Conventional physics has always tried to explain mechanics in terms of motion and interaction among particles. At first, everything looked so simple with the introduction of the atom. The Greek root of the word atom, "atomon", means "that which cannot be divided." But it was discovered in the 1930s that these entities are made from even more fundamental particles: a nucleus and electrons, termed elementary particles. Since the nucleus appeared much smaller, solid, and dense, scientists originally thought that the nucleus was the fundamental building block of matter. Later on, they discovered that it was made of protons (p+), which are positively charged, and neutrons (n), which have no charge (although they have the same mass as protons). More recently, physicists have discovered that protons and neutrons are composed of yet smaller particles called quarks. As far as we know, quarks are the most elementary elements, and can be classified as fundamental - simple and structureless elements.
Historically, Isaac Newton derived the laws for forces and motion of masses, Albert Einstein modified them by adding the 'effective mass' factor for relativistic particles, and Niels Bohr complicated the atomic model by proposing that tiny particles (electrons) orbit around a massive nucleus. More recently, scientists have needed to describe more and more particles to explain the particulate nature of the atom. So far, these particles include quarks, gravitons, muons, mesons, kaons, pions - and scientists will surely need to invent more, as long as the real geometric rules of nature remain unknown. The problem here seems to be that, at the subatomic level, the behaviour of matter appears to be radically inconsistent with our daily experience. In fact, the more we examine it, the less and less tangible matter becomes. We cannot help but ask, "Is matter as real as we think it is?" As Feynman said, if we keep picturing electrons and atoms as little steel balls, we're always going to have trouble understanding what is happening at the quantum level.
Many of us have learned about Bohr's atomic model, which postulates electrons orbiting around a central nucleus. Thankfully, conventional physics has taken a step in the right direction by largely abandoning this model. These days, even conventional physics understands that an orbital has little resemblance to the orbit of a planet moving around the sun, but is instead better described as a structure of energy that has a shape, with a probabilistic distribution in space.
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As you can obviously conclude from the above electron 'orbitals', the energy shape cannot be accounted for by the path of an orbiting electron. Let's have a look at the simplest type of orbital - the spherically symmetrical type. The Hydrogen atom in its ground state is a very good example of this. Since it is spherically symmetrical, it must have zero total angular momentum. Were we to attempt to interpret this observation in classical terms, we would be forced to conclude that the electron must only move in and out towards the nucleus (radially), while at the same time covering the entire angular range! This, in fact, contradicts the "steel ball" or "classical" interpretations, including Bohr's. So how can an electron possibly produce an orbital path without having an orbit? The only reasonable way to visualise this would be to imagine a spherical balloon being periodically inflated and deflated, but then we cannot talk about orbitals any more, can we? . Undoubtedly these statements will continue to sound strange until we free ourselves from the confines of the 'hard particle' paradigm. I understand that for one to free himself from a 200 years old of non-quantum science, full of assumptions of a world occupied by solid particles, euclidian geometry, and other spoon feeded concepts, it is not an easy thing at all to do. So, before stepping onto new grounds, let's have a further look at what our current knowledge teaches us about matter.
Currently accepted scientific description of an atom
This is the currently accepted atom model.
So, let us first revise how the atom is currently described by modern physics. Electrons are said to be in constant motion around the nucleus, protons and neutrons jiggle within the nucleus, and quarks jiggle within the protons and neutrons. Electrons, protons and neutrons are considered to be 'hard' particles.
This above picture is not to scale. If we drew the atom to scale and made protons and neutrons a centimeter in diameter, then the electrons and quarks would be less than the diameter of a hair and the entire atom's diameter would be greater than the length of thirty football fields! 99.999999999999% of an atom's volume is just empty space! Do you really believe that over 99.99% of the building block of matter is just empty space? If you DO NOT, then you are on the right track. The following is a list describing the currently accepted model of the atom.
1. At the center of the atom is a small, dense positively charged nucleus consisting primarily of protons and neutrons. Protons consist of two up quarks and a down quark (uud). Neutrons consist of two down quarks and an up quark (ddu).
2. Moving around the nucleus are negatively charged electrons which account for only 1/5000 of the atom's mass -- the rest of the mass being in the nucleus. Most of the atom is empty space. The motion of the electrons is not described.
3. The electrons in an atom are allowed to have only certain energies. The allowed states are described by a set of "quantum numbers", which indicate their average distance from the nucleus, their angular momentum and its direction, and the electrons' spin direction.
4. Light of a specific color is emitted or absorbed when electrons change from one state to another.
5. The "Heisenberg Uncertainty Principle" states that the position and momentum of an electron cannot be simultaneously determined. Since Bohr's orbiting electron model failed to describe the actual orbital distribution of the electron cloud, it had been concluded that the electrons motion it not governed by any ordered motion, but is completely random. The interpretation of the Heisenberg principle is that the atom's structure and the interactions of its electrons are random and can be discussed only statistically. The orbitals are therefore just a probabilistic distribution of such a random motion.
6. Even though the electron's exact position cannot be determined, if its energy is known, the theory predicts the probability that an electron could be at a particular place.
7. If the probability location of an electron of known energy is plotted in space, the plot looks like a fuzzy cloud of varying density, the shape varying with differences in angular momentum. It always has a definite symmetry about the nucleus. Some of the clouds or orbitals are spherical, others are like dumbbells, while others are more complex.
8. In describing an atom with many electrons, the charge clouds of one shell are superimposed in space with those of other shells.
2. Moving around the nucleus are negatively charged electrons which account for only 1/5000 of the atom's mass -- the rest of the mass being in the nucleus. Most of the atom is empty space. The motion of the electrons is not described.
3. The electrons in an atom are allowed to have only certain energies. The allowed states are described by a set of "quantum numbers", which indicate their average distance from the nucleus, their angular momentum and its direction, and the electrons' spin direction.
4. Light of a specific color is emitted or absorbed when electrons change from one state to another.
5. The "Heisenberg Uncertainty Principle" states that the position and momentum of an electron cannot be simultaneously determined. Since Bohr's orbiting electron model failed to describe the actual orbital distribution of the electron cloud, it had been concluded that the electrons motion it not governed by any ordered motion, but is completely random. The interpretation of the Heisenberg principle is that the atom's structure and the interactions of its electrons are random and can be discussed only statistically. The orbitals are therefore just a probabilistic distribution of such a random motion.
6. Even though the electron's exact position cannot be determined, if its energy is known, the theory predicts the probability that an electron could be at a particular place.
7. If the probability location of an electron of known energy is plotted in space, the plot looks like a fuzzy cloud of varying density, the shape varying with differences in angular momentum. It always has a definite symmetry about the nucleus. Some of the clouds or orbitals are spherical, others are like dumbbells, while others are more complex.
8. In describing an atom with many electrons, the charge clouds of one shell are superimposed in space with those of other shells.
The big flaws of the currently accepted atom model
Unknown to many of us, it is a fact that Einstein rejected the discrete point particle and stated that matter must be spherical entities extended in space. He writes "Physical objects are not in space, but these objects are spatially extended. In this way the concept "empty space" loses its meaning. Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high." Erwin Schroedinger understood the requirements of particle structure when he wrote in 1937: "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just 'Schaumkronen'. ('Schaum' means foam, 'Krone' means crest). He believed that quantum waves were real, not probability distributions with a hidden particle wondering inside, and that the particles are formed by the appearence of crests over the sea of energy. He clearly saw that abolishing the discrete point particle would remove the paradoxes of 'wave-particle duality' and the 'collapse of the wave function'. No atoms had even remotely been seen visually until 1985, when IBM Research Almaden Labs was the first to use an electron tunneling microscope to actually photograph the organization of molecules of germanium in an ink-blot. Here what we see from this experiment are indistinct, fuzzy spherical objects that appear to have some non-spherical geometric qualities to their shape and are in an extremely geometric pattern of organization, which was definitely a surprise for conventional science. How could the random nature of atoms described by the Heisenberg principle, ever result in such an ordered pattern? Perhaps the probability distributions are not 'distributions' at all. The image shown below was artificially colored orange and green to allow the eye to discriminate between the two types of atom that were seen:
Actual photograph of atoms of germanium in an ink-blot.
Furthermore, when quantum physicists have studied the electrons of the atom, they have observed that they are not actually points at all, not particulate in nature, but rather form smooth, teardrop-shaped clouds where the narrowest ends of the drops converge upon a very tiny point in the center.
There are no Electron Orbits! Bohr's model, which started the notion of electrons traveling around the nucleus like planets has misled a lot of people and scientists. If you have learned such an idea, forget about it immediately. Instead, all calculations and all experiments show that no satellite-like orbital motion exists in the normal atom. Instead, there are standing wave patterns, very similar indeed to the polar plots of antenna radiation patterns. For example, see the case M=0 and L=0, where the standing wave pattern is entirely spherical, this being equivalent to a pure isotropic antenna radiation plot. Similarly for M=1, L=1, the pattern is exactly the same as that of a half wave dipole, and so on. No one ever asks or requires for an antenna's radiation pattern to be formed of orbiting electrons, and yet we know that the standing wave generated from a typical radio antenna, posseses inertia, and can act upon external matter by means of radiation pressure. The electron path is NOT around and far off the nucleus, nor is the atom made up of 99.999% empty space!. Instead, the center of the electron pattern is also the center of the proton pattern. This is the normal situation of the H atoms in the universe; they have spherical symmetry, not orbits. You see, particulate matter is not requirement to generate the effects known to define matter.
To complicate things further, we have got the particle-wave dual nature enigma. The classical double slit diffraction experiment using a beam of electrons instead of light, shows us that we still get a diffraction pattern. The interpretation of this is that matter travels as a wave. Further more if we arrange a setup for light to enter the slits one photon at a time, or even one electron at a time, in both cases, we still get a build up a diffraction pattern over time. One interpretation of this result is that a single photon or electron goes through both slits and interferes with itself. Thus the common statement accepted by todays textbooks is that "matter acts as both a particle and as a wave." This statement obviously leaves a lot of holes in physics, since no mechanism is defined for how the transformation from one entity to the other is actually done. So, is matter a particle or a wave in nature?. Actually none of them, both the wave and particle models are flawed and/or incomplete models for subatomic particles as will be shown in this research section.
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| Electron clouds from top-down view (L) and from side view (R). [Courtesy Wolff, 1990] | |
| Some of the many possible spherical harmonics showing the probability density of an electron in a hydrogen atom. | ||
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| |2,0,0> | |2,1,0> | |2,1,1> |
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| |3,0,0> | |3,1,0> | |3,1,1> |
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| |3,2,0> | |3,2,1> | |3,2,2> |
As you can immediately recognise from the above electron distribution probability, electron shells commonly used in chemistry, together with Heisenberg Uncertainty Principle are impossible attempts to describe the above three dimensional atomic standing waves in terms of particles in motion. Now, do you find it surprising that one cannot know both position and momentum of an electron?
Below are some 3D plots of antenna radiation patterns obtained for some common radio antenna configurations. Those of you who studied elementary electronic communication systems know that the pattern of an array of antennas is the product of the pattern generated by a single element, called the element factor, and the pattern generated due to the array of elements called the array factor.
Below are some 3D plots of antenna radiation patterns obtained for some common radio antenna configurations. Those of you who studied elementary electronic communication systems know that the pattern of an array of antennas is the product of the pattern generated by a single element, called the element factor, and the pattern generated due to the array of elements called the array factor.
All the above 'electron distribution probability clouds', can be generated by different combinations of element and array factors acting on electromagnetic waves. Presently, the science to describe such factors in matter is almost non-existing, with the little we know generally referred as 'solid state physics'. As time goes by, however, an increasing number of scientists are becoming aware of the idea that to understand nature, one needs first of all understand the basic principles that govern collective behaviour of vast assemblies of matter. As strange as it may sound, these basic principles must be founded on the behaviour of vast interactions of electromagnetic waves, starting off from simple EM wave effects such as reflection and interference. Once such principles have been fully studied and understood, the human society can finally have a complete understanding of how two seemingly similar, spherical and featureless atoms of different elements, can assemble into two completely different crystalline assemblies, and acquire their own respective electrical and mechanical properties.
Most of the currently accepted particles have been found by the use of a common basic tool - the particle accelerator. This is a gigantic instrument that detects the effects and products of collisions between very fast moving particles. High speed is necessary so that it is energetic enough to 'crack open' the particles in order to reveal the inner structures that make up the colliding particles. Some of these sub-particles may only exist briefly before they dissapear or change to other form of particles.
Most of the currently accepted particles have been found by the use of a common basic tool - the particle accelerator. This is a gigantic instrument that detects the effects and products of collisions between very fast moving particles. High speed is necessary so that it is energetic enough to 'crack open' the particles in order to reveal the inner structures that make up the colliding particles. Some of these sub-particles may only exist briefly before they dissapear or change to other form of particles.
The realities of mainstream science
When two particles collide, or even combine, their total mass is not conserved, and this effect is known as the mass defect. Surely enough, modern science accounts for this fact, applying the well known Einstein's equation E=mc2, and states that the mass lost or gained is balanced by the change in bonding energy within the formed structure. All particle accelerator experiment results are currently being wrongly interpreted, because the particles appearing after impact are NOT the inner structures of the particles before impact. As we will see, in this theory, a particle is a structure, made up of an elementary unit, and not of an infinite number of a mix of smaller particles. Breaking up a structure of matter, will result in other structures which may not have existed as separate structural entities within the original particle, and the fact that most particles resulting after an impact in a particle accelerator have a very short life strengthens this idea, since how could ever a bigger structure have been formed if the chances of existance of its components are so small or nearly impossible?
The backbone of a new proposed atom model
3D attempt for De Broglie model by Kenneth Snelson
It was Louis De Broglie, who for the first time in 1923, proposed that all objects have properties of waves. His hypothesis was soon confirmed in 1927 by Davisson and Germer, by the observation of diffraction patterns in the scattering of electrons from crystals, confirming the wave behaviour of electrons. The lighter the object, the more pronounced the wave effect. An object as small as the electron would act very much like a wave, forming stationary waves around the nucleus. Unfortunately, his was the last of the accepted "physical" models, since just 5 years later, Werner Heisenberg derived his "Uncertainty Principle" which states that it is impossible to determine simultaneously the momentum and position of an electron. Such a principle has been widely accepted and to the present day, science gave up the search for a 'physical' model. De Broglie model is correct in principle, but is too simplistic and cannot account for all the experimental observations done on atoms. For this model to be complete, we first need to transform the 2D Broglie diagram into a 3D spatial equivalent, because we know that an atom occupies a volume. Shown above is one such attempt by Kenneth Snelson to render such a model. Also, Milo Wolff's spherical space resonance model introduced in the 80's, shows us the requirement for incoming and outgoing waves for the production of spherical standing waves.
Video interview of Milo Wolff by Geoff Haselhurst about the wave structure of matterHere is a list of statements that I believe define a much more accurate model of the atom. This model is fully consistent with all experimental evidence (both wave and particle), the Heisenberg uncertainty principle, as well as quantum mechanics (QM). The backbone of this model is based on Louis De Broglie simple model, which is further elaborated and explored in the following pages. In the following pages we will explore together, refine this model and also solve a few enigmas introduced by this model.
Standing wave theory of matter
1. The universe is not made up of matter and vacuum, but instead is comprised of standing and travelling electromagnetic (EM) waves. A standing wave appears to have both momentum and inertia when interacting with another standing wave, thus giving us the impression of 'hard particles' hitting each other. The interaction between living organisms (which consist of cells, atoms, and standing waves) and other standing waves give us the sense of touch - the most misinterpreted sense of all!
2. All experimental attempts to probe the internal structure of the electron have proved futile. For that reason, despite its size, the electron is considered by conventional science to be an elementary particle - a particle with no internal structure!
3. The substantiality of mass (i.e., its hard particle nature) is redundant because it can always be converted to electromagnetic energy, which has no particle properties. This has a serious implication on Newtonian physics, as it would become merely a redundant branch of science.
4. No theory exists in quantum mechanics that can predict the size of an electron, its mass, or its charge. Moreover, there is no theory that quantifies the particle in a meaningful calculation. This implies that QM actually has no need for a particle concept, because all the calculations are the same whether or not you believe in hard particles. It is interesting to note that QM equations still hold true when applied to an electrical entity that can exhibit momentum and inertia.
5. The atomic nucleus, along with its electron cloud teardrop shapes, would be also seen if an electron microscope were used to view a resonant antenna. One would also see different electron wave patterns (or shells) with different types of antennas, within their nearfield region. But what you see is not necessarily real and what is real cannot necessarily be seen. If we define reality, as conventional physics does, as that which is tangible to our senses, many of our observations become mysterious and unexplainable, which is precisely the current situation.
6. A 3D standing electromagnetic wave can be thought of as a structured volume defined by three orthogonal electromagnetic energy vectors, equating to (T/S)x * (T/S)y * (T/S)z = T3/S3, the space-time dimensions of mass.
7. Electromagnetic waves possess the properties of momentum and inertia, whose values can vary in space due to the interference effect of two or more waves. Similarly, a 3D standing EM wave has the same characteristics. Thus momentum or pressure are expected from the interaction of a standing wave with either another standing wave or with an external travelling EM wave. Momentum is given by P = h / l, where l is the wavelength of each element forming the standing wave structure.
8. Spherical resonance is what drives the entire observable universe. Resonance determines the behaviour of the trapped EM waves in the form of atomic particles. Resonance also determines the behaviour of the electrons in a hydrogen atom. The various shells of the electron are simply the result of resonance. Only those orbits that create standing electric waves will be stable. Non-standing wave orbits disintegrate immediately, as they do in short half-life isotopes. It is not a matter of some mysterious "prohibited--permitted" decision; it is a matter of resonance that can easily be calculated without resorting to quantum theory or the like. Quantum mechanics' "prohibited orbits" are merely non-standing wave orbits that cannot exist.
The observed teardrop shape of an electron cloud is exactly what we would expect when seeing a 3D standing wave of vibration. We remember that the hydrogen atom's electron cloud was seen to have a spherical shape, which is the same shape as an isotropic antenna's radiation. So the nucleus is just a 3D structure of oscillating electrical elements, while the electron cloud is the nearfield standing wave of the resulting oscillation, and the point where the teardrop shape of the cloud converges is simply the node of the standing wave. The electron is in fact known to be a Broglie wave (wave of matter) that interferes with itself. The so called 'electron cloud' around the nucleus can only be stable when it meets the condition of a standing wave. As we will see further on, the consequence of all this is that only certain values of radius and energy are permitted.
Mathematical proof that the electron is a spherical electromagnetic standing wave
Let's find the 'mass' of a spherical standing wave having the same diameter and charge of the electron:
Starting from the equation for the capacitance of an isolated spherical charge: C= 4.p.e0.r
The total internal energy stored in an electromagnetic standing wave = Electric field energy + Magnetic field energy, where Electric field energy = Magnetic field energy, hence:
Total internal energy E = 2 * Electric field Energy = 2 * Magnetic field energy ... so it's enough if we solve for one of these to get the total internal energy for an electron.
Total internal energy E = 2 * Electrical Energy = 2* (1/2QV) = QV ... where V=Q/C
Total internal energy E = Q2/C ... substitiuting for C, we get
Total internal energy E = Q2/(4.p.e0.r), Substitiuting for Q=electron charge=1.602E-19 Coulombs, r=classical electron radius= 2.8179E-15 m, and e0 = permittivity of free space = 8.854E-12 F/m
Total internal energy E = 8.18735E-14 Joules
Using E=mc2, we get
Electron standing wave mass = 9.1096E-31kg ... which is the known electron mass.
This clearly shows that what we call electron mass is nothing but the electromagnetic effect of a spherical standing wave.
Let's find the 'mass' of a spherical standing wave having the same diameter and charge of the electron:
Starting from the equation for the capacitance of an isolated spherical charge: C= 4.p.e0.r
The total internal energy stored in an electromagnetic standing wave = Electric field energy + Magnetic field energy, where Electric field energy = Magnetic field energy, hence:
Total internal energy E = 2 * Electric field Energy = 2 * Magnetic field energy ... so it's enough if we solve for one of these to get the total internal energy for an electron.
Total internal energy E = 2 * Electrical Energy = 2* (1/2QV) = QV ... where V=Q/C
Total internal energy E = Q2/C ... substitiuting for C, we get
Total internal energy E = Q2/(4.p.e0.r), Substitiuting for Q=electron charge=1.602E-19 Coulombs, r=classical electron radius= 2.8179E-15 m, and e0 = permittivity of free space = 8.854E-12 F/m
Total internal energy E = 8.18735E-14 Joules
Using E=mc2, we get
Electron standing wave mass = 9.1096E-31kg ... which is the known electron mass.
This clearly shows that what we call electron mass is nothing but the electromagnetic effect of a spherical standing wave.
Synergetics
Replacing the outdated Cartesian system
Replacing the outdated Cartesian system
We are living in a period of such absurdly blind acceptance of the Cartesian system of co-ordinates, based on the cube structure with three axes in 90 degree co-ordination developed more than four centuries ago. Instead, more recently, Buckminster Fuller, came out with a much more natural way of co-ordinate system based on his invention of the geodesic dome, a structure of triangularly-interconnected elements that has the best ratio of weight to enclosed space of any artificial construction so far developed. More recently, Fuller has received much public acclaim for having predicted, with his geometry, the existence of spherical molecules. The experimental discovery of the Buckminster fullerene, a spherical and extraordinarily stable large molecule of carbon, is only a few years old.
 | Departing from convention, this geometry replaces the cube with the regular tetrahedron as its principal unit of volume. The four-sided tetrahedron is the simplest possible enclosure, which is why mathematicians call it a "simplex". Drawn as a cage, or wire frame, it has four windows, four corners and six edges. No space-enclosing network has fewer windows (facets) than four. The cube (or hexahedron), by contrast, has six facets, eight corners, and twelve edges.Given the status of the simplex as "simplest space-enclosing network", the decision to use its regular form as a unit of volume makes some sense. As a consequence of this decision, we obtain whole number volumes for other familiar shapes (including for the cube). |
| Fuller's geometry goes by the name of Synergetics and has been developed by experimentally observing the behaviour of spheres of equal diameter, when packed as close as possible to form regular geometric figures. The basic and most simple stable geometric configuration of synergetic geometry is the tetrahedron, formed by four spheres laying next to each other, in perfect triangular configuration forming four angles of 60 degrees. Other important elements are the octahedron (formed by six closest-packed spheres) and the vector equilibrium, which is the result of twelve spheres nested around a thirteenth, central sphere, in omnidirectional closest-packing, 60 degree co-ordinated configuration. The cube, which is at the basis of our present-day construction methods and of the x-y-z Cartesian co-ordinate system, is not in and by itself a stable configuration. Eight spheres forming a cube are inherently unstable. To gain stability, they must be artificially stabilised by interconnecting them in the way the tetrahedron is connected. In this way, two tetrahedra of four spheres each, joined at their respective centers, form one cube of eight spheres. The cube and dodecahedron are both space-fillers, meaning they fill space without gaps. The tetrahedron and octahedron fill space in complements with twice as many tetrahedra as octahedra. |  |
 | It happens that this geometry, as developed by Fuller, is in perfect accord with how crystals grow in their various forms, and that its application in engineering reveals to us the possibility of very efficient structures in terms of economy of raw materials and strength of the resulting construction. |
Now how could the discoveries of Fuller be utilised to form a co-ordinate system and why should we venture to do such a task, seeing that the Cartesian x-y-z co-ordinates have done perfect (or almost perfect) service for such a long time?
For one, Cartesian co-ordinates may be a convenient mathematical construct, but they do not accord with nature's ways any more than modern chemistry will ever be able to duplicate the conditions of living organisms.
For one, Cartesian co-ordinates may be a convenient mathematical construct, but they do not accord with nature's ways any more than modern chemistry will ever be able to duplicate the conditions of living organisms.
From waves to particles
by standing waves in space
by standing waves in space
We have shown that the atom can be perfectly modeled by a standing wave pattern much in common with that of a radio antenna. The problem to visualise matter as being composed of a volume of electromagnetic waves is the fact that matter has got a structure, whilst an EM wave does not. It is true that EM waves have no structure, and are continously vibrating, but EM waves can be 'trapped' within a volume of space, given their dimensions are exact multiples of Planck's half wavelength, forming what is commonly called a standing wave. The nodes within the standing wave form the structure. All objects have a frequency or set of frequencies with which they naturally vibrate when struck, plucked, or somehow given an impulse, these are called the natural frequencies. Each of the natural frequencies at which an object vibrates is associated with a standing wave pattern. When an object is forced into resonance vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave is formed within the whole object. A standing wave pattern is described as a vibrational pattern created within a medium when the vibrational frequency of a source causes reflected waves from one end of the medium to interfere with incident waves from the source in such a manner that specific points along the medium appear to be standing still. Such patterns are only created within the medium at specific frequencies of vibration; these frequencies are known as harmonic frequencies, with the first harmonic referred to as the fundamental. In our context, this fundamental harmonic is highly related to Planck's length. At any frequency other than a harmonic frequency, the interference of reflected and incident waves results in a resulting disturbance of the medium which is irregular and non-repeating. Our medium is the vacuum through which EM radiation is well known to be able to propagate and vibrate.
Tip of a platinum needle enlarged 750,000 times.
Are those 'hard particles' or standing waves?
Field ion microscope image of a 'single crystal' tungsten tip.
Are those 'hard particles' or standing waves?
Water standing waves formed with vertical oscillation in a circular dish
Image courtesy of Ray Tomes
On the first two photos, you can see typical images from field ion microscope for platinum and tungsten tips. The bright areas correspond to positions on the tip where the electric field is particularly high, i.e. where the local radius of curvature of the crest of the wave is particularly small. In the lower photo we see water waves formed with 280 Hz vertical oscillation in a 6.3 cm circular dish. The particle like waves travel about independently when a medium strength oscillation is applied. This is very suggestive that atomic particles are similarly formed as standing waves. Some non-linearity is necessary to have stability. In this case it is supplied by the different rate of acceleration applied to the water from above (by gravity) and below (by pressure). Surface tension applies in both directions.
So the natural frequencies of an object are merely the harmonic frequencies at which standing wave patterns are established within the object. These standing wave patterns represent the lowest energy vibrational modes of the object. While there are countless ways by which an object can vibrate (each associated with a specific frequency), objects favor only a few specific modes or patterns of vibrating. The favored modes (patterns) of vibration are those which result in the highest amplitude vibrations with the least input of energy. Objects favor these natural modes of vibration because they are representative of the patterns which require the least amount of energy. Objects are most easily forced into resonance vibrations when disturbed at frequencies associated with these natural frequencies.
 | The wave pattern associated with the natural frequencies of an object is characterized by points which appear to be standing still; for this reason, a pattern in 2D is often called a "standing wave pattern", whilst we may call a pattern in 3D, a "standing wave structure". The points in the structure which are at stand-still are referred to as nodal points (in 2D) or vertex positions (in 3D). These positions occur as the result of the destructive interference of incident and reflected waves. Each nodal point is surrounded by anti-nodal points, creating an alternating pattern of nodal and anti-nodal points. A classical two dimensional demonstration utilizes a square metal plate (known as a Chladni plate), a violin bow and salt. The plate is securely fastened to a table using a nut and bolt; the nut and bolt are clamped to the center of the square plate, preventing that section from vibrating. The salt is then sprinkled upon the plate in an irregular pattern. Then the violin bow is used to induce vibrations within the plate; the plate is strummed and begins vibrating. At a certain violin tone, a high-pitched pure tone is sounded out as the plate vibrated; and, remarkably the salt upon the plate begins to vibrate and forms a pattern upon the plate. The pattern formed by the salt on the plate is the standing wave pattern associated with one of the natural frequencies of the Chladni plate. As the plate starts to vibrate, the salt begins to vibrate and tumble about the plate until they reach points along the plate which are not vibrating. Subsequently, the salt finally comes to rest along the nodal positions. The diagrams show two of the most common standing wave patterns for the Chladni plates. The white lines represent the salt locations (nodal positions). Observe in the diagram that each pattern is characterized by nodal positions in the corners of the square plate and in the center of the plate. For these two particular vibrational modes, those positions are unable to move. In a 3D standing waves, a structure, with all charactesitics of a platonic solid, is formed for each standing wave mode. Within an atom, which is the building block of matter, the platonic solid is not formed by salt or known particles, but by electromagnetic waves in vacuum. The final result, the standing wave structure, is one which has a structure, an inertia, a reaction to other standing wave structures, and a reaction to external EM waves, all characteristics of what we use to call 'a particle', which can be felt and seen. As we shall see later on, particles are point effects of the standing wave nodes. |  |
 | Both the students of Buckminster Fuller and his protege Dr. Hans Jenny devised clever experiments that showed how the Platonic Solids would form within a vibrating / pulsating 3D sphere. In the experiment conducted by Fuller's students, a spherical balloon was dipped in dye and pulsed with pure sinewave sound frequencies. A small number of evenly-distanced nodes would form across the surface of the sphere, as well as thin lines that connected them to each other. If you have four evenly spaced nodes, you will see a tetrahedron. Six evenly spaced nodes form an octahedron. Eight evenly spaced nodes form a cube. Twelve evenly spaced nodes form the icosahedron and twenty evenly spaced nodes form the dodecahedron. The straight lines that we see on these geometric objects simply represent the stresses that are created by the closest distance between two points for each of the nodes as they distribute themselves across the entire surface of the sphere. |
Dr. Hans Jenny conducted a similar experiment, wherein a droplet of water contained a very fine suspension of light-colored particles, known as a colloidal suspension. When this spherical droplet of particle-filled water was vibrated at various diatonic musical frequencies, the Platonic Solids would appear inside, surrounded by elliptical curving lines that would connect their nodes together. As we shall see, these dark points, which are nothing but point of intersections of nodes are the supposed 'point bits of matter'.
Photos courtesy of Paul Umbanhowar (University of Texas at Austin)
When a bed of dry granular material or fluid is subject to vertical vibration at certain frequencies, pattern formations start to appear at the surface when the modulation exceeds a critical value. These waves have a frequency which is half that of the driving oscillations (the first sub-harmonic). This effect was first reported by Michael Faraday in 1831.
In ordinary Newtonian fluids, those that do not exhibit shear thickening or shear thinning, the wave patterns include ones with 1-fold symmetry (stripes), 2-fold symmetry (squares), and 3-fold symmetry (hexagons).
Many of the same patterns seen in the liquid version of Faraday's experiment are also seen in the granular material. These patterns are in fact the same phenomena observed on the chladni plates discussed earlier. At lower frequencies however, a new phenomena has been observed, that of localized structures called "oscillons". The granular version of this experiment is done at the University of Texas at Austin, and now also in several other places.
Oscillons can be seen in the image on the lower right of the photographs shown above. They resemble a splash of water in a puddle, but with one important difference: instead of spreading out, they slosh back and forth between a state that resembles a crater and a state that resembles a peak. When one oscillon in a crater state collides with an oscillon in the peak state, they can form a bound system, as shown in the image on the lower right.
In shear thinning non-Newtonian liquids, theory suggests that localized structures analogous to granular "oscillons" should be found. These have recently been observed in experiments using clay suspensions as shown below.
In ordinary Newtonian fluids, those that do not exhibit shear thickening or shear thinning, the wave patterns include ones with 1-fold symmetry (stripes), 2-fold symmetry (squares), and 3-fold symmetry (hexagons).
Many of the same patterns seen in the liquid version of Faraday's experiment are also seen in the granular material. These patterns are in fact the same phenomena observed on the chladni plates discussed earlier. At lower frequencies however, a new phenomena has been observed, that of localized structures called "oscillons". The granular version of this experiment is done at the University of Texas at Austin, and now also in several other places.
Oscillons can be seen in the image on the lower right of the photographs shown above. They resemble a splash of water in a puddle, but with one important difference: instead of spreading out, they slosh back and forth between a state that resembles a crater and a state that resembles a peak. When one oscillon in a crater state collides with an oscillon in the peak state, they can form a bound system, as shown in the image on the lower right.
In shear thinning non-Newtonian liquids, theory suggests that localized structures analogous to granular "oscillons" should be found. These have recently been observed in experiments using clay suspensions as shown below.
Simulating what happens when you shake a box of granular material such as sand, researchers at the University of Texas at Austin acoustically vibrate vertically an evacuated container of tiny bronze balls to make beautiful patterns such as the ones shown above. The pictures show patterns such as hexagons and states that resemble the stitches on a baseball.
Particle-like localised excitations in a bed of sand can form into molecules and even crystals structures. At a certain frequency the energy put into the system manifests itself as small isolated heaps of sand (about thirty grains in diameter) which also bob up and down. These heaps, termed "oscillons," are stable (holding together for thousands of shakings) and able to slowly drift across the sand bed. This is not like a travelling wave, were the moving peak is being shaped by different particles, but here the same grains drift around. And just as with electrical charges, when it comes to oscillons opposites attract. As long as their centers are within 1.4 diameters of each other, oscillons of opposite phase (one at its peak height and one at its shallowest depth) can enter into a dipole state to form a sort of molecule. This peak-crater pair binding may lead to more complex molecules and even long chains of oscillons which, under the right conditions, can grow into extended patterns. Current theories give us no definite answer as to how and why the oscillons form and interact, but such localized structures may exist in other dissipative systems (systems which steadily exchange energy), and not just in granular materials.
Particle-like localised excitations in a bed of sand can form into molecules and even crystals structures. At a certain frequency the energy put into the system manifests itself as small isolated heaps of sand (about thirty grains in diameter) which also bob up and down. These heaps, termed "oscillons," are stable (holding together for thousands of shakings) and able to slowly drift across the sand bed. This is not like a travelling wave, were the moving peak is being shaped by different particles, but here the same grains drift around. And just as with electrical charges, when it comes to oscillons opposites attract. As long as their centers are within 1.4 diameters of each other, oscillons of opposite phase (one at its peak height and one at its shallowest depth) can enter into a dipole state to form a sort of molecule. This peak-crater pair binding may lead to more complex molecules and even long chains of oscillons which, under the right conditions, can grow into extended patterns. Current theories give us no definite answer as to how and why the oscillons form and interact, but such localized structures may exist in other dissipative systems (systems which steadily exchange energy), and not just in granular materials.
Oscillons are a soliton-like phenomenon emerging from batches of vibrated particles. Basically, researchers are studying them mostly empirically at this point. They've shown a coupling effect where smaller oscillons join into larger ones via waves of attraction. These waves of attraction or repulsion between them propagate through vacuum and seem to be driven by a force whose aim is to complete a defined pattern. Schroedinger-wavelike phenomena ensue also. In general oscillons have been observed when a large number of balls of less than 0.1 millimetres in radius are vibrated in a tray at between 10 and 100 Hz. They have so far been produced using a wide range of materials, particle sizes and frequencies of vibration. Oscillons are very stable and long lived, some having been observed to last for millions of cycles. Oscillons pulse up and down in the same way as standing waves in a fluid, such as the water waves discussed in the previous section. Because these structures attract or repel each other in vacuum as well as in air, depending on their relatives phases, they appear to act as charged particles. This is clear evidence that two neighbouring standing waves show the property of charge attraction & repulsion.
