July 09, 2004

Thinking About Physics (Part 2)

This time I'll address the other topic in physics I've been thinking about lately, brought up in the comments of this post by Sean Carroll. The issue is "wave-function collapse." This is another case where I think that R. Newton in his book Thinking About Physics is mostly right, so if my account is insufficient, take a look there.

The question at hand is whether there exists a nonunitary "wave-function collapse" in quantum mechanics. As Aaron Bergman points out in the comments over at Preposterous Universe, this is an experimental question. That's an important point, and it's worth noting (as he does) that Penrose has interesting ideas relating wave-function collapse to quantum gravity. The details are a bit fuzzy for me as I've only heard about this idea once, in Penrose's colloquium at Chicago three and a half years ago, back when my knowledge of quantum theory was limited and wave-function collapse seemed orthodox and reasonable to me.

Since then, my thoughts on the matter have changed. Quantum mechanics -- and quantum field theory, its special relativistic extension -- seem to be complete theories, describing our world within the accuracy of any experiment we can do. The simplest reasonable way to interpret this is that we live in a quantum world. Any experiment we do, any object we perceive, no matter how classical it seems to our senses (which, after all, evolved to deal with a world of low energies and macroscopic objects, a world in which classical physics is good enough), is fundamentally quantum in nature.

I think that the difficulties arising in "interpreting" quantum mechanics, and in trying to understand "the measurement problem," largely arise from trying to couple a classical perspective with quantum reality. The idea of wave-function collapse is that, when a measurement is performed, a quantum state that is in a superposition of various eigenstates will be projected onto one eigenstate, chosen according to a probability given by this state's overlap with the original state. This "wave-function collapse" is nondeterministic and corresponds to nonunitary evolution. This perspective fits with the idea of being able to do a classical measurement and extract a single number from a state.

In reality, all states are quantum, and any measurement we can do is inherently quantum. For instance, consider an overly simplistic setup, but one that hopefully will illustrate the issues involved. Electrons have a spin; its z-component has two eigenstates, +1/2 and -1/2 (call them "up" and "down"). If we have a beam of electrons, we can do a Stern-Gerlach type experiment in which an inhomogeneous magnetic field splits them into two beams, one spin up and one spin down. We can then observe these beams.

What's happening here, from my point of view, is entirely described by QED. The inhomogeneous magnetic field is given by some configuration of the quantum electromagnetic field; the electron beam is interacting with (virtual) photons according to the rules of QED. Naively supposing we simply "see" the two beams that result, what we see are photons scattered off the beams. Again, this is electrons interacting with photons, according to QED. I see no reason to suppose anything nonunitary happens here. Instead we just have various quantum fields, interacting according to well-defined rules. Measurements are, in some sense, just scattering processes. Everything is unitary. I don't deny that, at the end, electrons will appear to have collapsed to eigenstates. But I see no reason to suppose that this happens with spooky physics going beyond ordinary quantum theory.

I think this is just a straightforward application of Ockham's razor; there's no need to assume that wave-functions collapse unless that gives us extra explanatory power. In Penrose's framework, it might, so it's worth pursuing this as an experimental question. But without further evidence, why not just assume quantum mechanics is completely unitary?

It's worth noting that, in this case, quantum mechanics is also deterministic. (As Newton emphasizes in his book.) Probabilities only arise in trying to understand complicated quantum states in terms of individual classical numbers of the sort we understand. Newton further argues that a lot of what people see as weirdness in quantum mechanics arises from thinking in terms of particles rather than quantum fields, an idea that I had been mulling over for a while, but that he probably argues more clearly than I could.

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