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Ruminations and Explanations

Hypercube Mathematics toward a Unified Field Theory

1. Introduction

The intent of this website is to introduce a unique interpretation of atomic structure towards a unified field theory. It begins with the structure of the isotopes Helium, moving into Neon in period 2 and Argon in period 3, which seemingly lays the necessary framework for an for periods 4-5, and periods 6-7 of the periodic table.

To provide an understanding of this model, do not assume that the 4th dimension is time, but is instead another function of distance. In particular, really small distances found solely within the nucleus of the atom.

2. The Essential Structure of Periods 2 and 3 is a 4d Hypercube

The 4d hypercube in period 2 is a natural progression from the 4d glome featured by the 4He alpha particle. A 4d hypercube has 8 cells, coinciding with the number of elements in this period. The true mathematical location (or probability) of the protons within this 4d hypercube are the vertices. The mathematics involved in a hypercube are similar to those proposed by Minkowski and his theories of a "space" grid. Theories regarding 8d Minkowski space are likely somewhat illustrative of the concept of the seven dimensions presented in this theory. However, unlike Minkowski space, the coordinates are not fixed within space or spacetime itself. Instead of space as what defines the dimensions and locations that matter wishes occupy, the creation of the atomic structure is not defined by space or time, other than it is "in" it, and the motions are defined by it. Instead, has to do with the center of the location of the atom itself. The center of the atom itself is the location from which an observer would see the entire atom at mass rest but see the movement of the nucleons and electrons. The "wishes" of the particles are not dissimilar to those of chemistry based upon the electromagnetic charges in a molecule. Like charges want to be far apart.

While this relationship of adding nucleons and dimensions appears to us to be spherical in nature, spheres by their very nature have no vertices and therefore we must use the faces and nature of the hypercube in these calculations.

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As we walk from opposing cells in the hypercube, the ones furthest away from each other, we go to lithium where the alpha particle engine is disturbed enough that it is a solid at room temperature, and then to Beryllium. For Be, imagine what would be two superimposed alpha particles. As we walk to the next element, to boron, a p orbital appears. This p orbital is the first one to appear. Positionally, the introduction of a proton at this position would appear in 4d space to occupy the position furthest away from or the most equidistant to the other 4 protons as an intersection of a regularly positioned alpha particle and inverted alpha particle.

The p-shaped orbital of boron's 5th electron is the first indication of the magic described by the hyperposition of the 5th proton to be added to the structure. The magic is that the electron appears in 3d to be in two places at once. While the orbit has been described in textbooks as a figure 8, it appears in 2d more as a snowman, without intersecting paths. If we can imagine that the p shaped orbital would be spherical in 4 dimensio and a snowman in 3 dimensions, this orbit is our first glimpse of what the fourth dimension looks like. One electron, in two places. The protons of lithium and beryllium do not inherit these additional properties.

2.1 Hyperposition and the distance from the center

Of course, P shaped orbitals are not unique to period 2. Excitement of deuterium, a hydrogen atom with one neutron and one proton, can cause a P orbital. As the atom is heated, and the proton and neutron increase in energy and spin. As it absorbs energy, it enters 4d space, resulting in a 4d orbital. Higher energies result in higher classes of orbitals. It would be assumed by this theory that the energy required to enter these states is a direct relationship to the energy required to create the states of the higher elements.

2.2 Repeating Squares and Period 3.

At period 3, it should be noticed that the repeating pattern of the squares, but at a higher level of energy, seems to be the easiest method of arranging additional protons within the nucleus. Always nestled in the middle of this spheroid shape that follows the mathematics of a hypercube, is 4He, once again acting with its 3d-4d motor, but now completely tied into the structure above it.

3. Helium's Multidimensional Spin Engine and Lower Melting Point Than Hydrogen is a Result of 3d interpretatioon of a 4 dimensional structure

Imagine 4He layed out so that it looks like carbon tetrachloride. In 3d space, the atomic charges of the protons will always be next to each other no matter the configuration. This should cause a constant repulsion, and in all actuality should cause the structure to flatten out. At period 1 in the periodic table, this proposes a 4th dimension of space, represented by a 4d glome, such that the effect in 4d is that the protons of the nucleus are actually as far away from each other as they can be. The number of vertices a 4d glome is 4.

This interaction of the particles, co-existing within 3d- where they are close together- and 4d to spin and to reduce the melting point of Helium to that below Hydrogen. No matter what position of the protons and the neutrons within the nucleus, an alpha particle of helium seeks to keep spinning as the 4d layout interacts with the 3d result. This "engine" is what causes the noble gasses to have the melting points that they do. In this fashion, the disruption of the spin generated by the model may predicts thermodynamic changes between the elements as it relates to melting point.

Higher dimensions are also consistent with the creation of matter from energy and the second law of thermodynamics, if it is to be assumed that the higher dimensions are systems with more entropy.

