Question about photon experiments

[gonzo]

I posted this in reply to another topic in the relativity forum, but I realized this might be better as its own thread here in QP forum.

I have some questions on photons being able to go faster than c.

I just finished reading QED by Feynman (great book). One of the things he talks about is that when using QM pobability amplitudes to predict results you have to throw out any "common sense" notions of physics ... which, he says, includes the idea that photons move in a straight line, AND that they always travel at c.

He shows this clearly for the straight line bit with the standard wall with two small holes between a source and a detector. When the the holes are small enough, then the probabilities for going straight aren't so overwhelming anymore compared to the probability for going in some weird path through another hole off to the side somewhere.

However, he doesn't mention any related experiment with photon speeds, instead being careful to say for each experiment that the distances are relatively large that the photon travels, so we can assume it averages out to go c.

My question is, are there experiments where the distances aren't so large where you can show that photons move faster than c? Something analogous to the 2 small holes in a wall for the path, but for the speed instead? And if so, doesn't having something moving faster than c cause all sorts of other problems?

Thanks.

 

[selfAdjoint]

No, there are no such experiments. The motions Feynman is talking about here are not observable, that is you can't make up an experiment that will show them. It's only the average that is observable, and the the average is always c. That can be calculated from Feynmann's method (called "sum over histories" or "path integrals"), as well as shown by experiment. Feynman left out the math as much as he could in his book QED.

 

[gonzo]

But he showed it could be observed for the path changes using the wall with two holes experiment. His point was that the probablities average to going straight, but this is largely because all the paths for a photon "close" to straight have large contributions in the same direction. With a small enough hole, those contributions are removed, and the straight path probability becomes the same as a weird "other" path probability, which can be obsevered by experiment (and yes, I know this is an example of the "wave-like nature of photons", but Feynman's point was that you never needed to think of photons as anythin but particles as long as you used the QM probablitiy amplitudes correctly).

He also implies that for very short distances, the speed average will not necessary be c, just as for going through a very small hole the path isn't most likely to be straight ahead.

So it seems there should be some way to construct an analogous experiment with speed, or is not even something we can imagine doing even with a bit better technology?