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In a recent publication, Experimentally Faking the Violation of Bell’s Inequalities (Gerhardt 2011) (arXiv version), the statistics of quantum mechanics is faked using classical light sources. But if it is possible for physicists to fake an experiment to imitate QM, how can we be sure that nature doesn't do the same trick on us? Can it be that QM is a fake, and in the end QM turns out to be an artifact of our imperfect measurement devices?

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I am not going to post it as a full answer because I think that this question is a provocation to punish those who dare to consider quantum mechanics as a fact by those who have irrational reasons to dislike it. However, when one insists on locality (slower-than-light propagation of signals), and locality follows both from the field-theory nature of low-energy physics as well as special relativity, then the quantum EPR correlations simply can't be "faked". That was exactly why Einstein invented EPR to protest QM in the first place. One may only fake it by violating other rules of the game too. – Luboš Motl Nov 16 '11 at 6:49
So one may do many tricks just like David Copperfield but physics is not about tricks and "faking" things: physics is about the search for theories that agree with all the observations. There exists no non-quantum theory that would agree with the observations of elementary particles, including their wave-like properties and their respect for the Lorentz invariance. So "faking" papers are on par with various other papers trying to create "illusions" that something is moving faster than light, and so on, and so on. They're just illusions and we know how they differ from the real world. – Luboš Motl Nov 16 '11 at 6:52
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youtube.com/watch?v=P6MOnehCOUw – Georg Nov 16 '11 at 10:26
I am fairly sure that in the recent neutrino experiment, Nature is indeed faking faster-than-light travel, but I also believe that it's not going to stand up to as many replications of the experiment as quantum mechanics has. – Peter Shor Nov 17 '11 at 17:10

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I'm not sure it makes sense to ask if Nature is "imitating" Quantum Mechanics.

Quantum mechanics is a mathematical model that gives predictions that are in excellent, well so far perfect, agreement with what we actually see.

I guess the question is whether QM is just a good approximation to the real world or whether it's an exact description of the real world. We'll never be able to prove it's an exact description, but someday someone may find an experiment where QM gives the wrong answers. If so this would prove it's just an excellent approximation.

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I think this is spot on. There is no and never will be a way to test if Nature is faking it or not. The same is true if you would ask if God or anything like that just wants us to believe that QM works. Important is that QM makes testable predictions that have repeatedly been shown as correct. – Alexander Nov 17 '11 at 12:59
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I think this is a little pessimistic--- you can be sure in a scientific sense even when you are not absolutely sure in a philosophical sense, the same way you are sure of the big-bang or of the existence of the planent Neptune. If you have a classical model down beneath, faking quantum mechanics, it should obey some reasonable limits on classical computation. If the classical computation is reproducing quantum mechanics just by being enormously huge (as it is for example in DeBroglie Bohm quantum mechanics), then it might as well be quantum mechanics from a physics point of view. – Ron Maimon Nov 17 '11 at 16:22
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Can you fake Shor's factorization algorithm for a many digit product of two large primes on a quantum computer on a classical computer without noticeable slowdowns?

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Until now I believe the biggest number factorized by a quantum computer was of the order of 10. I believe every classical computer can easily do that without noticeable slowdown... – asmaier Nov 15 '11 at 21:32
Factoring is not known to be NP-Complete (and is, in fact, in the intersection of NP and co-NP) nor is it known whether BPP is equal to BQP so this answer might very well be "yes". – user834 Nov 15 '11 at 21:34
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Good answer, @Kelr, +1. The comments beneath it are implausible. Asmaier: Shor's algorithm would clearly work for high numbers to be practical; it hasn't been realized because of technological, not physical, limitations. The simple reason is that we have tested the same laws in other systems. User834: Kelr's question asks whether you (or Asmaier) can fake it so the answer is certainly No. But even if someone in the future could factorize large numbers classically, it would still not classify as faking of a quantum computer. So the answer to Kelr's question is No: it is really a rhetorical one. – Luboš Motl Nov 15 '11 at 22:11
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@user834: Even if there were a factoring algorithm which is classical, it would have to be relatively simple for nature to use. The Zurek algorithm or Grover's algorithm clearly require nonclassical resources, although there the growth isn't exponential. – Ron Maimon Nov 15 '11 at 22:29
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Kelr, though you're making a good point, this doesn't really answer the question... – David Zaslavsky♦ Nov 16 '11 at 6:39
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We can't be 100% sure that quantum mechanics is exact until we are able to do a quantum computation in a real system that would be impossible to perform on a classical computer roughly of size the universe. This looks like it is possible, there is no indication that quantum mechanics is only approximate, and there is no known classical theory which limits to quantum mechanics for small systems, but becomes something else for large ones.

But our tests of quantum mechanics are limited to a certain extent by our ability to compute predictions of the theory. By definition, we cannot predict the behavior of a quantum mechanical system which takes exponential resources, because the computation is too big. We must resort to approximations which might disguise a failure of the theory. So while it is unlikely, it is possible that nature is not fundamentally quantum mechanical, and that we just have not seen the breakdown of QM yet.

This type of statement is predictive--- it requires that a quantum computer will have mysterious unaccounted for sources of decoherence which are not due to known interactions, but which are fundamentally due to the breakdown of quantum mechanics. If a quantum computer is built which can regularly factor 100,000 digit numbers, this is good enough to establish that our universe is not classical down below, because such a feat would require too big a classical computer to realistically implement inside our universe, were it classical.

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I don't think your first sentence holds up logically. Even if we were able to do a quantum computation in a real system that is impossible to perform on a classical computer roughly the size of the universe, how do we know that there's not a part of the universe invisible to us that is contributing to the computation? Also, how could the entire universe be contributing to a computation that is taking place in a small room on Earth? – Peter Shor Nov 17 '11 at 14:44
@Peter Shor: I am not speaking as a philosopher, but as a physicist. I agree that it is logically possible that the universe is being simulated on an enormous computer, but this would not be physical. The reason for allowing the whole universe to contribute is the holographic principle--- the room is spread out over a cosmological horizon, and in principle some fraction of the whole horizon could be contributing to the process. Any more bits than what can fit on the cosmological horizon is physically impossible. BTW, this argument is due to t'Hooft, not me personally. – Ron Maimon Nov 17 '11 at 14:48
I would personally be convinced by factoring 1000 digit numbers, or even a few hundred. It is very implausible to get such an exponential speed up in any imaginable "beable" model even spread out nonlocally on the cosmological horizon. But Grover's algorithm, or any other square-root type speedup, could be imaginably fake for essentially any system size (although it likely isn't--- I tend to believe QM is exact--- it just would be nice to be sure). – Ron Maimon Nov 17 '11 at 15:05
Good point about the cosmological horizon. But if the universe is expending all its computing power on this little room on earth with a quantum computer that's factoring a large number, where is it getting the computing power to power the quantum computers being used by alien civilizations (let alone processing ordinary physics)? – Peter Shor Nov 17 '11 at 15:26
@Peter Shor: sure, this is implausible. This is why small numbers are already enough to convince me. But I imagine that if you can factor 1000 digit numbers, there is no harm in going to 100,000, just to convince the die-hard skeptics. – Ron Maimon Nov 17 '11 at 16:00
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