One of the neatest aspects is that the models predict 'mass' for the fundamental oscillons. I know of no modern physics theory that can claim this. All other theories assume fundamental particle masses as given constants. So, again, the 3D standing wave theory is fully compatible with the soliton mass predictions, because it defines the mass property as a property of space structure and not as a built in constant of particles. Again, despite continous research since 1996, oscillons seem to have totally escaped the attention of mainstream particle physicists as a model or direction of pursuit.
One of the neatest aspects is that the models predict 'mass' for the fundamental oscillons. I know of no modern physics theory that can claim this. All other theories assume fundamental particle masses as given constants. So, again, the 3D standing wave theory is fully compatible with the soliton mass predictions, because it defines the mass property as a property of space structure and not as a built in constant of particles. Again, despite continous research since 1996, oscillons seem to have totally escaped the attention of mainstream particle physicists as a model or direction of pursuit.
Sonoluminescence
Ionising gas into plasma by resonance
Ionising gas into plasma by resonance
Sonoluminescence (SL) was first observed in an ultrasonic water bath in 1934 by H. Frenzel and H. Schultes at the University of Cologne, an indirect result of wartime research in marine acoustic radar. By focusing ultrasonic waves of high intensity into a liquid, thousands of tiny bubbles appear. This process of breakup of the liquid is called acoustic cavitation. The bubbles begin to form a fractal structure that is dynamically changing in time. They also emit a loud chaotic sound because of their forced nonlinear oscillations in the sound field. The large mechanical forces on objects brought into contact with the bubbles enable the usage of cavitation in cleaning, particle destruction and chemistry. Marinesco and Trillat found that a photo plate in water could be fogged by ultrasound. This multi bubble sonoluminescence (MBSL) has been analyzed by many researchers, and a great amount of knowledge has been gained. Study of sonoluminescence then made little progress until 1988, when D. Felipe Gaitan succeeded in trapping a stable sonoluminescing bubble at the centre of a flask filled with degassed purified water, energised at its acoustic resonance - single-bubble sonoluminescence (SBSL). However their interest soon waned, and the research was subsequently taken up by Dr S. Putterman et. al., at UCLA, California. The discovery of Gaitan has been encouraging scientists to explore the phenomenon and the associated effects with a multitude of experiments, theories and simulations. The experimental results show picosecond synchronicity, quasiperiodic and chaotic variability of inter-pulse times, a black body spectrum and mass transport stability. The theories to explain the source of SBSL range from hotspot, bremsstrahlung, collision induced radiation and corona discharges to non-classical light. Numerical simulations have been focusing on the bubble dynamics, behavior of the gas content, properties in magnetic fields and the stability of the bubble. However, the final answer concerning the nature of SBSL still remains open. Putterman pursued SBSL, published numerous papers, and established many of the characteristics which are now taken for granted. Once per acoustic cycle (1/30kHz), coincident with a sharp decrease in bubble size, bluey-white light is emitted in a brief flash in the order of 10 picoseconds in duration, with incredible regularity, and broadband spectrum, including at least the UV range. The spatial images show a bright spot in the source with a diameter of about 3 microns, or less, and a larger diffused region with a diameter of 50 to 100 microns. Scientists don't even know whether the bubbles emit X rays, a sign of very high temperatures. Water absorbs X rays, making it futile to try to detect them from outside the flask. Despite the results that have been obtained, the actual mechanism by which sound is converted to light remains elusive, not least because of the difficulty in measuring the conditions inside a pulsating bubble whose diameter is measured in micro-meters. It is known that the bubble contracts violently, and at the same time the brief flash is emitted, after which it expands again and oscillates about its original equilibrium radius, until it is again stable, ready for another pulse. The addition of a small amount of noble gas (such as helium, argon, or xenon) to the gas in the bubble increases the intensity of the emitted light dramatically. Conventional physics tries to explain SL as the adiabatic compression of the bubble which leads to very high interior temperatures. The issue is still hotly debated and possible explanations include shocks, plasmas, ionisation and photo-recombination, Bremsstrahlung radiation, and even fusion.
Considering one needs just about one watt of audio power to start observing such effects, sonoluminiscense is to say the least a very efficient energy converter. As you will see in the 'States of matter' table given below, the next higher energetic state of a gas is indeed plasma. But how on earth may one totally ionise a bubble into plasma with just one Watt of power. The trick is resonance, same as shattering a glass with singing, pulverising a kidney stone with ultrasonic or collapsing a bridge with resonant wind vibrations. Once you subject the octahedron structure of a gas to the correct resonance frequency, you need just enough power to 'get loose' the constituent tetrahedrons (plasma) from the gas structure. Current estimations for the bubble temperature and pressure indeed confirm plasma formation. Temperatures have been estimated to range from 10 to 100eV (1eV = 11,600K or 20,420 degrees F); that is as hot as the corona of our sun. The pressures are as high as 200Mbar (1Mbar = 1011 Pa) in the core of the imploding bubble. This pressure is equal to 1.974*108Pa or 19,743,336 atmospheres. The only state of matter which can exist under these conditions is plasma.
Considering one needs just about one watt of audio power to start observing such effects, sonoluminiscense is to say the least a very efficient energy converter. As you will see in the 'States of matter' table given below, the next higher energetic state of a gas is indeed plasma. But how on earth may one totally ionise a bubble into plasma with just one Watt of power. The trick is resonance, same as shattering a glass with singing, pulverising a kidney stone with ultrasonic or collapsing a bridge with resonant wind vibrations. Once you subject the octahedron structure of a gas to the correct resonance frequency, you need just enough power to 'get loose' the constituent tetrahedrons (plasma) from the gas structure. Current estimations for the bubble temperature and pressure indeed confirm plasma formation. Temperatures have been estimated to range from 10 to 100eV (1eV = 11,600K or 20,420 degrees F); that is as hot as the corona of our sun. The pressures are as high as 200Mbar (1Mbar = 1011 Pa) in the core of the imploding bubble. This pressure is equal to 1.974*108Pa or 19,743,336 atmospheres. The only state of matter which can exist under these conditions is plasma.
The Glass shattering experiment
Weakening glass' intermolecular structure
Weakening glass' intermolecular structure
This Quicktime movie shows the classical shattering of a wine glass when in resonance using a 5 Watt sine wave audio tone in the range of 800Hz. Play the movie and watch carefully the motion of the glass rim. You will see that the radius of the rim of the wine glass is actually deforming by as much as 5 mm!! There is no way that such thing could be done under non resonant conditions without heating up the glass in a furnace. At room temperature, the glass is normally so brittle that it would shatter as soon as the rim is deformed by 1 or 2mm. This 'jellification effect' indicates that resonance weakened the actual intermolecular force and made them similar to those within liquids, thus inreasing the elasticity of glass. So, the audio energy in this experiment is used to modify the solid state of glass into the next higher state of matter, to give it liquid state characteristics, making it more elastic. At this point I have to point out that there is no overunity here. In an oscillating system at resonance, one pours power in small amounts, but the energy thus transferred gets accumulating in the system (actually in the standing wave). It is a common misperception to think that with few energy we produce lots of work. We just keep accumulating slowly the energy, by putting a little power over a relatively long time, and then we release the same amount of energy in a relatively short time, giving a tremendous energy per unit time, that is power. Same applies to sonoluminiscense and all other resonance phenomena mentioned here.
How to conduct the experiment
This demonstration requires a fair amount of equipment. A 10Watt stereo amplifier, whose output goes to a horn driver near the wine glass to be broken, can be switched between a frequency generator, easily tuned through a broad spectrum, a video camera, and a frequency synthesizer which can generate a very accurate frequency, at about 0.1Hz steps. Alternatively, if your frequency generator is of the digital type and accurate to 0.1Hz and is powerful enough, you can use it instead of the synthesiser. The response of the wine glass to the sound is monitored with a microphone connected to an oscilloscope. The first four steps can be prepared before the lecture, but most instructors like to run through them with the class so the students can see the entire operation.
1.. Flick the wine glass with you finger to "ring" it. With the amplifier set at low hearing volume, tune the frequency generator until you hear a similar pitch.
2.. Watching the response on the scope, tune the frequency generator until you hit the resonance of the wine glass where the signal on the oscilloscope becomes much larger.
3.. Read off the approximate resonance frequency from the frequency counter and enter this number on the frequency synthesizer. Switch the amplifier over to the frequency synthesizer input.
4.. With the synthesizer in the "edit" mode, change the frequency one hertz at a time until you hit the resonance again. Now tune by tenth hertz until you reach the maximum peak.
5.. Move the microphone away from the wine glass and place the Plexiglas shield in front (to prevent broken glass from spraying into the class and the video camera).
6.. Start video recording and turn up the amplifier volume to quite loud and the glass will break. The sound is loud, but not painful to the operator. At the position of the glass, it is approximately 140 dB. View video in slow motion to see what's happening.
How to conduct the experiment
This demonstration requires a fair amount of equipment. A 10Watt stereo amplifier, whose output goes to a horn driver near the wine glass to be broken, can be switched between a frequency generator, easily tuned through a broad spectrum, a video camera, and a frequency synthesizer which can generate a very accurate frequency, at about 0.1Hz steps. Alternatively, if your frequency generator is of the digital type and accurate to 0.1Hz and is powerful enough, you can use it instead of the synthesiser. The response of the wine glass to the sound is monitored with a microphone connected to an oscilloscope. The first four steps can be prepared before the lecture, but most instructors like to run through them with the class so the students can see the entire operation.
1.. Flick the wine glass with you finger to "ring" it. With the amplifier set at low hearing volume, tune the frequency generator until you hear a similar pitch.
2.. Watching the response on the scope, tune the frequency generator until you hit the resonance of the wine glass where the signal on the oscilloscope becomes much larger.
3.. Read off the approximate resonance frequency from the frequency counter and enter this number on the frequency synthesizer. Switch the amplifier over to the frequency synthesizer input.
4.. With the synthesizer in the "edit" mode, change the frequency one hertz at a time until you hit the resonance again. Now tune by tenth hertz until you reach the maximum peak.
5.. Move the microphone away from the wine glass and place the Plexiglas shield in front (to prevent broken glass from spraying into the class and the video camera).
6.. Start video recording and turn up the amplifier volume to quite loud and the glass will break. The sound is loud, but not painful to the operator. At the position of the glass, it is approximately 140 dB. View video in slow motion to see what's happening.
Huge atom structures
From SL micro-metre bubbles to 1 metre Light balls
From SL micro-metre bubbles to 1 metre Light balls
Light balls are sometimes called Ball Lightning which is a misnomer since they do not look like or relate to lightning. Actually is looks more like a huge sonoluminescent bubble floating in air. It usually appears as a mysterious glowing sphere which drifts through the air. It can also appear to bounce along the ground. Light balls are described as glowing balls of plasma. The phenomena usually lasts for only 5 seconds, but sometimes remains longer for up to a few minutes. Some of the balls are blindingly bright, others have almost no illumination and appeared grayish. The temperature within was evaluated to be a little bit higher than the solar temperature; 6,500 Kelvin degrees, however these were also reported to pass through glass and being touched with no burning effects, and also do not float up as would do a hot object. These plasmas can suddenly change in size and shape without any change in their measured temperature. Nominal size of reported light balls being the size of an orange or grapefruit. The diameter of the balls range from a few centimeters to a few meters, with the average around 20 cm. They are sometimes oval, cylindrical, flame, pear, ring, blob shaped or even cornered shapes like a cube. Cylindrical forms can sometimes be flattened, bent, or twisted into a variety forms. Sometimes they have halos, sparks, or radial streamers around them. Some appear to be fibrous. Some are solid in appearance, others are hollow.
 | An enlarged picture of the rectangular plasma formation after changing from a sphere, as well as the corresponding 3-D Point Spread Function (PSF) that is used in order to simultaneously obtain the peak intensity and the apparent dimension, in pixels, of the target. Date: August 18, 2001. Image processing by M. Teodorani. |
Various colors of ball lightning have been seen. Sometimes the colors change as well. The phenomena usually occurs during or right after a thunderstorm. In most surveys about 70% occured right after a lightning strike.
Ball lightning has also been seen without any detected electrical storm. In a shockingly high percentage of cases the balls actually entered in buildings - through windows and doors. Sometimes they cause no damage to property - yet other times they burn holes. Balls have been reported as eminating from tornadoes, cyclones, and hurricanes. In these cases high electric fields are present.
Light balls have been seen on many occasions traveling along fences or power lines. Sometimes they appear to roll, spin, hop, or vibrate. Some of them have been possible to view only under infrared vision and they were observed to continously flip their shape from spherical to cube.
Some people believe that ball lightning movement is guided by electric fields EM energies), which might explain their attraction to conductors. There movement doesn't seem related to wind speed or velocity. Ball lightning sometimes carries a significant charge, and sometimes no charge. Some witnesses have reported being seriously shocked and others not at all. People have sometimes gotten burns similar to those caused by ultraviolet radiation from touching ball lightning. Most reports show no evidence of radiant heat from the balls, even at close range. Most researchers agree that ligtning balls are real, but no one knows exactly what they are. Researchers are also unable to reproduce free floating ball lightning, however you may try to create a plasma ball in your microwave oven. More details here. This experiment shows that plasma balls are real and that energy can be trapped in a bubble or 3D space. We know that these light balls in general emit light, and can be considered to be a huge 3 dimensional electromagnetic standing wave structure. It has the same properties as an unstable mass, in that it radiates light, and most probably other forms of radiation. Due to it being unstable, it is very similar to a fast decaying radioactive substance. Unlike a stable atom, following our atom model, the structure will not be stable, but will break down slowly from a complex structure (resembling a sphere) to simpler structures similar to the basic platonics. Once the basic platonic breaks down, the light ball disappears. This also explains the fact that people saw these light balls change into cornered shapes before they disappear. In a way, the decay of a light ball is similar to dismantling a crystal structure back into its elementary components.
Ball lightning has also been seen without any detected electrical storm. In a shockingly high percentage of cases the balls actually entered in buildings - through windows and doors. Sometimes they cause no damage to property - yet other times they burn holes. Balls have been reported as eminating from tornadoes, cyclones, and hurricanes. In these cases high electric fields are present.
Light balls have been seen on many occasions traveling along fences or power lines. Sometimes they appear to roll, spin, hop, or vibrate. Some of them have been possible to view only under infrared vision and they were observed to continously flip their shape from spherical to cube.
Some people believe that ball lightning movement is guided by electric fields EM energies), which might explain their attraction to conductors. There movement doesn't seem related to wind speed or velocity. Ball lightning sometimes carries a significant charge, and sometimes no charge. Some witnesses have reported being seriously shocked and others not at all. People have sometimes gotten burns similar to those caused by ultraviolet radiation from touching ball lightning. Most reports show no evidence of radiant heat from the balls, even at close range. Most researchers agree that ligtning balls are real, but no one knows exactly what they are. Researchers are also unable to reproduce free floating ball lightning, however you may try to create a plasma ball in your microwave oven. More details here. This experiment shows that plasma balls are real and that energy can be trapped in a bubble or 3D space. We know that these light balls in general emit light, and can be considered to be a huge 3 dimensional electromagnetic standing wave structure. It has the same properties as an unstable mass, in that it radiates light, and most probably other forms of radiation. Due to it being unstable, it is very similar to a fast decaying radioactive substance. Unlike a stable atom, following our atom model, the structure will not be stable, but will break down slowly from a complex structure (resembling a sphere) to simpler structures similar to the basic platonics. Once the basic platonic breaks down, the light ball disappears. This also explains the fact that people saw these light balls change into cornered shapes before they disappear. In a way, the decay of a light ball is similar to dismantling a crystal structure back into its elementary components.
Hutchison Effect
Melting solids into liquids without heat
Melting solids into liquids without heat
We know that the state of matter can be changed from one to the other of the four states in the order: Solid - Liquid - Gas - Plasma, by means of increasing or decreasing external energy supplied to the structure. The most common example is water, which when heated changes from liquid to gas and when cooled changes into a solid block of ice. But heating and cooling are just the most inefficient ways to change the state of matter. The state of matter shift occurring with the change of temperature, seems to be only a by-product of the heating, which means that only a part of the energy accumulated in the system is used on weakening the molecular bonds, the most of it going to Brownian kinetic energy in atoms and molecules as large bodies. Therefore, finding the resonance frequency (or harmonics) of the molecular bonds would be indeed a much more efficient way of changing the state of matter.
The Hutchison Effect is a collection of phenomena which were discovered accidentally by John Hutchison during attempts to study the longitudinal waves of Tesla back in 1979. The Hutchison Effect occurs as the result of radio wave interferences in a 3 dimensional zone space volume radiated by two or more high voltage sources, usually a Van de Graff generator, and two or more Tesla coils. The results are levitation of heavy objects, fusion of dissimilar materials such as metal and wood (as shown in the upper right corner of the photo), the anomalous melting (without heating) of metals without burning adjacent material, spontaneous fracturing of metals (which separate by sliding in a sideways fashion), and both temporary and permanent changes in the crystalline structure and physical properties of metals as shown above. The fusion of dissimilar materials, which is exceedingly remarkable, indicates clearly that the Hutchison Effect has a powerful influence on intermolecular forces. Dissimilar substances such as steel and copper or wood can simply "come together," yet the individual substances do not dissociate. A block of wood can simply "sink into" a metal bar, yet neither the metal bar nor the block of wood come apart or carbonise. On the lower left corner of the photo, you may see the imprint left over by coins which were sitting on top of the steel bar during the effect.
The anomalous melting of metal without any evidence of heating, burning or scorching of the adjacent materials (usually wood) can be easily explained if one considers the external high voltage intermediate frequency source to be resonant with the molecular structure of the metal. In such a case, resonance will efficiently use up the external energy to change the metal structure, to the next higher energy level structure which is the liquid state. Thus the metal structure will take over liquid properties, and any foreign solid material, such as wood or different metal, will 'sink' into it. Once the oscillation is switched off, the foreign material will be permanently trapped within the solid structure. The radio wave interferences involved in producing these effects are produced from at least two radio sources, with the correct frequency difference, both operating at low power. However, the zone in which the interferences take place is stressed by hundreds of kilovolts oscillating at the intermediate resonant frequency.
Platonic Solids & States of matter
What's so important about them?
What's so important about them?
Plato's Timaeus conjectures on the composition of the four elements which the ancient Greeks thought made up the universe: earth, water, air, and fire. Plato conjectured each of these elements to be made up of a certain Platonic solid: the element of earth would be a cube, of air an octahedron, of water an icosahedron, and of fire a tetrahedron. Each of these perfect polyhedra would be in turn composed of triangles. Only certain triangular shapes would be allowed, such as the 30-60-90 and the 45-45-90 triangles. Each element could be broken down into its component triangles, which could then be put back together to form the other elements. Thus, the elements would be interconvertible, so this idea was a precursor to alchemy. Plato's Timaeus posits the existence of a fifth element (corresponding to the fifth remaining Platonic solid, the dodecahedron) called quintessence, of which the cosmos itself is made. In three dimensional space, there are ONLY FIVE natural frequency modes for spherical EM standing wave, resulting in the formation of the five Platonic solids shown below. Each platonic would be perceived as the formation of a stable form of matter, anything in between will tend to be unstable, and will degrade to its nearest stable form, giving off its extra elements as EM energy, with radioactive elements being such an example.
| SHAPE | ELEMENT | STATE | PROPERTIES |
Cube/ Hexahedron  | Earth | Solid  | Molecules are limited to vibration about fixed position. Solids have a definitive volume and shape and high density. When energy is applied to a solid (eg heated) the solid becomes a liquid at its melting point. The solid phase is the lowest energy state of matter. See Hutchison effect. Speed of sound in steel is 5960m/s, for glass 5640m/s. |
Icosahedron  | Water | Liquid  | Molecules free to move throughout the liquid but held by intermolecular forces, giving it a definitive volume but no definite shape and a lower density. When energy is applied, evaporation occurs and it becomes a gas at its boiling point. If energy is lowered it becomes a solid at its freezing point. Speed of sound in water is 1482m/s. |
Octahedron  | Air | Gas  | In gas state, molecules are free to move in every direction, and a gas has no definite shape or volume and its density is lower than liquids. When energy is applied, electrons gain enough energy to leave the atom structure and a gas starts getting ionised. When fully ionised it becomes a plasma. See sonoluminescence. If energy is lowered a gas becomes a liquid. Speed of sound in air is approx 343m/s but dependant on pressure, temperature. For Helium it is 965m/s! |
Tetrahedron  | Fire | Plasma  | When a gas is given energy, molecules are torn apart into their component atoms and individual electrons are pulled away. This highly energised mixture of electrons and ions forms the plasma. If energy is lowered, plasma becomes gas. If plasma is given further energy, the atom structure within it is broken into its constituent electromagnetic energy and can no longer be considered a state of matter. Indeed the Plasma phase is the highest energy state of matter. |
Dodecahedron  | Universe | Vacuum  | The vacuum (or ether) has a structure as well. Vacuum is made up of pure electromagnetic energy, which can be re organised in any of the other platonic structures to be perceived as one of the other states of matter. Vacuum is a sea of electromagnetic energy which cannot be detected unless an imbalance is created (example: casimir plates). |
Euclid, 300 BC and the Ancient Greeks, in their inherited love for geometry, called the five solids shown below, the atoms of the Universe. In the same way that we today believe that all matter, is made up of combinations of atoms so the Ancient Greeks also believed that all physical matter is made up of the atoms of the Platonic Solids and that all matter also has a mystical side represented by their connection with earth, air, fire, water and aether. Similar to our conventional atom model which shows a nucleus surrounded by electrons in orbits creating spheres of energy, the Greeks felt that these Platonic solids also have a spherical property, where one Platonic Solid fits in a sphere, which alternately fits inside another Platonic Solid, again fitting in another sphere. It is fascinating to see how any one of these solids can fit inside one another. The concept of one sphere fitting inside another sphere is surprisingly frequently seen in different cultures. Indeed, the mechanism of platonic solids is so perfect, that perhaps as we are approaching in this study, their concept of platonics as being the building blocks of matter, might be more evolved than our present knowledge of the atom model. As shown in the photograph below, as in so many other aspects of their science and philosophy, the Greeks were not the originators of these concepts. The photograph is of a collection Neolithic stones, unmistakably showing the same basic "platonic" shapes. These (from the Ashmolean Museum, Oxford, UK) are at least 3,000 years old (>1000BC). Indeed, we know that from the Vedic times, around 3000 B.C. to 1000 B.C., Indians (Indo-Aryans) had classified the material world into the four elements; earth (Prithvi), fire (Agni), air (Maya) and water (Apa). To these four elements was added a fifth one; ether or Akasha. According to some scholars these five elements or Pancha Mahabhootas were also identified with the various human senses of perception; earth with smell, air with feeling, fire with vision, water with taste and ether with sound. Whatever the validity behind this interpretation, it is true that since very ancient times Indians had perceived the material world as comprising these 5 elements. The information one can get from these carved out shapes shows that a highly developed generation of human kind gave a lot of scientific importance to these shapes, and perhaps carving out these stones was one of their attempts to pass over their knowledge to others, including us!
What's so special about these geometric shapes? Here are the main rules for these geometric solids:
- Each formation will have the same shape on every side.
- Every line on each of the formations will be exactly the same length.
- Every internal angle on each of the formations will also be the same.
- Each shape will fit perfectly inside a sphere, all the points touching the edges of the sphere.
The platonic solids are those polyhedra whose faces are all regular polygons, which means they have congruent legs and angles. Leonhard Euler (1707-1783) who was a Swiss mathematician, noticed that no matter how one cuts a sphere into polygons, sometimes called a triangulation, there is a quantity which remains constant; in other words, there is a number related to the sphere independent of the triangulation. This number is now called the Euler characteristic. Each of the platonic solids is in fact a triangulation of the sphere into polygons.The Euler characteristic is given by F-E+V, where F is the number of polygonal faces, E is the number of edges, and V is the number of vertices in the triangulation. Euler showed that for any triangulation of the sphere, we get an Euler characteristic equal to 2, no matter which platonic solid is chosen. Euclid proved around 200 B.C. that there are exactly five regular solids in three dimensions. Ludwig Schlafli proved in 1901 that there are exactly six regular solids in four dimensions, and also proved that the only regular solids in dimensions greater than or equal to five are the generalized tetrahedron, cube, and octahedron.
 | Each shape can be attached to a multiple number of the same shape or other platonic shape to generate a bigger platonic solid or even a non platonic one, as happens during generation of crystals. In a way, one may regard a crystal lattice structure as a picture of the mechanism within the atom itself. So as you see, this theory works well at quantum level as well as at molecular level, which makes it unique. |  |
Similar to the two-dimensional case of the Chladni plate, the Platonic Solids are simply representations of waveforms in three dimensions. Each tip or vertex of the Platonic Solids touches the surface of a sphere in an area where the vibrations have canceled out to form a node. Thus, what we are seeing is a three-dimensional geometric image of vibration / pulsation within a sphere.
This explains why an atom does not necessarily look spherical. It does not however indicate that an atom is restricted to any particular size, and this means that an atom mechanism can be 'grown' as much as its spherical boundary is set. We know, from the art of growing crystals, that a crystal tends to use up similar atoms to grow up, retaining its original structure. Sonoluminescence, described earlier, we see how a mechanism in all respects similar to an atom can be setup to work in the size of a small bubble, many times greater than any known atom. As we can see, we no longer have to restrain atoms to a certain size; they are capable of existing on various scales and maintaining the same properties. Once we fully understand what is going on in the vibrating sphere, we can design materials that are extremely hard, extremely light, or extremely unstable at our wish.
As we know, most physics parameters cannot fit in a 3 dimensional space, but in addition to space, require a further dimension we call time. So, although a 3D platonic may give us a good picture of what an elementary particle looks like, it will not give us any indication about its movement in time. As we will see later on, a moving 3D shape can be integrated over time and be fully described by a stationery 4D shape. Thus in order to understand the motion of 3D platonics we need to consider platonics of a higher dimension. In four dimensions, the five Platonic Solids have six analogues. Interestingly enough higher dimensions have only three platonic solids, so the 4th dimension is the special case with the largest variety. In 4D, Polyhedra are called polytopes. The Simplex and the Hypercube are relatively easy to understand, and illustrated with projections, as analogues of the Tetrahedron and the Cube.
This explains why an atom does not necessarily look spherical. It does not however indicate that an atom is restricted to any particular size, and this means that an atom mechanism can be 'grown' as much as its spherical boundary is set. We know, from the art of growing crystals, that a crystal tends to use up similar atoms to grow up, retaining its original structure. Sonoluminescence, described earlier, we see how a mechanism in all respects similar to an atom can be setup to work in the size of a small bubble, many times greater than any known atom. As we can see, we no longer have to restrain atoms to a certain size; they are capable of existing on various scales and maintaining the same properties. Once we fully understand what is going on in the vibrating sphere, we can design materials that are extremely hard, extremely light, or extremely unstable at our wish.
As we know, most physics parameters cannot fit in a 3 dimensional space, but in addition to space, require a further dimension we call time. So, although a 3D platonic may give us a good picture of what an elementary particle looks like, it will not give us any indication about its movement in time. As we will see later on, a moving 3D shape can be integrated over time and be fully described by a stationery 4D shape. Thus in order to understand the motion of 3D platonics we need to consider platonics of a higher dimension. In four dimensions, the five Platonic Solids have six analogues. Interestingly enough higher dimensions have only three platonic solids, so the 4th dimension is the special case with the largest variety. In 4D, Polyhedra are called polytopes. The Simplex and the Hypercube are relatively easy to understand, and illustrated with projections, as analogues of the Tetrahedron and the Cube.
| 3 Dimensional Platonics | |||||
|---|---|---|---|---|---|
| Polytope | cells | vertices | edges | faces | duals |
| 1. Tetrahedron | triangle | 4 | 6 | 4 | self-dual |
| 2. Octahedron | triangle | 6 | 12 | 8 | cube |
| 3. Cube | square | 8 | 12 | 6 | Octahedron |
| 4. Icosahedron | triangle | 12 | 30 | 20 | dodecahedron |
| 5. Dodecahedron | pentagon | 20 | 30 | 12 | Icosahedron |
| 4 Dimensional "Platonic" Polytopes | |||||
|---|---|---|---|---|---|
| Polytope | cells | vertices | edges | faces | duals |
| 1. 5-cell, Pentatope or Simplex | tetrahedra | 5 | 10 | 10 | self-dual |
| 2. 8-cell, Tesseract or Hypercube | cubes | 16 | 32 | 24 | 16-cell |
| 3. 16-cell | tetrahedra | 8 | 24 | 32 | 8-cell |
| 4. 24-cell | octahedra | 24 | 96 | 96 | self-dual |
| 5. 120-cell | dodecahedra | 600 | 1200 | 720 | 600-cell |
| 6. 600-cell | tetrahedra | 120 | 720 | 1200 | l20-cell |
| n-Dimensional "Platonic" Polytopes, n > 4 | ||||
|---|---|---|---|---|
| Polytope | number of (n-1) D cells | vertices | duals | 3-d analogue |
| 1. (n + 1) cell | n + 1 n-cells | n + 1 | self-dual | Tetrahedron |
| 2. 2n-cell | 2n (2n-2)-cells | 2n | 2n-cell | Cube |
| 3. 2n-cell | 2n n-cells | 2n | 2n-cell | Octahedron |
Very interesting is the fact that, in ALL dimensions greater than four, there are exactly three analogues to the Platonic Solids. Also these 3 analogues: the Tetrahedron, cube and octahedron, exist in all dimensions. This is, curiously, exactly half the forms we find in 4 dimensions. Also, note that the 3D platonics (or their duals) are found in the cells making up the 4D polytopes. In a way, we can say that the 4 dimensional state, has the highest structural entropy of all, and that is where we live in!. In 1908, a Russian physicist, Minkovsky gave a new concept of space-time continuum, which may be regarded as the geometrical interpretation of the Special Relativity Theory. Minkovsky considered that space and time, being relative, describe a fourth dimension. The space-time is composed of individual events each of which is described by four complex numbers, three space coordinates x, y and z, and one time coordinate t. How does our brain react to 4D space? We tend to see the universe around us as a 3D space, changing in time. What actually our brain is doing, is to take one of the 4D axis as reference (=time) and differenciate (or photograph) the other 3 dimensions with respect to it. This results in a sequence or 3D images over time, but the reference dimension (time) is arbitrarily taken as reference only in our perspective, whilst in reality it is a space dimension in its own right.
The duals
| Tetra <-> Tetra | Hexa <-> Octa | Dodeca <-> Icosa |
 |  |  |
| Edge length to circumscribed sphere radius for tetrahedron= 163.3% | Edge length to circumsribed sphere radius for hexahedron (cube)= 115.47% & octahedron = 141.42% | Edge length to circumscribed sphere radius for icosahedron = 105.15% and dodecahedron = 71.364% |
| Inscribed to Circumscribed sphere radius ratio for tetrahedron= 33.33% | Inscribed to Circumscribed sphere radius ratio for BOTH hexahedron (cube) & octahedron = 57.735% | Inscribed to Circumscribed sphere radius ratio for BOTH icosahedron and dodecahedron = 92.624% |
| Inscribed to Circumscribed sphere volume ratio for tetrahedron= 3.7% | Inscribed to Circumscribed sphere volume ratio for BOTH hexahedron (cube) & octahedron = 19.245% | Inscribed to Circumscribed sphere volume ratio for BOTH icosahedron and dodecahedron = 79.465% |
| Inscribed Planck's spherical volume for tetrahedron= 1.8793E-107 m3 | Inscribed Planck's spherical volume for hexahedron (cube) = 2.762E-106m3 and for octahedron= 1.503E-106m3 | Inscribed Planck's spherical volume for icosahedron= 9.538E-106m3and dodecahedron = 3.05E-105m3 |
A very interesting characteristic of these five platonic solids, is the so called DUALITY. The dual of a platonic is the shape formed having its vertices at the centre of each face of the parent platonic. The importance of duality is re-confirmed in the 1000 BC old stones shown above, by the presence of white dots, that show the vertices of the dual platonic within each stone. As shown above, you can see that the tetrahedron is the dual of itself, whilst an octahedron is the dual of a hexahedron/cube (and vice versa), and a dodecahedron is the dual of the icosahedron (and vice versa). Thus each platonic can have nested platonics within it of diminishing sizes down to an infinetely small side lengths, and yet every nested structure will still have all characteristics of a platonic solid. In the case of the tetrahedron, where the number of faces is equal to the number of vertices, its dual will be the same shape of its parent platonic shape. From the above calculations, it is shown that the ratios between both radius and volume of any circumcribed sphere to its inscribed sphere is a constant, not only for the case tetra-tetra, but also to the other two dual platonics, even if the platonic shape of the duals is not the same.The limiting edge size of any platonic is equal to half Planck's length (1.616E-35m), since each side of the platonic is vibrating at its fundamental frequency, where node to node distance is equal to half a wavelength.
This length is the lower limit at which the classical description of gravity ceases to be valid, and below which 'length', and time to travel it, have no meaning. At this value of length, the theories of quantum mechanics and general relativity become incompatible, and so it seems reasonable that it should be at this value that our platonic standing wave should interact with gravity, otherwise it will be, at best, only as good as the present theories. There is a corresponding Planck time associated with the Planck length which is the time required for an EM wave or photon to travel the elementary Planck length at the speed of light, which equates to 5.39E-44 seconds. In the Duals table above, a value named Planck's spherical volume has been worked out for each platonic shape, representing the volume inside the inscribed sphere for the particular platonic shape with edge length equal to half Planck's length. This will later on be shown to be the matter-antimatter interface volume, known in Superstring theories as the light cone.
Picturing the standing wave atom model
by visualising rotating platonics
by visualising rotating platonics
Now that we know that indeed, to say the least, there is striking evidence that the atom structure is a standing wave, we need to describe in terms of this new concept, each observable conventional particle and picture how the real atom looks like.We know that the atom has a high density core at the centre surrounded by a cloud of electrons. However, even in the case of atoms with a single electron, we still see a cloud, and never has anyone been able to track any electron orbiting around. We have also shown that no orbital electrons exist and therefore electrons can never collide to each other. In this theory there is no room either for a particulate nucleus or anything else described as particulate matter within the atom. The whole atom is a standing wave in three dimensions, and all known effects have to be described by electromagnetic standing wave geometry. So, where does this leave us with the picture of an atom? Surely we have got no neutrons, protons or electrons, but our model should still account for their effects in terms of 3D standing wave geometry.
