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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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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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