The Seven Dimensions of Physics

THE SEVEN PLANES OF EXISTENCE

There are seven planes of existence in all of creation, in which each plane is a higher level order than the one that preceded it. Moreover, the former plane always acts as the foundation for the following plane. The seven planes of existence I propose are a modified version of what Young proposed in the Reflexive Universe, and taken together it forms a foundation for a theory of everything. I am labeling this series of blogs with "Universal Order" if you want to review some of the earlier blogs (see blog Label column on the left). The smallest part is the microcosm of the whole, and what we see is a symbolic representation of a higher order of existence. This correspondence between different planes can be seen in the planes that have been explored by science. Thus it is related to Emanuel Swedenborg's Doctrine of Correspondences, where everything that exists is a symbolic representation of something higher. The seven planes are:

1. Space-time
2. Subatomic particles
3. Atoms
4. Molecules
5. Plants
6. Animals & Man
7. (an unknown state of existence)

Before I get into the seventh plane, I want to first establish a foundation. So I have been going through each plane, and within each plane there are seven smaller substages. We did this for subatomic particles, atoms, molecules, plants, and animals.  For the latter two scientific advances have been made in molecular phylogenetics, which is refining or redefining taxonomies that were done earlier based on morphology alone. There is one last gap that needs to be filled: and that is space-time. I brought up some various theories before, but as they are incomplete (and somewhat confusing, especially String Theory) I wanted to return back to this plane one more time.

THE SEVEN DIMENSIONS OF SPACE-TIME

Let us start with the dimensions that we know from Euclidean geometry:

1. 0 dimensions. This is represented by a point.
2. 1 dimension. This is represented by a line.
3. 2 dimensions. This is represented by a triangle.
4. 3 dimensions. This is represented by the four sided tetrahedron.

Let us assume these dimensions represent the first four substages of the space-time plane. These four geometric symbols, point, line, triangle and tetrahedron, were regarded as important among the ancient Pythagoreans. They can be taken to represent not only the first four substages of space-time, but also the first four planes of existence. Space-time can be taken to have 0 dimensions as it is everywhere, particles travel in a wave similar to a line, atoms are built on top of three quarks per proton and neutron, as well as require a minimum of three types of subatomic particles (proton, neutron, electron), and we saw earlier that there are four molecular bonds which can be used to classify all molecules in the form of a tetrahedron. This is no accident: we see how the microcosm explains the whole.

According to the pattern that we have been seeing, there should be seven substages of space-time, thus there should be higher dimensions than the ones we see. While this sounds like science fiction, in high level physics it is not. In fact, in order to explain certain phenomenon physics requires these other dimensions to exist. So, let us proceed to higher dimensions, according to our current knowledge of physics.

THE FOURTH DIMENSION

What is the fourth dimension? In higher physics, the fourth dimension is what we experience as time. To imagine this, flatten 3-dimensional space into a plane. As this plane moves to fill in a cube, that is what we experience as time. Time can only move in one direction to maintain causality. In Einstein's theory of special relativity, time is the fourth dimension. Time as the fourth dimension is what is known as "Minkowski Space-Time."  This was proposed by Minkowski to complement Einstein's theory of relativity, and although at first Einstein thought it was just a mathematical device, he eventually accepted it as it is necessary in order to understand how special relativity works. When he introduced the theory in 1908, Minkowski said the following:

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

Here is an image of Minkowski Space:

So how does this model help in the theory of Special Relativity? The best way to explain it, is to see it.  See the following video, which also explains the relationship between Einstein's theory of Special Relativity and the Lorentz transformations:

To sum up the theory of Special Relativity I will quote from Wikipedia:

This theory has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity. It has replaced the classical notion of invariant time interval for two events with the notion of invariant space-time interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc^2, where c is the speed of light in vacuum. The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared with the speed of light. Special relativity reveals that c is not just the velocity of a certain phenomenon—namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. One of the consequences of the theory is that it is impossible for any particle that has rest mass to be accelerated to the speed of light.

However, there are limitations to the theory. Special Relativity, and Minkowski Space, work as long as there is no significant gravitation.  Where there is strong gravitation, space-time becomes curved, in which case we must move on to the General Theory of Relativity which takes into account gravitation.