It has been already stated that a sphere has got just five natural frequency modes of vibration, and each of these frequencies gives rise to the formation of a platonic standing wave structure. Each 2 dimensional face of these structures is a standing EM wave node. Here on the left, a tetrahedron is shown. You may notice this shape has got 4 Vertices, 4 Faces, and 6 Edges. Euler's characteristic, as with the other four platonics is equal to F-E+V= 4-6+4 =2. It is understood that everything that we apply for this shape will apply for the other four platonics. Each platonic, when rotated in all possible angular directions about its centre, will form two spheres, one inscribed within its faces and one circumsribed by its vertices, as shown in the diagram. The inscribed sphere, will in turn be the circumscribed sphere of a smaller nested platonic structure, and so on, until a point is reached where the actual sides of the platonic equates to the smallest possible vibrating length in space, relating to planck length. The vertices of the internal nested platonic (the dual) will form at the centre of each face of the parent platonic. Curiously enough, this point is shown by dots on the 3,000 year old stones shown previously. This makes the inscribed sphere look very dense, in terms of standing wave structures. Unlike the conventional model, where the space between electron shells is described as a void and empty space, in our model it is the space in between the inscribed and circumscribed spheres, which contain the inward and outward going spherical waves forming up the 3D standing wave shape. Thus such a volume will be less opaque, and less dense than the standing wave shells. This volume, that is the volume trapped between the two spheres is what most call the 'electron cloud'. The internal inscribed sphere is as you might have guessed, what most call the nucleus. To reassure us of such an idea, we have to mention that one stable solution to Maxwell's equations is equivalent to a continuous standing electromagnetic wave arranged concentrically about a point. Standing waves of intermediate sizes explain the Rydberg constant and the fine and superfine structures of spectral lines, and may explain the valency shells of each atom. Since both nucleus and electrons in this model are made up of 3D standing waves, both of them will have common characteristics such as inertia (detected as mass), charge, and magnetic moments. Same characteristics, but not same values, as the energy density of the wave is inversely proportional to the square of the distance from the centre.
If an electric field is sweeping over a sphere, it induces a magnetic field at right angles. Integrating the cross product of the two fields -- over the surface of a sphere -- is equivalent energy divided the speed of light squared -- which is equal to mass. (This is a variation of Gauss's law of gravity.) It follows that the smallest entity which can have all characteristics of a particle should be one the simplest of the basic platonics described above. If this entity is unique, then it must be one whose dual is itself, and which has got its analogue existing in all dimensions. There is just one platonic satisfying this criteria and this is the Tetrahedron (in 3D), called the Simplex in 4D. Of course the atom is not as simple as one tetrahedron and consists of many such elementary particles and so need not be simply composed of nested tetrahedrons, but the above description gives the basic idea of how our model could eventially explain both nuclear and electron shells. Chemists all know about the existence of so called nuclear magic numbers, and atomic magic numbers, and these strongly indicate a kind of geometric structure governing both the built up of the nucleus and that of the electron cloud.
| The TETRAHEDRON is the most basic of the platonic bodies. It has four corners and four regular triangles as sides. There are three pairs of othogonal edges, the total number of edges is six. It may be considered the fundamental platonic shape, since as shown below, all platonic & archimedian shapes can be constructed by mathematical functions operating over this shape. The shortest path from one point to another on a spherical surface is along the arc of a great circle. This shortest path is called a geodesic. In particular the edges of a polyhedron can be replaced by arcs of great circles to obtain a spherical polyhedron. Each plane polygon that is a face of the polyhedron is thus transformed into a spherical polygon that is a face of the spherical polyhedron. The TETRAHEDRAL SPHERE is the central projection of the tetrahedron onto the surface of the unit sphere. The triangular sides of the tetrahedron become spherical triangles on the surface of the sphere, a spherical tetrahedron. |
 Diagram showing how all 5 Platonic & 13 Archimedian shapes are derived from a Tetrahedron |
Move your mouse over the image to rotate in 3D. Two points define a line (one dimension), three a plane (two dimension). This plane may have any orientation in space. Therefore, to define three-dimensional isotropic space, four nodes are required. We recognise a standing wave from a travelling wave from stationery nodes and antinodes, and that's the way we detect matter from EM energy. Each node will eventually contribute to the characteristics of the particle, including its charge and spin. |
Weyl, Clifford, Einstein, and Schroedinger agreed that the puzzle of matter would be found in the structure of space, not in point-like bits of matter. They speculated, "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. The complexity of physics and cosmology is just a special geometry." Perhaps it is about time we take such thoughts more seriously.
| Elementary spherical distribution showing the probability density of electrons in a Hydrogen atom in its first excited state (n=2). | |
| |  |
| 2,0,0 | 2,0,0 |
Schrödinger assumed that the electron's behavior could be described by a three dimensional standing wave. He derived an equation which described the amplitude of this wave. The simplest solution for the Schrödinger Equation for the ground state (1s) energy of a hydrogen atom is:
Y= Ae-Br
where A & B are constants, e is the base of the natural logs, and r is the radial distance from the nucleus.
The cross product (ExB) of two similar waves gives (Y2) tells the probability of finding an electron at any given location, or the 'mass' distribution of the electron cloud.
Y= Ae-Br
where A & B are constants, e is the base of the natural logs, and r is the radial distance from the nucleus.
The cross product (ExB) of two similar waves gives (Y2) tells the probability of finding an electron at any given location, or the 'mass' distribution of the electron cloud.
One may note that the dimension of the nodes is always one less than the dimension of the system. Thus, in a three-dimensional oscillating system the nodes would be two-dimensional rotating surfaces. The square of an electron's wave equation gives the probability function for locating the 'point' electron in any particular region. The orbitals or shells used by chemists describe the shape of the region where there is a high probability of finding a particular electron. Electrons are confined to the space surrounding a nucleus in much the same manner that the standing waves in the platonic are constrained to its surfaces. The constraints of each platonic forces each side to vibrate with specific frequencies, in the case of the tetrahedron each parent platonic will have 3 times the side length of its nested shape. So, an electron, which is equivalent to one of these rotating platonics, can only vibrate with specific frequencies, called eigenfrequencies and the states associated with these frequencies are called eigenstates or eigenfunctions. The set of all eigenfunctions for an electron form a mathematical set called the spherical harmonics. There are an infinite number of these spherical harmonics, but they are specific and discrete. Thus an atomic electron can only absorb and emit energy in specific in small packets called quanta. It does this by making a quantum leap from one eigenstate to another.
 | We found a strickingly similar model to the one we are approaching here in Dr. Robert J. Moon's model of the nucleus, a nesting of four of the five Platonic solids similar to that conceived by Johannes Kepler to describe our solar system. Even though this model does not show the tetrahedron as the inner platonic, we know that every cube implies a tetrahedron. Four diagonally opposite vertices of the cube form the vertices of the tetrahedron, and in fact two equal tetrahedrons may be positioned inside a cube, touching all 8 vertices of the cube. The combination of two such tetrahedrons is known as Stella Octangula. |
| Here is a photograph of a working mechanical model of this nucleus, made for Moon by retired machinist George Hamann in 1986. As we shall discuss later on in this section, the radial distance from the core, represents time, somewhat similar to the concept of measuring distance in light years. As we shall also see, positive time and positive entropy cannot be separated, thus it makes sense, that platonic shapes as time goes forward, will have a higher entropy, which result in a higher number of vertices. |  |
 | The periodicity of the atomic volumes of the elements (the ratio of their atomic weight to density) - a measurement of structure compactness guided Lothar Meyer in the 19th-century in developing the periodic table. The maxima in the graph at atomic numbers 3, 11, 19, 55, and 87 identify the Group 1A elements that begin each period. However, minima occur in the same graph at or near the atomic numbers 8, 14, 26, and 46, which mark the completed platonic shapes of this nucleus model. Moon equated each vertice in his model to a proton. Eight protons, corresponding to the Oxygen nucleus, occupy the vertices of a cube which is the first nuclear shell. Six more protons, corresponding to Silicon, lie on the vertices of an octahedron which contains, and is dual to, the cube. The octahedron-cube is contained within an icosahedron, whose 12 additional vertices, now totalling 26 protons, correspond to Iron. The icosahedron-octahedron-cube nesting is finally contained within, and dual to, a dodecahedron. The 20 additional vertices, now totalling 46 protons, correspond to Palladium, the halfway point in the periodic table. |
Beyond Palladium, a second dodecahedral shell begins to form as a twin to the first. After 10 of its 20 vertices are filled at Lanthanum (atomic number 56), a cube and octahedron nesting fill inside it, accounting for the 14 elements of the anomalous Lanthanide series.
Next, the icosahedron forms around the cube-octahedron structure, completing its 12 vertices at Lead (atomic number 82), which is the stable, end-point in the radioactive decay series. Finally the dodecahedron fills up, and the twinned structure hinges open, creating the instability which leads to the fissioning of uranium.
The completed shells of the Moon model, correspond to the elements whose stability is attested by their abundance in the Earth’s crust: Oxygen, Silicon, and Iron. These elements also occur at minima in the graphs of atomic volume, and of other physical properties (viz. compressibility, coefficient of expansion, and reciprocal melting point) as established by Lothar Meyer in the 1870s to 1880s. Palladium, which is an anomaly in the modern electron-configuration conception of the periodic table because it has a closed electron shell, but occurs in the middle of a period is not anomalous in the Moon model. Further, all four closed-shell elements in the Moon model occur at maxima on the graph of paramagnetism (versus atomic number), as reported by William Draper Harkins.
The Moon model is thus consistent with much of the same experimental data which underlies the periodic table of the elements, and explains additional features not explained by the modern, electron-configuration presentation of the periodic table. However, it seems to be inconsistent with the evidence from spectroscopy (upon which the electron-configuration conception rests) which suggests the periods of 2, 8, 18, and 32; it is also not consistent with the older law of octaves, which was developed to explain the phenomena of chemical bonding, and was subsumed in Mendeleyev’s conception. So, although Moon's model has introduced important geometric ideas, its accuracy is not good enough to match with experimental evidence. This means that his basic assumption - that vertices correspond to particles - may not be quite right.
Next, the icosahedron forms around the cube-octahedron structure, completing its 12 vertices at Lead (atomic number 82), which is the stable, end-point in the radioactive decay series. Finally the dodecahedron fills up, and the twinned structure hinges open, creating the instability which leads to the fissioning of uranium.
The completed shells of the Moon model, correspond to the elements whose stability is attested by their abundance in the Earth’s crust: Oxygen, Silicon, and Iron. These elements also occur at minima in the graphs of atomic volume, and of other physical properties (viz. compressibility, coefficient of expansion, and reciprocal melting point) as established by Lothar Meyer in the 1870s to 1880s. Palladium, which is an anomaly in the modern electron-configuration conception of the periodic table because it has a closed electron shell, but occurs in the middle of a period is not anomalous in the Moon model. Further, all four closed-shell elements in the Moon model occur at maxima on the graph of paramagnetism (versus atomic number), as reported by William Draper Harkins.
The Moon model is thus consistent with much of the same experimental data which underlies the periodic table of the elements, and explains additional features not explained by the modern, electron-configuration presentation of the periodic table. However, it seems to be inconsistent with the evidence from spectroscopy (upon which the electron-configuration conception rests) which suggests the periods of 2, 8, 18, and 32; it is also not consistent with the older law of octaves, which was developed to explain the phenomena of chemical bonding, and was subsumed in Mendeleyev’s conception. So, although Moon's model has introduced important geometric ideas, its accuracy is not good enough to match with experimental evidence. This means that his basic assumption - that vertices correspond to particles - may not be quite right.
| At this point, we may have a look at what might be happening in a bose-eintein condensate (BEC). What happens when such a platonic structure is cooled down to zero Kelvin and screened from all external energies, does the structure collapse? The effect of external EM radiation, such as heat, on a standing wave structure, is exchange of momentum. It is a known fact that EM radiation exerts momentum on matter. Such impacts of heat energy upon the platonic arrives randomly from its surroundings, but gives the same average momentum impulses to each edge, which results in rotation of the platonic about its centre. In this way the platonic vertices will be able to span a whole sphere over time. The whole integral of momentum over the time taken to span one whole sphere is zero. Indeed if we lower the temperature to absolute zero, and shield our atom from all EM radiations, the atom will no longer rotate, and there will be no more volume of space trapped between any two spheres, hence no electron cloud, but the structure does not breakdown, it simply becomes one huge entity made up of stationary platonic standing waves. In 1995, Ketterle cooled a gas made of sodium atoms to a few hundred billionths of a degree above absolute zero and created the first Bose-Einstein condensate. In such condition, the atoms do not need the spherical boundary between them, since they are not rotating. This means that the atoms will eventually pack side by side to each other forming a single compact standing wave structure. No wonder that since all platonic shapes have an even number of vertices, BEC are only possible with atoms with even number of electrons + protons + neutrons, normally referred to as bosons. The Bose Einstein plot shown here (top) shows the distribution of atoms in volume as temperature is decreased from 400nK to 200nK down to 50nK, in the order from left to right. Another variation of this state of matter is the fermionic condensate (lower plot). This substance has been created by cooling a cloud of 500,000 potassium-40 atoms to less than a millionth of a degree above absolute zero. In a BEC, the atoms are bosons. In a fermionic condensate the atoms are fermions. Bosons are sociable; they like to get together. Fermions, on the other hand, are antisocial. Any atom with an odd number of electrons + protons + neutrons, like potassium-40, is a fermion. To overcome the antisocial problem in the fermionic condensate, an external magnetic field has to be applied. |   |
In the above diagram, the cooling down of the gas is shown in three steps. The patterns represent a platonic with its outer circumscribing sphere. When the gas is cooled down, the atoms slow down their rotating movement, impacts due to external travelling EM waves get weaker, as do the impacts with each other, thus reducing their intermolecular distance. Reducing the temperature further, the gas structure will resemble more that of a liquid, with atoms touching each other at their spherical 'shell' that is formed by the slowly rotating platonics inside. Approaching absolute zero, the platonics stop rotating, thus the circumscribed spherical space no longer exists, and they can pack next to each other node to node in the most efficient & compact way. In such condition, the atoms lack their electron cloud, and actually cannot be identified from one another, forming the so called Bose-Einstein condensate or superatom.
Fractional electron charges
Most of the matter we see around us is made from protons and neutrons, which are each composed of 3 quarks. There are six quarks, or quark flavours, but physicists usually talk about them in terms of three pairs: up/down, charm/strange, and top/bottom. Top and bottom types are the most elementary of them all, and are the ones that make up protons and neutrons. Quarks have the unusual characteristic of having a fractional electric charge, unlike the proton and electron, which have integer charges of +1 and -1 respectively. The up, charm and top quarks have a charge of +2/3, whilst the down, strange and bottom have a charge of -1/3. Although individual quarks have fractional electrical charges, they normally combine into 'hadrons' such that these hadrons have a net integer electric charge. Protons and neutrons are good examples of quark grouping or hadrons. Researchers at the Weizmann Institute of Science have provided the first unambiguous evidence that electrons can behave in an intriguing way that seems to defy the idea of the electron being an indivisible charged elementary unit.
An electron is by convention considered to be a tiny indivisible hard particle that carries the smallest negative charge in nature. Yet a daring theory of physics developed 15 years ago argues that under certain conditions, an electric current behaves as if it were made up of fractions of electronic charges. In an experiment described in September 11,1997 issue of Nature, Weizmann Institute physicists measured fractional charges one-third that of an electron.
"Mind-boggling as this may seem, this phenomenon is real," says study author Rafael de-Picciotto. "Of course, electrons don't split into fragments in an electric current, but under certain conditions it is indeed possible to measure a charge smaller than that of an electron." This means, that although the electron charge is always the same well known value, it can no longer be stated that this value is the smallest possible value for electrical charge.
Almost 100 years ago, ever since American physicist Robert Millikan first measured the charge of an electron as equal to 1.602E-19C, this value has been widely regarded as a basic unit of electric charge. Scientists have consequently come to view electrons that make up an electric current as a flow of negatively charged, indivisible elementary charged "balls." A current made up of fractions of an electronic charge, therefore, would seem not to fit in Millikan's findout.
However, if electrons are always regarded as a "whole" or fundamental, as understood by current science, it is extremely difficult to understand and describe their behavior under certain conditions. For example, some particular instances of this behavior, as in a phenomenon known as the fractional quantum Hall effect, observed in a strong magnetic field, remain unexplained.
In 1982, physicist Robert Laughlin of the United States proposed a theory that explained this effect and provided a very simple way of describing highly complex interactions between electrons. However, this explanation came at a cost for physics community: the theory made the bizarre assumption that an electric current can be made up of 1/3 fractions of an electron charge.
In a new experiment, Weizmann Institute scientists designed a sophisticated system to measure such fractional electric charges, should they exist. The system makes it possible to measure so-called "shot noise." In day-to-day environment, this noise results from random variations in the number and velocity of electrons and causes popping sounds in radio receivers and snow effects in television pictures. Under special laboratory conditions, "shot noise" can be analyzed to reveal the make-up of the electric current. This is possible because the noise has "ripples" left by the flow of electrons in a conductor. The size of each "ripple" is proportional to the unit of electric charge: the smaller the ripple, the smaller the charge, and vice versa.
The scientists passed an electric current through a semiconductor immersed in a high magnetic field, under conditions in which the fractional quantum Hall phenomenon is observed. They used sophisticated equipment to eliminate all extraneous sources of noise. The "shot noise" made by the current was then amplified and measured. It turned out to be made of charges one-third that of an electron.So this confirms that an electron is not a fundamental particle, since such element should be indivisible, simple and structureless.
An electron is by convention considered to be a tiny indivisible hard particle that carries the smallest negative charge in nature. Yet a daring theory of physics developed 15 years ago argues that under certain conditions, an electric current behaves as if it were made up of fractions of electronic charges. In an experiment described in September 11,1997 issue of Nature, Weizmann Institute physicists measured fractional charges one-third that of an electron.
"Mind-boggling as this may seem, this phenomenon is real," says study author Rafael de-Picciotto. "Of course, electrons don't split into fragments in an electric current, but under certain conditions it is indeed possible to measure a charge smaller than that of an electron." This means, that although the electron charge is always the same well known value, it can no longer be stated that this value is the smallest possible value for electrical charge.
Almost 100 years ago, ever since American physicist Robert Millikan first measured the charge of an electron as equal to 1.602E-19C, this value has been widely regarded as a basic unit of electric charge. Scientists have consequently come to view electrons that make up an electric current as a flow of negatively charged, indivisible elementary charged "balls." A current made up of fractions of an electronic charge, therefore, would seem not to fit in Millikan's findout.
However, if electrons are always regarded as a "whole" or fundamental, as understood by current science, it is extremely difficult to understand and describe their behavior under certain conditions. For example, some particular instances of this behavior, as in a phenomenon known as the fractional quantum Hall effect, observed in a strong magnetic field, remain unexplained.
In 1982, physicist Robert Laughlin of the United States proposed a theory that explained this effect and provided a very simple way of describing highly complex interactions between electrons. However, this explanation came at a cost for physics community: the theory made the bizarre assumption that an electric current can be made up of 1/3 fractions of an electron charge.
In a new experiment, Weizmann Institute scientists designed a sophisticated system to measure such fractional electric charges, should they exist. The system makes it possible to measure so-called "shot noise." In day-to-day environment, this noise results from random variations in the number and velocity of electrons and causes popping sounds in radio receivers and snow effects in television pictures. Under special laboratory conditions, "shot noise" can be analyzed to reveal the make-up of the electric current. This is possible because the noise has "ripples" left by the flow of electrons in a conductor. The size of each "ripple" is proportional to the unit of electric charge: the smaller the ripple, the smaller the charge, and vice versa.
The scientists passed an electric current through a semiconductor immersed in a high magnetic field, under conditions in which the fractional quantum Hall phenomenon is observed. They used sophisticated equipment to eliminate all extraneous sources of noise. The "shot noise" made by the current was then amplified and measured. It turned out to be made of charges one-third that of an electron.So this confirms that an electron is not a fundamental particle, since such element should be indivisible, simple and structureless.
The search for the elementary particle
As you see, the one-third electron charge keeps popping up from every experimental evidence we have. Weyl, Clifford, Einstein, and Schroedinger once speculated, "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space." Our spherical tetrahedron model shown above is indeed based on this speculation and clearly indicates that the six quarks connecting up the protons & neutrons are equivalent to the six sides of the spherical tetrahedron. Protons and neutrons are just the point effects of their points of intersection, and these types of hadrons can therefore be defined as the intersection point of 3 standing wave planes.
Remember that the six sides of this tetrahedron are in fact a picture of the fundamental standing wave nodes which appear on any 3D vibrating sphere. So, if the sides of our model are the 1 dimensional quarks (6 off), then, each vertex connecting a group of 3, will define a hadron (a group of 3 quarks). In the diagram you see the three blue elements are equivalent to down quarks and the 3 red ones to up quarks. By joining together these two frames, a three dimensional closed platonic structure consisting of two neutrons and two protons is formed, equivalent to the simplest & strongest stable nucleus of Helium, namely the Alpha particle. This model also clearly explains why neutrons and protons never collide within a nucleus, despite being so close. Once the platonic structure is completed, the protons and neutrons act as a single entity - the one we call nucleus. It also gives a new meaning to the strong nuclear bonds, since a tetrahedron is the most stable, and compact geometric 3D shape.
At first, it might seem a little bit confusing that a 'solid' nucleus, is made up of a fixed 3D geometric shape of 2D planes and no 3D hard particles, but the fact that we can now explain a quark in terms of a 1 dimensional nodal string connection makes sense and reassures us that we really found the most fundamental elements - simple elements with no structure. The charge on each of these hadrons is simply the addition of the charges of the quarks, or sides making up the frame of the particular hadron. This spherical tetrahedron model has some interesting attributes not the least of which is the fact that spheres which resonate in phase are known to "attract" one another, while those with unlike phase angles will repel. We have established that atoms are EM vibrating spheres and this gives a new more clear meaning to the gravitational force between atoms. It is known that two spheres vibrating in phase attract. If all matter in the universe is a differential of the same 4D hyperspherical EM singularity, then it makes sense that all matter gets attracted to each other since all matter would be vibrating in phase.
Remember that the six sides of this tetrahedron are in fact a picture of the fundamental standing wave nodes which appear on any 3D vibrating sphere. So, if the sides of our model are the 1 dimensional quarks (6 off), then, each vertex connecting a group of 3, will define a hadron (a group of 3 quarks). In the diagram you see the three blue elements are equivalent to down quarks and the 3 red ones to up quarks. By joining together these two frames, a three dimensional closed platonic structure consisting of two neutrons and two protons is formed, equivalent to the simplest & strongest stable nucleus of Helium, namely the Alpha particle. This model also clearly explains why neutrons and protons never collide within a nucleus, despite being so close. Once the platonic structure is completed, the protons and neutrons act as a single entity - the one we call nucleus. It also gives a new meaning to the strong nuclear bonds, since a tetrahedron is the most stable, and compact geometric 3D shape.
At first, it might seem a little bit confusing that a 'solid' nucleus, is made up of a fixed 3D geometric shape of 2D planes and no 3D hard particles, but the fact that we can now explain a quark in terms of a 1 dimensional nodal string connection makes sense and reassures us that we really found the most fundamental elements - simple elements with no structure. The charge on each of these hadrons is simply the addition of the charges of the quarks, or sides making up the frame of the particular hadron. This spherical tetrahedron model has some interesting attributes not the least of which is the fact that spheres which resonate in phase are known to "attract" one another, while those with unlike phase angles will repel. We have established that atoms are EM vibrating spheres and this gives a new more clear meaning to the gravitational force between atoms. It is known that two spheres vibrating in phase attract. If all matter in the universe is a differential of the same 4D hyperspherical EM singularity, then it makes sense that all matter gets attracted to each other since all matter would be vibrating in phase.
| 3 Dimensional Platonics | |||||
|---|---|---|---|---|---|
| Polytope | vertices | edges | faces | duals | hadron pairs |
| 1. Tetrahedron | 4 | 6 | 4 | self-dual | 2 |
| 2. Tetradual | 4 | 6 | 4 | Tetrahedron | 2 |
| 3. Octahedron | 6 | 12 | 8 | cube | - |
| 4. Cube | 8 | 12 | 6 | Octahedron | 4 |
| 5. Icosahedron | 12 | 30 | 20 | dodecahedron | - |
| 6. Dodecahedron | 20 | 30 | 12 | Icosahedron | 10 |
Look closely at the hadron pair coloumn: 2,2,4,10.
If we start off with the tetrahedron, and add up shells with the next platonic, we will get the series: 2,2,2+2+4,2+2+4+10 = 2,2,8,18.
We know that the number of electrons is equal to the number of protons, hence to the number of hadron pairs. Spectroscopy data gives the sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d,... or 2,2,6,2,6,2,10,6,2, which may also be grouped as 2,2,8,18, similar to the shell build up sequence of Tetra, tetra, cube and dodecahedron.
So we have seen that a simple tetrahedron is the most accurate picture for a Helium nucleus, which has the strongest nuclear bond of all elements and is better known the alpha particle. The Alpha particle thus consists of 4 hadrons, two protons and two neutrons, with a total charge of +2. Protons and neutron are equivalent to the vertices of the standing wave shapes. We can also extend the same model to construct the Be4 nucleus, which has a total binding energy of twice that of 4He2. This is done by fitting another tetrahedron as shown below to obtain the 8Be4 nucleus, with its vertices common to a cube, representing its 4 protons and 4 neutrons. Note that these structures should not be considered as solid structures but as nodes on spinning spherical surfaces, with each edge element equivalent to a quark, and each vertex to a nucleon. At all times, tt should be kept in mind that these shapes are actually 3D standing EM waves, which can also share nodes.
If we start off with the tetrahedron, and add up shells with the next platonic, we will get the series: 2,2,2+2+4,2+2+4+10 = 2,2,8,18.
We know that the number of electrons is equal to the number of protons, hence to the number of hadron pairs. Spectroscopy data gives the sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d,... or 2,2,6,2,6,2,10,6,2, which may also be grouped as 2,2,8,18, similar to the shell build up sequence of Tetra, tetra, cube and dodecahedron.
So we have seen that a simple tetrahedron is the most accurate picture for a Helium nucleus, which has the strongest nuclear bond of all elements and is better known the alpha particle. The Alpha particle thus consists of 4 hadrons, two protons and two neutrons, with a total charge of +2. Protons and neutron are equivalent to the vertices of the standing wave shapes. We can also extend the same model to construct the Be4 nucleus, which has a total binding energy of twice that of 4He2. This is done by fitting another tetrahedron as shown below to obtain the 8Be4 nucleus, with its vertices common to a cube, representing its 4 protons and 4 neutrons. Note that these structures should not be considered as solid structures but as nodes on spinning spherical surfaces, with each edge element equivalent to a quark, and each vertex to a nucleon. At all times, tt should be kept in mind that these shapes are actually 3D standing EM waves, which can also share nodes.
 |  |
| The 8Be4 nucleus platonic combination & equivalent spherical standing wave structure. | |
- Binding Energy for 4He : 28295.673 keV (Single tetrahedron)
- Binding Energy for 8Be : 56499.506 keV (Two compound tetras)
- Twice binding energy for 4He : 56591.346 keV
- The difference Be - 2*He = -91.84 keV is due to the energy interaction of the two similar tetrahedrons.
- Spin for both 4He & 8Be: Zero
- Half life for 8Be: 6.8 EV
- Mode of decay for 8Be: 2 Alpha
- Decay energy for 8Be: 0.092 MeV
Even though very light, 8Be is a very stable metal. Its elasticity is larger than that of steel, its strength four times that of aluminum. The melting point at nearly 1600 K is very high. In the gas phase Beryllium is monoatomic.
The above structure is the compound of two tetrahedra called the stella octangula, discovered by Kepler. The vertices define a cube and the intersection of the two an octahedron, which shares the same face-planes as the compound. Thus it is a stellation of the octahedron, and in fact, the only stellation thereof. The probability of natural existance of such a structure is fully confirmed by many photos of vibrating fluids taken by Dr. Hans Jenny in his Cymatics study of sound vibrations in liquids. In this self explanatory diagram, you can see how two standing wave spherical tetrahedrons combine within the same 'shell', forming the double spherical tetrahedron structure. The two tetrahedrons are no longer independent, and any clockwise movement of one tetrahedron must be accompanied by an anticlockwise movement of its dual so that the stella octangula moves as a whole body.
In ancient times, this shape was given great importance, and was known as MerKaBa. The Merkaba is a symbol from the sacred geometry and is the symbol upon which the Star of David is based. The Merkaba has significance in different ancient cultures around the world. In the Bible’s book of Ezekiel, it is referred to as the chariot of Gods and in Hebrew, Merkaba means chariot. Some refer to the Merkaba as the 'vehicles of vehicles', or the tool for ascension. The ancient Egyptian (18th dynasty) meaning is even more interesting as it stands for MER= counter rotating fields of light in the same space, KA=spirit and BA=soul. How could ancient Egyptians know of 'counter rotating fields of light'?
In ancient times, this shape was given great importance, and was known as MerKaBa. The Merkaba is a symbol from the sacred geometry and is the symbol upon which the Star of David is based. The Merkaba has significance in different ancient cultures around the world. In the Bible’s book of Ezekiel, it is referred to as the chariot of Gods and in Hebrew, Merkaba means chariot. Some refer to the Merkaba as the 'vehicles of vehicles', or the tool for ascension. The ancient Egyptian (18th dynasty) meaning is even more interesting as it stands for MER= counter rotating fields of light in the same space, KA=spirit and BA=soul. How could ancient Egyptians know of 'counter rotating fields of light'?
Development of the new model
A proper model has to be compliant with experimental evidence and so be in perfect agreement with the spectral data for each atom. It is evident from our previous discussions that each shell is equivalent to a polyhedra shell, and getting the right sequence of shells is of primary importance in order to further develop the correct sequence of polyhedra transformations for each equivalent quantum number. If quantum numbers are unique, it then follows from our knowledge about the 6 unique basic platonics (5+dual tetra), that all basic elements can be described by no more than 6 pricipal quantum numbers.
Let us first see what the present theory says. Conventionally, the maximum number of electrons in the set of orbitals, defined by the principal quantum number n = 1, 2, 3, 4 etc., (also known by their spectroscopic designation K, L, M, N, etc., ) is given by the formula Z max = 2n2 and it is presented in table below.
Let us first see what the present theory says. Conventionally, the maximum number of electrons in the set of orbitals, defined by the principal quantum number n = 1, 2, 3, 4 etc., (also known by their spectroscopic designation K, L, M, N, etc., ) is given by the formula Z max = 2n2 and it is presented in table below.
| Principal quantum number | Number of electrons in a subshell | Maximum number of electrons in a shell | ||||||
| n> | symbol | s (l=0) | p (l=1) | d (l=2) | f (l=3) | g (l=4) | h (l=5) | Z max |
| 1 | K | 2 | - | - | - | - | - | 2 |
| 2 | L | 2 | 6 | - | - | - | - | 8 |
| 3 | M | 2 | 6 | 10 | - | - | - | 18 |
| 4 | N | 2 | 6 | 10 | 14 | - | - | 32 |
| 5 | O | 2 | 6 | 10 | 14 | 18 | - | 50 |
| 6 | P | 2 | 6 | 10 | 14 | 18 | 22 | 72 |
Electron configuration
The electron configuration of an atom might be presented by the number of electrons in each subshell, by the order of filling.
The conventional electron occupancy of the subshells of all atoms is as follows:
The electron configuration of an atom might be presented by the number of electrons in each subshell, by the order of filling.
The conventional electron occupancy of the subshells of all atoms is as follows:
giving maximum shell capacity sequence 2,8,18,32,50... etc. Theoretically, with such a theory, additional subshells such as the g, h and so on, can exist, but they are not required for any real atoms. See the scheme below:
| 1 |  | 1s | 2 | ||||||
| 2 | | 2s | 2p | 8 | |||||
| 3 | | 3s | 3p | 3d | 18 | ||||
| 4 | | 4s | 4p | 4d | 4f | 32 | |||
| 5 | | 5s | 5p | 5d | 5f | 5g | 50 | ||
| 6 | | 6s | 6p | 6d | 6f | 6g | 6h | 72 | |
| 7 | | 7s | 7p | 7d | 7f | 7g | 7h | 7i | 98 |
 | But, by just observing the electron shells of heavy atoms, one can observe that we soon run into problems, because higher shells start to be filled up before the respective lower shell has attained its full capacity. It is a well known nightmare for chemistry teachers, that, beginning with Z=19, a vivid struggle between normal filling and exeptional filling of subshells starts. Also, according to the experimental spectral data, in the ground state, electrons fill the quantum states in the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d ... respectively, giving maximum shell capacity sequence 2,8,8,18,18,32,32. If you try to follow this sequence on the above table, you will encounter 'jumping' back and forth between quantum levels, which does not make sense, since quantum levels must be filled in the same sequential order as the shells. If you imagine building up nested platonic shapes, it makes no sense for a sequence to start within the inner structure of a completed platonic to compose the next higher shell. Once an inner structure is complete (shell filled up or 'sealed'), higher shells cannot add any part within it. We therefore see, that the conventional way of shell capacity sequencing s->p->d->f is wrong. The scheme below shows a new way, which although still uses the conventional shell & electron method, describes in a different way which shells go with each respective quantum number, and as you see it is exactly the same order shown by the sequence we got from the experimental spectral data! |
| 1 | | 1s | 2 | ||||
| 2 | | 2s | 2p | 8 | |||
| 3 | | 3s | 3p | 8 | |||
| 4 | | 4s | 3d | 4p | 18 | ||
| 5 | | 5s | 4d | 5p | 18 | ||
| 6 | | 6s | 4f | 5d | 6p | 32 | |
| 7 | | 7s | 5f | 6d | 7p | 32 | |
The above table matches the sequence given from spectral data, and also the maximum number of elements of 118 matches the conventional periodic table. But if we try to analyse it in terms of shell build up, there seems to be something still wrong. For example, lets take shell number 7, first we find subshell 7s (l=0), then instead of moving to the next subshells in the order s,p,d,f (l=0,1,2,3..) we see that we are first filling subshell s, and then the remaining subshells in the reverse order f,d,p. It makes sense that higher subshells (lower energy levels) get filled up before the lower subshells (higher energy levels) for each quantum shell number. This means that the table has to be shifted all by one term, in order to move the 's' subshells at the end of each shell build, thus making all shells fill up in the same order f,d,p,s as follows:
| 1 | | 1s | 2 | ||||
| 2 | | 2s | 2 | ||||
| 3 | | 2p | 3s | 8 | |||
| 4 | | 3p | 4s | 8 | |||
| 5 | | 3d | 4p | 5s | 18 | ||
| 6 | | 4d | 5p | 6s | 18 | ||
| 7 | | 4f | 5d | 6p | 7s | 32 | |
| 8 | | 5f | 6d | 7p | 8s | 32 | |
 | With the new scheme the quantum numbers will match the lowest energy level subshell of the shell. Quantum number 1 will thus match those subshells with total electron count of 2, quantum number 2 will match those subshells with electron count of 8 and so on. This new quantum numbering scheme now has the same filling order of the subshells and the problem of jumping is totally eliminated during the subshells' filling, with the electrons in full accordance to the present experimental data. In the conventional model, this problem occurs for example at the filling of element with atom no. 19 Calcium, instead of 3d subshell filling, the subshell 4s is filled. The same surprise occurs at the elements with atom no.37 - Rubidium and atom no.55 - Cesium). Also, in contrary to the conventional way of electron shell configuration, with this new scheme, up to 56 basic elements can be contained within the first 6 shells or 3 principle quantum numbers, and up to 120 basic elements can be contained within 8 shells or 4 principle quantum numbers. The new model, apart from being much neater, can thus contain all known elements by using just s,p,d,f shells, without the need to resort to higher shells g,h.. whose existence is not proven. Below is a table summarising the proposed model. |
| Principal quantum number | Shell quantum number | Number of electrons in a subshell | Maximum number of electrons in a shell | Maximum number of electrons in a level | Maximum number of electrons in atom | ||||
| n | symbol | ns | f (l=3) | d (l=2) | p (l=1) | s (l=0) | Zsmax | Zlmax | Zmax |
| 1 | K | 1 | - | - | - | 2 | 2 | 4 | 2 |
| L | 1' | - | - | - | 2 | 2 | 4 | ||
| 2 | M | 2 | - | - | 6 | 2 | 8 | 16 | 12 |
| N | 2' | - | - | 6 | 2 | 8 | 20 | ||
| 3 | O | 3 | - | 10 | 6 | 2 | 18 | 36 | 38 |
| P | 3' | - | 10 | 6 | 2 | 18 | 56 | ||
| 4 | Q | 4 | 14 | 10 | 6 | 2 | 32 | 64 | 88 |
| R | 4' | 14 | 10 | 6 | 2 | 32 | 120 | ||
This new sequence is totally in agreement with experimental spectral data sequence:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s ... , which with the new quantum shell renumbering becomes:
1s, 1s', 2p, 2s, 2p', 2s', 3d, 3p, 3s, 3d', 3p', 3s', 4f, 4d, 4p, 4s, 4f', 4d', 4p', 4s' ...
