A thought that is not at all original

[mmcirvin]

bram was just talking about somebody's ideas concerning the need to de-emphasize states in a relativistic treatment of quantum mechanics. This reminds me of something that many people who work in quantum field theory have surely understood for years, and were in fact trying to tell me, but that I never really got until I was well out of graduate school. Namely, that the bogus classical sources that we plug into quantum field theories in order to formally derive n-point correlation functions are actually the true relativistic counterpart of the notional "classical measuring devices" of nonrelativistic quantum mechanics.

These calculations are usually done by figuring the amplitude for the field to evolve from vacuum in the distant past to vacuum in the distant future, while tickled by the presence of unspecified processes outside of our calculation that can create and absorb particles (or more complex field excitations). Those vacuums in the past and future aren't particularly important. No longer do we imagine setting up the quantum state by some unspecified process at time t₁ and measuring it by some other unspecified process at time t₂. Our unspecified set-up/measuring processes can occur anywhere in space and time; they can be sharply localized or spread out over spacetime; and some of them could even be interpretable as set-up in some reference frames and measurement in others, and in fact these are the very situations that result in weird-ass EPR correlations. This is how, at least in principle, we can think about moving beyond scattering-theory problems.

So you're therefore really better off thinking of problems in relativistic quantum theory as just dealing with vacuum at positive and negative infinity, and abandoning the Schrödinger picture of an evolving state at a given point in time. Who cares about a given point in time? It's just an arbitrary slicing of spacetime anyway.

When I was studying QFT in grad school, I kept wondering when we would get away from these ridiculous classical sources that were obviously just pretend, and start looking the quantum world full in the face. I might have well have demanded that Bohr and Heisenberg stop talking about measurements and uncertainties and tell me what is really going on.

Comments

[darkphonics.livejournal.com]

"People not interested in reading arcane thoughts about relativistic quantum theory can skip this."

Really, Matt...who *isn't* interested in such things? Why, just the other day I was at the grocery store purchasing some essentials and when I asked the cashier how she was doing, she replied in a melancholy voice "I'm fine, though I'd much rather be reading arcane thoughts about relativistic quantum theory than bagging people's groceries." We shared a rich belly laugh and a tender moment that only fellow lovers of quantum theory can share and parted ways, reassured that we weren't alone in the world.

So, how's the new job?