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This is a reformulation of two previous questions that seem to have been misunderstood, or most likely, I failed to make them clear. I thank all people that answered, even the belligerent ones.

Some terminology first: by classical I mean non-quantum, and I assume anybody trying to answer this questions do understand that difference. When we discuss if QM can be written in classical terms we mean a full description in terms of at least local hidden variables. Also by theory I mean what anybody means as a theory: some equations or computer algorithms written in paper, or anything equivalent to a formal system. I also assume we all know what is the difference between a theory (a simulation is also a special kind of theory) and the actual physical world.

For those unfamiliar with the violent discussions on this subject you can read this question, and this review article. Also a good popular science article with lots of references to the experimental results on oil droplets can be found here.

The question is pretty simple. The experiment on oil droplets show that what thought as a culprit of QM, the double slit interference experiment, could never be explained in classical terms. The oil droplets experiments showed that to be incorrect. Now the argument has moved to the statement that oil droplets will never be able to reproduce entanglement. Thus, entanglement is the new actual territory when we battle quantum vs. classical.

My question is not about oil droplets though. I take them as an example of a classical system that can reproduce behaviors that were previously thought to be exclusive of quantum systems.

My question is about another toy model, rule 110 cellular automata (CA). It is Turing universal thus it can simulate the behavior of any digital computer. The question is simple: digital computers can simulate entanglement and so can the 110 CA. Thus we have at least a toy model that has local rule hidden variables and reproduce entanglement.

Specific question: given this fact, what is wrong in claiming that entanglement could also be a classical phenomenon?

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  • $\begingroup$ And do you read my answer to your first or second question? $\endgroup$
    – HolgerFiedler
    Commented May 14, 2015 at 14:01
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    $\begingroup$ I heavily suspect your definition of "quantum" and "non-quantum/classical" is very different from mine, because my answer would be exactly this again. That we can simulate QM (in the sense of getting numerical predictions) with "classical" machines is not surprising - QM, after all, does not require in and of itself nastier math than classical mechanics. Perhaps I'm also misunderstanding what you mean by "simulating". $\endgroup$
    – ACuriousMind ♦
    Commented May 14, 2015 at 14:14
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    $\begingroup$ It seems to me you are having a hard time taking "no" for an answer. Why ask, then? $\endgroup$
    – CuriousOne
    Commented May 14, 2015 at 20:44
  • $\begingroup$ "given this fact, what is wrong in claiming that entanglement could also be classical phenomena?" - that "hidden variables" approaches can be ruled out as the cause / mechanism of entanglement? Bell's theorem - "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics." $\endgroup$
    – Xeren Narcy
    Commented May 14, 2015 at 23:25
  • $\begingroup$ There are simulations of almost-entanglement. I have my own ones. Even if these solutions are wrong, their results are interesting. $\endgroup$
    – user46925
    Commented Jun 8, 2015 at 19:05

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It seems that you're confusing, perhaps rightfully, the difference between exhibiting entangled behavior and describing entangled behavior. It's no surprise that a classical system can describe entanglement. As you point out, a digital computer can simulate an entagled system.

However, there is no meaningful entanglement happening in the computing process; it's just a classical Turing machine. I would suggest that the computer is describing an entangled behavior (given the right lens through which to process the data it produces), but it isn't exhibiting it on a level-0 physical hardware kind of way. I emphasize that it takes a certain post-processing by an observer for the computer to meaningfully be "describing" entanglement. Only a rational agent, equipped with an understanding of how to interpret the computer's output, can say "ah---there is entanglement".

A simpler example is pencil and paper. Given the right kind of observer who knows what to look for and how to interpret the output, simply writing down the Schrodinger equation seems to display entanglement if you know how to decode the "data". Perhaps a good metric here is to consider an alien species with no knowledge of our alphabet and perhaps a wildly different set of sensory organs. Such a species could look at two entangled particles and say "yes, that is entanglement", but if they look at our graphite-scribbled paper or at the weird glyphs being printed out by a computer program, they would be totally meaningless. Therefore, it seems that your assertion that entanglement "is" a classical phenomenon is a confusion between a real physical process and our understanding of it; the latter can of course be described classically, but the former is truly quantum.

As a side note, you may appreciate a chapter in David Deutsch's book "The Fabric of Reality"; I can't remember which chapter it is, but he describes "virtual reality generators", i.e. simulations, and even uses the idea to assert certain physical boundaries on reality.

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  • $\begingroup$ Thanks Daniel, but what you describe about between the difference between a description and the actual world, is not valid for every theory? I know that the simulation of a fluid in a computer is not "wet", nor the Navier-Stokes equations written on pencil. What I am talking about is if there can be a theory that "displays" a simulated behavior and the question is if the theory can be classical. $\endgroup$
    – user66432
    Commented May 14, 2015 at 14:06
  • $\begingroup$ I didn't really understand parts of what you were asking, so I apologize if I answered the wrong question. But it seemed that at the end of your question, you presented a toy model (the 110 CA) which you claimed was classical (it has "local hidden variables"; it is obviously classical since it can be simulated on a classical Turing machine) but also can "reproduce entanglement" (via simulation). Therefore, I thought you asserted, it seems that we have an example of a classical system with entanglement, so is entanglement classical? I meant to refute your example with my answer. $\endgroup$
    – danielsmw
    Commented May 14, 2015 at 14:42
  • $\begingroup$ Which is to say that I didn't try to generally refute the idea that you can have classical entanglement, I only meant to show that your proposed toy model doesn't satisfactorily exhibit entanglement in a meaningful way, for reasons I described in my answer. $\endgroup$
    – danielsmw
    Commented May 14, 2015 at 14:43
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When we discuss if QM can be written in classical terms we mean a full description in terms of at least local hidden variables.

I can create a simulation of quantum mechanics on a classical computer, but I can't make it correctly simulate entanglement using only local data AKA local hidden variables.

That is, if I want to simulate an EPR measurement on an entangled particle at point $(x_0,t_0)$, I must use simulation data from outside the light cone region $|x - x_0| < c(t - t_0)$. Specifically I'll have to use some information from the other EPR particle at coordinates $(x_1, t_1)$ outside the lightcone from $(x_0,t_0)$, meaning $|x_1 - x_0| > c(t_1 - t_0)$.

A simulation can use this non-local data to produce correct results, but there is no local data it can track in order to reproduce real EPR correlations.

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