Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory.
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There is lots of mathematical evidence that every quantum state maps 1-to-1 on a physical state¹, or at least be uniquely determined by the physical state². The main assumption both make is that there is some physical state.
So it doesn't really matter if it's a map or not - it tells you something about the territory.
[1] The completeness of quantum theory for predicting measurement outcomes, https://arxiv.org/abs/1208.4123
[2] On the reality of the quantum state, https://arxiv.org/abs/1111.3328v3
Thanks for the link![1] I should have been more precise.
What is settled science is that the collapse of the wave function happens due to different causes for different observers. Example: Take two detectors A and B and place an apparatus in the middle that emits two entangled photons in opposite directions. In the lab frame, both particles will reach the detectors at the same time, so that both detectors cause the collapse of psi simultaneously. In contrast to that, two observers moving to the left and right respectively will see one of the photons reach its respective detector before the other photon reaches his. Thus, for one observer it's detector A causing the…
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collapse (and B then only receives a disentangled photon) and for the second observer it's the other way around. Hence the causal chain of events is reversed (which is forbidden by special relativity).
Now, the problem here is obviously the collapse of the wave function itself (and the faster-than-light propagation of the disentanglement which, however, is widely accepted). Since we still don't know how the collapse actually works[2], it's likely (and I think assumed by most physicists nowadays) that the non-unitary(!) collapse should be replaced with a different mechanism. (Such as decoherence[3] but there are still a lot of questions remaining.)
So it is in this sense that I say that the wave function (in our formalism today) cannot be an actual part of reality because it only works until a collapse occurs. That doesn't mean, though, that the quantum states themselves (given by the wave function in intermediate times) can't correspond to reality. In fact, as I said myself, quantum uncertainty doesn't have anything to do with a lack of knowledge. That is, the view that quantum states merely represent statistical properties of an underlying state (which a priori might be part of a hidden variable theory) is wrong. While I think this was known before 2012, the PBR theorem gives a very general proof of that.
[1] The full article without pay wall can be found here: https://arxiv.org/abs/1111.3328v1
[2] https://en.m.wikipedia.org/wiki/Measurement_problem
[3] https://en.m.wikipedia.org/wiki/Quantum_decoherence
The original paper
http://arxiv.org/abs/1111.3328
was previously discussed on HN
https://news.ycombinator.com/item?id=3260445
and Matt Leifer's blog post
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-i...
is the best explanation out there of all this. The short answer is that the authors have ruled out an interpretation of quantum mechanics which very few experts believed in to begin with. Nevertheless, the tenability of that interpretation was previously unknown and this paper highlights exactly what is necessary for an epistemic interpretation of the wavefunction. That make this the most important result to come out of the quantum foundations field in a few years.
This article is about a new theorem that was uploaded to the preprint server earlier this week[1], and the article quotes several quantum theorists who describe this new result as important (or even ‘seismic’). On what basis do you think it’s been around for decades?
1. http://arxiv.org/abs/1111.3328
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
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