THE PENTACHORON

Considering how we can represent dimensions 0-3 as a point, line, triangle and tetrahedron, how can we represent the fourth dimension?  When I thought about it, there was only one geometric shape in which we could represent the fourth dimension of space-time: the pentachoron, also known as the pentatope or hyperpyramid or "4-simplex":

The pentachoron or pentatope is a tetrahedron, except now there is an extra vertex in the middle.  Inside the pentachoron are four tetrahedrons, which form the outer figure of a bigger tetrahedron. It is also known as the "5-cell".  Its described as a "four-dimensional object bounded by five tetrahedral cells." A four dimensional object?  I then found this entry on the Pentatope from Wolfram Mathworld:

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it consists of five vertices, or pentachoron. The pentatope is the four-dimensional simplex, and can be viewed as a regular tetrahedron  in which a point  along the fourth dimension through the center of  is chosen so that . 

To map out higher dimensional objects, mathematicians create an orthographic projection of the vertices and edges onto a Coxeter plane. Here is the pentachoron projected onto a flat Coxeter plane:

Which of course is the sacred symbol of the pentagram.  It was regarded as sacred by the ancients as well as  the Pythagoreans. The phi ratio is present where each inner line intersects the other inner line. Some take it as a negative symbol used in occult practices, but it was not so originally.

THE FIFTH DIMENSION

The fifth dimension is the curvature of space-time due to matter, and this is where the theory of General Relativity comes in. Why is this another dimension?  Suppose we live in a 2-dimensional world.  If we draw a triangle on our 2-dimensional plane, all the angles should add up to 180 degrees. But suppose it was not true that we were living on a 2-dimensional plane, but instead a sphere. The angles of the triangle would add up to 270 degrees:

As a result of measuring the angles, we would conclude that there was a dimension beyond the 2-dimensional world.  But it is not something we would be able to imagine, as our imagination is limited to 2-dimensions.  Similarly, we are seeing that large masses cause the curvature of space and time.  This is explained in the theory of General Relativity.  It also indicates that there is a dimension beyond the three space dimensions that we know and the fourth time dimension. Here is a description of the theory of General Relativity:

General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.

As far as I know, General Relativity does not speak of the curvature of space-time as the fifth dimension. But other theories do. The Kaluza-Klein theory makes use of five dimensions to unify gravity with the electromagnetic force. While it successfully does this, it has one weakness:

However, an attempt to convert this interesting geometrical construction into a bona-fide model of reality founders on a number of issues, including the fact that the fermions must be introduced in an artificial way (in nonsupersymmetric models).

In other words, it is incomplete. It does not account for the existence of matter. Also, it is not clear how to experimentally verify this theory. But the math checks out. From Kaluza, Klein and their story of a fifth dimension:

This Kaluza-Klein Theory had many fascinating consequences. Things that have charge under electromagnetism are would just be things that are moving in this circular fifth dimension. The radius of this extra dimension would be related to the electric charge of particles. A charged particle would be move in one direction in the fifth dimension, and an oppositely charged particle would move in the other. And as the momentum of two oppositely charge particles would cancel out when they collide, they would no longer move in the fifth dimension making their combined charge neutral.

This is interesting: things that occur in other dimensions would manifest in different ways in our own dimension. Such lower level orders explain why we have charge.  Science explains the behaviour of charge, but not why there is charge. Another more recent five dimensional theory to explain gravity is the Randall-Sundrum model. I found this other article entitled Higgs Field as Weak Boson in five Dimensions, which would seem to validate my earlier guess of putting the scalar Higgs field in the space-time plane.