Renumbering the quantum shell levels does not change the original basic sequence:
2, 2, 6, 2, 6, 2, 10, 6, 2, 10, 6, 2, 14, 10, 6, 2, 14, 10, 6, 2 ...
Note that the sequence is now very simple and no non-sense jumping between quantum levels is required to agree with experimental spectral data. Also, a new kind of symmetry now becomes evident. It becomes very noticable the fact that each principle quantum level is now composed of a paired structure, a double shell, which must be fully filled before the level can be 'sealed'. Once 'sealed' or completed, the next quantum level will have no effect on the sealed level during its growth. Since every two consequtive shells are composed exactly the same, quantum numbers can now be halved, and each quantum number is given a property of 'spin' where the first shell of each level shall be arbitrarily be the positive quantum spin denoted by the usual notations 1s, 2s, etc.. and the second shell will be the negative quantum spin and is denoted by 1s', 2s', etc.. The new sequence thus becomes:
(1s 1s') (2p 2s, 2p' 2s') (3d 3p 3s, 3d' 3p' 3s') (4f 4d 4p 4s, 4f' 4d' 4p' 4s')
Thus the electron configuration now consists of only four shells, each shell being a double-structure with twice as many electrons per shell as in the conventional electron configuration. This double quantum structure is clearly shown by plotting various physical characteristics for the elements. Similar graphs for density, ionisation energy, electronegativity, etc.. all show the same characteristic of twin quantum levels, immediately obvious at first glance at the paired curves for each quantum level. Shown below is the density vs atomic number graph, which makes it clear that all elements can be built up by nesting 4 paired structures.
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s ... , which with the new quantum shell renumbering becomes:
1s, 1s', 2p, 2s, 2p', 2s', 3d, 3p, 3s, 3d', 3p', 3s', 4f, 4d, 4p, 4s, 4f', 4d', 4p', 4s' ...
Renumbering the quantum shell levels does not change the original basic sequence:
2, 2, 6, 2, 6, 2, 10, 6, 2, 10, 6, 2, 14, 10, 6, 2, 14, 10, 6, 2 ...
Note that the sequence is now very simple and no non-sense jumping between quantum levels is required to agree with experimental spectral data. Also, a new kind of symmetry now becomes evident. It becomes very noticable the fact that each principle quantum level is now composed of a paired structure, a double shell, which must be fully filled before the level can be 'sealed'. Once 'sealed' or completed, the next quantum level will have no effect on the sealed level during its growth. Since every two consequtive shells are composed exactly the same, quantum numbers can now be halved, and each quantum number is given a property of 'spin' where the first shell of each level shall be arbitrarily be the positive quantum spin denoted by the usual notations 1s, 2s, etc.. and the second shell will be the negative quantum spin and is denoted by 1s', 2s', etc.. The new sequence thus becomes:
(1s 1s') (2p 2s, 2p' 2s') (3d 3p 3s, 3d' 3p' 3s') (4f 4d 4p 4s, 4f' 4d' 4p' 4s')
Thus the electron configuration now consists of only four shells, each shell being a double-structure with twice as many electrons per shell as in the conventional electron configuration. This double quantum structure is clearly shown by plotting various physical characteristics for the elements. Similar graphs for density, ionisation energy, electronegativity, etc.. all show the same characteristic of twin quantum levels, immediately obvious at first glance at the paired curves for each quantum level. Shown below is the density vs atomic number graph, which makes it clear that all elements can be built up by nesting 4 paired structures.
Binding Energy Curve
 | This curve shows the nuclear binding energy vs mass (P+N) number. As one can see, the most stable nucleui are those shown at the peaks which are 2He4, 6C12, 8O16 and 28Fe56. Incidentally these are the most cosmic abundant elements. The heaviest most stable element is iron, element number 28, which also sets the divisor between fusion & fission elements. As you will see, in our model this element is achieved when quantum level 3 is fully completed and 'sealed'. |
Nuclear Stability & Hybrid Tetrahedral fractal formation
| Stable nuclei generally have the same number of protons and neutrons (or Z=N, where Z is the number of protons and N is the number of neutrons in the nucleus). This is more strictly observed for light nuclei with fewer than 20 protons (Z<=20) (see figure on the right). For heavier nuclei with more than 20 protons (Z>20), the nuclear structure takes over more complicated geometry with increasing number of protons. The most common combination of neutrons and protons for stable isotopes is an even number of protons and an even number of neutrons. In a chart of neutrons (N) vs. protons (Z) for stable isotopes, a region of stability (shown in white) can be drawn. The stability line shows that nuclei with Z<=20 have a balanced number of protons and neutrons, and thus indicate a highly symmetric structure. Spatial symmetry, obtained on completion of a quantum level is a possible driving force for structuring the electron configuration in such a way, and also the driving force for chemical reactions and molecular bonds. Atomic build up for Z=20 will follow the growth of shells {1s,2s},{2p,3s,3p,4s} or with the new model {1s, 1s'}, {2p 2s 2p' 2s'}. As you may follow in the below diagram, in our model, a 1s shell is a simple tetrahedron (2P+2N), the 1s' (conventional 2s) shell is then a bigger tetrahedron, which inscribes the first tetrahedron. The 2p (conventionally known to contain 6 electrons, 3 upspin and 3 downspin) is actually made up of 3 x 2s tetrahedrons, which together with the original 2s tetrasphere, will pack together into a hybrid tetrahedral formation, to be inscribed in a bigger spherical tetrahedron, which is the 2s shell (conventional 3s). This mechanism will repeat itself in exactly the same way for the opposite spin quantum level. 3s shell will take the place of 2s shown in the diagram, 3p that of 2p, and 4s that of 3s. This hybrid tetrahedron shell build up is no longer followed after shell 4s, where the octahedron will emerge, and that explains why the balance between protons and neutrons is lost for Z>20. Our model, also explains the 'staircase' plot shown in the graph. When Z satisfies the conditions for a complete tetrahedron to form, whether s type or p type, the atom recovers it stability. The last point where the proposed structure touches the stability line coincides to the completion of the pair of hybrid tetrahedrons of quantum level 2. |  |
The fundamental hybrid tetrahedral structure
I am now going to explain the real origin of subshells s,p,d,f and also show that Zmax for shells g and h are somehow different than those defined for the conventional theoretic subshells. It is also shown that the empirical equation for the maximum number of electrons in level n = 2n2 just happens to give the correct answers only to the first four shells and such equation has no fundamentals. In fact the conventional equation implies that we can have an infinite number of subshells s,p,d,f,g,h,i.... whilst our proposed structure limits the shells to h, at which point the model can handle 412 atomic numbers. We will also go further to explain why nature abhors the existence of elements with Z>120.
At this point we no longer need Pauli's exclusion principle to explain subshells, since the limit of two opposite spin electrons per 'orbit' is built in the structure of the tetrahedron. In no electromagnetic standing wave structure could we ever have two vertices touching each other, so this principle is built inherently in our new definition for matter. In the preceeding sections I have explained that a tetrahedron, having 4 vertices, is equivalent to an atom having 2 Protons + 2 Neutrons. We also know that the number of electrons of such a stable atom will be equal to the number of protons. So for example, a tetrahedron structure we have 2 electrons. For each platonic, we can work out the number of electrons which is equal to half the number of vertices Z/2, as shown in the table below. Note that at each complete shell stage, that is a formation of a complete platonic shape, one of the spherical standing wave will always be a complete sphere formed by the previous higher energy levels. For higher atomic numbers, one of the vertices of each complete platonic shell will always be formed by a spherical platonic, which in turn can nest other spherical platonics within it. It's a fractal build up. For example, in the above diagram, you can see that the inscribed tetrahedron is made up of 4 spheres, three of which are 2p spheres and one 1s' sphere. So for the formation of a tetrahedron (4 vertices), you only need to have three extra spherical tetrahedrons. In general, you will always need the formation of n-1 new spheres which together with the existing complete spherical standing wave, will form the new platonic with n vertices. The quantum number dictates the energy level, seperated by s levels, so for example a 3s, a 3p or 3d subshell spheres will have the same quantum number. In the example shown, we see that although each of the 4 vertices of the tetrahedron looks electrically the same, one of them will result in a higher equivalent mass due to its internal structure. The higher the atomic number, the higher is such imbalance, which results in deviation of the nuclear stability line from the curve N=Z, as shown further above. Thus this model accounts for another experimental fact, which is otherwise unaccounted for in the conventional model. On the last column, Zavail shows the available electrons for each complete structure. Zavail= 2,10,18,36,54,86 and 118 represent all the noble gases, namely: Helium 2, Neon 10, Argon 18, Krypton 36, Xenon 54, Radon 86, and the still unknown ultimate element 118. Being complete platonic structures, these are the most inert elements to exist in nature.
At this point we no longer need Pauli's exclusion principle to explain subshells, since the limit of two opposite spin electrons per 'orbit' is built in the structure of the tetrahedron. In no electromagnetic standing wave structure could we ever have two vertices touching each other, so this principle is built inherently in our new definition for matter. In the preceeding sections I have explained that a tetrahedron, having 4 vertices, is equivalent to an atom having 2 Protons + 2 Neutrons. We also know that the number of electrons of such a stable atom will be equal to the number of protons. So for example, a tetrahedron structure we have 2 electrons. For each platonic, we can work out the number of electrons which is equal to half the number of vertices Z/2, as shown in the table below. Note that at each complete shell stage, that is a formation of a complete platonic shape, one of the spherical standing wave will always be a complete sphere formed by the previous higher energy levels. For higher atomic numbers, one of the vertices of each complete platonic shell will always be formed by a spherical platonic, which in turn can nest other spherical platonics within it. It's a fractal build up. For example, in the above diagram, you can see that the inscribed tetrahedron is made up of 4 spheres, three of which are 2p spheres and one 1s' sphere. So for the formation of a tetrahedron (4 vertices), you only need to have three extra spherical tetrahedrons. In general, you will always need the formation of n-1 new spheres which together with the existing complete spherical standing wave, will form the new platonic with n vertices. The quantum number dictates the energy level, seperated by s levels, so for example a 3s, a 3p or 3d subshell spheres will have the same quantum number. In the example shown, we see that although each of the 4 vertices of the tetrahedron looks electrically the same, one of them will result in a higher equivalent mass due to its internal structure. The higher the atomic number, the higher is such imbalance, which results in deviation of the nuclear stability line from the curve N=Z, as shown further above. Thus this model accounts for another experimental fact, which is otherwise unaccounted for in the conventional model. On the last column, Zavail shows the available electrons for each complete structure. Zavail= 2,10,18,36,54,86 and 118 represent all the noble gases, namely: Helium 2, Neon 10, Argon 18, Krypton 36, Xenon 54, Radon 86, and the still unknown ultimate element 118. Being complete platonic structures, these are the most inert elements to exist in nature.
| Level (Quantum number) | Lowest level Platonic | Vertices | No. of inscribed tetrahedrons | No. of tetrahedron vertices P+N=Z | Electrons in subshell= Z/2 | Zsmax | Zlmax | Zmax | Zavail |
| 1 = s,s' | Tetrahedron + | 4 | 1 | 4 | 2 (s) | 2 | 4 | 2 | 0 |
| Tetrahedron - | 4 | 1 | 4 | 2 (s) | 2 | 4 | 2 | ||
| 2 = (p,s)(p,s)' | Dual Tetrahedron + | 4 | 3 | 12 | 6 (p) | 8 | 16 | 12 | 10 |
| Dual Tetrahedron - | 4 | 3 | 12 | 6 (p) | 8 | 20 | 18 | ||
| 3 = (d,p,s)(d,p,s)' | Octahedron + | 6 | 5 | 20 | 10 (d) | 18 | 36 | 38 | 36 |
| Octahedron - | 6 | 5 | 20 | 10 (d) | 18 | 56 | 54 | ||
| 4 = (f,d,p,s)(f,d,p,s)' | Cube + | 8 | 7 | 28 | 14 (f) | 32 | 64 | 88 | 86 |
| Cube - | 8 | 7 | 28 | 14 (f) | 32 | 120 | 118 | ||
| 5 = (g,f,d,p,s)(g,f,d,p,s)' | Icosahedron + | 12 | 11 | 44 | 22 (g) | 54 | 108 | 174 | 172 |
| Icosahedron - | 12 | 11 | 44 | 22 (g) | 54 | 228 | 226 | ||
| 6 = (h,g,f,d,p,s)(h,g,f,d,p,s)' | Dodecahedron + | 20 | 19 | 76 | 38 (h) | 92 | 184 | 320 | 318 |
| Dodecahedron - | 20 | 19 | 76 | 38 (h) | 92 | 412 | 410 |
Why 118 elements not 412 ?
In the above table we see, that we can model all known elements with the proposed fractal structure by just using the first four structures: Tetrahedron, Dual Tetra, Octahedron and Cube. The two 'extra' structures containing icosa & dodeca structures, which could result in a total of 410 elements, seem not to be applied in nature. Why? The answer is quite simple, and you may understand it better as you follow this section. I have hinted in various sections that our reality is just a 'projection' of a unified higher dimensional reality in our 3D vision of the universe. In simple words, those things that cannot be found in higher dimensions, are most probably unstable and usually abhored by nature. The tetrahedron, cube, and octahedron all occur naturally in crystal structures. These by no means exhaust the numbers of possible forms of crystals. However, neither the regular icosahedron nor the regular dodecahedron are amongst them! As we have discussed earlier during the introduction to platonics, the icosa & dodeca structures are limited to exist in 3D, whilst the first four, and ONLY the first four structures exist in all dimensions. The fact that no stable elements with Z>118 have ever been found in nature, is in itself a clear indication that atoms, of which the universe is known to be made of, exist as a projection of a higher dimension than 4. So our proposed model gets truncated to the 4th quantum level, and the shaded part of the chart is deleted.
Magic numbers and Quantum shell capacities derived from VPM nuclear model
Magic numbers derived from a Variable Phase nuclear model - by Ing. Xavier Borg (1.2Mb PDF) The etymology of the term nucleus is from 1704, meaning “kernel of a nut”. In 1844, Michael Faraday used the term to refer to the central point of an atom. The modern atomic meaning of the term was proposed by Ernest Rutherford in 1912, following the detection of a central massive entity by the scattering experiments of Hans Geiger and Ernest Marsden, carried out under his own supervision[1]. To the present day, this important component of the atom has been bombarded by more energetic probes in an almost desperate attempt to reveal its internal physics. Today, almost a century after its discovery, both mechanism and phase of matter of the nucleons are still an enigma. Various models have been developed to understand selective properties of the nuclei. Some of the most popular are the shell [2], liquid drop [3] , cluster[4], Moon’s[5], and double tetrahedron[6] models, which assume a gas, liquid, semi-solid, platonic solid and tetrahedral solid phase for the nuclei respectively. It is interesting to note that each of these models is able to describe very successfully certain selected properties of the nuclei; however, none of them is able to give a comprehensive description. Most of the characteristics of the different phases are mutually exclusive. I shall here introduce the Variable Phase Model of the nucleus[7], based on the projection of a hypertetrahedral nuclear structure into our view of perception, which is limited to the observation of three dimensions. In this model, the phase of the nucleus varies between the various phases of matter according to the angle of projection of the hyper dimensional nuclear entity, thus redefining mass as a physical parameter having both real and imaginary components.
History of the magic numbers
"Magic numbers" were first discovered by physicist Maria Goeppert-Mayer[8]. Careful observation of the nuclear properties of elements showed certain patterns that seemed to change abruptly at specific key elements. Mayer noticed that magic numbers applied whether one counts the number of neutrons (N), the atomic number (Z), or the sum of the two, known as mass number (A). Examples are Helium Z=2, Lead Z=82, Helium N=2, Oxygen N=8, Lead N=126, Neon A=20, Silicon A=28. Magic numbers in the nuclear structure have been coming up during all this time, but no plausible explanation for their existence has ever been given. Interestingly, there are peaks and dips for binding energy, repeating every fourth nucleon. This periodicity is one clear indication of a geometrical structure within the nucleus. In particular, those nuclei that can be thought of as containing an exact number of alpha particles (2P+2N), are more tightly bound than their neighbours. This effect is more pronounced for the lightest nuclei, but is still perceptible up to A = 28. For those nuclei with A > 20, the number of neutrons exceeds the number of protons, so some sort of distortion occurs within the cluster, as we shall discuss.
It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. This comes from the fact that the physical structure must have an even number of vertices. A type of regular polyhedron would satisfy this condition, since no regular polyhedron exists with an odd number of vertices. These specific "magic numbers" of neutrons or protons which seem to be particularly favoured in terms of nuclear stability are:
"Magic numbers" were first discovered by physicist Maria Goeppert-Mayer[8]. Careful observation of the nuclear properties of elements showed certain patterns that seemed to change abruptly at specific key elements. Mayer noticed that magic numbers applied whether one counts the number of neutrons (N), the atomic number (Z), or the sum of the two, known as mass number (A). Examples are Helium Z=2, Lead Z=82, Helium N=2, Oxygen N=8, Lead N=126, Neon A=20, Silicon A=28. Magic numbers in the nuclear structure have been coming up during all this time, but no plausible explanation for their existence has ever been given. Interestingly, there are peaks and dips for binding energy, repeating every fourth nucleon. This periodicity is one clear indication of a geometrical structure within the nucleus. In particular, those nuclei that can be thought of as containing an exact number of alpha particles (2P+2N), are more tightly bound than their neighbours. This effect is more pronounced for the lightest nuclei, but is still perceptible up to A = 28. For those nuclei with A > 20, the number of neutrons exceeds the number of protons, so some sort of distortion occurs within the cluster, as we shall discuss.
It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. This comes from the fact that the physical structure must have an even number of vertices. A type of regular polyhedron would satisfy this condition, since no regular polyhedron exists with an odd number of vertices. These specific "magic numbers" of neutrons or protons which seem to be particularly favoured in terms of nuclear stability are:
2,8,20,28,50,82,126
Note that the structure must apply to both protons and neutrons individually, so that we can speak of "magic nuclei" where any one nucleon type, or their sum, is at a magic number.
We find magic numbers in the elements most abundant in nature:
2H1 (Hydrogen, 1st most abundant - 74% of the universe) 1+1 = 2 = magic
4He2 (Helium, 2nd most abundant - 24% of the universe) 2,2 = both magic
16O8 (Oxygen 3rd most abundant - 1% of the universe) 8,8 = both magic
Maria Goeppert-Mayer proposed that magic numbers should be explained in the same way as the electron shell model applies to electrons. So, in such a nuclear shell model, when a nuclear shell is full and the structure is formed (equivalent to saying that the nucleons have used up all of the possible sets of quantum number assignments), a nucleus of unusual stability forms. This concept is similar to that found in an atom where a filled set of electron quantum numbers results in an atom with unusual stability, usually an inert gas. When all the protons or neutrons in a nucleus are in filled shells, the number of protons or neutrons is called a "magic number." Visualizing the densely packed nucleus in terms of orbits and shells seems much less plausible than the corresponding shell model for atomic electrons. You can possibly accept the fact that an electron can complete many orbits without running into anything, but you would expect protons and neutrons in a nucleus to be in a continuous process of collision with each other. Despite the expectations, dense-gas models of nuclei with multiple collisions between particles didn't fit the data, and remarkable patterns like the "magic numbers" in the stability of nuclei suggested the seemingly improbable shell structure, which defines nuclei in layers similar to those of the electron shell model (Fig.1). In our model, a shell is built up of a structured layer.
We find magic numbers in the elements most abundant in nature:
2H1 (Hydrogen, 1st most abundant - 74% of the universe) 1+1 = 2 = magic
4He2 (Helium, 2nd most abundant - 24% of the universe) 2,2 = both magic
16O8 (Oxygen 3rd most abundant - 1% of the universe) 8,8 = both magic
Maria Goeppert-Mayer proposed that magic numbers should be explained in the same way as the electron shell model applies to electrons. So, in such a nuclear shell model, when a nuclear shell is full and the structure is formed (equivalent to saying that the nucleons have used up all of the possible sets of quantum number assignments), a nucleus of unusual stability forms. This concept is similar to that found in an atom where a filled set of electron quantum numbers results in an atom with unusual stability, usually an inert gas. When all the protons or neutrons in a nucleus are in filled shells, the number of protons or neutrons is called a "magic number." Visualizing the densely packed nucleus in terms of orbits and shells seems much less plausible than the corresponding shell model for atomic electrons. You can possibly accept the fact that an electron can complete many orbits without running into anything, but you would expect protons and neutrons in a nucleus to be in a continuous process of collision with each other. Despite the expectations, dense-gas models of nuclei with multiple collisions between particles didn't fit the data, and remarkable patterns like the "magic numbers" in the stability of nuclei suggested the seemingly improbable shell structure, which defines nuclei in layers similar to those of the electron shell model (Fig.1). In our model, a shell is built up of a structured layer.
Fig.1
Quoting Maria Mayer in "The shell model": "One of the main nuclear features which led to the development of the shell structure is the existence of what are usually called the magic numbers. That such numbers exist was first remarked by Elsasser in 1933. What makes a number magic is that a configuration of a magic number of neutrons, or of protons, is unusually stable whatever the associated number of the other nucleons. When Teller and I worked on a paper on the origin of the elements, I stumbled over the magic number. We found that there were a few nuclei which have a greater isotopic, as well as cosmic, abundance than our theory, or any other reasonable continuum theory, could possibly explain. Then I found that those nuclei had something in common: they either had 82 neutrons, whatever the associated proton number, or 50 neutrons. Eighty-two and fifty are magic numbers. That nuclei of this type are unusually abundant indicates that the excess stability must have played a part in the process of the creation of the elements..."
Doubly Magic nuclei
Doubly magic nuclei, are those nuclei which have both neutron number and proton number equal to a magic number. All such nuclei are particularly highly stable and are called "doubly magic".
Doubly magic nuclei, are those nuclei which have both neutron number and proton number equal to a magic number. All such nuclei are particularly highly stable and are called "doubly magic".
Lead-208 is one such example of a "doubly magic" nucleus as it has both 82 protons and 126 neutrons. Calcium it yet another example of this exceptional stability quality since it has two of them. The existence of several stable isotopes of calcium is due to its magic proton count of 20. The two highlighted isotopes have neutron numbers 20 and 28 and a proton count of 20, all magic numbers. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy than that calculated from the semi-empirical Weizsaecker formula, and also anomalously low masses and high natural abundances.
The existence of these magic numbers suggests some special shell configurations, like the electron shells in the atomic structure. They represent one line of reasoning which led to the development of a shell model of the nucleus. Other forms of evidence suggesting a geometrical structure include the following [9]
The existence of these magic numbers suggests some special shell configurations, like the electron shells in the atomic structure. They represent one line of reasoning which led to the development of a shell model of the nucleus. Other forms of evidence suggesting a geometrical structure include the following [9]
- Enhanced abundance of those elements for which Z or N is a magic number.
- The stable elements at the end of the naturally occuring radioactive series all have a "magic number" of neutrons or protons.
- The neutron absorption cross-sections for isotopes where N = magic number are much lower than surrounding isotopes.
- The binding energy for the last neutron is a maximum for a magic neutron number and drops sharply for the next neutron added.
- Electric quadrupole moments are near zero for magic number nuclei.
- The excitation energy from the ground nuclear state to the first excited state is greater for closed shells.
Tetrahedral stacking
Following the interpretation of Maria Mayer, the striking evidence for a structure in the nucleus was surprising at first, because common sense tells us that, a dense collection of strongly interacting particles should be bumping into each other all the time, resulting in redirection and perhaps loss of energy for the particles. This idea at first seems to violate Pauli's exclusion principle, but it does not. Keep in mind that the exclusion principle itself has been devised in the first place due to the lack of information about the geometrical structure of the electron shells.
Fig.2
Let us have a closer look at the nucleus. Assuming some sort of close packing arrangement for the nucleons, and assuming that the nucleus is perceived as a three dimensional object, it can be shown that the least number of nodes a three dimensional structure can have is equal to four, and that the simplest stable stacking structure is that of a tetrahedron (Fig.2). Four nucleons are thus required to fill the nodes of a tetrahedron. A nucleus with two protons and two neutrons would thus satisfy the most basic stable three dimensional structure, which would in fact give the nuclear structure of Helium 4 - otherwise known as the alpha particle.
Pauling tetrahedron nuclues [12]
Calculations of potential model, constrained by the hadrons spectrum for the confinement of the relativistic quark[10] and coloured quark exchange model[11], are also consistent with a tetrahedron formation of the nucleus. Also note that this tetrahedron structure is not something new, but dates back to 1964 in the work of Linus Pauling.[12] Once all four nodes of a tetrahedron are occupied, the next nucleon cannot be permitted at the same energy level, and the next spherical standing wave[13] (spherical tetrahedron) has to start forming. Recently, tetrahedron structures have regained interest in the study of the nuclear structure.[6] This theory also explains the emission of alpha particles from the nucleus. Many radio-nuclides achieve increased nuclear stability by emitting an alpha particle (a tetrahedral structure) rather than a single proton or neutron. This suggests that many isotopes contain one or more alpha particles in their nucleus.
Fig.3
If you consider every particle, being it a proton, neutron, or electron, as being restricted in space relative to its neighbour particle by the shape of a particular structure (spherical standing wave), there would be no need for any principle to show how and why these particles can never collide with each other, since they would be seating within the nodes of the frame. We know that collisions between electrons or nucleons in a particle are very infrequent. As I shall discuss later on, the possibility that matter exists in higher dimensions than three must not be excluded, in which case, two distinct three dimensional objects can overlap within the same three dimensional space without colliding. In fact from my own space time conversion system [14] one can easily deduce that mass is a three dimensional structure of energy, that is a six dimensional unit, and not a structure of point particles.
Note in the above diagram (Fig.3) that each nucleon is itself a spherical tetrahedron, each of which has three of its nodes touching the neighbouring nucleons, and one touching the external spherical tetrahedron of the formation. Thus the nodes of the spherical tetrahedral standing wave, are formed at the points where the stacked nucleons touch the external sphere. In a three dimensional nucleus, a tetrahedral stack consisting of four nucleons, such as an alpha particle, can accommodate an infinite number of stacked layers, while keeping the same properties of a tetrahedron. For example if six other nucleons are added at the base of a four nucleon tetrahedral stack, a new tetrahedral structure consisting of ten nucleons will be formed, having its three outermost nucleons touching a bigger external spherical tetrahedron.
What does an incomplete tetrahedron standing wave look like
Up to now we have considered filled up shells which equate to a complete spherical tetrahedron, equivalent to the Helium-4 nucleus (Fig.3). But what does the standing wave look like when the number of nodes is not equal to the number of vertices, for example in a Hydrogen nucleus? Does this result in a non-uniform structure within the spherical standing wave? How can a spherical wave contain one, two or three nodes? In the analogous situation of the electron shell model, chemists just put up the next shell and place the extra electrons orbiting around, but this picture is totally wrong.
Let us assume that a complete shell structure, say shell 's' has just been completed and a spherical tetrahedron has formed. We know that three similar spherical standing waves (known as subshell p) are now required until we have enough nodes to create a bigger tetrahedron shell. An analogous example to this process is with the case of using an oscilloscope trace while increasing the input frequency. If the wave signal frequency at its input matches exactly its time base frequency f, then, a single wave will appear at a standstill on the screen. If we double the input frequency to 2f , we see two standstill waves on the screen. But what do we see in between the two frequencies? If one increases the frequency slowly from f to 2f, the result is that the single wave will start moving across the screen until it slows down again and ‘morphs’ into the shape of two waves. This is exactly what happens at the nuclear level as extra nodes are added. This movement of the standing wave results in ROTATION or spin of the structure, until it builds up further nodes and 'slows down' into the new zero spin complete shells. Another analogy, this time mechanical, is that of a two spoke wheel being viewed under the light of a stroboscope. Slowing down the speed of the wheel will result in the observation of a stationary two, four, six, eight … spoke wheel. For revolutions which are not exact integer fractions of the stroboscope frequency, the spokes will appear to be either in random positions, or rotating and the observer cannot determine the actual number of spokes.
All incomplete, spherical, 3d standing waves have non-zero spin values and are pictured as various standing wave components. Zero spin and complete shells are achieved at the same time for the same reason - the number of nodes are equal to the number of nodes of a spherical platonic. Hydrogen(2) has a non zero spin since it has 1/2 the nodes required to complete the smallest and simplest spherical tetrahedron, which is achieved by a minimum of four nodes equivalent to the alpha particle, which in fact does have a zero spin. For many years, physicists have known that energy particles spin as they travel. For example, electrons appear to be continually making sharp 180-degree turns or half spins as they move through the atom. Quarks are often seen to make one thirds and two thirds spins when they travel. No one in the mainstream has provided a truly adequate explanation as to why this is happening. In our model, spin is just the movement of the spherical standing wave whenever the structure of nodes does not ‘lend itself’ to create a complete three dimensional structure.
What’s wrong with the standard model
The conventional 'bunch of grapes' nuclear structure (Fig.4) described in the standard model [15] has big flaws, and lacks to predict too many well known characteristics of the nucleus. One of its biggest flaws, is that it regards all elementary particles as point particles (zero dimension), which results in infinite energy when electric field energy is taken into account. However, it does give us a vague clue that multiple spherical standing waves can combine into another bigger entity, while maintaining themselves as separate identifiable similar structures. Evidence for this clustered structure comes from electron and alpha particle emissions from the atom.
Note in the above diagram (Fig.3) that each nucleon is itself a spherical tetrahedron, each of which has three of its nodes touching the neighbouring nucleons, and one touching the external spherical tetrahedron of the formation. Thus the nodes of the spherical tetrahedral standing wave, are formed at the points where the stacked nucleons touch the external sphere. In a three dimensional nucleus, a tetrahedral stack consisting of four nucleons, such as an alpha particle, can accommodate an infinite number of stacked layers, while keeping the same properties of a tetrahedron. For example if six other nucleons are added at the base of a four nucleon tetrahedral stack, a new tetrahedral structure consisting of ten nucleons will be formed, having its three outermost nucleons touching a bigger external spherical tetrahedron.
What does an incomplete tetrahedron standing wave look like
Up to now we have considered filled up shells which equate to a complete spherical tetrahedron, equivalent to the Helium-4 nucleus (Fig.3). But what does the standing wave look like when the number of nodes is not equal to the number of vertices, for example in a Hydrogen nucleus? Does this result in a non-uniform structure within the spherical standing wave? How can a spherical wave contain one, two or three nodes? In the analogous situation of the electron shell model, chemists just put up the next shell and place the extra electrons orbiting around, but this picture is totally wrong.
Let us assume that a complete shell structure, say shell 's' has just been completed and a spherical tetrahedron has formed. We know that three similar spherical standing waves (known as subshell p) are now required until we have enough nodes to create a bigger tetrahedron shell. An analogous example to this process is with the case of using an oscilloscope trace while increasing the input frequency. If the wave signal frequency at its input matches exactly its time base frequency f, then, a single wave will appear at a standstill on the screen. If we double the input frequency to 2f , we see two standstill waves on the screen. But what do we see in between the two frequencies? If one increases the frequency slowly from f to 2f, the result is that the single wave will start moving across the screen until it slows down again and ‘morphs’ into the shape of two waves. This is exactly what happens at the nuclear level as extra nodes are added. This movement of the standing wave results in ROTATION or spin of the structure, until it builds up further nodes and 'slows down' into the new zero spin complete shells. Another analogy, this time mechanical, is that of a two spoke wheel being viewed under the light of a stroboscope. Slowing down the speed of the wheel will result in the observation of a stationary two, four, six, eight … spoke wheel. For revolutions which are not exact integer fractions of the stroboscope frequency, the spokes will appear to be either in random positions, or rotating and the observer cannot determine the actual number of spokes.
All incomplete, spherical, 3d standing waves have non-zero spin values and are pictured as various standing wave components. Zero spin and complete shells are achieved at the same time for the same reason - the number of nodes are equal to the number of nodes of a spherical platonic. Hydrogen(2) has a non zero spin since it has 1/2 the nodes required to complete the smallest and simplest spherical tetrahedron, which is achieved by a minimum of four nodes equivalent to the alpha particle, which in fact does have a zero spin. For many years, physicists have known that energy particles spin as they travel. For example, electrons appear to be continually making sharp 180-degree turns or half spins as they move through the atom. Quarks are often seen to make one thirds and two thirds spins when they travel. No one in the mainstream has provided a truly adequate explanation as to why this is happening. In our model, spin is just the movement of the spherical standing wave whenever the structure of nodes does not ‘lend itself’ to create a complete three dimensional structure.
What’s wrong with the standard model
The conventional 'bunch of grapes' nuclear structure (Fig.4) described in the standard model [15] has big flaws, and lacks to predict too many well known characteristics of the nucleus. One of its biggest flaws, is that it regards all elementary particles as point particles (zero dimension), which results in infinite energy when electric field energy is taken into account. However, it does give us a vague clue that multiple spherical standing waves can combine into another bigger entity, while maintaining themselves as separate identifiable similar structures. Evidence for this clustered structure comes from electron and alpha particle emissions from the atom.
