A Theory of Pixelated Spacetime and of Reality as a Quasicrystalline Point Space
Projected From the E8 Crystal
Emergence theory is a unified first-principles theory currently in development by a Los Angeles-based team of scientists. Emergence theory weaves together quantum mechanics, general and special relativity, the standard model and other mainstream physics theories into a complete, fundamental picture of a discretized, self-actualizing universe.
At the root of emergence theory’s formalism is a concept quickly taking hold in the theoretical physics community––that all of reality is made of information. What is information? Information is meaning conveyed by symbols. Languages and codes are groups of such symbols that convey meaning. The various possible arrangements of these symbols are governed by rules. The language user makes free-will choices regarding how to arrange the symbols, in order to produce meaning, according to these rules. Fundamentally, then, the existence of information must therefore imply a “chooser,” or some form of consciousness, in order for it to be actualized.
We identify two classes of symbols. One class contains those symbols that subjectively represent something other than the symbols themselves. For example, the shape of two intersecting diagonal lines (“X”) can represent the mathematical concept of multiplication, it can represent an English letter, or it can represent a kiss. The shapes known as the letters “D-O-G” can represent a certain animal that we all know and love, but they can also represent anything else if we decide that they do. The second and arguably more fundamental class of symbols are those symbols that represent themselves with ultra-low subjectivity. An example is the shape of a square representing the shape of a square. Such a geometric language using geometric symbols could express geometric meaning.
Reality is experimentally observed to be geometric at all scales, from the Planck level to the largest structures. Our group hypothesizes that an entirely geometric language or code, using geometric symbolism, is the fundamental way in which meaning, in the form of our physical reality, is expressed by…well, we’ll get to that.
A central feature of reality behaving geometrically is that all fundamental particles and forces in nature, including gravity, can transform into one another, through a process called gauge symmetry transformation, in a manner that corresponds precisely to the vertices of the 8-dimensional polytope of a crystal called the E8 lattice. However, we do not appear to live in an 8-dimensional universe. Experimental evidence indicates that we live in a universe comprised of only three spatial dimensions.
What kind of geometric language or code, then, would express a geometric, 3-dimensional reality that is deeply linked to the 8-dimensional, E8 lattice?
We believe the answer is in the language and mathematics of quasicrystals. A quasicrystal is an aperiodic, but not random, pattern. A quasicrystal in any given dimension is created by projecting a crystal - a periodic pattern - from a higher dimension to a lower one. For example, imagine projecting a 3-dimensional checkerboard - or cubic lattice made of equally spaced and sized cubes - onto a 2-dimensional plane at a certain angle. This 3D cubic lattice is a periodic pattern that may stretch out infinitely in all directions. The 2D, projected object is not a periodic pattern. Rather, it is distorted due to the angle of projection, and instead of containing only one shape that repeats infinitely like the 3D crystal does, it contains a finite number of different shapes (called proto-tiles) that are oriented relative to one another in specific ways, governed by a set of mathematical/geometrical rules, to fill the 2D plane in all directions. By analyzing the 2D projection it is possible, with the correct mathematical and trigonometric toolkit, to actually recover the "mother" object in 3D (the cubic lattice crystal in this example.) A famous example of a 2D quasicrystal is the Penrose tiling conceived by Roger Penrose in the 1970’s, in which a 2D quasicrystal is created by projecting a 5-dimensional cubic lattice to a 2D plane.
Emergence theory focuses on projecting the 8-dimensional E8 crystal to 4D and 3D. When the fundamental 8D cell of the E8 lattice (a shape with 240 vertices known as the “Gosset polytope”) is projected to 4D, two identical, 4D shapes of different sizes are created. The ratio of their sizes is the golden ratio. Each of these shapes are constructed of 600 3-dimensional tetrahedra rotated from one another by a golden-ratio based angle. We refer to this 4D shape as the “600-Cell.” The 600-Cells interact in specific ways (they intersect in 7 golden-ratio related ways and “kiss” in one particular way) to form a 4D quasicrystal. By taking 3D subspaces of this 4D quasicrystal and rotating them from one another at a certain angle, we form a 3D quasicrystal that has one type of proto-tile: a 3D tetrahedron.