4. Potassium, Calcium and the D orbital of transition metals, Period 4.

Walking next to Potassium, we begin to build again. This time into the 5th dimension. We introduce, instead of one Proton, two, and we have the building block for the alpha particle, at the center. The alpha particle has truly been added to the outside of the atom, however, conceptually, it is also inside. The 5th dimension has already started, but just as with the periods before, an alpha particle alone isn’t going to do it. It is instead at Scandium that the 5d nature of the hypercube, is realized. The D orbital. Rather than being in 2 places at once, the probability cloud of a single 3d electron of scandium appears to be in 4 places at once, disconnected from one another. The additional slice of our 3d perception causes what appears to be a division of 4. For the next 10 cells, the electrons tied to the next 10 cells of a 5d supercube will be added. The protons settle on configurations of s orbitals and where there is an overlap they default to the s orbital, but never more than 2. The cells of the 5d hypercube cells until the sequence is complete and all cells of the 5d hypercube, finishing the D orbital sequence, filling the 10 cells with protons. This results in a 5d structure that craves another 4d structure and it begins to build one offering what amounts to an easing of hardness, all the way to the gas of Krypton, filling the 8 cells of the 4d hypercube below.

Metals are metals due to the disruption of the alpha particle motor, throwing off the balance, causing them to have different properties than gasses, or liquids.

4.1 Two squares are better than one.

Just as before, with the previous period, the 5d hypersphere repeats, resulting in different energy levels than the previous hypersquare. Protons position themselves within the 5d dimensions until the mathematics of 10 cells are filled. Again, the positions occupied by the protons correspond to how the charges are balanced in terms of the geometrical shape of the 5d super sphere and to the expected electron path. Again, the amount of the higher energy orbital never exceeds that of the rubidium and strontium before it. When the geometrical shape allows for the sharing of a point that does not exceed the charge of an alpha particle, the proton takes the opportunity to occupy that point in space. The electron then operates in that orbital.

4.2 Orbital mechanics

These overlaps of hyperposition within 5d space and 4d space should equate to the 2n2 format found within the overall pattern of 2, 8, 18, 32, 32, 18, 8 at the element of 118, 4th period. The 32 of the 32 vertices of a 5d tesseract that began with Potassium and fill to the brim at Radon.

5. Period 6 - the 6d Hypercube

The next level beginning with Cesium, the Barium, again builds an alpha particle, conceptually on the inside. In the 6th period, the 6d hypercube formed has 12 cells. The F orbital appears. Again, when the proton position can occupy an s orbital position, that coincides to an intersection of the 6d hypercube, if that position is better represented by the hypercube positions of an f, d, p, or s, it goes to an s orbital. If its definition is better positioned in the hypercube layered structure best by a p, then it is a p.

5.1. The Liquidity of Mercury

Liquidity of mercury - It is very close to becoming a perfect square. If it were anymore perfect, it’d be Radon.

6. Dimensions

The dimensionality that we are discussing is very small, occurring only between atoms, but the effect gives the characteristics that we view today. The current model based on the periodic table of elements ends with Element 118, Oganesson, and ends with a 6d hypercube. The shell orbital model given for this is 2, 8, 18, 32, 32, 18, 8. Given the current progression, Element 119 would begin with a 7th dimensional hypercube. There is nothing to suggest that this 7th dimensional hypercube that would begin at 119 does not exist, however.

As a product of the American education system, I had always conceived of time as the fourth dimension. In fact, one of Einstein’s early equations listed time fourth, after x, y, and z. When I stumbled into the idea of potential 4d atomic structures, I began a thought experiment about the 4th dimension and the idea that lithium, beryllium, and boron all have an extra degree or element of “timeyness” about them. I struggled to somehow relate this to Boron’s electron appearing with this mysterious double orbit. The structure of the universe, just like the structure presented here, must have mathematical sense behind it.

This brought me back to a fundamental inquiry about the nature of space. If a hydrogen atom with one neutron can be excited to a state where it mimics the orbitals of other elements, the key has to be the proton’s location when excited. It has to be related to distance.

If all matter follows Einstein’s equation, then the rest mass of an object equals the energy divided by the speed f light squared. Speed, as a unit of measurement, whether it is furlongs per fortnight or kilometers per hour, is a function of distance over time. The denominator here is always literally time. The numerator of speed is always literally, distance, something defined by x, y and z.

As my model started in the 4th dimension, with a 4d glome, the alpha particle, a tetrahedron. If that part of my theory was correct, then the next dimension should be the 3rd dimension. Since I’m in the 3rd dimension, I see the tetrahedron. That I see and experience existence in 3d, and the experience of the tetrahedron of 4He line up with the coordinates of x, y, and z (assuming I can look at it). This leaves time. Based on the model, instead of the variable of t for time, “w” would have been more appropriate based on alphabetical preference. Time, properly conceived, numerically, is the 0th dimension. It permeates all of space and is responsible for the wave motion of all particles that succumb to it. Matter is the 4th dimension, 5th dimension, and 6th dimension, that we can see and touch.