Fig.4
However due to the lack of a defined structure, the conventional 'bunch of grapes' model tends to be an overly complicated model. In such a model, there is the need for the nuclear binding energy to overcome the tendency of the nuclear components to fly apart, because of the mutual repulsion of the positive proton charges. The mass deficiency of atomic nuclei has been hypothesized as the cause of this nuclear binding, and for this to take place, a new type of strong force has been hypothesized to exist in the form of 'exchange forces' between nuclear components. To complicate the issue further, a new class of particles like the meson have been invented to account for the force exchange mechanism. This hypothesis has in fact never been proved. The standard model also gives no hint to the existence of the nuclear magic numbers and no way to predict, or even explain the existence of its obvious shell structure. Since Bohr's orbiting electron model failed to describe the actual orbital distribution of the electron cloud, it had been concluded that the electrons motion is not governed by any ordered motion or structure, but is completely random. The standing wave shape is called an 'Orbital' - quite a misnomer considering nothing is orbiting inside! We usually learn that these represent the volume of space of probability distribution of an electron in an atom, and whose momentum and position cannot be determined at the same time. This is quite confusing since one would expect any moving object to have both momentum and position. It would all make sense if instead of probability distribution of point particles, we refer to orbitals as the real electromagnetic standing waves. Even if today we no longer learn about ‘orbiting electrons’, Heisenberg principle has unfortunately been established into mainstream science. The interpretation of such principle is that the atomic structure and the interactions of its electrons are random and can be discussed only statistically as probabilistic distributions of a random motion. On the other hand, we have nature, that shows us otherwise - crystal lattices[16] do not build up in random shapes, but in very specific shapes like simple cubic, body centred cubic, cubic close packed etc..
Unfortunately, to the present day, science gave up the search for a 'physical' model and most people prefer to ignore hard evidence in favour of an outdated principle, referring to electromagnetic radiation patterns (Fig. 5) as probabilistic distribution of electron ‘clouds’.
Unfortunately, to the present day, science gave up the search for a 'physical' model and most people prefer to ignore hard evidence in favour of an outdated principle, referring to electromagnetic radiation patterns (Fig. 5) as probabilistic distribution of electron ‘clouds’.
Fig. 5 - Some ‘electron probability density’ plots for the Hydrogen atom
One can solve the binding force problem, by showing that the most stable nuclei, are tightly bound due to being in the stable nodal positions of a spherical standing wave. Before going into the actual hyper geometric structure model of the nucleus, we shall first hack the magic number sequence into a predictable three dimensional configuration.
Deriving the Magic Number sequence using a physical model
The first attempts to hack, or reverse engineer, the Magic number sequence into a geometric progression by the use of a physical model, date back to 1964 during Pauling's research[12]. From his records we can see that today’s magic numbers are exactly the same as those listed under his 'Observed' values. Unfortunately it seems that Pauling never got a solution to generate the correct sequence.
An interesting characteristic of the collection of protons and neutrons is that a nucleus of odd mass number A will have a half-integer spin and a nucleus of even A will have an integer spin. This highly suggests that the real structure is based on pairing of nucleons. The suggestion that angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin I=0. In this section, we will need to stack pairs of tetrahedrons in our nuclear structure, so I shall first cite the triangular and tetrahedron number sequences. [17,18] These are very simple numerical sequences which are very useful for this study.
Triangular Numbers
Deriving the Magic Number sequence using a physical model
The first attempts to hack, or reverse engineer, the Magic number sequence into a geometric progression by the use of a physical model, date back to 1964 during Pauling's research[12]. From his records we can see that today’s magic numbers are exactly the same as those listed under his 'Observed' values. Unfortunately it seems that Pauling never got a solution to generate the correct sequence.
An interesting characteristic of the collection of protons and neutrons is that a nucleus of odd mass number A will have a half-integer spin and a nucleus of even A will have an integer spin. This highly suggests that the real structure is based on pairing of nucleons. The suggestion that angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin I=0. In this section, we will need to stack pairs of tetrahedrons in our nuclear structure, so I shall first cite the triangular and tetrahedron number sequences. [17,18] These are very simple numerical sequences which are very useful for this study.
Triangular Numbers
A triangular number is a number that can be arranged in the shape of an equilateral triangle. The sequence of triangular numbers is
| 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 | 45 | 55 | ... |
The formula for the nth triangular number is given by
TRI(n)=(n/2)(n + 1)
Square Numbers - relation to triangle numbers
An important relation we will prove itself useful, is that relating square numbers to triangular numbers. The nth square number is the sum of two consequtive triangular numbers, for example 0+1=1, 1+3=4, 3+6=9, 6+10=16, 10+15=25, 15+21=36 ....=n2
The sequence of square numbers is thus
An important relation we will prove itself useful, is that relating square numbers to triangular numbers. The nth square number is the sum of two consequtive triangular numbers, for example 0+1=1, 1+3=4, 3+6=9, 6+10=16, 10+15=25, 15+21=36 ....=n2
The sequence of square numbers is thus
| 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 | ... |
The formula relating square to triangular numbers is given by
SQR(n) = TRI(n-1) + TRI(n) = n2
Tetrahedral numbers
Analogously, a tetrahedral number, is a number that can be arranged like a tetrahedron.
Analogously, a tetrahedral number, is a number that can be arranged like a tetrahedron.
Fig.6 - 3D view of tetrahedral stack
The nth tetrahedral number is the sum of the first n triangular numbers added up, for example 0+1=1, 0+1+3=4, 0+1+3+6=10, etc.. The sequence of tetrahedral numbers is thus
| 1 | 4 | 10 | 20 | 35 | 56 | 84 | 120 | 165 | 220 | ... |
The formula for the nth tetrahedral number is given by
TETRA(n)=(n/6)(n + 1)(n+2)
Hacking the Magic Number sequence using a physical model
The first attempts to hack or reverse engineer the Magic number sequence into a geometric progression by the use of a physical model, date back to 1964 during Pauling's research. From his records we can see that todays magic numbers are exactly the same as those listed under his 'Observed' values. Unfortunately it seems that Pauling never got a solution to generate the correct sequence.
Let's now see how these two number series apply to our tetrahedral pack of nucleons. Level n=1 is the top level - the black sphere, level n=2 is the red, n=3 is the yellow and so on... The first equation for the triangular numbers at n=3 gives us the number 6. So, 6 is the number of spheres in the yellow layer. Putting n=3 in the tetrahedral equation, gives us the number 10, and that is equal to the total of spheres making up the tetrahedron whose base is formed by the yellow spheres, that is the total of yellow, red and black spheres. If one wants to find the number of spheres required for the whole 5-layer tetrahedron, it will be the fifth number in the tetrahedron number series, that is 35. If you subtract the 4th triangular number from 35, you get the number of spheres of the whole tetrahedron, less the blue slice, which will be 35-10=25.Next we will apply two other facts, already described in the this section to hack the magic number sequence. Fact no.1 is that nuclei up to magic number Z=20 have equal numbers of protons and neutrons, whilst for Z>20, the balance is lost. Fact no.2 is that the nuclie build up as a double structure. From fact no.1 we deduce that up to the formation of the structure containing 20 nucleons, the nucleus will look as a perfectly symmetrical structure, in electromagnetic terms, a perfect dipole. From fact no.2, we deduce that each tetrahedron level, builds up in pairs, and the next level tetrahedron is not started unless both pairs of the previous stage have been completed. Applying these rules we can now start from level n=1 until we get to Z=20 at n=3.
Fig.7
For n=1 (black sphere) the Tetrahedron number=1, the double tetra structure closes at 1x2 = 2
For n=2 (red and black) the tetrahedron number=4, the double tetra structure closes at 4x2 = 8
For n=3 (yellow, red, black) the tetrahedron number=10, the double tetra structure closes at 10x2 = 20
You may have already noticed, that these are the first 3 of the magic number series:
For n=2 (red and black) the tetrahedron number=4, the double tetra structure closes at 4x2 = 8
For n=3 (yellow, red, black) the tetrahedron number=10, the double tetra structure closes at 10x2 = 20
You may have already noticed, that these are the first 3 of the magic number series:
Now that we are at Z=20 (n=3), we know that the geometrical symmetry from here over is lost, that is the double structure (or 3 dimensional dipole) will no longer act as two perfect tetrahedron structures and so, we can no longer assume a simple symmetric double tetra structure. However, things do not complicate much, because what happens from here is that the two terahedron pairs now couple or hinge together much like covalent bonds are known to 'hinge' in chemistry. In electromagnetic terms, the dipole will no longer act as a purely resistive electromagnetic standing wave, but become slightly reactive due to their overlap.
Fig.8
For example, if we take the above 35 nucleon tetrahedron (n=5) shown in Fig.8 (left), its companion tetra will be underneath it, in inverted position, with its green layer occupying the same space previously occupied by the blue layer (triangular level 4=n-1) of the top tetrahedron (Fig.8 right). The green layer of the latter, will also occupy the same space previously occupied by the blue layer of the inverted tetra. Thus, the total number of nucleons for the magic dual structure for n=5, would be given by Magic(n) = 2*[TETRA(n)-TRI(n-1)] = 2*(35-10) = 50. This simple rule is observed for all magic nuclei having Z>20, that is for n>3. The table below shows how these numbers can be easily worked out by subtracting the respective triangular hinge layer (n-1) from each tetrahedron number, and multiply the result by two to get the number of nucleons of the complete double structure. The bonding layer, as chemists would call it, is always one layer above the base of the tetrahedron.
| Level (n) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Tetrahedron number (level n) | 1 | 4 | 10 | 20 | 35 | 56 | 84 | 120 |
| Less triangular binding layer (level [n-1]) | - | - | - | 6 | 10 | 15 | 21 | 28 |
| Total nucleons per tetrahedron | 1 | 4 | 10 | 14 | 25 | 41 | 63 | 92 |
| Total nucleons per double structure Z (Magic number/closed shell Z sequence) | 2 | 8 | 20 | 28 | 50 | 82 | 126 | 184 |
Table 1
The lowest values 2, 8, and 20 agree with independent nucleon motion into a single particle potential, like a harmonic oscillator. Nucleons' stacking positions occur at the vertices of the two spherical standing waves or the resistive configuration, shown above in Fig.9. Mathematically the sequence of complete shell nucleon numbers for Z<=20 is given by the same equation that gives the total number of spheres of two symmetrical tetrahedron stacks forming an ideal 3D dipole:
For 3 ≥n≥ 1: Z = Magic(n) = (n/3)(n+1)(n+2)
For 3 ≥n≥ 1: Z = Magic(n) = (n/3)(n+1)(n+2)
For 3 ≥n≥ 1: Magic(n) = (n/3)(n2+3n+2)
giving series: 2, 8, 20The magic numbers 28, 50, 82, and 126 agree to those nuclei with a strong spin-orbit coupling (by Maria Mayer and Jensen) which have the mentioned nuclear co-valent bond type structure as discussed above. Nucleon stacking positions occur at the vertices of the two spherical standing waves shown on the right, or the reactive configuration of the above figure. So, for Z>20, the total number of nucleons is given by the above equation, less a pair of two triangular layers which represent the binding energy (or nuclear anomalous mass deficiency). In electromagnetic terms, this binding energy or missing mass is due to the reactive component of the capacitive dipole, a situation analogous to the real and apparent electric power in reactive loads we learn in electrical theory.
For n>3: Z = Magic(n) = (n/3)(n+1)(n+2) - n(n-1)
For n>3: Z = Magic(n) = (n/3)(n+1)(n+2) - n(n-1)
For n>3: Magic(n) = (n/3)(n2+5)
giving series: 28, 50, 82, 126, 184
Fig 9. - Resistive (left) & Reactive (right) dipole configurations
We have therefore finally hacked the magic number sequence into a physical model based on the double tetrahedron structure and simple dipole structure of the nucleus as proposed here. Not only do the above geometrical sequences derive all known magic numbers (2,8,20,28,50,82,126) but also derive the magic number 184, which is predicted by many scientists to be the next higher magic number. I have also showed how todays' classical 'bunch of grapes' nuclear model can be geometrically arranged while explaining the shells build up for the nucleus and giving a plausible explanation for the missing mass that is normally attributed to binding energy. This physical model also unveils a property of mass which is not so common in today's science literature - the imaginary component of mass. As is easily observed above, all magic number structures can be understood in terms of electromagnetic energy components, and since such components are complex in nature (complex means they have both real and imaginary parts), a structure which can be completely described in such terms will have the same properties of its constituents. Looking at the periodic table of elements, one should not only visualise nucleons simply bunching up as tetrahedral stacks of hard steel balls, but tetrahedral stacks of spherical electromagnetic standing waves with varying real and imaginary energy components. Only then, can one start to appreciate and predict the properties of the elements.
Deriving the Quantum theory nucleon and electron shell capacity
If we slice a stacked tetrahedron in two level layers, we find out that the total number of nucleons agrees with that predicted from Quantum Theory for each quantum shell, assuming that the number of protons and neutrons are equal.
Deriving the Quantum theory nucleon and electron shell capacity
If we slice a stacked tetrahedron in two level layers, we find out that the total number of nucleons agrees with that predicted from Quantum Theory for each quantum shell, assuming that the number of protons and neutrons are equal.
| Level n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Quantum Shell number N | 1(K) | 2(L) | 3(M) | 4(N) | ||||
| TRI(n) | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 |
| Nucleons in Quantum Shell = Nucleons in two level slice = TRI (2N) + TRI(2N -1) | 4 | 16 | 36 | 64 | ||||
| For the case Protons= ½*nucleons | 2 | 8 | 18 | 32 |
If we define each principal quantum shell number N, as a two level slice of a tetrahedron, then, the number of nucleons per slice = TRI(n) + TRI(n-1) where n=2N. As already mentioned, the sum of two consecutive triangular numbers is always the square number of the highest triangular level.
The total number of protons or electrons in such a slice = ½ * total nucleons in slice
So, Zmax = ½ [TRI (n ) + TRI (n-1) ]
Zmax = ½ n2
Zmax = ½ [ 4N2 ]
Zmax = 2N2 , giving the sequence 2,8,18,32,.. for principal quantum numbers 1,2,3,4…
This is the well known empirical formula which defines the maximum number of electrons in the set of orbitals, also known by their spectroscopic designation K, L, M, N, etc. ). We now reconfirm, that each quantum shell, is made up of two sub shells, or a two layer slice of a tetrahedral structure, which is composed of the triangular levels TRI(2N) and TRI(2N - 1). It thus follows, that the electron structure is closely related or simply a direct effect of the nuclear structure. This is the same as saying that the far field radiation pattern of a radio antenna, can be directly deduced by knowing either its near field pattern, or its dipole structure[20].
Nuclear structure of inert gases
Two independent tetrahedron stacks will each generate Zmax sequence 2, 8, 18, 32 …. A tetrahedron stack pair would generate Zmax sequence 2, 2, 8, 8, 18, 18, 32, 32 …. A simplex stack pair having their top simplex projected over the same space in 3D, will thus generate Zmax sequence 2, 8, 8, 18, 18, 32, 32 …. and be like two tetrahedral stack structures with their uppermost tetrahedrons overlapping the same space. It will also be equivalent to a conventional electron shell structure: s, sp, sp, spd, spd, spdf, spdf.
Building up the dual overlapping stack, gives the element sequence 2, 2+8, 2+8+8, 2+8+8+18, 2+8+8+18+18, 2+8+8+18+18+32, 2+8+8+18+18+32+32 which results in elements 2, 10, 18, 36, 54, 86, 118 - well known as the inert gases (including the recently discovered Unonoctium - element 118!). Again, the sharing of the top tetrahedron indicates higher dimensional entities. Taking into account both protons and neutrons, the structure will look like four tetrahedral stacks, sharing a common central tetrahedron. For the sake of clarity, figure 10 shows only two of the tetrahedral stacks, the other two would be stacked over the other two faces of the central tetrahedron.
The total number of protons or electrons in such a slice = ½ * total nucleons in slice
So, Zmax = ½ [TRI (n ) + TRI (n-1) ]
Zmax = ½ n2
Zmax = ½ [ 4N2 ]
Zmax = 2N2 , giving the sequence 2,8,18,32,.. for principal quantum numbers 1,2,3,4…
This is the well known empirical formula which defines the maximum number of electrons in the set of orbitals, also known by their spectroscopic designation K, L, M, N, etc. ). We now reconfirm, that each quantum shell, is made up of two sub shells, or a two layer slice of a tetrahedral structure, which is composed of the triangular levels TRI(2N) and TRI(2N - 1). It thus follows, that the electron structure is closely related or simply a direct effect of the nuclear structure. This is the same as saying that the far field radiation pattern of a radio antenna, can be directly deduced by knowing either its near field pattern, or its dipole structure[20].
Nuclear structure of inert gases
Two independent tetrahedron stacks will each generate Zmax sequence 2, 8, 18, 32 …. A tetrahedron stack pair would generate Zmax sequence 2, 2, 8, 8, 18, 18, 32, 32 …. A simplex stack pair having their top simplex projected over the same space in 3D, will thus generate Zmax sequence 2, 8, 8, 18, 18, 32, 32 …. and be like two tetrahedral stack structures with their uppermost tetrahedrons overlapping the same space. It will also be equivalent to a conventional electron shell structure: s, sp, sp, spd, spd, spdf, spdf.
Building up the dual overlapping stack, gives the element sequence 2, 2+8, 2+8+8, 2+8+8+18, 2+8+8+18+18, 2+8+8+18+18+32, 2+8+8+18+18+32+32 which results in elements 2, 10, 18, 36, 54, 86, 118 - well known as the inert gases (including the recently discovered Unonoctium - element 118!). Again, the sharing of the top tetrahedron indicates higher dimensional entities. Taking into account both protons and neutrons, the structure will look like four tetrahedral stacks, sharing a common central tetrahedron. For the sake of clarity, figure 10 shows only two of the tetrahedral stacks, the other two would be stacked over the other two faces of the central tetrahedron.
Fig. 10
This physical model also unveils a property of mass which is not yet conceived in today's science literature - the reactive or imaginary component of mass. As is easily observed above, all magic number structures can be understood in terms of electromagnetic energy components, and since such components are complex in nature (complex means they have both real and imaginary parts), a structure which can be completely described in such terms will have the same properties of its constituents. Looking at the periodic table of elements, one should not only visualise nucleons simply bunching up as tetrahedral stacks of hard steel balls, but (hyper)tetrahedral stacks of spherical electromagnetic standing waves with varying real and imaginary energy components. Spin and angular momentum are direct effects of the imaginary components. Only when we take these components into account, can we start to appreciate, predict and master the properties of the elements.
Tetrahedral or Hypertetrahedral stacking?
Tetrahedral or Hypertetrahedral stacking?
The structure for the pair of tetrahedrons for Z>20, shown in Fig.8, leads one to consider a hypertetrahedron (simplex or higher dimension) type of stacking, in favour of the simple tetrahedron stacking. To understand why, let's analyse a simpler situation with a pair of three dimensional spheres, as shown below in Figure 11:
Fig.11
You can see two different cases, showing the 3D spheres at a different angle of projection onto a 2D plane, one at say, time=t, and another at time t=t+Dt. The relation of their position with respect to the 2D projection plane is described by the projection or phase angle. In real life we can see the 3D view with no problem. If one takes photos from underneath them however, or simply projects their shadows on a screen, the result would be that shown in the 2D projection. Now, if one has got only a photo of the 2D projection, it will be confusing, since it will appear that two individual circles (lower left) are merging into two overlapping circles (lower right). The surface area of the two circles on the right is less than that of two separate circles, and can diminish to the surface area of a single circle, at which point the observer cannot even know whether there is one or two circles. The observer will call the effect as missing area, and if density (in a 2D world like Flatland) is defined as mass per unit area, the effect would be that of a missing mass. Now, you do not really have to imagine what a 4D hyper sphere would look like (it is impossible, even if you try), but just apply what you understood for the lower dimensional case, to the case, where the spheres exist in 4D, and the projection is on a 3D kind of screen. Two hyper spheres separated at a distance greater than their diameter, would look like two independent 3D spheres, and the image would look like it is the real thing. But when their horizontal distance is decreased, or the phase angle increases, strange things start to happen. They seem to be overlapping into the same space, until you can see only one sphere! One would actually see the two separate masses combining into a single mass, sharing the same space until their mass becomes that of a single sphere. The observer will call the effect of the missing volume as missing mass - a ‘mass defect’, as Einstein called it, accompanied with a respective increase in internal or binding energy. In the macro world, the effect will show as a decrease in density, or change of phase of matter from solid to liquid to gas to plasma and finally to vacuum, accompanied with a respective increase in internal energy. As you can surely understand, when such effect is observed, it is a clear indication, that your image is not the complete picture, and that the real thing is operating at a higher dimensional level. One cannot really know if it's just one or many levels up, but it is certain that the observed dimension is a limited projection of the entity being observed. And that's exactly what's happening with our tetrahedral stacking within the nucleus. For Z<20, we see pairs of 3D tetrahedral stacking operating as normal 3D stacks would do. Only as Z increases further, we realize that strange things start to happen, the pair of tetrahedral stacks overlap and partly share the same space, resulting in a mass defect. At that stage, it becomes clear that a tetrahedral nuclear model is just a limited projection in 3D, of a higher dimensional entity - a hypertetrahedral stack. You will now clearly understand, that if we define mass as a 3D entity, it will always be a shadow effect. In other words, the term mass refers to the apparent component of a much complex entity. This is the reason of the long time failure of generating a 3D physical model to represent the complete list of known elements. The variable phase angle is the reason for which a nuclear model cannot assume any single specific phase of matter. Similarly to electronic components, where in practice, no component can be assumed purely resistive or purely reactive, the phase of matter and hence of the nucleus, cannot be considered to be either purely solid, or purely vacuum energy, both of which are purely theoretical limits. Such model must be considered as a hyper dimensional structure, otherwise, all those elements which do not happen to project into a simple enough 3D structure like the case for magic numbered nucleons and inert gases, will have spin, which will result in a rotating/overlapping three dimensional projection of hypertetrahedral stacks popping in and out of the 3D ‘screen’.
References:
[1] E. Rutherford: Philosophical Magazine 21 699 (1911)
[2] M.G. Mayer: Phys. Rev. 75 (1969)
[3] E. Feenberg: Rev. Mod. Phys. 19 239 (1947)
[4] L.R. Hafstad, E. Teller: Phys. Rev. 54 681 (1938)
[5] 21st Century Science & Technology Magazine (http://www.21stcenturysciencetech.com/articles/moon_nuc.html)
[6] J. Garai: Double Tetrahedron structure of the nucleus (http://lanl.arxiv.org/abs/nucl-th/0309035)
[7] X. Borg: The Variable Phase Model of the nucleus (http://www.blazelabs.com/f-p-vpm.asp)
[8] Sachs, Robert G: "Maria Goeppert Mayer", Biographical Memoirs 50 (National Academy of Sciences, 1979).
[9] Hyper Physics, Georgia State University http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
[10] K. Maltman, G.J. Stephonson Jr. K. E. Schmidt: Nuclear Physics. 481 62
[11] D. Robson: Nuclear Physics. A 308 381 (1978)
[12] Linus Pauling: Research Notebooks 25,26 (http://osulibrary.orst.edu/specialcollections/rnb/index.html)
[13] X. Borg: Spherical Standing Waves (http://www.blazelabs.com/f-p-prop.asp)
[14] X. Borg: Space Time system of units http://www.blazelabs.com/f-u-suconv.asp
[15] Gordon L. Kane: Modern Elementary Particle Physics. Perseus Books (1987)
[16] Crystal lattice structure - Wikipedia (http://en.wikipedia.org/wiki/Crystal_structure)
[17] M. Abramowitz and I. A. Stegun, eds., Handbook of Math Functions, N.Bureau of Std Applied Math. S 55, 1964
[18] D. Wells, The Penguin Dictionary of Curious and interesting Numbers, pp 126-7, Penguin Books (1987)
[19] K. Neubert - Double shell structure of PSE , Institut Berlin, Z. Naturforschung 25a, 210-217 (1970)
[20] Constantine A. Balanis: “Antenna Theory, Analysis and Design”, John Wiley & Sons, Inc., 2nd ed. (1982)
References:
[1] E. Rutherford: Philosophical Magazine 21 699 (1911)
[2] M.G. Mayer: Phys. Rev. 75 (1969)
[3] E. Feenberg: Rev. Mod. Phys. 19 239 (1947)
[4] L.R. Hafstad, E. Teller: Phys. Rev. 54 681 (1938)
[5] 21st Century Science & Technology Magazine (http://www.21stcenturysciencetech.com/articles/moon_nuc.html)
[6] J. Garai: Double Tetrahedron structure of the nucleus (http://lanl.arxiv.org/abs/nucl-th/0309035)
[7] X. Borg: The Variable Phase Model of the nucleus (http://www.blazelabs.com/f-p-vpm.asp)
[8] Sachs, Robert G: "Maria Goeppert Mayer", Biographical Memoirs 50 (National Academy of Sciences, 1979).
[9] Hyper Physics, Georgia State University http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
[10] K. Maltman, G.J. Stephonson Jr. K. E. Schmidt: Nuclear Physics. 481 62
[11] D. Robson: Nuclear Physics. A 308 381 (1978)
[12] Linus Pauling: Research Notebooks 25,26 (http://osulibrary.orst.edu/specialcollections/rnb/index.html)
[13] X. Borg: Spherical Standing Waves (http://www.blazelabs.com/f-p-prop.asp)
[14] X. Borg: Space Time system of units http://www.blazelabs.com/f-u-suconv.asp
[15] Gordon L. Kane: Modern Elementary Particle Physics. Perseus Books (1987)
[16] Crystal lattice structure - Wikipedia (http://en.wikipedia.org/wiki/Crystal_structure)
[17] M. Abramowitz and I. A. Stegun, eds., Handbook of Math Functions, N.Bureau of Std Applied Math. S 55, 1964
[18] D. Wells, The Penguin Dictionary of Curious and interesting Numbers, pp 126-7, Penguin Books (1987)
[19] K. Neubert - Double shell structure of PSE , Institut Berlin, Z. Naturforschung 25a, 210-217 (1970)
[20] Constantine A. Balanis: “Antenna Theory, Analysis and Design”, John Wiley & Sons, Inc., 2nd ed. (1982)
The Variable Phase Model of the nucleus
The paired tetrahedron stacking mechanism of the nucleus gave perfect match and prediction with the known nuclear magic numbers. However, one cannot but ask what's really happening within the layers which seem to occupy the same space. Such phenomena is also known to occur with covalent bonding between atoms, in chemistry. When one stops to think about it, it is found that real and apparent values for most physical constants are part of everydays' experience. We know about rest mass, relativistic mass, time dilation, length contraction, apparent power, real power ... Those readers who already went through my introduction on higher dimensional levels, will appreciate how easy one can understand imaginary 3D mass components by projecting the shadow of a pair of 4 dimensional hypertetrahedrons (called a simplex) onto a 3D plane. The angle of projection of such a shadow will vary the ratio of reactive to resistive energy, or in other words, the ratio of hidden mass to measureable mass, very much analogous to the way we engineers calculate the power factor in electrical systems. This is the angle that to this date, physicists have been calling 'spin'. A closed shell situation, is the condition at which such an angle projects a simplex onto a 3D plane, such that the observer perceives it as a 3 dimensional tetrahedron. The above diagram shows this effect. Each angle gives a different ratio of real to imaginary components, defining the way we perceive matter. A variation of this angle does in fact change the whole perception of matter, changing it between the well known four phases or states of matter; plasma, gas, liquid, solid. You can now understand why different models of the nucleus, based on gas, liquid and semi-solid states respectively, have each been very successful in describing selected properties of the nuclei, but none of them on its own has been able to describe all its properties, since most characteristics of the various phases are mutually exclusive. The model shown here is a variable phase model and for this simple reason, succeeds in modelling the nucleus where all others have failed.
Where did Quantum Mechanics go wrong?
The difficulty in reconciling GR with QM, is not only limited to wrong assumptions in Einstein's GR, but also wrong assumptions in QM. This assumption got dragged along from the time of Descartes who famously defined matter as that which has mass and occupies space. Later on, Heisenberg proposed his 'Matrix Mechanics', in which mass and momentum took form of infinite-dimensional non commutative matrices. Although his method was good enough to calculate relative intensities of spectral lines from atomic energy level transitions, the requirement for the infinite dimensional matrices brought with it several other problems, some of which are still found in today's quantum mechanics theory. In Quantum mechanics, the physical state of a system is defined as an infinite dimensional Hilbert space, with physically observable quantities like mass and energy, being represented with Hermitian operators, which by definition can only be real numbered quantities. So, it seems that Heisenberg's matrices where doomed to infinite dimensions due to an old paradigm which has been dragged along from Descartes definition which requires matter to have real mass, occupying real space. But, the truth is that there is no reason why space, mass or energy should not be complex valued. In fact, if one defines both space and time dimensions as hyperdimensional vectors, any physical parameter we know of can take up complex (Re and Im) values. This was later on shown by Schrodinger in his complex wave equation, which automatically introduced complex valued functions and physical quantities. Indeed, his complex wave equations gave the same predictions as Heisenberg's infinite matrix mechanics, thus showing that our present assumptions for physically observable quantities to be represented with Hermitian operators is not a prerequisite for a correct theory. From there on however, things took a very wrong path, with the intervention of Bohr and Heisenberg who teamed up and gave birth to what is known as the Copenhagen interpretation. Schrodinger, Einstein and other pioneers opposed this doctrine, and insisted that all physical laws must have a direct and logical solution without resorting to probability functions and infinite dimensional matrices. However, all theories, including newer ones like the Quantum field theory, point towards the same solution, that of the consideration of mass being a complex value, able to have a real component residing in real space, and an imaginary component residing in imaginary space. This step comes at the expense of trashing Bohr's well-established principle of Quantum Mechanics , which states that we have no ability whatsoever to measure any imaginary anything and that all measurements are of real numbers, and complex wave functions are only mathematical constructs to help explain the purely real measurements. Once we understand the important physical role of imaginary components, especially the imaginary mass components as described in the variable phase nuclear model, we will finally be able to understand and predict the logical and direct actions involved in nature, and shall easily reconcile relativity with quantum mechanics, into a single unified theory based on a simple unified hyperdimensional yet finite system of units.
VPM predicts vacuum as the fifth state of matter and free Hydrogen for all planets and the sun
Where did Quantum Mechanics go wrong?
The difficulty in reconciling GR with QM, is not only limited to wrong assumptions in Einstein's GR, but also wrong assumptions in QM. This assumption got dragged along from the time of Descartes who famously defined matter as that which has mass and occupies space. Later on, Heisenberg proposed his 'Matrix Mechanics', in which mass and momentum took form of infinite-dimensional non commutative matrices. Although his method was good enough to calculate relative intensities of spectral lines from atomic energy level transitions, the requirement for the infinite dimensional matrices brought with it several other problems, some of which are still found in today's quantum mechanics theory. In Quantum mechanics, the physical state of a system is defined as an infinite dimensional Hilbert space, with physically observable quantities like mass and energy, being represented with Hermitian operators, which by definition can only be real numbered quantities. So, it seems that Heisenberg's matrices where doomed to infinite dimensions due to an old paradigm which has been dragged along from Descartes definition which requires matter to have real mass, occupying real space. But, the truth is that there is no reason why space, mass or energy should not be complex valued. In fact, if one defines both space and time dimensions as hyperdimensional vectors, any physical parameter we know of can take up complex (Re and Im) values. This was later on shown by Schrodinger in his complex wave equation, which automatically introduced complex valued functions and physical quantities. Indeed, his complex wave equations gave the same predictions as Heisenberg's infinite matrix mechanics, thus showing that our present assumptions for physically observable quantities to be represented with Hermitian operators is not a prerequisite for a correct theory. From there on however, things took a very wrong path, with the intervention of Bohr and Heisenberg who teamed up and gave birth to what is known as the Copenhagen interpretation. Schrodinger, Einstein and other pioneers opposed this doctrine, and insisted that all physical laws must have a direct and logical solution without resorting to probability functions and infinite dimensional matrices. However, all theories, including newer ones like the Quantum field theory, point towards the same solution, that of the consideration of mass being a complex value, able to have a real component residing in real space, and an imaginary component residing in imaginary space. This step comes at the expense of trashing Bohr's well-established principle of Quantum Mechanics , which states that we have no ability whatsoever to measure any imaginary anything and that all measurements are of real numbers, and complex wave functions are only mathematical constructs to help explain the purely real measurements. Once we understand the important physical role of imaginary components, especially the imaginary mass components as described in the variable phase nuclear model, we will finally be able to understand and predict the logical and direct actions involved in nature, and shall easily reconcile relativity with quantum mechanics, into a single unified theory based on a simple unified hyperdimensional yet finite system of units.
VPM predicts vacuum as the fifth state of matter and free Hydrogen for all planets and the sun
The variable phase model (VPM) of the nucleus, can totally describe matter in terms of electromagnetic field structures. The phase of the nucleus, giving different properties of 3D motion to its constituents, can be described by the real and imaginary components of electromagnetic fields. If the real component is much greater than the imaginary one, the phase will tend to be solid or semi solid. When the imaginary component increases, the phase will tend to be more gaseous or plasma. The VPM predicts that for the matter phase having negligible or no real component at all (the dipoles being purely capacitive), the nuclear phase will change into that of a vacuum. This brings vacuum into the list of phases of matter, matter with no real mass component. The idea may not be so new, as we find that Plato's Timaeus, long time ago had already proposed the existence of a fifth element which he called quintessence, of which the cosmos itself is made. Despite having no real mass components, VPM still requires that vacuum retains its electromagnetic properties, as we know it does. This explains enigmas like the observed matter popping in and out of empty space, and variations in energy levels and refractive index of empty space, for example close to a huge mass like the sun.
Generation of gases from vacuum
The VPM also predicts that since it is known that refractive index of space is being altered by strong gravitational fields (due to bending of light phenomena), the space around a huge body will have its real component gradually increased from that of vacuum to plasma, to gas. The first evidence for this is the fact that over 99% of matter in the universe is known to be in its plasma phase. Further phase change of such plasma would in fact generate a real gas atmosphere around each planet, starting from the lightest gases on the outer surface. Thus, using old terminology, the aether takes up the form of various forms of atmospheric densities, ranging from the mostly imaginary vacuum content, to the mostly real solid content. Mainstream physics explains this anomalous presence of gas surrounding all massive bodies in space as outgasing from their solid core.
Generation of gases from vacuum
The VPM also predicts that since it is known that refractive index of space is being altered by strong gravitational fields (due to bending of light phenomena), the space around a huge body will have its real component gradually increased from that of vacuum to plasma, to gas. The first evidence for this is the fact that over 99% of matter in the universe is known to be in its plasma phase. Further phase change of such plasma would in fact generate a real gas atmosphere around each planet, starting from the lightest gases on the outer surface. Thus, using old terminology, the aether takes up the form of various forms of atmospheric densities, ranging from the mostly imaginary vacuum content, to the mostly real solid content. Mainstream physics explains this anomalous presence of gas surrounding all massive bodies in space as outgasing from their solid core.
