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The Geometry of Quantum Gravity

faculty article Oct 29, 2014
Early Studies

My journey to the leading edge of Modern Physics and Quantum Gravity began when I was a teenager.

I had discovered that the human body had an energetic field. While the primary aspects and functionality of this field were explored in detail by a variety of cultural and spiritual traditions around the world, I realized it was entirely missing from the current scientific framework, and absent from my High School education.

Rather casting doubt on my experiences, this absence prompted my deeper investigation. I began to notice that many of the mysteries in sciences from biology to geology, astronomy to chemistry, had fundamental patterns that were similar, and also showed up in metaphysical studies of the “Ether” throughout the ages.

Like a detective sensing a secret waiting to be revealed, I decided to dive into a study of modern physics to see if there were any studies that could explain these patterns.

I began with a study of the macrocosmic world through Special and General Relativity, gaining a deeper understanding of the relative nature of spacetime, and our observation within it. Einstein pointed out that Gravity is simply the curvature of spacetime, and that acceleration is indistinguishable from Gravity (often explained in shorthand as “G-Force” by pilots and race-car drivers).

Einstein also explained that it would take infinite energy to accelerate to the speed of light, as this acceleration warps the fabric of Spacetime (creates curvature). The more you accelerate, the more Gravity it creates by curving spacetime, and the more energy it takes to push the envelope further.

I then dove into the study of the microcosm, and the strange world of Quantum Mechanics. QM established a few fundamental beliefs about reality, primarily through the Copenhagen Interpretation of the famous “double-slit” experiment. Scientists at the time were stumped by the results of the experiment. How could you shoot single particles at two splits, and witness waves with interference patterns coming out the other side? Their assessment: energy must act as both a particle and a wave. They then attempted to work out some calculations for this, and discovered that if you attempt to define the position of energy, you get a result that accurately describes a particle. If you attempt to discover the angular momentum or information about the movement of energy, you get information resembling a wave. The problem? You can’t do both simultaneously. The more precise you attempt to discover position, the more fuzzy its momentum gets, and vice-versa.

They called this the “Uncertainty Principle,” and it’s a major cornerstone of all Quantum Mechanics. Going forward, Quantum Mechanics has worked to discover all manner of particles, and developed highly complex equations to predict the probability of energy in certain states. However, I quickly discovered that this path of research diverged so drastically from the macrocosmic studies of Relativity that there seemed to be very little hope in true reconciliation.

To find a bridge, I began to explore studies in Quantum Gravity. How could one explain the curvature of spacetime, and effects of Gravity at large scales through the interactions of miniscule particles?


A Unified Picture Emerges

I read Lee Smolin’s book, Three Roads to Quantum Gravity. In it, I discovered that there was actually a great deal of progress made in bridging these macrocosmic and microcosmic worlds. Lee and his colleagues had begun to describe spacetime itself as a background independent system, meaning that seemingly empty Spacetime could be a lattice-like fabric filled with interconnected grids of energy. This would mean that the particles and waves we experience are just emergent patterns from this fundamental fabric. Immediately, I knew he was on the right track, as patterns in the fundamental energy flow and structure of Spacetime is exactly what I had been considering as a solution to describe how vastly different fields in science would have the same geometric patterns arising within them.

At this time, I also did a lot of reading into String Theory. While I found very important synergy in the idea that the most fundamental aspect of the universe is the vibration of incomprehensibly small strings, I was also turned off by certain aspects of the theory. Ideas that these strings are loops that float around freely in a void and vibrate through infinite modes, or stack and loop through 10 dimensions, or entangle themselves in shapes that can’t accurately be understood or modeled in 3D, all seemed like a waste of time to me. I found many other physicists who thought similarly, but found some inherent beauty in the mathematics of string theory. I found beauty in its study of vibrational resonance.

I began to see a unified picture emerging. What if the same fundamental patterns I had witnessed in nature through biology, geology, and cosmology were the basic patterns in the lace of spacetime? Spiral galaxies, hurricanes and nautilus shells map precisely to a spiral generated by the Phi ratio, but at vastly different scales. What if this pattern and others, like the “flower of life” or laws of equilibrium in circle packing were actually starting at the level of the fabric of space itself, and then having a fractal impact across scales until we see it in the blooming of a flower or the spinning vortices of wind.

I had already mapped the fundamental geometric patterns I was finding in every field of science, as well as nearly every spiritual tradition on the Planet. The primary patterns I found could be simplified as three basic geometries and their constituents: the pentagram (5-pointed-star), the hexagram (6-pointed-star) and the equilateral triangles that form it, and the heptagram (7-pointed-star).

