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Mark Andrew Smith’s PhD thesis from 1994 examines relativistic cellular automata models. Also a 1999 paper by Ostoma and Trushyck examines this topic. One topic not discussed is the information required in a cell to represent photons in transit. Suppose we have cells arrayed in a cube so that each cell has 26 neighbors. Suppose there are cells in the simulation. So it requires bits to represent a cell location. If a photon in motion is currently in a cell, it’s direction can be represented by the location of the farthest cell it will reach on it’s straight-line trajectory. Any cell can originate a photon and can receive photons passing through from any other cell. So each cell must be able to represent bits of information, to represent all photons in transit from all possible sources.
Question: Is there any schema that could represent the set of all photons passing through a cell using less information, with reasonable fidelity?
Question: According to the Pauli Exclusion Principle, any number of photons can occupy a single point in space. In the limit (real physical space), does each point in space contain an infinite number of photons? This would require infinite bits to represent. Storage of infinite bits requires infinite energy. If so, does this pose a challenge to the idea, expressed in Fredkin’s Digital Philosophy, that the universe is in fact a cellular automata, with the limiting speed of light simply coinciding with the “clock speed” of the automata, i.e. the rate at which photons can move from one cell to the next?