Photon flight times and the uncertainty principle

[kurros]

Ok I feel a bit silly asking about this, but I have gotten myself confused and need some help sorting something out. In QFT the operators of observable quantities commute over space-like intervals, so we cannot propagate effects faster than light, causality is safe, cool.
But I have somewhat convinced myself that it is perfectly ok for a single particle emitted at one place to be detected elsewhere after less than the required L/c time period. Right? Because Feynman propagators are non-zero outside the lightcone? Not to mention that the wavepacket of a photon is spread over space, which means that the flight times of a series of identical photons should follow some -probably gaussian-like- distrubution with a mean of L/c? (even in the absence of all equipment-related uncertainties)

Or have I just misled myself here?

Perhaps there is also some interesting interpretation of such an effect, something like you aren't really measuring the 'same' photon, it is just the there is some non-zero probability that the photon field will fluctuate in just the right way so that a photon pops out of the vacuum at just the right time to make it look like your original one went a little faster than c (or slower an equal amount of the time of course)?

 

[Jacques_L]

But I have somewhat convinced myself that it is perfectly ok for a single particle emitted at one place to be detected elsewhere after less than the required L/c time period. Right?

No.
And you have no ways to put this question experimentally.
Experimentally, you are tight by delays in the emitting and detecting apparatus, which ruin your ambitions.
Just beaches on the mountains...

 

[kurros]

I am not sure I understand your claim that this cannot be experimentally investigated. People do lots of photon flight time experiments, one just needs to get long enough flight path in order to measure small variations. If you are talking about fundamental restrictions due to uncertainty principle difficulties in measuring exactly when a photon is emitted or absorbed then I am interested to hear more, because it is this kind of argument that let me to imagine that because we probably can't help but know something about a photon's wavelength, we then cannot ever measure it's position perfectly, and thus there is always an uncertainty in it's flight time, which fundamentally -or so it seems to me- means that flight times cannot perfectly be c always.

Perhaps it is just that one cannot draw from this argument the conclusion that photons "really do" travel faster than c sometimes, it is just that we can't tell their flight time to better than a given accuracy.

 

[Drakkith]

Due to the uncertainty principle, you wouldn't be able to tell if the delay was because the photon's speed was less than c, because it was emitted slightly after you thought it was, or because of some random interaction with a stray molecule. The measured value of c is extremely tight, and not just through experiments. I believe it is possible to derive c using math as well. If it wasn't VERY VERY VERY close to what we say it is we would have known by now.