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Are computational models of the universe, like Stephen Wolfram's cellular automaton model of the universe (proposed in his book A New Kind of Science), somehow related to the Holographic Principle and the Bekenstein bound?

Are all these models compatible with Holographic Principle and the Bekenstein bound?

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    $\begingroup$ You might find this interesting : physics.stackexchange.com/q/4200/207455 $\endgroup$ – user207455 Jun 26 at 9:19
  • $\begingroup$ @SolarMike Thank you for the link, but there the holographic principle is only mentioned once and does not give much information about its relation to Wolfram's ideas. Do you know about anything else? $\endgroup$ – user234845 Jun 26 at 12:34
  • $\begingroup$ Have you searched on here to find anything else that may be relevant? $\endgroup$ – user207455 Jun 26 at 12:36
  • $\begingroup$ @SolarMike Yes, here and in internet in overall. I've only been able to find an article by Scott Aaronson (cds.cern.ch/record/559422/files/0206089.pdf) where he says ""Wolfram maintained to us that whether the number of degrees of freedom in a bounded region of spacetime is finite is unrelated to whether spacetime has a discrete structure of the sort he proposes." With was he saying that holographic principle was compatible but irrelevant to his model? I mean, did he said that holographic principle could be applied to his model but it was not a necessary part of it? $\endgroup$ – user234845 Jun 26 at 14:20
  • $\begingroup$ @SolarMike And also, referring to my original question: Has Wolfram said anything about the relation between his model and the holographic principle since then? $\endgroup$ – user234845 Jun 26 at 14:21
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There is at least one relation between the cellular automata and the holographic principle that is mostly historic. t'Hooft proposed in the following paper -- which is often considered as one of the origins of the idea of the holographic principle-- that black holes behave quantum mechanically like a evolving grid of boolean variables (i.e. a cellular automaton).

t'Hooft himself is still proposing these kind of models as a underlying model for quantum mechanics, but the idea of holography in its modern form of the AdS/CFT-duality was developed without any reference to these cellular automata.

The Bekenstein bound is a bound on the amount of entropy (i.e. the number of available microstates) for a system of given volume and energy.

I am not aware that the idea that cellular automata can describe physical systems matured to such an extent that you can actually speak of all these concepts (energy, volume, Hilbert spaces) in the framework of this model.

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  • $\begingroup$ thanks. But do you know if Wolfram has said something about the relation of his model and the holographic principle? I found an article by Scott Aaronson (cds.cern.ch/record/559422/files/0206089.pdf) where he says ""Wolfram maintained to us that whether the number of degrees of freedom in a bounded region of spacetime is finite is unrelated to whether spacetime has a discrete structure of the sort he proposes." With was he saying that holographic principle was compatible but irrelevant to his model? @Nontriviality $\endgroup$ – user234845 Jun 26 at 23:25
  • $\begingroup$ I mean, did he said that holographic principle could be applied to his model but it was not a necessary part of it? Has Wolfram said anything about the relation between his model and the holographic principle since then? @Nontriviality $\endgroup$ – user234845 Jun 26 at 23:25

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