Guest Post: David Wallace on the Physicality of the Quantum State
The question of the day seems to be, “Is the wave function real/physical, or is it merely a way to calculate probabilities?” This issue plays a big role in Tom Banks’s guest post (he’s on the “useful but not real” side), and there is an interesting new paper by Pusey, Barrett, and Rudolph that claims to demonstrate that you can’t simply treat the quantum state as a probability calculator. I haven’t gone through the paper yet, but it’s getting positive reviews. I’m a “realist” myself, as I think the best definition of “real” is “plays a crucial role in a successful model of reality,” and the quantum wave function certainly qualifies.
To help understand the lay of the land, we’re very happy to host this guest post by David Wallace, a philosopher of science at Oxford. David has been one of the leaders in trying to make sense of the many-worlds interpretation of quantum mechanics, in particular the knotty problem of how to get the Born rule (“the wave function squared is the probability”) out of the this formalism. He was also a participant at our recent time conference, and the co-star of one of the videos I posted. He’s a very clear writer, and I think interested parties will get a lot out of reading this.
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Why the quantum state isn’t (straightforwardly) probabilistic
In quantum mechanics, we routinely talk about so-called “superposition states” – both at the microscopic level (“the state of the electron is a superposition of spin-up and spin-down”) and, at least in foundations of physics, at the macroscopic level (“the state of Schrodinger’s cat is a superposition of alive and dead”). Rather a large fraction of the “problem of measurement” is the problem of making sense of these superposition states, and there are basically two views. On the first (“state as physical”), the state of a physical system tells us what that system is actually, physically, like, and from that point of view, Schrodinger’s cat is seriously weird. What does it even mean to say that the cat is both alive and dead? And, if cats can be alive and dead at the same time, how come when we look at them we only see definitely-alive cats or definitely-dead cats? We can try to answer the second question by invoking some mysterious new dynamical process – a “collapse of the wave function” whereby the act of looking at half-alive, half-dead cats magically causes them to jump into alive-cat or dead-cat states – but a physical process which depends for its action on “observations”, “measurements”, even “consciousness”, doesn’t seem scientifically reputable. So people who accept the “state-as-physical” view are generally led either to try to make sense of quantum theory without collapses (that leads you to something like Everett’s many-worlds theory), or to modify or augment quantum theory so as to replace it with something scientifically less problematic.
On the second view, (“state as probability”), Schrodinger’s cat is totally unmysterious. When we say “the state of the cat is half alive, half dead”, on this view we just mean “it has a 50% probability of being alive and a 50% probability of being dead”. And the so-called collapse of the wavefunction just corresponds to us looking and finding out which it is. From this point of view, to say that the cat is in a superposition of alive and dead is no more mysterious than to say that Sean is 50% likely to be in his office and 50% likely to be at a conference.
Now, to be sure, probability is a bit philosophically mysterious. …
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