-Comment on recent preprint by Pusey, Barrett and Rudolph.
A quantum system is said to have a state, also known as a wavefunction. The minimal interpretation of the state is that it encodes our knowledge about measurement outcomes. But many of us want to be able to think about some out-there reality. In particular, I would personally want to be able to visualize what happens in-between quantum measurements before I can say I feel I 'understand' quantum theory. I want what Schroedinger called 'Anschaulichkeit', which by my limited understanding of German combines the notions of visualizable and comprehensible into one word.聽
Different proposals for how to think of the wavefunction (called PSI) were labelled in a paper by Harrigan and Spekkens as either PSI-epistemic or PSI-ontic. The former means one thinks of the wavefunction as representing our knowledge about something (e.g. measurement outcomes, or a hidden variable that determines probabilities of measurement outcomes), and the latter that it is a real out-there object. The PSI-ontic approach, as exemplified by Bohmian mechanics (see, for instance, "The Emperor's New Swindle" for more on Bohmian mechanics) where the wavefunction plays the role of guiding classical particles around, does offer Anschaulichkeit. PSI-epistemic approaches seem to leave open the possibility of some tantalizing underlying reality which we have limited knowledge about, but which could if identified provide Anschaulichkeit. 聽
In a recent pre-print three researchers claim to disprove the possibility of PSI-epistemic interpretations, or, if one reads their claims more carefully, that an underlying hidden variable type of reality is impossible. The pre-print of Pusey, Barrett (and FQXi member, whose research on time and quantum mechanics is profiled here) and Rudolph was given extraordinary attention in an article in Nature, last month, and has since been the subject of many blog posts (including posts by FQXi members Matt Leifer and Scott Aaronson that are worth reading). The Nature article was so positive that it risks inducing a back-lash, and I think it should be noted that the authors (two of whom I see weekly) declined to be interviewed as the policy of some journals is to disallow papers that have been discussed in the media before publication. Thus any ire, whether of the jealous or righteous type, should not be directed at the authors. Perhaps with the exception that the title of their paper, 'the quantum state cannot be interpreted statistically,' could have been more specific.
Let me try to summarise their argument. They suppose a particular kind of PSI-epistemic model is possible and then show a contradiction with quantum statistics. The kind of model they consider is essentially a hidden-variable one. The idea is that at the time of preparation of a quantum system one also sets the value of some hidden variable q. This is *not* assumed to be local as far as I can tell. Here q is assumed to determine the probabilities of different outcomes. But, also for the sake of argument, q is assumed not to uniquely determine the quantum state, i.e. the same value of q can be associated with the preparation of several different quantum states.聽
To show a contradiction with quantum statistics, they consider a setting where the same value of q is associated with four possible states (state 1, state 2, state 3 and state 4), i.e. there is some non-zero probability that that particular value of q, call it qx, is prepared for each of the four states under consideration. A measurement is then considered. It has four outcomes. They design the measurement such that if state 1 is prepared outcome 1 never happens, if state 2 is prepared outcome 2 never happens and so on. This now gives a contradiction with the idea that qx can be realised for all four states as well as determine the measurement probabilities. This is because for q=qx we would have to have the probability of outcome 1,2,3 and 4 all being zero, yet one of them must always happen!
So the argument, modulo potential subtleties like hidden assumptions, puts another nail in the coffin for hidden variable theories, adding to the contributions by Bell and others. As it is quite clean and does not appear to assume the hidden variable is local, one can imagine it turning up in text-books at some point.聽
I view it as consolidating existing paradigms rather than forcing a significant rethinking. To get the reaction from someone who is strongly associated with PSI-epistemic interpretations, I also聽emailed Chris Fuchs. He is a key defender of the idea of the quantum state representing our knowledge of something, and in talks he frequently writes the wavefunction on a piece of paper and puts it on his head to emphasize this point! Chris Fuchs says that although he likes the result it was quite clear from previous results that the hidden variable approach would not work, and "...there has been a particularly thriving community of researchers the last few years trying to argue that nonetheless---i.e., even without hidden variables---quantum states should be given a statistical or epistemic interpretation, and that one achieves the greatest clarity of what quantum theory is about by doing so.聽For those non-hidden-variable epistemicists, the theorem makes no difference (i.e., it knocked down a straw man)."聽聽
In any case many interested in foundations will agree that the paper reinvigorates a fundamental debate and deserves attention. A very interesting paper by Colbeck and Renner has just appeared (arXiv:1111.6597v1) apparently deriving a very similar result from even more minimal assumptions, and I know that at least one more related paper will appear on the arXiv soon. My personal inclination remains to not think of the wave-function as a real object. It appears to me that Bohmian mechanics (as well as many-worlds) go wrong by taking the theoretical description as their starting point as opposed to the experimental phenomena. I guess this is the reason these interpretations tend to be associated with theorists while experimentalists, who never see wavefunctions apart from in calculations, often opt for the Copenhagen approach. (I also don't see how one can reconcile the wavefunction and its collapse being real with the relativity of simultaneity but that is another discussion). But whilst I criticize aspects of these ideas I am also very sympathetic to anyone trying to come up with a good way of thinking about quantum effects. The new no-go theorem of Pusey et. al. can help to guide such efforts.