The pentagram contains the Phi ratio, which describes meteorological patterns in weather like tornadoes and hurricanes, growing patterns in plants, galactic spiral arcs, and even the wavelength to width ratio of our DNA.

Hexagrams are formed from the most simple possible packing of circles and spheres, and are formed by equilateral triangles in equilibrium with each other. This basically describes the most balanced possible state of energy in the universe, and so could be understood as the “ground state” of any highly-efficient energy lattice. It shows up from the structure of carbon molecules (essential to all life) to honeycombs, leaves, flowers, all the way up to the poles of Saturn.

Heptagrams are most often seen in integrative symbolism throughout human society and culture. Perhaps archetypally rooted in the seven planets visible to the naked eye from Earth, the expressions of seven are found throughout Christianity, Hinduism, Islam, Judaism, Norse Mythology, Greek Mythology, Alchemy, Kabalah, Egyptian Magic, Astrology, and many many more. In nature, it is commonly found in leaves, flowers, and feathers. It’s also found in musical scales, color perception, crop circles, and even police badges.

It turns out that when you consider these geometries in terms of a fundamental energy lattice in the fabric of space, as the quantum geometry of the vacuum, they describe the most basic operations of a highly energized system in nearly perfect balance.

First, let's look at the fundamental structure of the fabric of space-time. If we consider the most basic possible information structures at the Planck scale, a Planck length line is the most fundamental representation of distance (1D), and a triangle made from three of these lines would form the most fundamental structure of area (2D).  Note that a triangle also forms the most stable arrangement of energy in a highly energized lattice, and they can stack in a fractal (and bidirectional) arrangement. Moving up to the next most fundamental dimensional structure, we obtain a Planck scale tetrahedron (3D). From here, we obtain a component that can form a lattice structure that has both planar surfaces and extruded depth, both of which are measured in both space and time.

Each unit of Planck space is also a unit of time, since the distance itself cannot exist in measurement without some measure of time. In this way, we could say that the dimension of time (4D) is embedded, entangled, or folded into each of these three spacial dimensions.

It is also important to look at our most fundamental building block, the triangle, more closely. Through the laws of thermodynamics, we know that energy and matter is always trying to reach the most balanced state. Heat will continue to flow into cool space until the temperature is equalized. Spheres thrown into a box will continue to compact with each other until they reach the maximum state of spacial density, which at the same time is the lowest state of potential energy (or mobility).

When discussing a lattice of energy, each node (or intersection point) will try to reach the position in which it has the most equal balance with all surrounding points. This is simply another way of describing why the equilateral triangle, and its 3D projection, the tetrahedron, is the most fundamental and equalized structural form for space-time.

If energy, and thus the fabric of spacetime, is always trying to maintain an equilibrium state, then any condition outside of that state of equilibrium will produce force (an influence that may cause a body to accelerate, or produce Gravity).

From here, we may begin to review each of the permutations of this fundamental lattice that would produce different levels of force, and thus produce Gravity.

"Any polygon with more than three sides is unstable. Only the triangle is inherently stable. Any polyhedron bounded by polygonal faces with more than three sides is unstable. Only polyhedra bounded by triangular faces are inherently stable

- Buckminster Fuller


Curvature 1:

In any equilateral triangular lattice surface, if you remove one of the triangles, the entire surface will bend in order to keep the equilibrium intact.It is this principle that holds the secret to Buckminster Fuller's work, and allows the curvature of structures to be modulated by adjusting the distance between the areas where this triangle has been removed. In these places, the Hexagonal "plate" has now "warped" into a Pentagonal plate, and this change in geometry in a single position allows curvature for the entire surface. At maximum Pentagonal curvature, these Pentagonal plates are directly adjacent to each other, which will tighten into an Icosahedron.

Because of this simple modulation to the equilateral surface, curvature has been established, and we might identify this as a basic "unit of Gravity" in the structure of spacetime.


We often see this in the surface of domes.  Most of the triangles in the dome structure are balanced with each other, forming hexagons, yet what causes the curvature of the dome itself is the placement of the joints where only five triangles come together (a Pentagonal plate).  If these joints are close together (with less triangles between them) the curvature will be greater, and the dome will be smaller.  The smallest dome of this form would simply be an Icosahedron.  As the Pentagonal plates move further apart, the dome's curvature will be reduced.  There are usually only a few Pentagonal plates spread out at extreme distances to form a "superdome" like those found on some stadiums.