It is an accepted fact that all of the planets in our solar system started out with atmospheres of Hydrogen and Helium. The outer four planets (Jupiter, Saturn, Uranus, and Neptune) were able to keep their original atmospheres with minimal to no gas by-products from their interiors. They have very thick atmospheres with proportionally small solid cores and their atmosphere consists of 89% Hydrogen and 11% Helium, element numbers 1 and 2 respectively. Recently it was also found that even small moons, including our moon have a a very thin layer of atmosphere composed of the same light gases. The phase shift mechanism proposed in this model, does in fact show how the ionosphere and earth's own atmosphere are maintained. Hydrogen and Helium were never a gas by-product released from planet's or moon's interiors, and presently my VPM is the only physical model that explains their presence on all the planets, including the sun. If one could go on Neptune or Jupiter, and start pumping out Hydrogen from Neptune's atmosphere into space, or somehow utilising it as an energy source, he would find out that the supply of Hydrogen will be inexhaustible. This is because, the thickness of Hydrogen around a planet is simply vacuum with its phase shifted to the lightest gas phase, so a new layer of Hydrogen will be instantly converted by the gravitational field from the surrounding vacuum, resulting in an inexhaustible supply of hydrogen. The same of course applies to our sun, and explains its inexhaustible supply of hydrogen. As you see, the term 'phase' of matter fits perfectly with its equivalent electromagnetic phase angle, and the old term of 'aether' (a gas like medium) for vacuum was not that bad at all!
More experimental evidence of vacuum phase turning into gas phase
The following is the introduction to a 1905 article by Clarence Skinner of the University of Nebraska:
While making an experimental study of the cathode fall of various metals in helium it was observed that no matter how carefully the gas was purified the hydrogen tested spectroscopically, persistently appeared in the cathode glow. Simultaneous with this appearance there was also a continuous increase in the gas pressure with time of discharge. This change in gas pressure was remarkable because of its being much greater than that which had been observed under the same conditions with either nitrogen, oxygen or hydrogen. Now the variation in cathode fall with current density and with gas pressure in helium was found to be so like that obtained with hydrogen that it appeared necessary to maintain the helium free of the latter in order to make sure that the hydrogen present was not the factor causing this similarity in the results. Futile endeavors to attain this condition led to the present investigation, which locates the source of the hydrogen in the cathode, shows that the quantity of hydrogen evolved by a fresh cathode obeys Faraday’s law for electrolytes, and that a fresh anode absorbs hydrogen by the same law.1
Skinner employed various metals as cathode and found that most tarnished during discharge in helium and each produced hydrogen. Metals tarnish in the presence of atomic hydrogen, but not in helium. The following quote is from his article:
Altogether about two cubic centimeters of gas have been given off by this silver disk, which is 15 mm in diameter and about 1 mm thick. It shows no sign of having its supply of hydrogen reduced in the least.2
Many respected experimenters have reported the surprising appearance of hydrogen gas in their experiments. The following quote is from a 1914 article by Sir J.J. Thomson:
I would like to direct attention to the analogy between the effect just described and an everyday experience with discharge tubes. I mean the difficulty of getting these tubes free from hydrogen when the test is made by a sensitive method like that of positive rays. Though you may heat the glass tube to the melting point, may dry the gases by liquid air or cooled charcoal and free gases you let into the tube as carefully as you will from hydrogen, you will get hydrogen lines by the positive ray method, even when the bulb has been running several hours a day for nearly a year.3
Since the gases tested by Thomson were subjected to electrical discharge prior to test, he may have produced hydrogen by the same mechanism as Skinner. If the medium proposed by Maxwell is a matrix of protons and unpaired electrons, atomic hydrogen might be produced from the medium by electrolysis. If so, the hydrogen would be produced at a fresh cathode at the rate predicted by Faraday’s laws. Atomic hydrogen is extremely reactive and would be expected to tarnish metal cathodes and form diatomic hydrogen gas, as noted by Skinner.
In a 1914 article4, George Winchester of Washington and Jefferson College gave results of electrical discharge experiments using cp aluminum electrodes approximately one millimeter apart and pressures as low as one millionth of a millimeter. He obtained hydrogen and traces of helium and neon early in the experiments. He proposed that helium and neon had been occluded in the electrodes.
The case of hydrogen is different; I have sparked tubes until the electrodes were entirely wasted away and this gas can be obtained as long as any metal remains.5
A 1928 article6 by Stearcie and Johnson of McGill University reports on an exhaustive study of the solubility of hydrogen gas in silver. They reported that, at 25° C, silver absorbed 0.007 volumes of hydrogen per volume of silver. As pointed out above, Skinner’s silver cathode, which had volume of about 0.08 cc produced 2 cc of hydrogen gas or 25 times its volume of hydrogen and,'It shows no sign of having its supply of hydrogen reduced in the least.'2
The cathode could have contained only 0.08 X 0.007 = 0.00056 cc of hydrogen. The hydrogen Skinner produced could not have been initially present in his silver cathode
References
1. Skinner, C.A. The Evolution of Hydrogen from the Cathode and its Adsorption by the Anode in Gases., Phys. Rev. 21, 1-15 (1914)
2. ibid p. 6
3. Thomson, J.J., Nature, 90, pp. 645-647, (1914)
4. Winchester, G., On the continued Appearance of Gases in Vacuum Tubes, Phys. Rev. 3, pp. 287-94, (1914)
5. ibid. p. 290
6. Stearcie, E and Johnson, F., The Solubility of Hydrogen in Silver, Proc. Roy. Soc., London, A, 101, pp. 290-299, (1928)
More experimental evidence of vacuum phase turning into gas phase
The following is the introduction to a 1905 article by Clarence Skinner of the University of Nebraska:
While making an experimental study of the cathode fall of various metals in helium it was observed that no matter how carefully the gas was purified the hydrogen tested spectroscopically, persistently appeared in the cathode glow. Simultaneous with this appearance there was also a continuous increase in the gas pressure with time of discharge. This change in gas pressure was remarkable because of its being much greater than that which had been observed under the same conditions with either nitrogen, oxygen or hydrogen. Now the variation in cathode fall with current density and with gas pressure in helium was found to be so like that obtained with hydrogen that it appeared necessary to maintain the helium free of the latter in order to make sure that the hydrogen present was not the factor causing this similarity in the results. Futile endeavors to attain this condition led to the present investigation, which locates the source of the hydrogen in the cathode, shows that the quantity of hydrogen evolved by a fresh cathode obeys Faraday’s law for electrolytes, and that a fresh anode absorbs hydrogen by the same law.1
Skinner employed various metals as cathode and found that most tarnished during discharge in helium and each produced hydrogen. Metals tarnish in the presence of atomic hydrogen, but not in helium. The following quote is from his article:
Altogether about two cubic centimeters of gas have been given off by this silver disk, which is 15 mm in diameter and about 1 mm thick. It shows no sign of having its supply of hydrogen reduced in the least.2
Many respected experimenters have reported the surprising appearance of hydrogen gas in their experiments. The following quote is from a 1914 article by Sir J.J. Thomson:
I would like to direct attention to the analogy between the effect just described and an everyday experience with discharge tubes. I mean the difficulty of getting these tubes free from hydrogen when the test is made by a sensitive method like that of positive rays. Though you may heat the glass tube to the melting point, may dry the gases by liquid air or cooled charcoal and free gases you let into the tube as carefully as you will from hydrogen, you will get hydrogen lines by the positive ray method, even when the bulb has been running several hours a day for nearly a year.3
Since the gases tested by Thomson were subjected to electrical discharge prior to test, he may have produced hydrogen by the same mechanism as Skinner. If the medium proposed by Maxwell is a matrix of protons and unpaired electrons, atomic hydrogen might be produced from the medium by electrolysis. If so, the hydrogen would be produced at a fresh cathode at the rate predicted by Faraday’s laws. Atomic hydrogen is extremely reactive and would be expected to tarnish metal cathodes and form diatomic hydrogen gas, as noted by Skinner.
In a 1914 article4, George Winchester of Washington and Jefferson College gave results of electrical discharge experiments using cp aluminum electrodes approximately one millimeter apart and pressures as low as one millionth of a millimeter. He obtained hydrogen and traces of helium and neon early in the experiments. He proposed that helium and neon had been occluded in the electrodes.
The case of hydrogen is different; I have sparked tubes until the electrodes were entirely wasted away and this gas can be obtained as long as any metal remains.5
A 1928 article6 by Stearcie and Johnson of McGill University reports on an exhaustive study of the solubility of hydrogen gas in silver. They reported that, at 25° C, silver absorbed 0.007 volumes of hydrogen per volume of silver. As pointed out above, Skinner’s silver cathode, which had volume of about 0.08 cc produced 2 cc of hydrogen gas or 25 times its volume of hydrogen and,'It shows no sign of having its supply of hydrogen reduced in the least.'2
The cathode could have contained only 0.08 X 0.007 = 0.00056 cc of hydrogen. The hydrogen Skinner produced could not have been initially present in his silver cathode
References
1. Skinner, C.A. The Evolution of Hydrogen from the Cathode and its Adsorption by the Anode in Gases., Phys. Rev. 21, 1-15 (1914)
2. ibid p. 6
3. Thomson, J.J., Nature, 90, pp. 645-647, (1914)
4. Winchester, G., On the continued Appearance of Gases in Vacuum Tubes, Phys. Rev. 3, pp. 287-94, (1914)
5. ibid. p. 290
6. Stearcie, E and Johnson, F., The Solubility of Hydrogen in Silver, Proc. Roy. Soc., London, A, 101, pp. 290-299, (1928)
he nucleus - the most basic naturally occuring fractal
As discussed earlier, the above is equivalent to an atom fullfilling its shell 2s, equivalent to atom Be8, which is known to decay in exactly two alpha particles, each of which we explained, take the shape of a tetrahedron. We also know that the second tetrahedron is an exact mirror image of the first one about a central mirror core. Now these two shapes are similar but not the same entity and somehow need to be identified. It's like having to define an uphill from a downhill, so we will call the one with its pointed vertex upwards as the positive tetra and the other as negative tetra. Once the two counter rotating tetrahedrons are summed up in the same spherical space, one gets the geometric shape shown below.
These interactive 3D graphics were created with the help of some Mathematica code written by Robert M. Dickau available on his homepage.
The shape is called the Sierpinski tetrahedron and is the three-dimensional version of the famous Sierpinski gasket. You can rotate this graphic in 3D using your mouse. If you study the shape you will find the the inner shape enclosed between the positive and negative tetrahedrons is in fact a perfect octahedron. This hidden octahedron plays an important role in nature as we shall see later on. For the sake of clarity, the three vertices of the negative tetrahedron are not shown in the 3D diagrams. This fractal is of immense importance as it is probably the key not only to generation of particles but to nature's secret mechanism of growth itself. With the help of this graphic, one can easily understand how nature works out the way from a single entity, in this case the parent tetrahedron (positive), into an opposite parent tetrahedron (negative), and adding them onto the same space coordinates to get three similar structures, each of which have the same 'reproducing' mechanism of their parent structure. Remember that the tetrahedron represents the most basic spherical solution existing in 3D and is thus the best candidate for natures mechanism. Now the wavelength of the EM standing wave generating the structure is equal to twice the distance between vertices, oscillating at a frequency F. What would happen if the structure is twice as energetic? Each positive tetrahedron will replicate itself into its image negative tetrahedron, and four tetrahedrons each oscillating at 2F will take place each parent tetrahedron. Such a mechanism might easily explain the fact that there are peaks and dips of energy per nucleon repeating every fourth nucleon.
| Doubling the standing wave EM frequency 'mates' each tetrahedron to its opposite polarity tetrahedron and replaces the original with four similar tetrahedrons. The original structure of four tetras is now replaced with sixteen similar tetrahedrons. Doubling the frequency further, gives a structure of 64 positive tetrahedrons as shown on the right. The process of fractal generation does not go for infinity but is restricted by planck's length which defines the shortest wavelength for the distance between vertices of the smallest hidden octahedron. Nature does not in fact set a higher limit for wavelength and that's why we can generate dc (zero frequency currents) in the first place. It is now clear that any possible energy combination within this structure will be a multiple of planck's wavelength represented by the smallest tetrahedron in the fractal structure. |
Black Hole within matter
The matter-antimatter interface core
The matter-antimatter interface core
Considering the atom as multiple nesting of 3D platonic solids, all rotating as a single object, gives us a whole new clearer picture of how the atom looks like, and explains in a more obvious way many rules which had to be adopted without any previous plausible reason. Each of the outer spherical shells circumscribed by the outer platonics is analogous to electron energy levels or shells in the conventional model. Inner spherical shells represent various known (and unknown) conventional particles, the smaller the shell, the shorter the platonic edge length, the higher the frequency of its vibration and thus the higher its energy level, frequency and 'mass'.
If one looks closer to this new model however, one can notice that at the very centre of any atom, there will always exist a platonic whose side lengths are equal to Planck's length, and whose inscribed spherical volume CANNOT nest any further platonic shape, in fact it cannot nest anything at all, since units of wavelength (space) and time are meaningless within such a volume. This is not vacuum, since we know that EM waves CAN be handled in vacuum. This 3D volume is in fact NOT a space time volume, it behaves very similarly to a black hole and is NOT REAL. This means that unlike Wolff's assumption about wavecentres, the ingoing waves never reach to a single centre point, but a central sphere whose natural resonance wavelength is equal to plank's length.
We know that a black hole is a region of space whose attractive gravitational force is so intense that no matter, light, or communication of any kind EXCEPT GRAVITY can escape. This means that two stars on opposite sides of a black hole can never 'see' (property of EM radiation) each other but would still 'feel' (property of gravity) each others gravitational force!. A black hole would thus appear black from the outside real world. However, gas around a black hole can be very bright, indicating an elevated energy level at its periphery.
Returning back to our atom model, this small 3D sphere, of which one is present in every standing wave structure (particle), has a very special purpose, and is the only interface between the real and imaginary components of the standing wave, will similarly look black, and will be surrounded by the highest energy level within the atom. As we shall see this spherical core of sub-quantum dimensions has a special function within matter. But at this point we must explore the imaginary world of the particle nature.
Most of you have one time or another worked with imaginary terms, or complex numbers. Conventional physics makes use all the time of imaginary components for voltage, impedance, currents, permittivity, permeability, refractive index, but no one ever stops thinking of the consequences of the existence of these terms, in terms of our restricted 4 dimensional space-time universe.
As with normal travelling EM waves, standing EM waves have an 'imaginary' component equivalent to an imaginary mass, as in the square-root of (-1), times its real mass (jm). Imaginary particles are not something new to physics, although most textbooks barely mention them due to lack of knowledge, and because they have never been (and can never be) isolated. For example, it is known that the anti-electron or positron has exactly the same mass as a regular electron, but has a positive charge and negative entropy, rather than a negative charge and positive entropy. The anti-proton has the same mass as a regular proton, but carries a negative electric charge and opposite entropy. There are also quarks and anti-quarks which carry opposite color-charge, but otherwise are identical to regular quarks. Anti-neutrinos carry opposite 'neutrino-charge' from ordinary neutrinos. As Feynman correctly described, these imaginary particles are as real as the real counterparts but travel backwards in time. This statement may be confusing at first but it's just about the simplest & best description one could could come up with for these particles. These antiparticles are not to be found as a cluster in somepart of the universe. Some people think that such clusters, of antimatter are being formed elsewhere in the universe, whilst leaving all real particles clustered in our own universe. This is totally wrong as the anitparticle is just the mirror image of the particle travelling in a reverse time direction - something we humans cannot ever experience.
We have no idea how regular matter and 'imaginary' or anti matter interact, but all forces between real and imaginary matter involving their mass would be 'imaginary', rather than 'real', forces which means that the big chances are there are no effects from one onto the other, gravitationally. This would not be true if their interaction is passed through an imaginary function medium, that is a medium which looks like a mirror to both the imaginary and real sides. In such a case, an imaginary mass through an imaginary function would result in a real effect on the real mass (j x j x m = 1m), and a real mass through an imaginary function would result in an imaginary effect on the imaginary mass!(1 x j x jm = 1m).
From the Spacetime conversion table we know that all physics parameters, including those known to have both real and imaginary components, can be described in terms of Space (length) and Time. For this to remain mathematically consistent, both space and time must handle both real and imaginary components. The terms +j and -j do not mean that the component is orthogonal to the left or right of the real vector. That is in real 3D space, the vector jx is not equivalent to either y nor to z. Same applies to time. This means that our 4D space-time model is not even enough to handle our known physics, since both space and time are normally being assumed 100% real, which is definetely not the case.
It is about time, that both mathematical and scientific analysis give more importance and meaning to all imaginary terms. In multitudes of important derivations, in both maths and physics, we find imaginary roots and solutions literally dropped off or disregarded, just because they are not real. Disregarding imaginary components in the physical world has serious consequences and is what makes things look to behave weird or showing overunity. If one does not fully understand that the imaginary components EXIST as much as the real components, he may be easily tricked, and could never for example, explain why a seemingly genuine overunity device can never be made self running.
The implications are rather obvious, an imaginary space-time dimension has to be defined along with the four real space-time dimensions to fully represent all physics parameters. This shall upgrade all physics units into a set of space-time dimensions, one with real and the other with imaginary, resulting into at least one complex 4 dimension space time. This requires no major change in physics, but from thereoff, ALL quantities have to be assumed to be complex values, that is, have BOTH REAL & IMAGINARY COMPONENTS of space-time.
- Real 3D Space vectors: x,y,z
- Real time vectors: t
- Imaginary 3D Space vectors: xj,yj,zj
- Imaginary time vector: jt
As I have illustrated above, the centre of each particle of matter cannot be defined as a dimensionless point but one which inscribes a spherical solution singularity (another platonic), in which real wavelengths and real time do not fit.
As we have seen in the fractal description of the most inner part of the nucleus, the mirror core required to perfectly get a mirror image for the tetrahedron must have the shape of an octahedron. And you must also keep in mind that such octahedron is in itself a solution of an incoming and outgoing spherical waves, that is a spherical standing wave. This octahedron core is illustrated by one of the nice models from Gayla Chandler which shows the complement shape of the two interlaced tetrahedrons (the tetrahedron and its reflection, or antiparticle counterpart). The imaginary component of matter can be visualised as being the exact mirror image of its real counterpart, being reflected through this interface core. Similarly to the real side, the imaginary component is made up of imaginary rotating platonics, and the central interface core has the same size as that in the real matter. Thus the virtual particle is on one side and the real particle is on the other side of this spherical volume. Although, the two spheres seem to occupy the same spherical volume, they are not, and the 'mirror surface' at the centre is real on the real side and imaginary on the virtual side, it has 3 dimensions of its own, but it's not a space volume but rather an interface.
Each particle has got this mirror core at the centre, which cannot be defined in terms of our known space-time dimensions, and so it is independant of both time and length. Now, we define two different points in space by their location, and the only way to do that is to define the distance from each other. If we imagine that each of two independent particle cores are forming part of a time independent gigantic mirror, how could we measure the distance between these cores if their dimension is less than any measureable dimension? You cannot. This means that such mirror cores within two separate particles cannot be identified from one another, are separated by a non-measureable distance apart, and from our 4D point of view can thus be considered as the same entity existing from beginning to end of our time. Also, the time taken for light to travel from one such core to the other cannot be measured because light cannot travel without a time dimension.
This has various implications in the real world. It means that all matter in the universe is interfacing or communicating with its virtual matter through the same medium, and that all matter in the universe communicates through the same singularity which has no time dimension. This medium is responsible for the instantaneous action noticed even at astronomical distances between two masses, and also for the EPR experimental evidence, and the lack of aberration of gravitational force. Such theory may finally give significance to the gravitational constant which seems to depend on the total mass of particles within the whole universe, which is of course interfacing through this single entity.
As we have seen in the fractal description of the most inner part of the nucleus, the mirror core required to perfectly get a mirror image for the tetrahedron must have the shape of an octahedron. And you must also keep in mind that such octahedron is in itself a solution of an incoming and outgoing spherical waves, that is a spherical standing wave. This octahedron core is illustrated by one of the nice models from Gayla Chandler which shows the complement shape of the two interlaced tetrahedrons (the tetrahedron and its reflection, or antiparticle counterpart). The imaginary component of matter can be visualised as being the exact mirror image of its real counterpart, being reflected through this interface core. Similarly to the real side, the imaginary component is made up of imaginary rotating platonics, and the central interface core has the same size as that in the real matter. Thus the virtual particle is on one side and the real particle is on the other side of this spherical volume. Although, the two spheres seem to occupy the same spherical volume, they are not, and the 'mirror surface' at the centre is real on the real side and imaginary on the virtual side, it has 3 dimensions of its own, but it's not a space volume but rather an interface.
Each particle has got this mirror core at the centre, which cannot be defined in terms of our known space-time dimensions, and so it is independant of both time and length. Now, we define two different points in space by their location, and the only way to do that is to define the distance from each other. If we imagine that each of two independent particle cores are forming part of a time independent gigantic mirror, how could we measure the distance between these cores if their dimension is less than any measureable dimension? You cannot. This means that such mirror cores within two separate particles cannot be identified from one another, are separated by a non-measureable distance apart, and from our 4D point of view can thus be considered as the same entity existing from beginning to end of our time. Also, the time taken for light to travel from one such core to the other cannot be measured because light cannot travel without a time dimension.
This has various implications in the real world. It means that all matter in the universe is interfacing or communicating with its virtual matter through the same medium, and that all matter in the universe communicates through the same singularity which has no time dimension. This medium is responsible for the instantaneous action noticed even at astronomical distances between two masses, and also for the EPR experimental evidence, and the lack of aberration of gravitational force. Such theory may finally give significance to the gravitational constant which seems to depend on the total mass of particles within the whole universe, which is of course interfacing through this single entity.
Instantaneous (non local) Action
Without violating Causality
Without violating Causality
In all textbook physics we learn that masses, including planets, obey fixed laws of nature. Until the last decade, these laws were measured properties of nature, no theoretical or physical origin was known. These measurements indicated that the movement of energy and information, which are needed to carry out the laws, travel consistently at the speed of light, and that nothing (no information) can travel faster than light. This motion satisfied our rule of causality; that is: Events always occur after their causes. 
However, some events have repeatedly seemed to violate the rule of causality. One such force is called Quantum entanglement. This term is used to describe the way that particles of energy/matter can become correlated to predictably interact with each other regardless of how far apart they are. Also, events such as gravity pull between planets seem to be transmitted instantaneously, otherwise it can be shown that any two planets will spiral into each other. As shown by Sir Arthur Eddington, this means: "If the Sun attracts Jupiter towards its present position S, and Jupiter attracts the Sun towards its present position J, the two forces are in the same line and balance. But if the Sun attracts Jupiter toward its previous position S', and Jupiter attracts the Sun towards its previous position J', when the force of attraction started out to cross the gulf, then the two forces give a couple. This couple will tend to increase the angular momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observations if the speed is at all comparable with that of light." (Eddington, 1920, p.94).
Evidence of infinite gravitational phase speed at zero frequency has been also recently observed by a few other researchers by noting the high stability of earth's orbit about the sun. Light from the sun is not observed to be collinear with the sun's gravitational force. Astronomical studies indicate that the earth's acceleration is toward the gravitational centre of the sun even though it is moving around the sun, whereas light from the sun is observed to be aberated. If the gravitational force between the sun and the earth were aberated, then gravitational forces tangential to the earth's orbit would result, causing the earth to spiral away from the sun, due to conservation of angular momentum. Current astronomical observations estimate the phase speed of gravity to be greater than 2x1010c. This value could very well indicate the limit of the measuring equipment in trying to time a force which unlike EM waves does not travel, but acts at two distant points at the SAME TIME regardless of how far apart they are.
Indeed, even Newton's equation for the force of gravity, F=GMm/r2, indicates that the gravitational force is not a function of time, that is d/dt(GMm/r2)=0. This is not the same for EM induced forces, where radiation momentum on matter = hf/c, which as you see depends on frequency which IS time dependent. The Newtonian gravity has two special traits. One, there is no event horizon for Newtonian gravity. Two, it transmits its force in a manner of immediate (non local) action at a distance. So, the non-locality is fully compliant with Newtonian gravity. All these events, which indicate the transmission of energy and information at superluminal speeds (or infinite speeds), are somehow all related to the gravitational force. Accepting that something can travel at infinite speed makes no sense, however one may explain this effect if the medium through which it travels cannot be differentiated with respect to time dimension, and hence have no aberration. Indeed, General Relativity suggests that gravity is not a force that propagates. Also, it is widely accepted, even if less widely known, that the speed of gravity in Newton's Universal Law is unconditionally infinite. But since there has not been a good scientific explanation of how this could ever be possible, we still learn that gravity forces travel at the speed of light, and the reason given is that no information can travel faster than the speed of light. This is definitely wrong, as no one has yet been able to show that gravity information 'travels along'.
The fact that the gravitational effect is felt before its cause is 'seen' at the observer does not mean that causality is actually being violated. Instead, the strange event is merely due to the fact that gravity effect and EM waves are not travelling through the same medium, or better, through the same spatial dimensions. It is quite similar (although not really analogous) to the delay between a lightning flash and its thunder, if one assumes that nothing travels faster than sound, one would say that the lightning occurred before the strike. The interpretation of violation of causality is created by our incomplete knowledge of the Standing Wave Structure of Matter, and of the special energy exchanges taking place within matters' central sub-quantum core and its periphery. All electromagnetic communication (radiation & radiation pressure on masses), detected in 3D space, still travel at c, the speed of light. Action at a distance can be completely understood if one considers the fourth spatial dimension. As already discussed here, the only way we humans get to percieve this 4th spatial dimension is through the perception of time. Any energy fields in this dimension will appear to us to be time independent. Our mind normally perceives speed as the rate of change of a spatial dimension with respect to time, but what happens if we try to detect the rate of change of time with respect to time itself? Gravitational forces are taking place in this 4th spatial dimension, which is orthogonal to all 3D spatial dimensions, the one we normally perceive as 'time' and therefore the concept of 'travelling' in 3D space makes no more sense for such a force.
The speed of gravity information is still hotly debated, but the EPR experiment is a well accepted scientific experiment which proves instant action at a distance. The EPR experiment (named after Einstein, Podolski and Rosen) in which two quantum particles A and B which were once together fly apart and are measured at two distant locations A and B. In the Quantum Theory, observer A's choice of what kind of measurement to make on particle A instantly changes the state description of particle B--a general feature of quantum theory called "quantum phase entanglement". In the theory a particle is represented by possibility amplitudes and relative phases. When the particles separate, so do the amplitudes, but the phases of particle A remain entangled with the phases of particle B. Any action on A--such as reaching the observation sensor--changes not only A's phases but the phases of B as well. This action of observer A on distant particle B does not diminish with distance, cannot be shielded and travels faster than light. This distant influence is unmediated, unmitigated and immediate. Such quantum connection between two particles once together now apart is a lot like voodoo--no known force connects particles A and B--just the fact of their once being together suffices to mingle their phases. Such instant voodoo influences are called "non-local"; all ordinary light-speed-limited forces are called "local". All interactions taking place in the fourth dimension will of course look like voodoo to a 3D observer, as long as the observer does not recognise TIME as a real SPATIAL dimension.
This 4th dimension is common to all particles and establishes an interesting feature in the whole universe : the cosmic wavelength. The resulting 'heart beat' is the same for all matter, because the homogeneity of the medium of the waves produces a fixed wave frequency. That's why Planck's constant is a constant through galaxies light years away from each other, since for gravity or quantum entanglement, a light year distance and 1 mm make no difference. The thickness (one planck wavelength or one timeframe) & homogeneity (G-gravitational constant) of this medium, sets a standard frequency of vibration for the smallest electric entities (dielectric entities) across the universe, as well as a relation between them for their action at a distance. An other interesting property of this cosmic clock is that it is always in phase at every particle boundary. This means that if you get two electrons, any two in the whole universe, their in-going and out-going waves will be EXACTLY in phase. Same applies for all matter in the universe being it an electron, proton, neutron or whole particle.
The notion of such universal clock has been suggested by deBroglie. He stated that the universal frequency of the electron is fe = mec2/h, and that this will be the same for any electron that exists anywhere. This frequency standard based on Planck's constant is a property of the special subquantum core we have defined earlier in this section and, thus, as we already stated, it is the same for all particles. Similarly this uniform medium thickness also provides a measure of minimum quantum length, time interval and speed of light. In a way this medium gives a sense for the existence of both real and imaginary space-times. Without it, there would be no boundary limits for the existence of length and time and the standing wave structures we refer to as the 'elementary building blocks of matter', and hence no universe, nothing at all. So, how do particles 'feel' each other within this medium?
The spherical wave structure of particles provides range and location information for the force laws. Nautical navigation teaches us that the curvature of a wave front is sufficient to determine the range and position of the center of the source of the wave fronts. This is the simple mechanism available to two particles to find their relative range and position. But what about wavefronts in a time independent medium; they should not exist. That's right, but since the homogeneity of the medium is constant (G), and all sources have the same intensity at the interface, the attenuation level would give their relative position without the requirement of a wavefront.
The fact that the gravitational effect is felt before its cause is 'seen' at the observer does not mean that causality is actually being violated. Instead, the strange event is merely due to the fact that gravity effect and EM waves are not travelling through the same medium, or better, through the same spatial dimensions. It is quite similar (although not really analogous) to the delay between a lightning flash and its thunder, if one assumes that nothing travels faster than sound, one would say that the lightning occurred before the strike. The interpretation of violation of causality is created by our incomplete knowledge of the Standing Wave Structure of Matter, and of the special energy exchanges taking place within matters' central sub-quantum core and its periphery. All electromagnetic communication (radiation & radiation pressure on masses), detected in 3D space, still travel at c, the speed of light. Action at a distance can be completely understood if one considers the fourth spatial dimension. As already discussed here, the only way we humans get to percieve this 4th spatial dimension is through the perception of time. Any energy fields in this dimension will appear to us to be time independent. Our mind normally perceives speed as the rate of change of a spatial dimension with respect to time, but what happens if we try to detect the rate of change of time with respect to time itself? Gravitational forces are taking place in this 4th spatial dimension, which is orthogonal to all 3D spatial dimensions, the one we normally perceive as 'time' and therefore the concept of 'travelling' in 3D space makes no more sense for such a force.
The speed of gravity information is still hotly debated, but the EPR experiment is a well accepted scientific experiment which proves instant action at a distance. The EPR experiment (named after Einstein, Podolski and Rosen) in which two quantum particles A and B which were once together fly apart and are measured at two distant locations A and B. In the Quantum Theory, observer A's choice of what kind of measurement to make on particle A instantly changes the state description of particle B--a general feature of quantum theory called "quantum phase entanglement". In the theory a particle is represented by possibility amplitudes and relative phases. When the particles separate, so do the amplitudes, but the phases of particle A remain entangled with the phases of particle B. Any action on A--such as reaching the observation sensor--changes not only A's phases but the phases of B as well. This action of observer A on distant particle B does not diminish with distance, cannot be shielded and travels faster than light. This distant influence is unmediated, unmitigated and immediate. Such quantum connection between two particles once together now apart is a lot like voodoo--no known force connects particles A and B--just the fact of their once being together suffices to mingle their phases. Such instant voodoo influences are called "non-local"; all ordinary light-speed-limited forces are called "local". All interactions taking place in the fourth dimension will of course look like voodoo to a 3D observer, as long as the observer does not recognise TIME as a real SPATIAL dimension.
This 4th dimension is common to all particles and establishes an interesting feature in the whole universe : the cosmic wavelength. The resulting 'heart beat' is the same for all matter, because the homogeneity of the medium of the waves produces a fixed wave frequency. That's why Planck's constant is a constant through galaxies light years away from each other, since for gravity or quantum entanglement, a light year distance and 1 mm make no difference. The thickness (one planck wavelength or one timeframe) & homogeneity (G-gravitational constant) of this medium, sets a standard frequency of vibration for the smallest electric entities (dielectric entities) across the universe, as well as a relation between them for their action at a distance. An other interesting property of this cosmic clock is that it is always in phase at every particle boundary. This means that if you get two electrons, any two in the whole universe, their in-going and out-going waves will be EXACTLY in phase. Same applies for all matter in the universe being it an electron, proton, neutron or whole particle.
The notion of such universal clock has been suggested by deBroglie. He stated that the universal frequency of the electron is fe = mec2/h, and that this will be the same for any electron that exists anywhere. This frequency standard based on Planck's constant is a property of the special subquantum core we have defined earlier in this section and, thus, as we already stated, it is the same for all particles. Similarly this uniform medium thickness also provides a measure of minimum quantum length, time interval and speed of light. In a way this medium gives a sense for the existence of both real and imaginary space-times. Without it, there would be no boundary limits for the existence of length and time and the standing wave structures we refer to as the 'elementary building blocks of matter', and hence no universe, nothing at all. So, how do particles 'feel' each other within this medium?
The spherical wave structure of particles provides range and location information for the force laws. Nautical navigation teaches us that the curvature of a wave front is sufficient to determine the range and position of the center of the source of the wave fronts. This is the simple mechanism available to two particles to find their relative range and position. But what about wavefronts in a time independent medium; they should not exist. That's right, but since the homogeneity of the medium is constant (G), and all sources have the same intensity at the interface, the attenuation level would give their relative position without the requirement of a wavefront.
Time and spherical wave solutions
Perception of time through vortices (CP) asymmetry
Perception of time through vortices (CP) asymmetry
We measure time by clocks, but clocks do not really measure time. If time slows down, everything will slow down, including the clock, and we could never detect or feel any change. If time slows down by a factor of ten, a clock in the same time-frame will still show a 24 hour day. We can only measure the difference between our time-frame and another. How would we know if time flows backwards. In the universe the time flow can be noticed by the direction of waves in space, inward or outwards from a source, outward being the normal positive time. Similarly, if the real electric and real magnetic fields are in the form of a spherical standing wave, their real cross product always points to the center of the sphere, and we call this real mass, which would always be positive. But how does matter flow through time? We know that when a slight imbalance in standing wave mechanism occurs, the standing wave will surely but slowly drift either towards or away from the source. In our real & imaginary spherical standing wave, the drifting nodes will be the platonic shapes, which will either drift outwards or inwards the sphere, depending upon the symmetry imbalance between the real & reflected waves. This effect is perceived by matter as flowing through time. Wheeler and Feynman (1945) modelled the electron as spherical inward and outward electromagnetic waves, seeking to explain radiation forces, however they failed, because as it was illustrated, the spherical wave is hidden, and is only clearly visible when rotating the standing wave structure. Once you have the standing spherical wave front, you have also got the ingoing and outgoing spherical EM waves and can then account for radiation forces. The major deficiency of the classical force laws is that they have no theoretical or physical mechanism for energy transfer. The formulae contain only constants, "mass" and "charge," - no function & no mechanism. This was an inherent defect of the static point particle model. Einstein, Wheeler and Feynman knew this, recognizing that there must exist a continual dynamic means for forces to transfer energy, and sought it in electromagnetic waves. Unfortunately there are no spherical solutions for the travelling vector e-m wave equation. Hence the mechanism had to await the scalar waves.
 | The above diagram shows a 3D view of a tetrahedron rotated 360 degrees simultaneously about each of its three axis, as viewed from a frozen time axis. This is the complex vortex one would get from a standing wave structure based on the tetrahedron. If one had to view such rotation, while giving depth to the image as time flows, the tetrahedron flowing past time would get smaller and smaller. The resulting plot of its vertices as viewed from a camera fixed over one of the vertices, would be exactly as shown on the left, which happens to be the well known Treble Julia Set crop circle found overnight in the UK. |
The wave equation must be written in spherical coordinates because cosmological space has spherical symmetry. Uniform density of the medium (space) is assumed, which yields a constant speed of the waves (and 'light'). Then the only two solutions describe the charge waves of common charged particles including the electron, positron, proton, and anti-proton. They are:
IN-wave amplitude = {A/r} e(iwt + ikr)
OUT-wave amplitude = {A/r} e(iwt - ikr)
A= wave amplitude peak
r = radius from wave center
w = 2.pi.f
t = real time
k = mc/h = wave number
Energy = E = hf = mc2.
