CELLULAR AUTOMATA
THEORY AND PHYSICS

We wish to thank R. Mongrain (P. Eng.) for his encouragement, constructive criticisms, and for the lengthy conversations on the nature of space, time, light, matter, and CA theory.

ABSTRACT

A new paradigm for the unification of physics is described. It is called Cellular Automata (CA) theory (ref. 2,4 & 6), which is the most massively parallel computer model currently known to science. We maintain that at the tiniest distance and time scales the universe is completely deterministic, and utterly simple. Our universe is a Cellular Automaton consisting of a huge array of cells capable of storing numeric information. These cells form a vast, 3D 'geometric' CA, where each cell has 26 surrounding neighboring cells that influence the state of a given cell. One set of common mathematical rules exists for each given cell, and the rules are applied to the inputs of the numeric state of the cell's immediate 26 neighbors and on the numeric state of the cell itself. The result of this 'computation' is then stored back in the cell on the next 'clock cycle'. In this way, all the cells are updated simultaneously, everywhere (not in the context of our measure of time) This process repeats itself for all cells, and for each and every 'clock cycle'. The CA structure automatically has a built-in, low-level space and time in the form of cells and 'clock cycles'. This can be thought of as a special kind of absolute and quantized 3D space, and separate, quantized absolute time. Low-level space and time units are totally inaccessible to direct measurement, and are independent of the usual 4D relativistic space-time units (which can be affected by motion and by gravitational fields). Here we reconcile the known relative nature of Einstein's 4D space-time of special and general relativity with the absolute nature of the quantized 3D CA space and quantized, time of the cellular automaton.

CA theory directly implies that all the laws of physics must result from interactions that are strictly local, therefore forbidding any form of action at a distance. CA theory suggests that space, time, matter, energy, and motion are all the same thing: the end result of information changing state in the CA. Matter in motion is an illusion resulting from the 'shifting' of stable particle-like information patterns from cell to cell in low-level 3D CA space. The CA model automatically contains an inherent maximum speed limit for which information can be moved from place to place. At the CA level we can represent CA low-level space as a rectangular array of integers or cells; C_{i, j, k} with respect to an arbitrary cell that acts like the origin. The entire array of numbers is updated at every new CA 'clock cycle' t, where Nt is the measure of the number of CA low-level time periods elapsed between two events. The 26 inputs surrounding a given cell C_{i, j, k} act to modify the state of the cell at the next 'clock cycle' according to a fixed (possibly integer) function or algorithm F acting on the 27 inputs (and on the state of the cell itself) as follows: C_{i, j, k} = F C_{i+x, j+y, k+z}; where x, y, z take on all combinations of -1,0, and 1. CA low-level space or time are not affected by any physical interactions, and are inaccessible by direct measurement.

We propose that light (photon) motion is the fixed, simple shifting of a photon information pattern from cell to adjacent cell at every 'clock cycle'. Thus photons 'travel' only at one fixed speed, which is unaffected by any possible source motion. By adopting absolute CA space and time coordinates for the description of a pair of observers in inertial reference frames with a relative velocity 'v', then the Lorentz transformation follows mathematically. We argue that 4D flat space-time is a direct consequence of the behavior of the universal CA, as seen by inertial observers who are not aware of, and cannot access the absolute low-level CA units of space and time. We also provide some speculative arguments that may reconcile the apparent non-local character of entangled quantum particle interactions in quantum theory, and the strictly locality that is required for particle 'motion' in relativity and in CA theory.