While the mathematical symmetry is nice and neat for placement of time at the 0th dimension, the arrangement of time to this position seems necessary as derived from the atomic structure of the periodic table.

Matter, itself, is the 4th dimension because the mathematics of the 4d structure start at the beginning, with Hydrogen.

7. Tensors

A physicist feeling uncomfortable with matter representing the 4th dimension may argue that this theory does not hold up because the four dimensional divergence of an antisymmetric second rank tensor equals zero. They might also simultaneously argue that the organization of time to the 0th dimension is somehow unnecessary because it does not change the mathematics of the vector matrix.

The model that I am proposing regarding matter is:

0th Dimension - Time
1st Dimension - X
2nd Dimension - Y
3rd Dimension - Z
4th Dimension - Matter (Periods 1 (4d glome), 2, 3)
5th Dimension - Matter (Periods 4, 5 incorporating the lower dimensions) (Only those protons making up the transition metals, and accompanying neutrons to satisfy the empty cells and then the furthest vertices of the 5d hypercube in the order provided above)
6th Dimension - Matter (Periods 6, 7 incorporating the lower dimensions) (Only those protons making up the lanthanides and actinides, and accompanying neutrons to satisfy the vertices of a 6d hypercube)

While the 4th dimension is matter, its operation is ordinally that of the 5th dimension. I believe that this is the reason that the 5th dimensional mathematics of the Klauza-Klein model begins to work in a vector mathematical senseand why string-theory calculations based upon multi-dimensional Minkowski space begin to work.

Time, from what can be deduced, would have a wave function consistent with the speed of light, setting the speed limit of the universe. Positioning time in the 0th position fits with the mathematics of the beginning of the periodic table. 1 dimension, then 3 dimensions, incorporating the first, to make 4, space time. It is my hope that the reorganization of time to the 0th dimension and may provide a valuable model moving forward. It seems logical and is admittedly the only way that this hypercube model of the atom can be correct in the ordinal.

There is no doubt that the four dimensional divergence of an antisymmetric second rank tensor equals zero. This represents space with nothing in it. There is a question of where you should start counting those dimensions. This model proposes putting time 0th only so that all matter can properly be a property of the 4th dimension and up.

8. Suggested ways to Disprove this Theory - From here on down is a whiteboard, not a theory.

1. Prove mathematically in a (by use of a tensor?) that an alpha particle with a square configuration in 4d would not show appear in 3d as a tetrahedron.

2. Prove mathematically that the electromagnetic charge of a opposite proton in 4d square and interaction in 3d space, would not cause spin.

3. Proving the negative is hard, but showing no relationship between the excited state of deuterium resulting in a p-orbital and the mass energy state of Boron. As well as disproving the relationship between the other orbitals displayed by deuterium and their corresponding state. All of these calculations need to not destroy the alpha particle engine at the center of the atom.

4. Prove that the relationship between an electron P orbital has nothing to do with positioning in the cell of a hypercube.

5. Prove that this geometry cannot produce a dipole magnet at Fe, or Nd.

9. Possible holes in this theory

1. This theory requires a constant interaction between 3d, 4d, 5d and 6d space, such that the coordinates can intersectlogically as not to least disrupt the "alpha particle" engine. It is highly likely that as the dimensions overlap, there would be atomic isomers, chiral looking (left hand, right hand formations). At higher levels, given the overlap, it may also be possible that that elements of differing qualities exist despite the same atomic number.

2. Vector mathematics, in general.

3. This theory requires a spatial relationship of compaction in multiple dimensions to present in 3d as a function of the preservation of the alpha particle.

4. This theory requires a somewhat arbitrary "definition" change of particles. For example, if a proton is added to calcium, an inner most proton, will need to "switch" to the 5th dimension to produce Scandium's d orbital.

5. This theory could be much more mathematically tight when addressing the mixtures of 4d, 5d, 6d space within the atom. and explaining what "distance" is between dimensions.

6. This theory denies M-theory, and states that an atom is a dimension where you create it in space time, not a dimension of space time. It is not on a membrane manifold other than that provided by the structure of the atom. The only membrane is 3d space and the 0th, time.

7. The theory focuses on the cells of the hypercube, and then it pushes out to the vertices, without giving detailed explanation as to why, or explain the geometrical layout of the hypercube in sufficient detail and lacks true description location and structure of neutron configurations nor does it particularly address neutron variations of isotopes, but might make such predictions automatically.

8. The theory suggests that squareness and cubeness, as a function in 4d, 5d, or 6d is, when viewed from that dimension, square or cubeness, but that in 3d it will be "smeared".

9. The theory suggests that roundness and sphereness, as a function, in 4d, 5d, or 6d, is, when viewed from that dimension roundness or sphereness.

10. The theory is incomplete regarding the concept of the function of the cylinder in Kaluza-Klein, unless somehow this translates to the geometry of a hypercube.

11. This theory also supposes that the furthest a proton may be from another proton, is within the same dimension rather than a mixture of the two.