It is also important to note that in most spherical domes, there will be five Pentagonal joints that match the position of the five vertices in the upper hemisphere of an icosahedron, as well as one at the very top of the dome.  Similarly, if the dome extended into the ground, you would also see a total of six Pentagonal joints in the lower hemisphere, five around the "Tropic of Capricorn" and one on the "South Pole."
Curvature 2:
With enough energy, after the Pentagonal curvature reaches its maximum state (Icosahedral arc), the structure of spacetime can be forced to curve even further, and another triangle in the equilibrium "pressed" off of the surface lattice. This will tighten the four remaining triangles of the surface into a pyramid shape. This state of compression and change in the lattice has a rippling effect, as each of the vector planes curve to adjust to the insertion of a "square" unit.  This forms the basic octahedron, one of the strongest crystalline formations in the universe.

This effect is intimately involved with the series of energetic alterations that produce physical matter from energy within the fabric of space-time, but we will not go into depth here on that process. However, we must recognize that at this level of curvature there is no longer a gradual spherical curve on spacetime, just an abrupt compression point of energy. This may b e the key to the vector equilibrium form, and may form the entry point into a black hole or singularity.

"There are only three possible cases of fundamental omnisymmetrical, omnitriangulated, least-effort structural systems in nature: the tetrahedron with three triangles at each vertex, the octahedron with four triangles at each vertex, and the icosahedron with five triangles at each vertex. If there are six equilateral triangles around a vertex we cannot define a three-dimensional structural system, only a 'plane."

- Buckminster Fuller

Producing Spin:

Any time a triangle is "removed" from one plane of equilibrium, or from a curvature, it cannot simply be "added" to another Hexagonal lattice. If you attempt to insert an additional equilateral triangle into a Hexagon, you will find that there is no amount of angular adjustment you can make to allow it to fit.

Therefore one of two things must happen:


(1) The equilateral triangles in the set "warp" and become acute triangles in order to accomodate the new trianglular energy field, which would take a vast amount of energy since these structures want to remain in equilibrium and this would change the balance of the entire fabric.

(2) The equilateral triangle connects to one of the triangles in the set, and the new triangle now "rotates" into a position connecting with one of the other vector equilibrium planes. The initial act of this rotation into position would cause the torsion forces in the fabric of space-time described by Nassim Haramein and others.

Being that the latter option would require far less energy, it is certainly the more likely scenario, and generates other notable effects. First of all, the rotation of a new triangle, or more specifically a single "point" of force (since it is actually only one node or intersection on the structure that needs to be removed) from one surface into any other plane of the Hexagonal vector equilibrium would produce a chain reaction, in which that Hexagonal plane would then transfer one of its own "points" to the next adjacent plane, and so on.

This would look like a ripple effect, in which a point of energy in the fabric of space-time would go spinning through the lattice until it found a stable position to rest, or "nest." Energy transference in this form is limited to the speed at which each Planck unit of distance in the structure can exchange with the next, which would be the fundamental measure of the speed of energy exchange through the fabric of space-time. This speed of course, is the "speed of light," which in turn provides the fundamental unit of "time" to the vector equilibrium of space, as it provides the relative measure of separation between any point in the lattice with any other point.

It is also important to note that the origin point for radiated energy would also be missing an energy node when one is radiated, forming curvature and gravity wherever there is radiation and spin (or electromagnetism).

Frequency and Change:

Now if we consider each one of the individual points in this lattice, we see that while in a vector equilibrium state, there are 12 radials extending to other points in the matrix along spacial dimensions. The points are intersections of energy, bridging dimensions. Each point in the lattice may fluxuate as energy passes through it, as vibration travels through these dimensional radials.

The state of a point or intersection at any given moment is determined by the combination of vibrations moving through it. Each structural intersection is not only a position, but also resonates at a specific frequency. In this way, even the planck scale structure of space-time is not a static and rigid system, but is flexible and acts in accordance with the properties of waveforms and fluid dynamics.

Energy will always attempt to reach an equilibrium state, so the dynamics at this scale are in a constant flux, working to return balance to the fundamental fabric. Each change that precipitates this "returning" ripples through the fabric, and can be seen from microcosmic to macrocosmic scales.



Many of these ideas were drafted over ten years ago, but they are even more relevant to my research today as I work with the Resonance Science Foundation and Nassim Haramein.  I'm providing this article as an additional resource to people taking the Delegate LVL1 course, in order to set the stage for understanding more of the dynamics of the geometry of space.  As you may have seen in this article, visualizing structures through 2D geometries can be useful when those geometries are reapplied to seeing the 3D forms of which they are component parts.  In a later article I will apply these principles to a complete discussion on the geometry of the proton itself, based on the mathematics of Nassim Haramein's recent paper, "Quantum Gravity and the Holographic Mass," as well as my own research.


Article by Adam Apollo


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