# Relativistic Cellular Automata

Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics.

Google Scholar still gives more than 2.000 results when searching for "quantum cellular automata".

But it gives only 1 (one!) result when searching for "relativistic cellular automata", i.e. cellular automata with a (discrete) Minkoswki space-time instead of an Euclidean one.

How can this be understood?

Why does the concept of QCA seem more promising than that of RCA?

Are there conceptual or technical barriers for a thorough treatment of RCA?

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Have you implemented anyother languages in your searches? For example German, for they were the pioneers of modern physics. –  Waqar Ahmad Oct 28 '13 at 12:14

Lattice Boltzmann take on 1+1 dimensional quantum field theory:

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Search term "relativistic lattice boltzmann" gives over 9000 results on Google Scholar. For example:

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In cellular automata I do know there is explicit dependence on step/time. In quantum mechanics (and other many other theories) it is natural to write local evolution with respect to time.

On the contrary, in 'pure' relativity, time is not that different from position. And thus there is no such natural interpretation like 'the next step is the next time'.

However, there are relativity-based equations (e.g. Dirac Equation, Maxwell Equation) in which time can be taken to be an independent variable. And for sure there are more papers on the topic than one, e.g.:

Furthermore, some relativistic aspects are easily implemented, like $c=\hbox{(pixel size)}/\hbox{(time step)}$. One cellular automaton-like thing is so-called Feynman Checkerboard, which bases on the assumption that every particle always travels at $c$ but also sometimes gets bounced (it turns that effective mass depends on the amplitude of bouncing).

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Question on FC here too physics.stackexchange.com/questions/4048/… And if you can do 1+1 checkerboard, could you go down to Space Time in dimensions 10 and 26? –  arivero Jan 30 '11 at 4:25

I asked this very same question at mathoverflow, too (do the policies of PSE have anything against this?), and got one further answer, which I leave to your attention:

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