# the relation between entropy and probability at quantum levelu

by dhillonv10
Tags: entropy, levelu, probability, quantum, relation
 P: 83 Hi all, I have been reading some new stuff recently on the holographic principal and I have a question, I seem to understand that entropy and probability must have some relation to each other, I am not sure what exactly but it seems like they just do, can anyone please explain what it is? Now to continue that chain of thought, is the following scenario possible: The outer edges of the universe exist in 2 dimensions (AdS/CFT) and in the inside we feel 3 dimensions. Now because of this we have holographic noise which Carl Hogan wants to detect at the holometer. We know that our universe had to start with low entropy and there are several theories that pertain to that, but could it be that because of the holographic principal, entropy also emerged? I understand that my question sounds completely absurd but then again there are a lot of absurd things around :) Also if entropy emerged, could it be that probability also emerged from entropy in quantum systems? Thanks for your time.
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 P: 83 thanks for the link qsa, could you also possibly comment on the emergence of entropy? Thanks.
P: 739

## the relation between entropy and probability at quantum levelu

Quantum randomness is holographic noise caused by an entropic force. If that's the idea, then wow, not bad for a random crackpot idea. :-) I could lecture you about how entropy and probability are actually related, or about problems with the ideas of Erik Verlinde and Craig Hogan, but I just wanted to get the main idea into view first.
 P: 83 haha thanks mitchell, yes i couldn't say in proper words but you hit the bull's eye. I think that probability must have emerged from holographic noise and that if you take the universe as a system, at its boundaries (which always keep moving away) you will find no probability because that region has complete information. Inside that system however, because there is holographic noise, quantum systems have randomness. I have more on this idea so would you like to hear it? or perhaps explain how entropy and probability are actually related and problems with the ideas of Erik Verlinde and Craig Hogan? Thanks, Vikram
 P: 83 actually mitchell, i think the way i presented this idea and the way you understood it are a little different, can you please expand what you wrote in #4 a little more? it'll help me clarify somethings before we proceed. Thanks.
 P: 83 no that was not what i was thinking but the last few lines are exactly what i tried to say, I need a bit more time to look up the stuff you've mentioned before I can reply back with how this idea is evolving :) - V
 Sci Advisor P: 7,407 Without holography, there's conventional speculation about quantum mechanics and thermalization eg. http://arxiv.org/abs/1007.3957 , which also gives a nice overview of the literature in its introduction.
 P: 83 thanks for the link atyy. mitchell: if its okay with you, could we possibly move to a private conversation? perhaps PM? I wouldn't PM anyone without their permission, that's simply rude, if not than that's cool too, i'll just post here.
 P: 739 It can't be rude to PM someone; they can always ignore you! Anyway, PM me if you wish. I'll just add that I found some papers relating AdS/CFT to "stochastic quantization" (this paper, also its ref #1). That's the closest thing to a holographic explanation of quantum theory that I've seen.
 P: 83 Also I found another paper describing a lot of what I'll need http://arxiv.org/abs/1103.3427
 P: 83 mitchell, I send you a message in PM if you get time please reply back to that, also with the description of local interactions turning into non local ones, i think there's another way to approach the idea through the use of the paper i posted a link to, that paper describes the whole process in terms of PEPS and here's the abstract: In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models, like a deformed AKLT [1], an Ising-type [2], and Kitaev's toric code [3], both in finite ladders and infinite square lattices. In the latter case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary. Seems like someone else has already done a lot of the work required, now from what I understand of this, the paper proposes a method to relate interactions (at least entaglement) on the bulk to boundary. Although we need to generalize the following: - This method is proposed in lattice theory, does it really matter what framework is being used, our concern is holography. - The holographic framework being proposed, see how quantum randomness arises from that, going back to your original idea - Is entanglement enough as a type of interaction? Explore how to generalize to all types of interactions, for that the Hamiltonian would have to be modified. - Explore other implications.
 Sci Advisor P: 7,407 I think the holographic principle mentioned in the OP was AdS/CFT. However, there are other examples of holography, such as the above mentioned paper by Cirac et al. Some discussions of how the various types of holography may be related are found in Gukov et al's http://arxiv.org/abs/hep-th/0403225 and Swingle's http://arxiv.org/abs/0905.1317 .
P: 83
thank you very much for the link atty, after the comments by mitchell the idea that i put up in the OP has evolved, I am trying to focus on what was brought up:

 Could a purely local interaction in a classical boundary field theory turn into a nonlocal interaction in its holographic image? In that case, could you understand quantum randomness in the bulk theory as arising from the holographic transformation of a local interaction on the boundary?
 Sci Advisor P: 7,407 Isn't there a Euclidean-Euclidean version of AdS/CFT? In which case the boundary should have a Bohmian interpretation, shouldn't it? But of course this wouldn't be a derivation of QM, since it the Bohmian interpretation is QM.
P: 7,407
 Quote by mitchell porter However, in Arkani-Hamed's recent talks, he interprets their work as the discovery of a third framework, neither string theory (bulk) nor field theory (boundary), but something else outside space-time entirely (twistor space - perhaps it is as simple as that - twistors are the answer). And this is the framework where neither space-time locality nor quantum unitarity is "manifest", i.e. visible - you have to switch to the other perspectives to see them.
Couldn't one say also say that unitarity isn't manifest in the Lagrangian description, compared to the Hamiltonian one?

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