To be honest, I hate this sort of question. I don’t know what “real” means, and I always have a suspicion that the people advocating for one answer or another to this question don’t know either.
There’s a new preprint by Pusey, Barrett, and Rudolph that is being described as shedding light on this question. According to Nature News, “The wavefunction is a real physical object after all, say researchers.”
The debate over how to understand the wavefunction goes back to the 1920s. In the ‘Copenhagen interpretation’ pioneered by Danish physicist Niels Bohr, the wavefunction was considered a computational tool: it gave correct results when used to calculate the probability of particles having various properties, but physicists were encouraged not to look for a deeper explanation of what the wavefunction is.
Albert Einstein also favoured a statistical interpretation of the wavefunction, although he thought that there had to be some other as-yet-unknown underlying reality. But others, such as Austrian physicist Erwin Schrödinger, considered the wavefunction, at
least initially, to be a real physical object.
The Copenhagen interpretation later fell out of popularity, but the idea that the wavefunction reflects what we can know about the world, rather than physical reality, has come back into vogue in the past 15 years with the rise of quantum information theory, Valentini says.
Rudolph and his colleagues may put a stop to that trend. Their theorem effectively says that individual quantum systems must “know” exactly what state they have been prepared in, or the results of measurements on them would lead to results at odds with quantum mechanics. They declined to comment while their preprint is undergoing the journal-submission process, but say in their paper that their finding is similar to the notion that an individual coin being flipped in a biased way — for example, so that it comes up ‘heads’ six out of ten times — has the intrinsic, physical property of being biased, in contrast to the idea that the bias is simply a statistical property of many coin-flip outcomes.
As far as I can tell, the result in this paper looks technically correct, but it’s important not to read too much into it. In particular, this paper has precisely nothing to say, as far as I can tell, on the subject known as the “interpretation of quantum mechanics.”
When people argue about different interpretations of quantum mechanics, they generally agree about the actual physical content of the theory (specifically about what the theory predicts will happen in any given situation) but disagree about what the predictions mean. In particular, the wavefunction-is-real camp and the wavefunction-isn’t-real camp would do the exact same calculations, and get the exact same results, for any specific experimental setup.
This paper considers a class of theories that are physically distinct from quantum mechanics — to be specific, a certain class of “hidden-variables theories,” although not the ones that were considered in most earlier hidden-variables work — and shows that they lead to predictions that are different from quantum mechanics. Therefore, we can in principle tell by experiment whether these alternative theories are right.
This is a nice result, but it seems to me much more modest than you’d think from the Nature description. I don’t think that people in the wavefunction-isn’t-real camp believe that one of these hidden-variables theories is correct, and therefore I don’t see how this argument can convince anyone that the wavefunction is real.
I admit that I’m not up-to-date on the current literature in the foundations of quantum mechanics, but I don’t know of anyone who was advocating in favor of the particular class of theories being described in this paper, and so to me the paper has the feel of a straw-man argument.
Personally, to the limited extent that I think the question is meaningful, I think that the wavefunction is real (in the ontological sense — mathematically, everyone knows it’s complex, not real!). But this preprint doesn’t seem to me to add significantly to the weight of evidence in favor of that position.