On a TV or computer screen the smallest, indivisible unit is a 2D pixel. In our 3D quasicrystalline reality, the tetrahedron is the smallest, indivisible unit. A 3D pixel of reality, if you will. Each tetrahedron is the smallest possible 3D shape that can exist in this reality: the length of each of its edges is the Planck length (the shortest possible length known in physics - over 10^35 times smaller than a meter) These 3D pixels combine with one another according to specific, geometric rules, to populate all of space.
On a 2D screen, the pixels never move. They simply have different brightness and color values, and an illusion of meaning (in the form of a picture) is created by their combined values. Similarly, the tetrahedra in the 3D quasicrystal never move either. Instead, they act as a binary language: in any given moment, each tetrahedron can be chosen by the code operator to be either “on” or “off.” If it is “on,” it can be in one of two states: “rotated left” or “rotated right.”
Imagine a single, frozen moment in time throughout the entire universe. Let’s call this moment “moment 1” for the purposes of illustration. In moment 1, the 3D quasicrystal filling the entire universe is in “state 1” and in this state, some tetrahedra are on, some are off, some are rotated left and some are rotated right. Now imagine the next frozen moment in time, “moment 2.” In moment 2, the quasicrystal is in “state 2.” In this new state, many of the tetrahedra are in different states from their states in moment 1. Now imagine a hundred of these moments. Now imagine an animation of all of these frozen moments.
If you think of a movie, the moving-image is composed of single, frozen frames that are filmed and projected at a certain speed (24 frames per second in most modern movies). In our model, one second contains 10^44 frozen frames. Over many of these frames patterns emerge on the 3D quasicrystal. These patterns become more and more meaningful and sophisticated with time. Gradually patterns resembling and acting as particles form on the quasicrystal. In fact, one of the most groundbreaking predictions Emergence theory will make is about a specific, pixelated substructure of electrons––particles currently thought of, without proof, as dimensionless. With time, these particles take on more and more complex forms, and eventually the reality we all know and love emerges.
Emergence theory views spacetime in a way that builds on Einstein’s spacetime model, in which the future and past exist simultaneously in one geometric object. We view this object as a system in which all frames of spacetime interact with all other frames all the time. In other words, there is a constant, dynamic, causality loop relationship between all moments in time, in which the past influences the future and the future influences the past.
We view consciousness as both emergent and fundamental. In its fundamental form, consciousness exists inside every tetrahedron/pixel in the 3D quasicrystal in the form of something we call viewing vectors. Think of viewing vectors as micro-scale observers in the traditional quantum mechanical sense. These observers actualize reality by making ultra-fast, Planck scale choices about the binary states of the pixels (on, off, left, right) at every moment in time. This fundamental, primitive, yet highly sophisticated, form of consciousness steers the patterns on the quasicrystalline point-space toward more and more meaning. Eventually consciousness expands into higher degrees of order such as nature and life as we know it. From there life and consciousness keep expanding, growing exponentially, into all corners of the universe. Imagine humankind one day populating trillions of galaxies, its instantaneous communicative channels and high levels of consciousness growing over time into a massive, universal-scale neural network––a collective consciousness of sorts. This collective consciousness conceives the fundamental, “primitive” consciousness that powers the quasicrystal from which it emerges.
A creates B.
B creates C.
And C creates A.
There are no known laws in physics that place an upper limit on what percentage of the universe can exponentially self-organize into freewill systems such as us humans. Indeed, physics allows the possibility that all the energy of the universe can be converted into a single, conscious system that itself is a network of conscious systems. Given enough time, what can happen will eventually happen. By this axiom, universal emergent consciousness has emerged via self-organization somewhere ahead of us in 4D spacetime. And because it is possible, it is inevitable. In fact, according to the evidence of retro-causality time loops, that inevitable future is co-creating us right now just as we are co-creating it.