At the center (the mirror), the in/out waves are joined by rotating the in-wave to transform it to the out-wave. Superposition of the two amplitudes to produce a standing wave can occur in two ways depending on rotation, CW or CCW. One is the electron, the other the positron, with opposite spins. Writing the rotation operators as CCW or CW ,then the two resonance amplitudes are:
Rotating standing wave electron = E(-) = {IN-wave - OUT-wave} CCW
Rotating standing wave positron = E(+) = {OUT-wave - IN-wave} CW
IN-wave amplitude = {A/r} e(iwt + ikr)
OUT-wave amplitude = {A/r} e(iwt - ikr)
A= wave amplitude peak
r = radius from wave center
w = 2.pi.f
t = real time
k = mc/h = wave number
Energy = E = hf = mc2.
At the center (the mirror), the in/out waves are joined by rotating the in-wave to transform it to the out-wave. Superposition of the two amplitudes to produce a standing wave can occur in two ways depending on rotation, CW or CCW. One is the electron, the other the positron, with opposite spins. Writing the rotation operators as CCW or CW ,then the two resonance amplitudes are:
Rotating standing wave electron = E(-) = {IN-wave - OUT-wave} CCW
Rotating standing wave positron = E(+) = {OUT-wave - IN-wave} CW
The above diagram, is equivalent to the complex vortex diagram, based on the same rotating tetrahedron, but with the time dimension represented in the shell distance from the core. Thus the outer shells represent the present and inner ones represent the past. The diagrams thus represent time reversal.
To perform an entropy or time inversion, change CCW to CW, which converts the time factor from positive to negative, and the positron into an electron. You will see that a positron is a mirror image of the electron viewed from the real space-time. To change a particle to an anti-particle (real to imaginary), switch the in-waves and the out-waves, it's like viewing the real particle in the mirror.
If they collide, the electron standing wave structure and anti-particle (positron) standing wave structure disappear, to leave only a non-standing (travellling EM wave) energy - an act of mutual destruction, called annihilation. Experiments have since demonstrated that most other particles, protons, neutrons, muons and so on, have anti-particles. Note that in all such cases energy is not destroyed or created, but rather their structure is destroyed, releasing the energy within it.
When particle and anti-particle meet, a spontaneous burst of pure energy is produced, such process called annihilation. Let's go a step further. Since anti-matter is the reflection of matter, and vice-versa, in this central core black hole or singularity, one would expect that matter and anti-matter exist in equal amounts, referred to as symmetry. This indicates that way back to the era when the universe is created, which should have huge energetic conditions, the amount of matter should be equal to that of anti-matter...but something unusual happened, which resulted in the existence of space & time itself. If symmetry had been conserved, why did the anti-matter not completely annihilate the matter, leaving only energy in the universe? Or why does nobody ever encounter stable anti-matter or maybe anti-matter planets? At this point we should know the answer, because anti-matter EXISTS but is NOT REAL - it can be observed as matter through its reflection in the cetral core of each elementary particle.
So why do we live and observe the matter side (REAL part) of things, and not the other. It is believed that there is a breakdown in the symmetry, called the charge-parity, CP-violation. It is this violation that causes the amount of matter to be slightly more than anti-matter. For this reason we, and all the matter around us, can exist, and anti-matter always lags behind matter in time. If you have read carefully up to this point, you will now understand why action on a particle will always cause a motion AFTER (NOT before) the force has been applied. This is the law of causality, and seems quite obvious - but such law would be reversed if anti-matter leads matter in time, or simply exists in higher abundance than matter. In such a case, having a CP-violation of the opposite value, would make us live in and observe an anti-matter universe, but still exist. 'Existence' shall only stop when time itself stops, and that can only happen when the CP-violating factor is exactly null.
In 1964, scientists got another anti-matter surprise, when a team of physicists, studying neutral kaons in experiments at DOE's Brookhaven Laboratory, discovered a slight but definite assymmetry in the behaviour of the neutral kaon and its anti-particle - an assymmetry called charge-parity, or CP, violation. Until that discovery, physicists had believed that particles and anti-particles behaved symmetrically, like mirror reflections of each other.
At Fermi Labs during 1999, it was announced that epsilon prime over epsilon equals 28 E -4. Now SLAC is offering a more robust measurement of the CP-violating parameter, referred to as sine (2beta); the value it reports is 0.59 with an uncertainty of 0.14. From this result we can conclude that there are less than 3 chances in 100,000 (<0.003%) that the actual, physical assymmetry could be equal to zero. This is a direct measure confirming charge parity assymmetry or violation between the real and imaginary components of the same particle, which is the only measure of the arrow and rate of time - perhaps the reason why we live on the real side and why real mass exists in positive time & entropy, whilst virtual particles exist in negative time & entropy.
To perform an entropy or time inversion, change CCW to CW, which converts the time factor from positive to negative, and the positron into an electron. You will see that a positron is a mirror image of the electron viewed from the real space-time. To change a particle to an anti-particle (real to imaginary), switch the in-waves and the out-waves, it's like viewing the real particle in the mirror.
If they collide, the electron standing wave structure and anti-particle (positron) standing wave structure disappear, to leave only a non-standing (travellling EM wave) energy - an act of mutual destruction, called annihilation. Experiments have since demonstrated that most other particles, protons, neutrons, muons and so on, have anti-particles. Note that in all such cases energy is not destroyed or created, but rather their structure is destroyed, releasing the energy within it.
When particle and anti-particle meet, a spontaneous burst of pure energy is produced, such process called annihilation. Let's go a step further. Since anti-matter is the reflection of matter, and vice-versa, in this central core black hole or singularity, one would expect that matter and anti-matter exist in equal amounts, referred to as symmetry. This indicates that way back to the era when the universe is created, which should have huge energetic conditions, the amount of matter should be equal to that of anti-matter...but something unusual happened, which resulted in the existence of space & time itself. If symmetry had been conserved, why did the anti-matter not completely annihilate the matter, leaving only energy in the universe? Or why does nobody ever encounter stable anti-matter or maybe anti-matter planets? At this point we should know the answer, because anti-matter EXISTS but is NOT REAL - it can be observed as matter through its reflection in the cetral core of each elementary particle.
So why do we live and observe the matter side (REAL part) of things, and not the other. It is believed that there is a breakdown in the symmetry, called the charge-parity, CP-violation. It is this violation that causes the amount of matter to be slightly more than anti-matter. For this reason we, and all the matter around us, can exist, and anti-matter always lags behind matter in time. If you have read carefully up to this point, you will now understand why action on a particle will always cause a motion AFTER (NOT before) the force has been applied. This is the law of causality, and seems quite obvious - but such law would be reversed if anti-matter leads matter in time, or simply exists in higher abundance than matter. In such a case, having a CP-violation of the opposite value, would make us live in and observe an anti-matter universe, but still exist. 'Existence' shall only stop when time itself stops, and that can only happen when the CP-violating factor is exactly null.
In 1964, scientists got another anti-matter surprise, when a team of physicists, studying neutral kaons in experiments at DOE's Brookhaven Laboratory, discovered a slight but definite assymmetry in the behaviour of the neutral kaon and its anti-particle - an assymmetry called charge-parity, or CP, violation. Until that discovery, physicists had believed that particles and anti-particles behaved symmetrically, like mirror reflections of each other.
At Fermi Labs during 1999, it was announced that epsilon prime over epsilon equals 28 E -4. Now SLAC is offering a more robust measurement of the CP-violating parameter, referred to as sine (2beta); the value it reports is 0.59 with an uncertainty of 0.14. From this result we can conclude that there are less than 3 chances in 100,000 (<0.003%) that the actual, physical assymmetry could be equal to zero. This is a direct measure confirming charge parity assymmetry or violation between the real and imaginary components of the same particle, which is the only measure of the arrow and rate of time - perhaps the reason why we live on the real side and why real mass exists in positive time & entropy, whilst virtual particles exist in negative time & entropy.
In/out waves origin
The Final Enigma
The Final Enigma
Well, we have seen that both mathematical evidence and experiments agree with the notion of matter being made up of a standing wave structure of energetic waves in space. The new model offers logical mathematical and common sense explanations for many laws which had previously no origin other than experimental evidence. These include the conservation of energy, quantum theory, special relativity, origin of charge and mass, Newton's law and Feynman diagrams. However, as we have said in the introduction to this section, a new discovery always brings with it a few more enigmas. The positive side of it is, that one enigma is better than many enigmas which is the present situation of modern science. This theory leaves us with a single enigma - Where do in waves come from and out waves go to? Let's hear what Milo Wolff has to say about this.
According to Milo Wolff, the inwave of a particle must come from the outwave of another, but the actual origin of the incoming and final destination of outgoing wave is still unknown, the imaginary part of the waves is still a confusing issue and this should hold the key to the whole standing wave model. Personaly, I find Wolff's argument about the ingoing waves generated by the outgoing waves of other particles not particularly convincing though, as it implies that no single particle can exist in the absence of another particle. The standing wave model proves to solve most enigmas in physics, it explains all paradoxes present in today's modern physics, yet it seems to suffer the same problem as the chicken & egg paradox - which came first and from where? I believe, and you shall learn within the following pages, that things are far more different from what we think they are, but we are getting closer to the truth.
Let us start to visualise a simple situation, in which a sphere is slowly immersed in a tray of water.
Let us start to visualise a simple situation, in which a sphere is slowly immersed in a tray of water.
On the right of the diagram, we see what's 'visible' at the water surface, that is the varying cross sectional area of the sphere being immersed. What we see is the volume of the sphere sliced sequentially into 2D flat disks of varying radii. Now imagine that the original motion consists of immersing the sphere under the water level, and that the part showing it going up again is just a 'reverse playback' of the movie. The time during which the sphere is being immersed is the positive going time, whilst the reversed movie part is the negative going time. If you think about that, you will understand that the cross sectional area at time=t during reverse playback is actually as real as the cross sectional area at time=t during the first playback. There should however be some mathematical way to show which cross sectional area we are refering to. Although they are the same, their motion is opposite to each other, that is during the time the positive time area is expanding the negative time area is contracting and vice versa. We only perceive with our senses the positive time going events, but each negative time going event is there as well since if the negative flat disk slice does not contract back in time, the positive one cannot expand forward in time! It is VERY important you understand this concept. Then you will understand that in such a situation you cannot refer to the positive going part without the knowledge of the negative going counterpart. The whole situation is fully defined only if you describe both the events as happening in both positive and negative time. Whilst the normal playback is showing a cross sectional area coming into existence, the reverse playback is showing the area going out of existence...ingoing, outgoing. At this point you should have guessed what the description of the forward and reverse playback events represent... they do represent the outgoing and incoming waves respectively. Depending whether your mind sees the outgoing wave to represent positive or negative time, will eventually determine which standing wave pattern your mind will select as the REAL and which it selects as IMAGINARY. The imaginary counter part of the standing wave is the virtual particle or antiparticle counterpart of the standing wave and its existence cannot be ignored! For a particle to exist, you need both ingoing and outgoing waves. This implies by logic that you cannot generate an electron without having at the same time generated its imaginary counterpart, the positron. Again this logic deduction is backed by experimental evidence as shown in the bubble chamber photo below.
Part of a bubble chamber picture (Fermilab'15 foot Bubble Chamber', found at the University of Birmingham), showing electron & positron pair generation. The curly line which turns to the left is an electron. Positron looks similar but turns to the right. The magnetic field is perpendicular to the picture plan. Remember, a photograph has the exceptional ability to integrate different events happening at different instances in time over the same picture.
The following animation shows how the superposition of both the area flowing forward in time and the area flowing backward in time, together with their complex (real + imaginary) superposition which creates the standing EM wave. The first two animations are the 'playback' and 'reverse playback' of the same sphere being slowly immersed under the surface of the water.
The following animation shows how the superposition of both the area flowing forward in time and the area flowing backward in time, together with their complex (real + imaginary) superposition which creates the standing EM wave. The first two animations are the 'playback' and 'reverse playback' of the same sphere being slowly immersed under the surface of the water.
 |  |
Concentric spherical standing waves graphics by Gabriel LaFreniere.
If you have problems understanding how the positive and negative time counterparts can create the above sequence, imagine you are in the front seat of your car driving inside a tunnel. This will create the effect shown in the middle animation. Now imagine that you are looking back either from the rear window or from your mirror, you will see the animation shown on the left. Both are realities, but we tend to term the one from the front seat as the real, and the one from the back seat as the imaginary, one cannot exist if the other ceases to exist, isn't it? If you see the tunnel approaching from the front seat, and you see no tunnel from the rear window, then it would mean that the tunnel is being absorbed into the car!! The animation on the right is just the mathematical addition of both experiences, which therefore contains all the information of the two separate views. It is interesting to note, that if at any point in time, the real & imaginary animations are interchanged, the resultant standing wave will not change at all. So, if we apply this fact to the above mentioned sphere being immersed in and out of the water surface, the final standing wave during the whole oscillation will be unchanged. Also, let's take this one step further, if instead of a moving sphere, you have got a moving observation plane, the standing wave will still remain unchanged. This is another important point to understand the universe, since it is not the ultimate dimension of the universe that is changing but only the observer's point of view.
Now if you are still with me to this point, you must have one important question. "How can we have the 'reverse playback' video before we finish the first playback video, in order to produce the superimposed standing wave?" Good question which will take us to the next interesting topic. In order to be able to costruct the above standing wave animation we cheated a bit. We assumed that both past and future are known already. Does this not usually make sense to us humans, because we only perceive the positive going time direction, and thus our mind is capable only of recording the past. But picture this: if within the next minute you will be reading the next paragraph, then you can say that one minute in the future from now you ARE already there reading it, while at the present you are reading this sentence. Also, it means that if a minute ago you were reading the previous paragraph, then one minute in the past from now you ARE reading the previous paragraph. Notice, we are not saying you WERE and you WILL, but you ARE. I understand this might be puzzling at first, but do not give up. To re assure you that I am right, I will just mention the name of the experimental evidence for this: the EPR experiment, in which it is clearly shown that the particles involved in the experiment know there past and future during their whole journey from source to detector. Here is a very relevant quote from Louis De Brolie, which explains the same effect :'In space-time everything which for us constitutes the past, the present, the future is given in block... Each observer, as his time passes, discovers, so to speak, new slices of space-time which appear to him as successive aspects of the material world, though in reality the ensemble of events constituting space-time exist prior to his knowledge of them.'
As you will see in the following section, this mechanism can be explained in terms of differentiating a higher dimensional space. Don't get confused with the term multidimensional or higher dimensions. Here we are not talking about science fiction parallel worlds existing independently in different dimensions. You will soon see, that the existence of higher dimensions will eventually be the key to solve the ultimate enigma and a few more that are not yet very clear with the 3D standing wave idea.
If you correctly understood the above diagram, then the answer to the Enigma; "Where do in/out going waves come from, or go to?" should be quite straight forward, they come from and go to one space dimension higher than our observation 3D point of view. Having understood this, you will now find it much easier to explain how elementary particles are found to pop in and out of the nothingness into nothingness, as experimental evidence shows. Without the existence of higher dimensions, the 3D standing wave model on its own is not enough to explain this hard evidence.
At this point, one can tackle another enigma regarding the origin of the relativistic energy diagram, which states that:
Total energy E2= (Rest mass energy mc2)2 + (Relative motion energy pc)2
The main enigma here is "why should these two energies use the squares of each energy term to give the total true energy?" Looking again at our animated sphere, the answer is quite easy to deduct. The two energies are orthogonal, not in 3D but in 4D. Thus the true energy is calculated using pythagoras theorem from 475BC as in a right angle triangle to find the hypotenuse.
Now if you are still with me to this point, you must have one important question. "How can we have the 'reverse playback' video before we finish the first playback video, in order to produce the superimposed standing wave?" Good question which will take us to the next interesting topic. In order to be able to costruct the above standing wave animation we cheated a bit. We assumed that both past and future are known already. Does this not usually make sense to us humans, because we only perceive the positive going time direction, and thus our mind is capable only of recording the past. But picture this: if within the next minute you will be reading the next paragraph, then you can say that one minute in the future from now you ARE already there reading it, while at the present you are reading this sentence. Also, it means that if a minute ago you were reading the previous paragraph, then one minute in the past from now you ARE reading the previous paragraph. Notice, we are not saying you WERE and you WILL, but you ARE. I understand this might be puzzling at first, but do not give up. To re assure you that I am right, I will just mention the name of the experimental evidence for this: the EPR experiment, in which it is clearly shown that the particles involved in the experiment know there past and future during their whole journey from source to detector. Here is a very relevant quote from Louis De Brolie, which explains the same effect :'In space-time everything which for us constitutes the past, the present, the future is given in block... Each observer, as his time passes, discovers, so to speak, new slices of space-time which appear to him as successive aspects of the material world, though in reality the ensemble of events constituting space-time exist prior to his knowledge of them.'
As you will see in the following section, this mechanism can be explained in terms of differentiating a higher dimensional space. Don't get confused with the term multidimensional or higher dimensions. Here we are not talking about science fiction parallel worlds existing independently in different dimensions. You will soon see, that the existence of higher dimensions will eventually be the key to solve the ultimate enigma and a few more that are not yet very clear with the 3D standing wave idea.
If you correctly understood the above diagram, then the answer to the Enigma; "Where do in/out going waves come from, or go to?" should be quite straight forward, they come from and go to one space dimension higher than our observation 3D point of view. Having understood this, you will now find it much easier to explain how elementary particles are found to pop in and out of the nothingness into nothingness, as experimental evidence shows. Without the existence of higher dimensions, the 3D standing wave model on its own is not enough to explain this hard evidence.
At this point, one can tackle another enigma regarding the origin of the relativistic energy diagram, which states that:
Total energy E2= (Rest mass energy mc2)2 + (Relative motion energy pc)2
The main enigma here is "why should these two energies use the squares of each energy term to give the total true energy?" Looking again at our animated sphere, the answer is quite easy to deduct. The two energies are orthogonal, not in 3D but in 4D. Thus the true energy is calculated using pythagoras theorem from 475BC as in a right angle triangle to find the hypotenuse.
We note that if side 'a' represents the relative motion energy in 3D, whilst side 'b' represents the orthogonal 'mass' energy analogous to the above animated sphere penetrating the 2D dimensional plane from a higher dimension, then side 'c' will represent the true total energy of the moving particle. Also, since the speed of light is a property of space, any point on the circular cross sectional area on the surface will see the inwaves of the sphere approaching down at the same speed, whatever relative speed is involved between the two points on the surface. Since the inwaves are EM waves, the speed is always equal to the speed of light 'c'. Despite other expectations from scientists, the verified experimental facts support this concept since if two experimenters measure the speed of light, they always both get the same value for 'c' independent of their relative speed to the source.
Existence of Higher dimensional space & Perception of time
The observation that spatial dimensionality is limited to three dimensions has been for long a puzzle to scientists. Our mathematics do not limit us to three dimensions. Why are there only three dimensions? We are 3D observers, and this makes it easy for us to conceive the observed reality as 3D. We can also quite easily conceive a 2D universe as a subset of our 3D universe, and we see how complex the explanations can get in a 2D universe, for events we find simple in our 3-D universe.
The relativity theory made spatial dimensionality elastic. The space-time continuum was conceived. Four dimensional space-time was proposed and attempts to visualize a 4-D space, as an extension of our 3-D world, became popular. We talk about 3-D space being curved around some 4-D sphere like the atmosphere around the earth.
In science fiction, discussion of alternate planes, or dimensions of existence, have become ingrained. Religious "Heaven" has been moved from the stars and galaxies to these alternate dimensions. In this section I will show you how to scientifically understand higher dimensions, which will hopefully lead you to better understand the higher dimensional universe which we all form part of.
Many modern physicists, in their attempts to unify theory, have proposed the existence of many space dimensions beyond three. The multi-dimensional efforts at grand unification have indeed mathematically helped describe theory and predict experimentally observed facts, but attempts at 4D visualization seem hard indeed. We talk of extra dimensions being curled into minute 3D spaces.
One should keep in mind what we are with respect to the space around us. The answer is that each one of us is a 3 dimensional spatial observation point in space, and that dimensionality is not a property of 'reality', but of the being, the observer. Instead, our spatial dimensionality is a characteristic of our conceptions, our mind. This means it is a characteristic, or property, of knowledge rather than of reality. Spatial dimensionality is a property of the observer rather than of the observed.
So, is everything observed around us just an illusion? Not at all, the things around us will still exist even if no one looked at them. To say spatial dimensionality is a very powerful tool may be one of the all-time greatest understatements. However, if spatial dimensionality is a property of our knowledge, then it is not a complete universal truth, but just a shadow of the truth (look at the animation to see what I mean). The answer, of course, is that our spatial dimensionality is based upon what we see. Of all the senses which a typical person possesss, sight is the one which plays the greatest role in the perception and conception of reality. The perception of spatial dimensions does not have to be based upon sight, hearing or any of the other senses. Our eyes are essentially 2D arrays which sense light reflected from viewed objects. Therefore, we never actually 'see' three spatial dimensions. We see (perceive) stereographic 2D pictures. In our mind, we conceive the existence of a third dimension using two stereographic pictures. As you see, our mind is already 'too busy' converting 2D sensed data to reconstruct a 3D observation picture of reality. For humans to visualize a world in more dimensions than 3D is no trivial task. It may even be impossible, without physically modifying ourselves. If dimensionality is not a property of the universe, but of ourselves, then our attempts to 'visualize' 2D and 4D universes in terms of our 3D abilities is not only futile, it is nonsense. The reality perceived by a 2D being is the same reality as perceived by a 3D being and a 4D being. Their methods of description will vary greatly, but they are each attempting to describe the same thing.
This alternative perspective on spatial dimensionality has offered a rational answer to the question of why do we conceive the universe to be limited to three spatial dimensions. The answer is the universe is not limited to 3D, and most scientific evidence points to higher dimensional universe, but it is we who are limited, due to our senses. Another dimensionality issue that is answered is that of the co-existence of multiple dimensions beyond three. This issue becomes nonsense. An object cannot pass to another plane or dimension of existence, because these planes or dimensions do not exist. No dimensions exist except in our minds.
Dimensions are powerful tools which we use to organise, live and understand the universe. It seems reasonable to believe that a being who can conceive an "n"*D universe can develop more elegant knowledge that a being who can only conceive an "n-1"*D universe. In essence, the more dimensions we can conceive, the more about the universe we can understand. TIME is only a way to organise information about the n*D universe, for all those mysteries which we have not been able to fit entirely into our (n-1)D spatial dimensionality framework. Remember the initial hypothesis was that a being who perceives "x" dimensions, will conceive the universe in "x+1" dimensions. We are now expanding the hypothesis to say that a being who perceives "x" dimensions, will conceive the universe in "x+1" dimensions where the "+1" is "time." Therefore, as beings may increase the total number of dimensions in which they perceive and conceive the universe, there will always be a temporal dimension to the universe for the beings. In the case of a limited dimensional universe of n*D dimensions, then the universe (reality) will be the being (the n*D observator) itself and that is the only possible non-temporal dimension.
If we could increase our perception to 3-D so we could then conceive a 4-D universe, many phenomena which we now describe as occurring at different times would then be described as occurring at different spatial locations. The progressive increase in spatial dimensionality moves explanations from the infinite reservoir of "time" to spatial locations. However, even though the number of spatial dimensions may increase without bound, the conception of "time" remains constant for all beings, from 0D to 3D to "n"D.
From these ideas one can deduct, that we are 3D spatial observation points observing a multidimensional universe around us. For us 3D observers, the "+1" dimension cannot be spatially observed, so our mind perceives different 3D pictures changing through 'time'. Time being the "+1" dimension is so embedded in our minds, that subconscious brain functions may be "hardwired" to better enable its "conception".
Current scientific knowledge is based on a 3D based reality which seems to get in trouble when small dimensions of length or time are involved. Science is now talking of energetic particles that randomly pop in and out of existence, which doesn't make sense if we do not try to understand how higher dimensional universe may work. It is a fact that at the time of writing, the best candidate unified theory is fully compatible with this higher dimensional space theory, namely the supersymmetry.
Supersymmetry is an idea that has been around for decades. It states that every boson has an associated fermion and vice-versa. So a quark, which is a fermion, has a supersymmetric imaginary partner called a squark, which is a boson. Likewise a photon, which is a boson, is teamed up with the photino, a fermion. None of the proposed supersymmetric particles have ever been detected. Scientists say this is because current particle accelerators are just not powerful enough. Science knows that these imaginary components MUST exist, but will never be able to detect/isolate them with the current methods, for the simple reason that they are imaginary. Note that the term 'imaginary' is a mathematical term and does NOT mean 'non-existent'. Any form of matter interpreted in our space-time dimension can be mathematically expressed as a complex (Complex = Re+Im) function of space and time. Lately, some evidence that supersymmetry is real may have emerged from a study of gold and platinum atoms. Teams from the Ludwig-Maximilians University in Munich and the University of Kentucky in the United States have used the Tandem accelerator in Munich to bombard gold atoms with sub-atomic particles. The results of the interactions between the targets and the projectiles, they say, can only be explained by supersymmetry. This is the way to go, since we can only observe these imaginary particles through the motion of the real part.
The relativity theory made spatial dimensionality elastic. The space-time continuum was conceived. Four dimensional space-time was proposed and attempts to visualize a 4-D space, as an extension of our 3-D world, became popular. We talk about 3-D space being curved around some 4-D sphere like the atmosphere around the earth.
In science fiction, discussion of alternate planes, or dimensions of existence, have become ingrained. Religious "Heaven" has been moved from the stars and galaxies to these alternate dimensions. In this section I will show you how to scientifically understand higher dimensions, which will hopefully lead you to better understand the higher dimensional universe which we all form part of.
Many modern physicists, in their attempts to unify theory, have proposed the existence of many space dimensions beyond three. The multi-dimensional efforts at grand unification have indeed mathematically helped describe theory and predict experimentally observed facts, but attempts at 4D visualization seem hard indeed. We talk of extra dimensions being curled into minute 3D spaces.
One should keep in mind what we are with respect to the space around us. The answer is that each one of us is a 3 dimensional spatial observation point in space, and that dimensionality is not a property of 'reality', but of the being, the observer. Instead, our spatial dimensionality is a characteristic of our conceptions, our mind. This means it is a characteristic, or property, of knowledge rather than of reality. Spatial dimensionality is a property of the observer rather than of the observed.
So, is everything observed around us just an illusion? Not at all, the things around us will still exist even if no one looked at them. To say spatial dimensionality is a very powerful tool may be one of the all-time greatest understatements. However, if spatial dimensionality is a property of our knowledge, then it is not a complete universal truth, but just a shadow of the truth (look at the animation to see what I mean). The answer, of course, is that our spatial dimensionality is based upon what we see. Of all the senses which a typical person possesss, sight is the one which plays the greatest role in the perception and conception of reality. The perception of spatial dimensions does not have to be based upon sight, hearing or any of the other senses. Our eyes are essentially 2D arrays which sense light reflected from viewed objects. Therefore, we never actually 'see' three spatial dimensions. We see (perceive) stereographic 2D pictures. In our mind, we conceive the existence of a third dimension using two stereographic pictures. As you see, our mind is already 'too busy' converting 2D sensed data to reconstruct a 3D observation picture of reality. For humans to visualize a world in more dimensions than 3D is no trivial task. It may even be impossible, without physically modifying ourselves. If dimensionality is not a property of the universe, but of ourselves, then our attempts to 'visualize' 2D and 4D universes in terms of our 3D abilities is not only futile, it is nonsense. The reality perceived by a 2D being is the same reality as perceived by a 3D being and a 4D being. Their methods of description will vary greatly, but they are each attempting to describe the same thing. This alternative perspective on spatial dimensionality has offered a rational answer to the question of why do we conceive the universe to be limited to three spatial dimensions. The answer is the universe is not limited to 3D, and most scientific evidence points to higher dimensional universe, but it is we who are limited, due to our senses. Another dimensionality issue that is answered is that of the co-existence of multiple dimensions beyond three. This issue becomes nonsense. An object cannot pass to another plane or dimension of existence, because these planes or dimensions do not exist. No dimensions exist except in our minds.
Dimensions are powerful tools which we use to organise, live and understand the universe. It seems reasonable to believe that a being who can conceive an "n"*D universe can develop more elegant knowledge that a being who can only conceive an "n-1"*D universe. In essence, the more dimensions we can conceive, the more about the universe we can understand. TIME is only a way to organise information about the n*D universe, for all those mysteries which we have not been able to fit entirely into our (n-1)D spatial dimensionality framework. Remember the initial hypothesis was that a being who perceives "x" dimensions, will conceive the universe in "x+1" dimensions. We are now expanding the hypothesis to say that a being who perceives "x" dimensions, will conceive the universe in "x+1" dimensions where the "+1" is "time." Therefore, as beings may increase the total number of dimensions in which they perceive and conceive the universe, there will always be a temporal dimension to the universe for the beings. In the case of a limited dimensional universe of n*D dimensions, then the universe (reality) will be the being (the n*D observator) itself and that is the only possible non-temporal dimension.
If we could increase our perception to 3-D so we could then conceive a 4-D universe, many phenomena which we now describe as occurring at different times would then be described as occurring at different spatial locations. The progressive increase in spatial dimensionality moves explanations from the infinite reservoir of "time" to spatial locations. However, even though the number of spatial dimensions may increase without bound, the conception of "time" remains constant for all beings, from 0D to 3D to "n"D.
From these ideas one can deduct, that we are 3D spatial observation points observing a multidimensional universe around us. For us 3D observers, the "+1" dimension cannot be spatially observed, so our mind perceives different 3D pictures changing through 'time'. Time being the "+1" dimension is so embedded in our minds, that subconscious brain functions may be "hardwired" to better enable its "conception".
Current scientific knowledge is based on a 3D based reality which seems to get in trouble when small dimensions of length or time are involved. Science is now talking of energetic particles that randomly pop in and out of existence, which doesn't make sense if we do not try to understand how higher dimensional universe may work. It is a fact that at the time of writing, the best candidate unified theory is fully compatible with this higher dimensional space theory, namely the supersymmetry.
Supersymmetry is an idea that has been around for decades. It states that every boson has an associated fermion and vice-versa. So a quark, which is a fermion, has a supersymmetric imaginary partner called a squark, which is a boson. Likewise a photon, which is a boson, is teamed up with the photino, a fermion. None of the proposed supersymmetric particles have ever been detected. Scientists say this is because current particle accelerators are just not powerful enough. Science knows that these imaginary components MUST exist, but will never be able to detect/isolate them with the current methods, for the simple reason that they are imaginary. Note that the term 'imaginary' is a mathematical term and does NOT mean 'non-existent'. Any form of matter interpreted in our space-time dimension can be mathematically expressed as a complex (Complex = Re+Im) function of space and time. Lately, some evidence that supersymmetry is real may have emerged from a study of gold and platinum atoms. Teams from the Ludwig-Maximilians University in Munich and the University of Kentucky in the United States have used the Tandem accelerator in Munich to bombard gold atoms with sub-atomic particles. The results of the interactions between the targets and the projectiles, they say, can only be explained by supersymmetry. This is the way to go, since we can only observe these imaginary particles through the motion of the real part.
Understanding 1 dimensional space
Supersymmetry involves the concept of multidimensional space. In order to understand dimensional spaces higher than three, let's start with the simplest 1D case, that of a 1D observer - a line. You might think, well that's quite easy. In fact it is quite easy, but if you really understand it, you might use your knowledge to understand higher dimensions. The animation below shows the observer as a grey line, who is trying to percieve a reality (a 2D circle in this case) in his 1D limited mind. The animated blue line is what he perceives. Note that the reality, the circle, is not changing in time, its radius, colour and all other properties are a part of the reality. The observed thing is quite different from this, it is a blue line varying in length WITH TIME. For the observer, it remains a mystery as to what happened to the original full length of line, why and how it changes length and 'pops in and out' of his 'observed reality'. Also, the 1D observer has no way to find out whether the oscillating line is due to observing a circle (2D), a sphere (3D) or hypersphere (D>3). Also, in order for an observation to take place, we need the grey line (1D) observer, to have a 'thickness'. This thickness is very small, just enough for the observed image to be projected on, similar to a projector screen, but has to be greater than zero.
Supersymmetry involves the concept of multidimensional space. In order to understand dimensional spaces higher than three, let's start with the simplest 1D case, that of a 1D observer - a line. You might think, well that's quite easy. In fact it is quite easy, but if you really understand it, you might use your knowledge to understand higher dimensions. The animation below shows the observer as a grey line, who is trying to percieve a reality (a 2D circle in this case) in his 1D limited mind. The animated blue line is what he perceives. Note that the reality, the circle, is not changing in time, its radius, colour and all other properties are a part of the reality. The observed thing is quite different from this, it is a blue line varying in length WITH TIME. For the observer, it remains a mystery as to what happened to the original full length of line, why and how it changes length and 'pops in and out' of his 'observed reality'. Also, the 1D observer has no way to find out whether the oscillating line is due to observing a circle (2D), a sphere (3D) or hypersphere (D>3). Also, in order for an observation to take place, we need the grey line (1D) observer, to have a 'thickness'. This thickness is very small, just enough for the observed image to be projected on, similar to a projector screen, but has to be greater than zero.
Understanding 2 dimensional space
Let's now start analysing a 2D case, that of the classic Flatland example, in which a person lives in a 2D universe and is only aware of two dimensions (shown as the blue grid), or plane, say in the x and y direction. Such a person can never conceive the meaning of height in the z direction, he cannot look up or down, and can see other 2D persons as shapes on the flat surface he lives in.
Let's now start analysing a 2D case, that of the classic Flatland example, in which a person lives in a 2D universe and is only aware of two dimensions (shown as the blue grid), or plane, say in the x and y direction. Such a person can never conceive the meaning of height in the z direction, he cannot look up or down, and can see other 2D persons as shapes on the flat surface he lives in.