If we were to continue our geometric representation for each dimension, we end up with something known as a hexateron or "5-simplex".  It has 6 vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 pentachoron facets. Here is what its projection looks like on Coxeter plane:

In other words, something coming close to the Star of David. The Star of David being used as a symbol for the Jewish nation is relatively recent, dating to around the seventeenth century. Earlier, it was simply a magical symbol known as the "Seal of Solomon", used to imprison or command spirits. Thus its somewhat similar in magical symbolism to the pentagram. Odd. Here is one version of the Seal of Solomon:

However this does not go back far enough. Earlier than this, it was known as a "hexagram" and appeared in Hinduism, Bhuddism and Jainism. Here is a possible meaning of the hexagram in ancient India, from Wikipedia:

Within Indic lore, the shape is generally understood to consist of two triangles—one pointed up and the other down—locked in harmonious embrace. The two components are called "Om" and the "Hrim" in Sanskrit, and symbolize man's position between earth and sky. The downward triangle symbolizes Shakti, the sacred embodiment of femininity, and the upward triangle symbolizes Shiva, or Agni Tattva, representing the focused aspects of masculinity. The mystical union of the two triangles represents Creation, occurring through the divine union of male and female. The two locked triangles are also known as 'Shanmukha'—the six-faced, representing the six faces of Shiva & Shakti's progeny Kartikeya. This symbol is also a part of several yantras and has deep significance in Hindu ritual worship and history.

THE SIXTH DIMENSION

We now arrive at the sixth dimension. So what in the world goes on here?  A curvature of the curvature of space-time.  In other words, matter in our 3 dimensional world may be a manifestation of the sixth dimension. The fifth dimension cannot handle fermions, the sixth dimension does. The Physics theory which uses six dimensions is known as the "Yang-Mills theory".  From Wikipedia:

Yang–Mills theory is a gauge theory based on the SU(N) group, or more generally any compact, semi-simple Lie group. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-Abelian Lie groups and is at the core of the unification of the Weak and Electromagnetic force (i.e. U(1)xSU(2)) as well as Quantum Chromodynamics, the theory of the Strong force (based on SU(3)). Thus it forms the basis of our current understanding of particle physics, the Standard Model.

I was looking for something to explain the Yang Mills theory simply, here is a geometric representation I could find which is partly in Russian. I am not trusting it completely, so see the other videos below for a more objective description of Yang Mills theory:

Comments on the video:  Some of this looks highly conjectural, but I am interested in some of the geometric interpretations of space-time. Interesting point: extra dimensions or fields are "round", and the unit of distance is the Planck length. It shows the relationship between the six dimensions and the six observed colors in quarks. One must understand the underlying geometry to understand why particles behave the way they do. Extensive use of triangles are made, and throughout several hexagrams are made. A graviton with +/- 2 spin is used to explain some subatomic interactions. It then moves on to some Russian research on some observed cyclicity in the macroscopic world (I get somewhat lost here)...but then interestingly, it makes use of geometric polyhedrons - including the tetrahedron and icosahedron - to explain the number of subatomic particles. These geometries explain the number of leptons and quarks, as they are properties of the underlying geometric membrane. It then moves onto the underlying geometry of biosystems - viruses often come in the form of one of the Platonic solids.

These six dimensions seem to be necessary before they manifest to us as "particles" or "fields" (the next plane of existence). The Yang-Mills theory is however incomplete. It  is supposed to explain the "color confinement" of quarks, that is, why we cannot directly observe quarks.  There is an unsolved mathematical problem called "Yang Mills existence and mass gap" and the Clay Mathematics Institute will give a one million dollar reward to anyone who solves it. While Yang Mills is strong enough theory for physics, the mathematics behind it is still incomplete. I wanted to understand this better, and I am not trusting that part-Russian video, so I found a series of lectures for a general audience on the Yang Mills theory and its problems. Some of this sums up some of the earlier material I had been discussing earlier. A lot of it is introduction before he finally gets to the Yang-Mills theory:

Comments on the video: science has simplified elements down to 118 atoms, and more recently, these have been reduced to about 16 elementary particles in the Standard Model.  He discusses the importance of symmetry in physics, which basically talks about changes of state in a physical system, which is important for describing these particles.

Comments on the video: continuation on the importance of symmetry, how it is used for classification (Group Theory). If you know what symmetry is, you can skip this.

Comments on the video: Conservation laws in physics are based on mathematical symmetry. Noether proved in 1915 how a mathematical symmetry leads to a conservation law. Space motion is to momentum, as time is to energy - which shows up in the theory of Special Relativity. Thus when Einstein combined space and time, he ended up with E = mc^2.

