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I would like to ask you about Tegmark's Mathematical Universe Hypothesis and its relation to the holographic principle: Could we use the holographic principle as a framework to Tegmark's MUH?

I mean, In holographic principle it is assumed that the information from a universe would be encoded in a "surface" (generally). Then, in principle, couldn't it be the case that information from every single mathematical model could be encoded in a holographic "surface"? Couldn't that reproduce every single universe of Tegmark's hypothesis? Couldn't every single mathematical structure be represented in D-1 dimensions?

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    MUH as such is not linked to a special phenomenon like holography, there is no need for a "surface" to even make sense in the universe's description. However, Tegmark advocates "infinity-free equations — the true laws of physics", and speaks approvingly on his website that "in quantum mechanics... the number of states appears to be finite even when taking general relativity into account, which is closely related to the holographic principle". So presumably holography provides suitable examples of his universes. – Conifold Jun 27 at 16:40
  • @Conifold thank you for your comment. There are a few more questions I have about it, though: With this, are you saying that Tegmark's MUH is not necessarily linked to holographic principle, but that holography would be compatible with his hypothesis? (i.e. that we could build holographic principle-models that could reproduce every single mathematical universe he proposes)? – Sue K Dccia Jun 27 at 19:43
  • Tegmark's MUH is not linked to holography at all, and saying that something is compatible with it is not really saying much, it is quite vague. But that something is compatible with X certainly does not mean that it can reproduce all of X, and holography certainly can not reproduce much, it is a very special effect. Even Tegmark himself does not know what "every single mathematical universe he proposes" might look like, he keeps his options open, but he obviously likes holographic models. – Conifold Jun 27 at 20:08
  • @Conifold yes, the holographic principle is usually defined in special situations where a space has a boundary. But holography can be applied to spaces which have not boundaries (arxiv.org/pdf/hep-th/9911002.pdf). These are "holographic screens" which can be present in any spacetime and in any dimension. Wouldn't that mean that literally all mathematical structures would obviously be compatible with holography? – Sue K Dccia Jun 27 at 21:49
  • As I understand, Tegmark leans towards digital philosophy, where the basis of reality is not spatial at all, with or without boundaries, it is discrete. Geometric models with holography are sometimes equivalent to such discrete structures, but certainly not even all of cellular automata can be implemented this way. – Conifold Jun 28 at 1:17

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