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John Baez: Things that Really Really Exist

Michael Weiss wrote:
By the way, a mighty battle has been raging over on sci.physics over whether Photons Really Exist.
I'll join in as soon as I figure out the difference beween things that Exist and things that Really Exist -- not to mention those that Really Really Exist.
Throwing out 98.462% of this, I realize that I have but the vaguest conception of the sense in which Photons Really Exist according to QED. They can't be localized (if I understand Haag's comments about the Newton-Wigner wavefunction), they don't have identity -- you can't say the photon absorbed by Nick Nitrogen over here is The Same Photon as was emitted a nano ago by Harry Hydrogen over there (do I have that right?) -- a fine excuse for a particle!
If photons seem a bit dodgy, it's because:

1) They are bosons, so they are gregarious and like to travel in packs where you can't tell which one is to blame for anything.

2) They are massless, so it's hard to tell where the hell they are, more so than for your average particle.

Remember how a while back I showed how you could rewrite the Klein-Gordon equation as a first-order differential equation, which boiled down to Schrödinger's equation in the nonrelativistic limit? [No, but I'm sure we'll get to it eventually.  --ed.]  You need to pull this trick to get a nice ``position operator'' for a particle in relativistic quantum mechanics, analogous to the good old position operator for nonrelativistic quantum mechanics. It's called ``Newton-Wigner localization''. It doesn't work well for massless particles -- which shouldn't be utterly surprising, since is no such thing as a nonrelativistic massless particle.

3) They carry no conserved charge, so it's easy to create or destroy a bunch of the rascals with the flick of a switch.

How unlike you and I, who Really Really Exist -- at least according to ourselves! We are made of charged massive fermions. The Pauli exclusion principle makes us individualistic: we can't both be in the same place at the same time. Our massiveness makes us easier to localize, and we don't have to be running around at the speed of light all day. Finally, conservation of baryon and lepton number makes it hard to create or destroy us -- or at least our underlying atoms. We naturally look with disdain on massless uncharged bosons.

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Michael Weiss