Comments on the video: Phenomenon as electricity, magnetism and light were initially viewed as separate things, but underlying all of this was one electromagnetic force. Quantum mechanics unified particles with fields. Quantum physics is probabilistic, not deterministic, at a fundamental level. Quantum physics deals with the fact that things that we expected to be continuous in nature are actually discrete.

Comments on the video: Now, we start to get into quantum weirdness. Particles have intrinsic spin, but this "spin" is discrete. Fermions always have half-spin, bosons have integer spin. This can be mathematically described by symmetry. For fermions, this means no two fermions can share the same state when they interact with each other (Pauli exclusion principle). Quantum Electrodynamics, or QED, is based on local symmetry. And finally, he begins (around 15 min) to discuss the Yang-Mills theory. It fit in well with QED, but it predicted that all force carriers were massless: which is not true for the weak and strong nuclear forces. It could not explain why some force carriers have mass. This is handled by the concept of "Broken Symmetry": assume physical laws are symmetrical, but the universe can be in an asymmetrical state. The Higgs Boson theory is an extension of this concept of broken symmetry, which explains why the Weak force carriers have mass.

Comments on the video: He now reviews the "Eightfold Way" by Gell-Mann (one pattern is the same as the Pythagorean Tetractys) fixed the problem of the "particle zoo." In order to reach this symmetry, there must be quarks, which are the most elementary matter particles known thus far. There was another problem, mathematical infinities, which was handled in Feynmann diagrams through a process of renormalization. Virtual particles that pop in and out of the vacuum may be an explanation for the mystery of "dark energy". Combined with the theories of Yang-Mills and Higgs, new particles were predicted and confirmed in the 1970s, although for the Higgs-Boson that was more recently confirmed in 2012. However the big problem with Yang-Mills is that the formulas only work with 2 space dimensions, the problem is to show that it works with 3 space dimensions. Also, more math is needed rigorously prove why particles have the properties that they do. (Evidently, of the six dimensions in Yang-Mills theory, only two of them are space dimensions. Unfortunately these videos do not discuss the six dimensions of the Yang-Mills theory).

To finish off the symbolism for each of the dimensions thus far, the geometric object that represents the sixth dimension is known as a heptapeton, a "6-simplex" or seven pointed star.  It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and 7 5-simplex 5-faces. Here is what it looks like on a Coxeter plane:

The seven pointed star is also known as a heptagram.  According to some, it represents the seven known planets, or the seven days of the week:

THE SEVEN DIMENSIONS OF SPACE-TIME

To sum things up, we have the following seven dimensions of space-time:

1. 0 dimensions. A point.
2. 1 dimension. A line.
3. 2 dimensions. A plane, or triangle.
4. 3 dimensions. A tetrahedron.
5. 4 dimensions (Special Relativity). This is space + time. A pentagram.
6. 5 dimensions (General Relativity, Kaluza-Klein theory). This is where gravity operates. A hexagram.
7. 6 dimensions (Yang-Mills theory). This is where matter operates. A heptagram.

That is looking better than what we had before. But interestingly, it ranges from 0 to 6 dimensions. What is the 0-dimension? That is either a point of singularity, similar to what happened at the Big Bang, or it simply represents higher dimensions that are so compact they appear as a singular point. Of course mathematically we can go up an infinite number of dimensions, but other physics state that there are only seven, as stated in earlier blog entries.

I have read some opinions stating that the 6th dimension is "all possibilities" of the universe, thus all the possible universes. This is not quite true - but what is true is that Quantum physics is probabilistic at its very nature: thus it is all possibilities, but constrained at a quantum level. But what is interesting is once we reach this level, physicists can then begin to explain some of the essential properties of the subatomic particles. We are not quite there yet...it is still an active area of research.

What I like about the descriptions of the seven substages of space-time is that the first four substages are "constraining" - in the same way that the first four substages of other planes are also constraining. Then reality begins to "escape" from its constraint, but this time in the form of time and gravity, until we finally reach the state of reality where matter can occur.