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Does 't Hooft's determinism work need the holographic principle in order to work or is it just an extension of his work?

Qmechanic
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lee hudson
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2 Answers2

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Determinism was a theme in 't Hooft's original paper on holography, and holography is a recurring theme in his papers on hidden variables e.g. http://arxiv.org/abs/quant-ph/0212095 section 2, http://arxiv.org/abs/gr-qc/9903084 section 8. The idea seems to be that quantum mechanics would emerge alongside gravity and the extra dimension, as a result of mathematically rewriting a lower-dimensional deterministic theory (reorganizing its variables and neglecting some degrees of freedom). So "holographic determinism" - or "holographic emergence of QM from a deterministic theory" is an idea, or an idea for an idea, but there's no working example of it.

I should point out that actual examples of holography like AdS/CFT involve a mapping between a quantum theory in a higher dimension and a quantum theory in a lower dimension. They don't involve an emergence of quantum mechanics on one side of the duality. Also, 't Hooft's most recent hidden variables papers (everything from 2012) do not mention holography, though one of them contains a version of the usual elementary string duality between "10-dimensional space-time" and "2-dimensional worldsheet" perspectives.

Mitchell Porter
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  • see I was right. The two points are linked in his theory. Mitchell are there any people or local hidden variable theories which dont rely on the holograpic principle or are set in a 3 dimensional world? – lee hudson Jan 15 '13 at 00:07
  • You would need something special to get around Bell's theorem, i.e. the correlations which in quantum mechanics arise from "entangled states" which can't be reduced to "a local state here and a local state there", even though "here" and "there" are arbitrarily far apart. The only idea for a local solution to that, that I can remember, is to have cause and effect going backwards in time as well as forwards, which is another idea on the fringe of physics that has been kicked around for decades... – Mitchell Porter Jan 15 '13 at 00:24
  • ... e.g. "transactional interpretation", but for which there is no truly working model. Personally, "quantum mechanics as side effect of emergent space" seems more plausible to me, since even physics orthodoxy now thinks that the space we know "emerges from" some other, more fundamental network of causes. – Mitchell Porter Jan 15 '13 at 00:28
  • there isnt backward causation in t hoofts model though is there? and it isnt confirmed space is emergent either? – lee hudson Jan 15 '13 at 00:37
  • We should move this to a chat room on the meta site but I don't know how to create the link. Anyway, there's no backward causation in 't Hooft, and there is no experimentally validated model of the world in which space is emergent. But 't Hooft also doesn't have a working model of the real world, either. – Mitchell Porter Jan 15 '13 at 01:08
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    @leehudson with all due respect, your statement "see I was right" does not follow from this answer, as it says, imo, that no clear connection between holography and determinism is demonstrated in 't Hooft's recent papers. Maybe you should conclude that he does not have one theory but many possible paths to explore. His recent work which has been discussed here http://physics.stackexchange.com/questions/7/will-determinism-be-ever-possible/43443#43443 and here http://physics.stackexchange.com/questions/30065/why-do-people-rule-out-local-hidden-variables . Holography is not in his recent works. – anna v Jan 15 '13 at 12:32
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It has been proved in [3] that a holographic description of extra-dimensional dynamics is equivalent to a semiclassical description of quantum behavior of elementary 4D fields, in agreement with AdS/CFT. In the holographic description the modes associated to the extra dimension turns out to describe quantum excitations (virtual particles), see AdS/QCD. For instance, the assumption of a flat extra dimension corresponds to quantize semiclassically a free field with mass equal to the fundamental Kaluza-Klein mass. Vice versa, quantum dynamics create a fictitious extra dimension called virtual extra dimension. This explains other mathematical beauties of extra dimensional theories.

[3] http://arxiv.org/abs/1110.0316

eureka
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    Dear eureka: Is arXiv:1110.0316 your own work? For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself. – Qmechanic Aug 13 '13 at 16:06
  • @Qmechanic: It seems to be. I had flagged this because the [3] looked suspicious (who starts counting with 3?) and this seems to be, as you said, talking about one's own work as if it's something that is well-established. – Abhimanyu Pallavi Sudhir Aug 14 '13 at 16:18