De-temporalizing the measurement process

[mmcirvin]

My previous post about what relativistic quantum field theory suggests about measurement is worth elaborating a little bit. Elementary treatments of the "measurement problem" in quantum mechanics, particularly the ones out to insist that there is a serious problem in the foundations of QM itself (I am thinking particularly of Roger Penrose), often say something like this: "We have two kinds of process in quantum mechanics. There's a smooth, continuous process represented by a linear unitary operator that makes the wavefunction evolve; that's pretty well-characterized. Then, there is this other process that John von Neumann represented with a projection operator, that happens when you measure something: the wavefunction collapses, the state vector is reduced, or whatever you want to call it, into an eigenstate of the thing you measured. This happens instantaneously throughout all space [edit: originally said "space and time" here—I was getting ahead of myself], and nobody understands, dynamically, how that works."

Sometimes it's argued that this mysterious collapse process is associated with human consciousness (a point of view riffed on by countless science-fiction authors, including me).

Then, it's a bit baffling that things seem to work out so that you can't precisely tell what kinds of events cause the collapse: you can do quantum-eraser experiments to show that this or that kind of event doesn't cause it, but those are delicate and limited experiments that don't end up saying a whole lot about people and laboratory equipment and half-dead cats. The magical collapse process always seems to be hidden behind a curtain of complexity and irreversibility: you can construct elaborate arguments about decoherence and density matrices that illustrate that, for anything you typically measure, it doesn't matter precisely when it happens.

Now, I've always suspected for these reasons and others that this whole view of wavefunction collapse as a dynamical process is wrong-headed. I wrote a summary of what I think a while ago.

Notice, though, that in that essay I'm still using this very nonrelativistic-QM formalism in which measurement is something that happens at a certain time. The wavefunction collapse is really just a transition between choices of model for the system under study: once the system becomes entangled with the measuring apparatus, it becomes very difficult to model the whole world including the apparatus that is actually superposed, so we back off to speaking of the system under study as having chosen an eigenstate, as a more approximate model. And it's possible to show that only the Born rule does this in a self-consistent way, and so on.

I think that a major stumbling block to my understanding of quantum field theory, way back in the early nineties, was that, even though I didn't really believe in a dynamical wavefunction collapse, I was stuck on the notion that it was convenient to represent measurements that way. So I kept waiting for the moment when Prof. Coleman would bring the initial and final states in from temporal infinity and start talking seriously about finite-time evolution. But the measurements weren't properly represented by initial and final states at all; they were represented by the "classical sources" that he had added artificially to the field Lagrangian. And the introduction of the measuring apparatus into the system was no longer associated with an abrupt state transition at all, since our transition amplitudes were always measured from t=minus infinity to plus infinity.

(In practice this kind of thinking is applied to scattering theory, in which the states of interest really are enormously before and after the events we are interested in. So there's this derisory thing you hear sometimes, that "in relativistic quantum mechanics we only know how to do scattering theory". That's true to some extent; the math of scattering theory is worked out better than everything else, in part because those are the experiments that scientists can do in high-energy physics. But there's nothing in the basic formalism of sources in Lagrangians that limits us to scattering theory. I used to have this uncomfortable feeling that, whenever somebody calculated something other than a scattering-theory result in QFT, they did it by translating it awkwardly into a scattering-theory problem. But it was because I was paying too much attention to the initial and final states.)

Here's the important thing about this formalism: it makes it particularly clear that what Wheeler called "the distinction between the probe and the probed" (your joke goes here) is completely physically arbitrary. What was a sharp break between the pre-measurement and post-measurement quantum worlds at the moment of measurement becomes smoothly absorbed into that distinction as the classical sources create and destroy quanta. Nobody really believes that real-world field equations have sources with hard-coded time evolution hard-wired into them. That's just the boundary at which we decided to stop modeling the apparatus in detail. We can even acknowledge this without abandoning the idea that the amplitude we end up calculating is the basis for a probability.

Hi, bram. I can probably put messages intended solely for you down here.

Comments

[bram.livejournal.com]

Ha, that last line was great!!

Although if I ever ween pbrane away from that K-theory obsession of his...

As I've said, I'm rusty of QFT, and almost everything I've read on the measurement problem has been about nonrelativistic QM. I'll read that link you provided and think about this some more!

Is the map the terrain?

[venividi.livejournal.com]

It strikes me, especially after reading Hawking & Penrose "The Nature of Space and Time", that Bohr should be shot with a quantum gun for the Copenhagen interpretation and all the confusion that follows. I would guess that the unreasonable effectiveness of mathematics in physics has been too much for too many for too long.

Re: Is the map the terrain?

[mmcirvin.livejournal.com]

Actually when Bohr talked about Copenhagen, my impression was that he was a lot cleverer and more subtle about it than most of the people who came after. He certainly didn't have this literalistic picture in which the wavefunction at time t is the only reality and observation makes it collapse through some unspecified physical process-- that was more von Neumann and Wigner-- but it later became thought of as "the Copenhagen interpretation".

Sort of like the way Everett's subtle musings on macroscopic superposition and "relative state" got popularized as the somewhat cruder many-worlds interpretation writings of DeWitt, etc., which tried to do things like count the rate at which worlds were spawning off; and then that was further bastardized by popular accounts that give the impression that it just replaces the mysterious "wavefunction collapse" with an equally mysterious cosmological process that spawns off new space-time continua whenever somebody observes something.