Now we know that 3D space exists, and can conceive that, because we see each other in 3D space. So, what does a 3D reality sphere look like into a 2D plane? The answer is again graphically shown in the animation, which shows a circle expanding and contracting depending on which slice of the sphere intersects the 2D observation plane. In the 2D plane, the thickness of the plane tends to zero, but again, cannot be absolute zero. There must be enough thickness for the circle to form and be observed. Thus, the 3D sphere is being differenciated with respect to one of its spatial dimensions (z in our case) across its diameter. Actually, in the special case of a sphere, it could be intersecting the plane at any angle to the z axis, and still be perceived as a perfect circle in 2D. For the person that lives in 2D, the only way to recognise such a 3D structure is through integrating all the circles he sees, on top of each other. But here is the problem, he cannot imagine anything 'on top of each other'. A clever 2D guy has just one simple way to refer to this z-axis, which is constantly differenciating the 3D object, and that is TIME.
I admit this concept is quite hard to grasp, especially when one moves on to describe a 4D universe differenciated by a 3D space, with both real and imaginary axis. The imaginary space dimensions can be pictured as follows. Just try to imagine a person in front of a 2D plane surface, but this time a mirror surface. The person is equivalent to the real part and his image in the mirror is equivalent to the imaginary part. Imagine also that such a mirror is present everywhere he can possibly move. So, the person becomes DEPENDENT on the existence of his imaginary component. That is, if the image is no longer present in the mirror, then one can deduct that the person can no longer exist in reality! In fact, beleive it or not, this is a fact. Now this was an example of a 3D image reflected on a 2D plane (the mirror).
I admit this concept is quite hard to grasp, especially when one moves on to describe a 4D universe differenciated by a 3D space, with both real and imaginary axis. The imaginary space dimensions can be pictured as follows. Just try to imagine a person in front of a 2D plane surface, but this time a mirror surface. The person is equivalent to the real part and his image in the mirror is equivalent to the imaginary part. Imagine also that such a mirror is present everywhere he can possibly move. So, the person becomes DEPENDENT on the existence of his imaginary component. That is, if the image is no longer present in the mirror, then one can deduct that the person can no longer exist in reality! In fact, beleive it or not, this is a fact. Now this was an example of a 3D image reflected on a 2D plane (the mirror).
Understanding 4 dimensional space
Recall ages ago, when most people believed that the earth was flat. Some thought that they would "fall off the edge" of the earth if they went out too far. No one ever thought, that if they kept on going, they could possibly end up where they started, having experienced the entire trip as being in a straight line! No matter how far the subject travels (by boat, train, or plane), he will never come to a boundary: there is no "edge" to fall off from!! It is because the earth exists on the surface of a sphere that these properties hold true. Let us now take this a step further.
Launched from the earth is a rocket ship that is travelling out into space. Its mission is to continue outward in a straight line in its current direction until it reaches the "outer edge" of the universe. When will the rocket ship reach the outer edge of space? In the previous example we find a similar situation: the concern of "falling off the edge" of a flat earth - an earth that in reality has no "edge" to fall off from. Now, if our universe reality is not 3D we will find out that the ship will never encounter an outer edge. Not only that, but it could also possibly end up where it started, having experienced the entire trip as being in a straight line! No matter how far the rocket ship travels through space, it will come across no boundary of any kind. These properties would hold true if the universe existed on the surface of a hypersphere in the same way that the earth exists on the surface of a sphere.
The hypershpere is the 4D analogue to a circle in 2D or of a sphere in 3D. How would we picture a hypersphere? The key to approaching something of the fourth dimension is by means of the tool of analogy: we rely upon corresponding lower-dimensional structures we have studied as the means by which their 4-dimensional analogue is constructed. A solid circle is a 2-dimensional object. When cut into 1 dimensional slices, you will see a line, that varies in length between the size of a single dot to its full length. A solid sphere, as shown above in the flatland animation, is a 3-dimensional object. When cut into slices, we find that a solid sphere is in essence an array of 2D solid circles that vary in cross sectional area. Having obtained the knowledge we have so far, we now possess the ability to bring these lower-dimensional structures "up a notch" through analogy to envision a 4D hypersphere.
Recall ages ago, when most people believed that the earth was flat. Some thought that they would "fall off the edge" of the earth if they went out too far. No one ever thought, that if they kept on going, they could possibly end up where they started, having experienced the entire trip as being in a straight line! No matter how far the subject travels (by boat, train, or plane), he will never come to a boundary: there is no "edge" to fall off from!! It is because the earth exists on the surface of a sphere that these properties hold true. Let us now take this a step further.
Launched from the earth is a rocket ship that is travelling out into space. Its mission is to continue outward in a straight line in its current direction until it reaches the "outer edge" of the universe. When will the rocket ship reach the outer edge of space? In the previous example we find a similar situation: the concern of "falling off the edge" of a flat earth - an earth that in reality has no "edge" to fall off from. Now, if our universe reality is not 3D we will find out that the ship will never encounter an outer edge. Not only that, but it could also possibly end up where it started, having experienced the entire trip as being in a straight line! No matter how far the rocket ship travels through space, it will come across no boundary of any kind. These properties would hold true if the universe existed on the surface of a hypersphere in the same way that the earth exists on the surface of a sphere.
The hypershpere is the 4D analogue to a circle in 2D or of a sphere in 3D. How would we picture a hypersphere? The key to approaching something of the fourth dimension is by means of the tool of analogy: we rely upon corresponding lower-dimensional structures we have studied as the means by which their 4-dimensional analogue is constructed. A solid circle is a 2-dimensional object. When cut into 1 dimensional slices, you will see a line, that varies in length between the size of a single dot to its full length. A solid sphere, as shown above in the flatland animation, is a 3-dimensional object. When cut into slices, we find that a solid sphere is in essence an array of 2D solid circles that vary in cross sectional area. Having obtained the knowledge we have so far, we now possess the ability to bring these lower-dimensional structures "up a notch" through analogy to envision a 4D hypersphere.
 | We cannot directly visualize a hypersphere for the very reason that it is a 4-dimensional object and goes beyond our senses. What we can visualize, however, is a hypersphere in the form of 3-dimensional slices (as is displayed to the left). A hypersphere is in essence an array of 3 dimensional solid spheres that vary in volume. This would represent our basic conception of the hypersphere, and is shown in the animated picture here. If one superimposes the time reversed animation over this one, a 3D spherical standing wave with 'shells' will result...matter will be formed. Unfortunately we 3D observers can never see the difference between a 4D and a 5D hypersphere, but accepting the knowledge of their existence is a big step. |
As I have said, in 4D space, our 'time' is integrated in a space dimension, and then action at a distance (gravity being the purest example), becomes much clearer to us. Just imagine, in the classic 2D example shown above, that the 2D person is somehow able to impart a force on the circle he sees on the plane. What would the consequences be? He would eventually move the whole sphere and would also change the position of the future circles in the plane. He would also move all points on the circle, as if all points are 'entangled', and the transmission of this force from the point of action to any other point on the circle does not depend on the time it takes for the sphere slice to pass through. So, to the question, is gravity a push, a pull or both, or does gravity act on a body, or is gravity generated by the mass of a body, there is no answer if the problem is analysed only in 3D space, as the interaction between two bodies is just an effect we see due to the interaction on a single body existing in a higher dimension. The interaction between the two different dimensions takes place in the 'mirror plane' where the time dimension does not exist, but is rather a perception of the observer. That also means that issues like 'the finite speed of gravity' clearly make no sense.
If you try to extend this to our existence and to the existence of all matter, you will find that all actions (including gravity) are at work at a higher dimension and we are here in 3D space observing the effects that are being played at this higher dimension(s). The 4D I am referring to, is quite different from Einstein's 4D Space time, in that it is a 4D space and no time. The time coordinate comes in as a false perception of the 4th space dimension, which we are unable to imagine, analogous to the flatland man who cannot understand height and depth. In this figure, you can see what a 4D sphere looks like when differenciated in 3D space. When one differentiates this 4D dimension with respect to an infinitely small mirror thickness (Plancks length being the best candidate), then you get the universe we observe, with Plancks time being the time taken for each 3D slice to pass through the 'thickness' of the mirror, and such universe is equivalent to Einstein's Space-time.
So, what is the speed of light? The speed of light can now make more sense, it is the thickness of the mirror divided by the time it takes for the next slice. It is the maximum speed of differenciating the 4D reality from a 3D spatial point of view. In our context, the value would be equal to Planck's length/Planck's time which is in fact equal to c, the speed of light. That's why Einstein's theory of relativity although correct, CAN NEVER give us all the answers to our questions, because it is NOT COMPLETE. As Rudolf Steiner stated: "Anything dead tends to remain within the three ordinary dimensions, while anything living constantly transcends them". Applying the same rule to everything, we may modify this statement as "Anything stationary exists in the ordinary 3D, whilst anything moving is being constantly differentiated in each 3D plane and hence exists in the fourth dimension". We also know that matter is made up of waves, and waves cannot be stationary, and this means that matter requires the existence of a higher dimension in order to exist.Click here for an excellent site discussing Space in motion.
If you try to extend this to our existence and to the existence of all matter, you will find that all actions (including gravity) are at work at a higher dimension and we are here in 3D space observing the effects that are being played at this higher dimension(s). The 4D I am referring to, is quite different from Einstein's 4D Space time, in that it is a 4D space and no time. The time coordinate comes in as a false perception of the 4th space dimension, which we are unable to imagine, analogous to the flatland man who cannot understand height and depth. In this figure, you can see what a 4D sphere looks like when differenciated in 3D space. When one differentiates this 4D dimension with respect to an infinitely small mirror thickness (Plancks length being the best candidate), then you get the universe we observe, with Plancks time being the time taken for each 3D slice to pass through the 'thickness' of the mirror, and such universe is equivalent to Einstein's Space-time.
So, what is the speed of light? The speed of light can now make more sense, it is the thickness of the mirror divided by the time it takes for the next slice. It is the maximum speed of differenciating the 4D reality from a 3D spatial point of view. In our context, the value would be equal to Planck's length/Planck's time which is in fact equal to c, the speed of light. That's why Einstein's theory of relativity although correct, CAN NEVER give us all the answers to our questions, because it is NOT COMPLETE. As Rudolf Steiner stated: "Anything dead tends to remain within the three ordinary dimensions, while anything living constantly transcends them". Applying the same rule to everything, we may modify this statement as "Anything stationary exists in the ordinary 3D, whilst anything moving is being constantly differentiated in each 3D plane and hence exists in the fourth dimension". We also know that matter is made up of waves, and waves cannot be stationary, and this means that matter requires the existence of a higher dimension in order to exist.Click here for an excellent site discussing Space in motion.
What's the evidence for the existence of higher dimensions?
So, are higher dimensions only theoretical? Not at all. In physics, the inverse square law relation is quite common. This relation is valid for the gravitational attraction between matter, for the electrical forces between charges and for magnetic forces between moving charges. A force that varies with the square of the distance means that the force will increase with the square of the distance if we reduce the distance, and it will decrease with the square of the distance if we increase the distance.
So, are higher dimensions only theoretical? Not at all. In physics, the inverse square law relation is quite common. This relation is valid for the gravitational attraction between matter, for the electrical forces between charges and for magnetic forces between moving charges. A force that varies with the square of the distance means that the force will increase with the square of the distance if we reduce the distance, and it will decrease with the square of the distance if we increase the distance.
Electromagnetic energy decreases as if it were dispersed over the area of an expanding sphere, 4piR2where radius R is the distance the energy has travelled. The amount of energy received at a point on that 3D sphere diminishes as 1/R2. This clearly shows the origin of the inverse-square law.
Here is a table showing the volume and surface area of hyperspheres of different dimensions:
| Dimension (n) | Shape | Volume | Surface Area |
|---|---|---|---|
| 2 | circle | π r2 | 2π r |
| 3 | sphere | (4/3)π r3 | 4π r2 |
| 4 | 4-sphere | (1/2)π2r4 | 2π2r3 |
| 5 | 5-sphere | (8/15)π2r5 | (8/3)π2r4 |
| 6 | 6-sphere | (1/6)π3r6 | π3r5 |
| 7 | 7-sphere | (16/105)π3r7 | (16/15)π3r6 |
As a result, a force that varies with the square of the distance can be considered as a conventional 1-dimensional force vector (x-axis) that is scattered into 2 additional dimensions (y, z). The square power of the distance indicates the projection of such a force over a 2D surface area. But what happens if the force is also acting in higher order dimensions? What if the originating force is being projected on a higher dimensional surface area? Are there forces which vary to other powers than the inverse square law?
Yes, there are. The Casimir force related by the above equation is known to vary as the inverse d4, keeping all other parameters constant, which is two orders of dimensions higher than the more common inverse square law forces, and coincides with a force projected over the surface area of a 4D hypersphere (see table above). Such force that varies with the fourth power of the distance can be thus considered as a force vector that is scattered in a 4-dimensional space. Therefore, it is evident that the field that originates the Casimir force is a 4-dimensional field, that it is in fact a hyperspace field that produces the corresponding effects in our restricted 3D vision of our universe.
Another force this time varying as the inverse seventh power is that of the force of attraction between two atoms. It is known that for all non polar molecules, in which all electrical charges are neutralised, the force of attraction is given by F=k/r7, where k is a constant depending on the molecule. So, in this case, we have evidence of a 7 dimensional field effect.
Can dimensions be limited, or is the universe really infinite
Can dimensions be limited, or is the universe really infinite
From our point of view, the universe seems to be infinite, and it seems that it's not only infinite but even ever expanding. Now that you should be able to understand how our seemingly 3D space time universe can all fit in a 4D hypersphere, which in turn can fit on a surface of a 5D hypershere and so on, where a difference in time is equivalent to a different point within its volume, you can understand why the universe as seen by a 3D observing creature/mind has no limits.
Just imagine one of those 2D creatures who cannot understand what is height in the z direction and put him on the surface of a sphere. He would walk round and round searching for an edge for ever, and finally he may conclude and even prove that the path is infinite. Same applies to a 1D creature going round a simple circle, and therefore same applies to us 3D creatures living and travelling around in a 4D universe! In general we can say that a creature with n*D observation capability, will observe an (n+1)D dimension universe as infinite. We also learn that for an n*D observer, the only way to observe a universe of a higher dimension than himself is to 'walk around it' and memorise. A 1D creature cannot understand what is a circle other than observing all the points making it up, one by one. Similarly a 2D creature cannot understand what is a sphere other by observing the flow of circles making it up. We see that in all cases, walking around, or observing the flow through time, is necessary to observe a higher dimensional space.
The question is, how can we know how many dimensions is the universe made up from. All the arguments mentioned above can be applied to any dimension and would imply the possibility of an infinite dimension space. However other known things as the relationship between the gravitational constant and all the matter in the universe indicate that the universe is closed and limited. Even mathematics shows us that there are yet unknown reasons for which an ultimate dimension may be reached. One very interesting curve is the plot of surface area of hyperspheres of different dimensions, shown below. One would easily think that as we go higher in dimensions, the surface area of the n-sphere would increase at each stage, and yet, something very strange occurs, as a maxima in its surface area is reached at the 7th dimension. This could easily be the reason for the relentless way the energy always seeks the lowest energy levels. Could this indicate the real ultimate dimension of the universe?. Most probably yes.
Just imagine one of those 2D creatures who cannot understand what is height in the z direction and put him on the surface of a sphere. He would walk round and round searching for an edge for ever, and finally he may conclude and even prove that the path is infinite. Same applies to a 1D creature going round a simple circle, and therefore same applies to us 3D creatures living and travelling around in a 4D universe! In general we can say that a creature with n*D observation capability, will observe an (n+1)D dimension universe as infinite. We also learn that for an n*D observer, the only way to observe a universe of a higher dimension than himself is to 'walk around it' and memorise. A 1D creature cannot understand what is a circle other than observing all the points making it up, one by one. Similarly a 2D creature cannot understand what is a sphere other by observing the flow of circles making it up. We see that in all cases, walking around, or observing the flow through time, is necessary to observe a higher dimensional space.
The question is, how can we know how many dimensions is the universe made up from. All the arguments mentioned above can be applied to any dimension and would imply the possibility of an infinite dimension space. However other known things as the relationship between the gravitational constant and all the matter in the universe indicate that the universe is closed and limited. Even mathematics shows us that there are yet unknown reasons for which an ultimate dimension may be reached. One very interesting curve is the plot of surface area of hyperspheres of different dimensions, shown below. One would easily think that as we go higher in dimensions, the surface area of the n-sphere would increase at each stage, and yet, something very strange occurs, as a maxima in its surface area is reached at the 7th dimension. This could easily be the reason for the relentless way the energy always seeks the lowest energy levels. Could this indicate the real ultimate dimension of the universe?. Most probably yes.
| Dimension | Volume | Area |
|---|---|---|
| 1 | 2.0000 | 2.0000 |
| 2 | 3.1416 | 6.2832 |
| 3 | 4.1888 | 12.5664 |
| 4 | 4.9348 | 19.7392 |
| 5 | 5.2638 | 26.3189 |
| 6 | 5.1677 | 31.0063 |
| 7 | 4.7248 | 33.0734 |
| 8 | 4.0587 | 32.4697 |
| 9 | 3.2985 | 29.6866 |
| 10 | 2.5502 | 25.5016 |
What would an n*D observer see if the universe in which he lives in is his own n*D dimensions ? - the answer is 'a still, or static (frozen in time) spatial shape of n*D dimensions'. A 2D creature does not need to move around the circle to recognise it or know anything else about it, and a 3D creature does not have to flow through circular slices of a sphere to recognise a sphere. Note that the actions move and flow both require the time dimension to make sense, but recognise is an act that reacts to the shape of a static structure and needs no time. For an n*D observer, the n-dimensional universe is static, lifeless, and does not change through time, but has all the knowledge of what's within all lower dimensions. Let's name this ultimate n*D observer as the universal observer. For the universal observer, time does not exist, since both himself and the universe are the same thing and neither himself nor the universe is effected by time in lower dimensions, and from a lower dimensional observer point of view he can be said to be existing from eternity to eternity.
For those mathematically minded, let's take a car accelerating in a road. If we integrate the observed acceleration m/s2 with respect to time we get a car driving at a velocity measured in m/s. We have thus moved the motion of the car one dimension up with repect to time. If we integrate further the velocity with respect to time, we get the total distance covered in metres, no time. So did the road distance exist before or after the car started acceleration? As you see the 'road', the time independent dimension is NECESSARY for all other actions (differentiations with respect to time) to take place, and hence the universe should be limited in its number of dimensions, with the highest dimension being time independent, and being the universal observer itself. This conclusion leads to an inevitable property of space, the property that seems to drive the whole universe and physics laws the way they are, which is the property of a SELF OBSERVING SPACE. Through observation points (central cores of each standing wave), space is observing itself and in the process move through higher dimensions, with increasing surface area and lower energy states, until each wavecentre interface reaches the ultimate time independent dimension.
For those mathematically minded, let's take a car accelerating in a road. If we integrate the observed acceleration m/s2 with respect to time we get a car driving at a velocity measured in m/s. We have thus moved the motion of the car one dimension up with repect to time. If we integrate further the velocity with respect to time, we get the total distance covered in metres, no time. So did the road distance exist before or after the car started acceleration? As you see the 'road', the time independent dimension is NECESSARY for all other actions (differentiations with respect to time) to take place, and hence the universe should be limited in its number of dimensions, with the highest dimension being time independent, and being the universal observer itself. This conclusion leads to an inevitable property of space, the property that seems to drive the whole universe and physics laws the way they are, which is the property of a SELF OBSERVING SPACE. Through observation points (central cores of each standing wave), space is observing itself and in the process move through higher dimensions, with increasing surface area and lower energy states, until each wavecentre interface reaches the ultimate time independent dimension.
Unification into a fractal dimension
Conventional science fails to unify the two seperate backbones of the most recent scientific revolutions: relativity and quantum mechanics. All our past knowledge seems to assure us is that 'Nature is simpe', and this should answer our questions as to where these two important concepts come from and where do they unify into a simple singular concept. It seems that the answer is beyond any human's mind imagination or knowledge, but nature offers a lot of clues, which as I will show you, will eventually let us explain the connection between the macro universe scale and microphysics, and that enormous simplifications of current science is possible through such unified concept.
The observations discussed in the previous pages, show that although matter is made up of standing waves of real and imaginary waves, flowing forward and backward in time, everything boils down to a single unified dimension in which time needs no longer to be perceived. Remember that the perception of time is a requirement in order to observe any dimension higher than the observers' dimension. This means, that although science shows the existence of waves, and here we showed that particles are nothing but standing waves, when observed from the ultimate dimension, we see that the ingoing and outgoing waves, are not dynamic waves at all, and that 'ingoing' and 'outgoing' no longer apply in the unified dimension. We will find that the properties of space, and of waves behaviour are built into the SHAPE of the ultimate space dimension. But what makes the universe so rich in diversity? If the universe is just a hypersphere, then why are things around us not all spherical? The answer is partly staring at us in the following curve.
The observations discussed in the previous pages, show that although matter is made up of standing waves of real and imaginary waves, flowing forward and backward in time, everything boils down to a single unified dimension in which time needs no longer to be perceived. Remember that the perception of time is a requirement in order to observe any dimension higher than the observers' dimension. This means, that although science shows the existence of waves, and here we showed that particles are nothing but standing waves, when observed from the ultimate dimension, we see that the ingoing and outgoing waves, are not dynamic waves at all, and that 'ingoing' and 'outgoing' no longer apply in the unified dimension. We will find that the properties of space, and of waves behaviour are built into the SHAPE of the ultimate space dimension. But what makes the universe so rich in diversity? If the universe is just a hypersphere, then why are things around us not all spherical? The answer is partly staring at us in the following curve.
Apart from the fact that the ultimate dimension is approximately 7, we see that the peek of the curve does not occur at an integer value, in fact its maxima can only be approximated by iteration and occurs about 7.25695... which is very different from 7. The consequence of this is very important, as it results in a FRACTAL ULTIMATE DIMENSION. This means that the wave equations and properties can all be described in terms of a FRACTAL SHAPE, yes, it means that reflection, refraction, attenuation and all properties of standing waves (and of the universe) can be described by a complex fractal shape in the 7.25695th dimension. It also means that all things surrounding us, as are solids, liquids, air, plasma, living objects and planets, all obey their underlying fractal equations which are embedded into the hyperdimensional fractal of which they form part. Self-similar replication and harmonic resonance are natural features of fractal structures and organizations. We can finally see how the quantum and macro world can be easily unified. Quit mind boggling, but let us see the clear evidence in nature.
Tungsten needle tip photo ---> Mathematical iteration zn+1 = zn2 modulus n
Platinum needle tip photo ---> Mathematical iteration zn+1 = zn2 modulus n
The above two photos on top and bottom left are actual field ion microscope images of single crystal tips of Tungsten and Platinum respectively. The two adjacent plots have been mathematically computed and plotted by the same fractal function based on the iteration zn+1 = zn2 modulus n.
The plots have been only adjusted in brightness to make the similarity more obvious, but otherwise are the same. This is fantastic, as it means that the pattern formed by 3D standing waves obey an underlying iterative function. Using just a simple iterative function, we do not even need to have any knowledge of inwaves, outwaves and wave properties such as reflection. This solves the enigma of which wave (incoming or outgoing) came first. In fact it explains how neither of them comes first, and although we perceive the standing wave as a resultant of an incoming and an outgoing wave, both waves are generated at the same time. This also explains why a wave seems to know its destination before reaching it... both the positive time going wave and negative time going wave form part of an underlying static fractal hyper structure.
In 1904, Swedish mathematician Helge von Koch defined a continuous curve that could not be differentiated. It was just another example of a discovery first made some years before by Karl Weierstrass, but it has lead to more general constructions.
The plots have been only adjusted in brightness to make the similarity more obvious, but otherwise are the same. This is fantastic, as it means that the pattern formed by 3D standing waves obey an underlying iterative function. Using just a simple iterative function, we do not even need to have any knowledge of inwaves, outwaves and wave properties such as reflection. This solves the enigma of which wave (incoming or outgoing) came first. In fact it explains how neither of them comes first, and although we perceive the standing wave as a resultant of an incoming and an outgoing wave, both waves are generated at the same time. This also explains why a wave seems to know its destination before reaching it... both the positive time going wave and negative time going wave form part of an underlying static fractal hyper structure.
In 1904, Swedish mathematician Helge von Koch defined a continuous curve that could not be differentiated. It was just another example of a discovery first made some years before by Karl Weierstrass, but it has lead to more general constructions.
Koch Snowflake fractal
Instead of using the same rule on every step, an element of chance can be introduced by allowing to switch to the opposite orientation. This simple effect leads to more irregular outlines resembling natural coastlines. However, the fractal dimensions of both figures remain the same: approximately 1.262. At first glance one does not notice that a coastline is in fact a fractal. Given a map one can sit down with a ruler and soon come up with a value for the length. The problem is that repeating the operation with a larger scale map yields a greater estimate of the length. If we actually went to the coast and measured them directly, then still greater estimates would result. It turns out that as the scale of measurement decreases the estimated length increases without limit. Thus, if the scale of the (hypothetical) measurements were to be infinitely small, then the estimated length would become infinitely large! Lewis Fry Richardson (quoted in Mandelbrot, 1983) noted this dependence of measured length to the measuring scale used.
Fractal Coastline
Fractals have one special property, self-similarity, which makes them independent of scale. In other words, if you zoom-in on a fractal or magnify a section to view it, it will appear as if you were looking at the original object. A great example of the self-similarity property that can be found in nature is that of the fern. If you examined one of the fronds of a fern, you would see that the frond actually looks like a smaller fern itself. Most fractals in nature however are not as perfectly self-similar as the fern is. Take a cloud for example. If we zoom in on a section of a cloud, cut it out and looked at it from far away, it wouldn’t look exactly like the original cloud but would still look like a cloud nonetheless. The importance of the self-similarity property of fractals is therefore not that the magnified portion of the original object looks exactly the same, but that it LOOKS SIMILAR. The intricate patterns embedded in fractals due to the self-similarity property are what make fractals so impressive to the eye. Most impressive is when we find a fractal in nature that is perfectly self-similar like the fern. One sort of fractal is known as the Iterated Function System, or IFS. This fractal system was first explored by Michael Barnsley at the Georgia Institute of Technology in the 1980s. You start with shapes plotted on a graph, and iterate the shapes through a calculation process that transforms them into other shapes on the graph. Starting with four shapes, one of which is squashed into a line segment (this becomes the fern's rachis or stalk), you apply the shapes to the calculation to generate more shapes, feed them back into the calculation process, etc. Eventually a pattern emerges that bears a startling resemblance to a fern, if you choose the right starting shapes and positions. The longer you continue the iteration process, the more intricate the tiny detail in the pattern becomes.
Barnsley's Fern generated by IFS fractal system
Cloud fractal dimension 2.5
Brownian Motion is an example of a process that has a fractal dimension of 2. It occurs in microscopic particles and is the result of random jostling by water molecules (if water is the medium). The path of such a particle is a "random walk" in which both direction and distance are uniformly distributed random variables. So in moving from a given location in space to any other, the path taken by the particle is almost certain to fill the whole space before it reaches the exact point that is the 'destination'. Again, for a time dependent observer, it would seem as if each and every particle has got the knowledge of the path taken of all other particles, very similar indeed to the enigmatic EPR experiment! Another aspect of brownian motion is its effect on the formation of aggregates such as crystals. The figure below shows structures formed under different assumptions about the relative rate of horizontal movement (h) and the probability (p) of a settling particle sticking to fized particles as it brushes past. In the figure the following values are shown: (a) h=1, p=0; (b) h=1, p=1; (c) h=10, p=0; (d) h=10, p=1.
Brownian 'random' motion predicted by fractal function
The most common random signal found in nature is called the 1/f noise. You can find electronic circuits which let you amplify and hear this naturally generated background noise. One may think that since nature generates a random signal, then there are some exceptions to the well regulated fractal concept as depicted here. But, no, this is no exception, 1/f noise is not chaotic as it looks like, and is just obeying its higher order fractal function. 1/f noise can in fact be created using deterministic functions. One such method is a finite difference equation proposed by I. Procaccia and H. Schuster. It is simply
A section of the time series is illustrated below.
The power spectra is shown below.
We are living in a period of such absurdly blind acceptance of the Cartesian co-ordinate system that we think of all things around us as made up of primitives such as lines, rectangles, polygons, and curves in 2 D or boxes and surfaces in 3D. One of the first lessons present children learn at their primary schools is to build up shapes of various things with such cartesian building blocks. Its not surprising to note that few of them, if any, will be able to build any natural occuring structure in this way, and a high percentage of the students will only be able to replicate other man-made structures as houses, robots, ships, etc.. Even commonly used computer graphic softwares are based on cartesian co-ordinates, and this explains why it is so difficult for anybody to draw for example a fern leave, or landscape or a simple insect with the cartesian based CADs. We often find that these geometric primitives and usual tools for manipulating them, typically prove inadequate when it comes to representing most objects found in nature such as clouds, plants, crystals, waves, or a simple piece of stone. Now we know the reason behind, simply because the universe is unified in a fractal dimension and not in two or three dimensions. Note that when I mention the universe, I am not refering to the stars and galaxies, but to everything from subquantum scale to the macroscale that exists. There has been considerable interest recently in chaos theory and fractal geometry as we find that many processes in the world can be accurately described using that theory. In fact the computer graphics industry is rapidly incorporating these techniques in dedicated graphic rendering CADs to generate stunningly beautiful images as well as realistic natural looking structures.
Fractal computer-generated landscape
Scientists have also noticed the great similarity between the structure of a brain cell and that of the universe. On the left photo is the fractal structure of neurons in a mouse brain. The other is a simulated image of the universe. Similar patterns are also found in different natural phenomena.
Similarity between brain cell and universe fractal (From the NY Times)
At this point, you should realize how the macro and quantum worlds are easily unified when one considers the fact that the universe we live in, and of which we are part of, exists in a fractal hyperdimension. All things we observe are just a small piece of this immense fractal function projected onto our 3D observation plane. When a fractal function 'separates' from another it is observed as a seperate entity (in 3D), but actually each one of them still forms part of one unified function in higher dimension.
Fractal generating 'seperate' entities
Sacred Geometry
The link between physics, mathematics & life
The link between physics, mathematics & life
 | Charles R. Henry , professor at the Dept. of Sculpture, Virginia Commonwealth University, in 1977 had discovered one stacking structure and viewpoint that produced a very convincing image of an archetypal human face. This structure of 10 spheres (two 5-ball pyramids) forming a cluster is shown here. Later, he realized that the most natural structure for enclosing would be another 10 sphere, two pyramid structure that would totally enclose a smaller but similar cluster. After working out the math he found that by multiplying the inner sphere's diameters by Pi gives the dimension for the outer sphere's diameters as shown here. One sphere is removed from the outer cluster to reveal the inner cluster. However, the inner cluster must be upside down with respect to the outer cluster to fit inside. The expansion by Pi reinforces the suspicion that this 10 sphere cluster is a fundamental unit that is linked to the properties of three dimensional space. |  |
 | Close-packed reflective spheres clustered in this concentric shell structure produce an optical distribution network that links the Golden Mean and Pi. The Golden Mean is expressed in the 52 degree angle pyramid structure and Pi is expressed in the ratio of the diameter to the circumference of each sphere of course; but it is also expressed in the ratio of the sizes of spheres in the ten-spheres-within-ten-spheres concentric shell structure that he discovered. This concentric shell structure could continue to expand with many shells and still retain the same ratio between shells. |
| R. Henry has rediscovered some of what was a highly developed understanding of mankind's relationship to the Universe, and this knowledge was utilized and documented in the geometry of ancient structures, with its origins probably dating back prior the last ice age. Sacred Geometry, the study of the unity of the cosmos, demonstrates relationships between Number and Space and the Human Form. It was used in the construction of ancient glyphs and monuments thereby aiming at preserving the knowledge of these principles of Natural Law for future generations. This construction of reflective spheres may embody the technology that produced the animated images of the deities in the temples of antiquity. |  |
 | Here we see a picture of a DNA. Looks familiar doesn't it? One question that becomes obvious to a highly developed human generation, is obviously 'How can we pass over all of our scientific knowledge in case of a cataclysm'. It is believed that such cataclysms have occured more than once in the past, probably wiping off each time whole human generations with all their knowledge. Unfortunately, it is beleived that these generations have either left no signs of their knowledge, or no traces were left of these. However, it is more probable that in our ignorance we are still not able to find and understand their messages, which might have been well visible to us for many years. |
A few years ago Feynman, a great scientist of the past century, stated that the message he would have passed for the continuation of all our present knowledge would have been 'all things are made up of atoms- little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another'. Indeed, such a statement would at the least accelerate the development of technology in such a situation, but what if we could convey a message showing the true geometric mechanism of the atom and the whole universe? Would that convey much more information? The next stage to convey the message is to convert it into a universal syntax, for generations separated by thousands of years from each other would certainly not communicate in the same way or language.
Mathematics is a universal language, and the easiest way to convert any message into a mathematical format is to change it into a geometric shape. The problem of any shape surviving a cataclysm has to be well addressed and two obvious solutions are (a) make the shape as rigid and visible as possible, and (b) replicate the shape on various parts of the earth's surface.
The pyramid as a model of the mechanism as desribed by my theory, requires us to visualize an octahedron by a regular pyramid and an inverted pyramid joined together at the base and surrounded by a sphere. This, in effect, is a 3D representation of the innermost core as stated in this theory, depicted by the Hermetic Principle "as above; so below.", a principle which somehow, mainly through various old religious beleifs, has survived through the ages. Another fascinating feature of some of the pyramidal structures is that they contain a broad, thick layer of mica, which had to be brought from Brazil, over 2000 miles away! Mica, is very flaky and fragile, yet it was brought in very large pieces from great distances (supposedly without wheeled vehicles). Then the mica was used on an inner layer of the pyramid, not where it could be seen. Why? Was this only a representation or a working model? Indeed, if we look carefully around the world we do find a few, but very similar geometric structures, which really tell us that a lot of work to convey scientific knowledge of an earlier unknown and technologically advanced human generation has been attemped, before known history began.
Mathematics is a universal language, and the easiest way to convert any message into a mathematical format is to change it into a geometric shape. The problem of any shape surviving a cataclysm has to be well addressed and two obvious solutions are (a) make the shape as rigid and visible as possible, and (b) replicate the shape on various parts of the earth's surface.
The pyramid as a model of the mechanism as desribed by my theory, requires us to visualize an octahedron by a regular pyramid and an inverted pyramid joined together at the base and surrounded by a sphere. This, in effect, is a 3D representation of the innermost core as stated in this theory, depicted by the Hermetic Principle "as above; so below.", a principle which somehow, mainly through various old religious beleifs, has survived through the ages. Another fascinating feature of some of the pyramidal structures is that they contain a broad, thick layer of mica, which had to be brought from Brazil, over 2000 miles away! Mica, is very flaky and fragile, yet it was brought in very large pieces from great distances (supposedly without wheeled vehicles). Then the mica was used on an inner layer of the pyramid, not where it could be seen. Why? Was this only a representation or a working model? Indeed, if we look carefully around the world we do find a few, but very similar geometric structures, which really tell us that a lot of work to convey scientific knowledge of an earlier unknown and technologically advanced human generation has been attemped, before known history began.
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