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).
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:
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.
|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.