We establish a deep connection between the CA model and the existence of virtual particles in the quantum vacuum. We find that the particle exchange paradigm of quantum field theory is also manifestly compatible with the CA model. However, classical Newtonian inertia is not compatible with CA, since it is a global law regarding the property of the total mass to resist being accelerated. We briefly present a new theory of inertia based on a proposal by R. Haisch, A. Rueda, and H. Puthoff (ref. 5) which we modified and called Quantum Inertia (QI). QI is also manifestly compatible with Cellular Automata theory. According to QI, inertia is due to the strictly local electrical force interactions of matter consisting of quantum particles with the surrounding electrically charged virtual particles of the quantum vacuum. The sum of all the tiny electrical forces (from photon exchanges) originating from each electrically charged particle in the mass with the surrounding electrically charged virtual particles of the quantum vacuum is the source of the total inertial force opposing accelerated motion in Newton's law 'F = MA'. QI resolves the problems and paradoxes of accelerated motion introduced in Mach's principle by suggesting that the state of acceleration of the electrically charged virtual particles of the quantum vacuum with respect to a mass serves as Newton's absolute space, for accelerated motion only.

We have developed a new quantum theory of gravity called Electro-Magnetic Quantum Gravity (EMQG) (ref. 1) for the purpose of unifying Quantum Inertia and gravity into one common quantum framework. EMQG theory is designed to be manifestly compatible with Cellular Automata theory. What is unique about EMQG as a quantum gravity theory is that it is based on two boson force exchange particles; the graviton and the photon. Furthermore, the photon and graviton are physically nearly identical, with the same quantum numbers, but varying greatly in the strength of the force coupling. We invoked Einstein's principle of equivalence of inertial and gravitational mass to understand the origin of gravitational mass from the perspective of Quantum Inertia. We concluded that gravity also involves the same 'inertial' electrical force component that exists for inertial mass. We proposed that the general relativistic Weak Equivalence Principle (WEP) is a physical phenomenon, originating from common 'lower level' quantum processes occurring in both gravitational mass and inertial mass. The magnitude of the gravitational mass results from the electrical force interactions of the electrically charged mass particles interacting with the surrounding electrical charged virtual particles of the quantum vacuum. However, now the quantum vacuum particles are falling due to graviton exchanges between the earth and the surrounding quantum vacuum particles, which posses mass. Thus, both the electrical force (photon exchanges) and the pure gravitational force (graviton exchanges) are involved in gravity. However inertial mass is strictly the result of only the electrical force process specified in quantum inertia (with negligible graviton processes present). For a gravitational test mass near the earth, the graviton exchange process occurring between the earth, the test mass, and the surrounding vacuum particles upsets perfect equivalence of inertial and gravitational mass, with the gravitational mass being slightly larger than inertial mass. Thus, for a large and a tiny test mass dropped simultaneously on the earth, the larger mass falls faster by a very small amount. This tiny deviation from perfect equivalence might be detected experimentally.

Since the virtual matter particles (specifically virtual fermions) of the quantum vacuum posses mass, they exchange gravitons with the earth and are therefore falling. This can be visualized as a downward directed accelerated 'flow' of electrically charged vacuum particles. The reversal in the relative accelerated state of the quantum vacuum particles with respect to a test mass in an accelerated or in a gravitational frame still leads to the same measure of mass. This is the reason why there is mass equivalence. 4D curved space-time is now understood as a consequence of the behavior of matter (particles) and energy (photons) under the influence of this (statistical average) downward accelerated 'flow' of electrically charged virtual particles of the quantum vacuum. This coordinated downward 'accelerated flow' can be thought of as a 'Fizeau fluid' that 'flows' through all matter subjected to a gravitational field. Like in the Fizeau experiment (which was performed with a constant velocity water flow), the behavior of light and measuring instruments is now affected by the accelerated flow of the 'Fizeau fluid' (virtual particle fluid). This is the root cause of 4D space-time curvature. This process also occurs in accelerated motion, where the quantum vacuum acceleration is an 'apparent' acceleration actually caused by the acceleration of the observer. In EMQG, space-time measurements based on instruments composed of matter are now affected by the action of this accelerated 'Fizeau-like' quantum vacuum fluid to give an 'apparent' 4D space-time curvature. Because our measuring instruments are incapable of measuring the true absolute and quantized CA 3D space and quantized CA time units, 4D space- time appears to be curved in accelerated frames and inside gravitational fields.

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