Can Photons travel faster than c?

[phinds]

I don't understand this.
Is it possible to prove something in physics using mathematical proof and concepts, yes or no?
I always thought it can.

To give a shorter version of vanhees71's excellent response, NO. Again and again I keep telling you, "proof" is a mathematical concept and does not apply to the physical world. The map is not the territory.

 

[Dadface]

I would express it by saying that every relevant theory and every relevant bit of scientific evidence we have at the present time seems to prove that the speed of light is a maximum. However the proof is not absolute and who knows, at a future time hyper light speeds may be detected. In the light of present knowledge the possibility of hyper light speeds may seem to be extremely unlikely but, however, the possibility remains.

 

[phinds]

I would express it by saying that every relevant theory and every relevant bit of scientific evidence we have at the present time seems to prove that the speed of light is a maximum. However the proof is not absolute and who knows, at a future time hyper light speeds may be detected. In the light of present knowledge the possibility of hyper light speeds may seem to be extremely unlikely but, however, the possibility remains.

This is incorrect on two fronts. First, no, it does NOT prove it. For the umpeenth time, there IS no proof in physics just in math. Second, it is not the speed of light that is the maximum, it is the universal speed limit, which as far as we know is the speed at which light travels but if photons were found to have a mass (which would have to be staggeringly tiny to be consistent with current observations) then the universal speed limit would not change but it would no longer be synonymous with "the speed of light".

 

[Dadface]

I would express it by saying that every relevant theory and every relevant bit of scientific evidence we have at the present time seems to prove that the speed of light is a maximum. However the proof is not absolute and who knows, at a future time hyper light speeds may be detected. In the light of present knowledge the possibility of hyper light speeds may seem to be extremely unlikely but, however, the possibility remains.

This is incorrect on two fronts. First, no, it does NOT prove it. For the umpeenth time, there IS no proof in physics just in math. Second, it is not the speed of light that is the maximum, it is the universal speed limit, which as far as we know is the speed at which light travels but if photons were found to have a mass (which would have to be staggeringly tiny to be consistent with current observations) then the universal speed limit would not change but it would no longer be synonymous with "the speed of light".

Sometimes it seems my posts are not read correctly. I did not claim that it "proved it". In fact the message I was trying to convey was the exact opposite of that. What i actually wrote was it "SEEMS to prove" it. There is a big difference between "proves it" and "SEEMS to prove it".

I think your reference to my use of the phrase "speed of light" is unnecessarily fussy for this particular thread particularly when I counted eight other respondents who referred to "speed of light", some indirectly. Take a look at earlier replies.

 

[phinds]

Sometimes it seems my posts are not read correctly. I did not claim that it "proved it". In fact the message I was trying to convey was the exact opposite of that. What i actually wrote was it "SEEMS to prove" it. There is a big difference between "proves it" and "SEEMS to prove it".

Good point. I'm frustrated by this need to "prove" physical things and so mis-interpreted your post.

I think your reference to my use of the phrase "speed of light" is unnecessarily fussy for this particular thread particularly when I counted eight other respondents who referred to "speed of light", some indirectly. Take a look at earlier replies.

Yeah, but fussy is one of my best things

 

[atyy]

Regardless, I have seen on the internet that for points outside of the light cone, the integral results in very low probability of photons being detected, but still nonzero.

In an exact relativistic theory, faster than light communication is impossible (see Demystifier's post #32 and vanhees71's post #33).

However, we can also find non-exact relativistic theories, where the Lorentz symmetry is emergent at low energies. In these cases, faster than light communication is in principle possible, but very difficult in practice: https://en.wikipedia.org/wiki/Lieb-Robinson_bounds.

 

[vanhees71]

I would express it by saying that every relevant theory and every relevant bit of scientific evidence we have at the present time seems to prove that the speed of light is a maximum. However the proof is not absolute and who knows, at a future time hyper light speeds may be detected. In the light of present knowledge the possibility of hyper light speeds may seem to be extremely unlikely but, however, the possibility remains.

This is an excellent example for the discussion we have here.

First of all there is not even a mathematical proof within relativistic QFT (assuming the usual set of symmetry, causality, and stability assumptions) for the masslessness of the photon. Even when restricting oneself to local gauge symmetry and renormalizable models in the case of an Abelian gauge group, nothing prevents one from giving the photon a mass (even without using the Higgs mechanism!). On the other hand, assuming the masslessness of the photon together with the other constraints on a relativistic QFT and Wigner's analysis of the representation theory of the proper orthochronous Lorentz group leads necessary to the idea of local gauge invariance.

As you see, already into the model building itself a lot of empirical input is needed to constrain the plethora of possibilities, and among other things the masslessness of the photon is such an empirical input. Of course, one has to test this assumption to ever higher accuracy to make sure that it is really describing Nature. There's of course never 100% accuracy, and in the case of the photon mass we have only an upper limit (although an amazingly low one of $m_{\gamma}<10^{-18} \mathrm{eV}/c^2$). So far there's no evidence for a finite photon mass and thus we set it happily to 0 in the Standard Model, as well in its classical limit, i.e., Maxwell's classical electrodynamics.

 

[PeterDonis]

what do you mean by evidence, @PeterDonis ??

Um, the stuff that you get by doing experiments and recording their results?

 

[phinds]

Um, the stuff that you get by doing experiments and recording their results?

[Sorry ... I just couldn't keep a straight face.]

 

[OCR]

Sorry ... I just couldn't keep a straight face.

Oh, my... !

 

[anorlunda]

seems to prove that

Semantic debates are so tedious and unnecessary. As in court, proof can mean sufficient evidence to convince. In mathematics (such as geometry) a proof means something very different.

@Dadface, you should have known better to say "seems to prove" (e.g. the courtroom sense) in a conversation about mathematical proof.

Is there any experimental proof for this?
I know no particle can, but I am interested in the proof.

@ISamson , you started the confusion. In your first sentence, you mean proof in the courtroom sense (i.e. a convincing mass of experimental evidence.) In the second sentence, "the proof" can only be interpreted in the mathematical sense. You used (perhaps unintentionally) two different meanings of proof in consecutive sentences. tsk tsk. If you had said, "Is there any experimental evidence for this? I would be interested in the evidence." Then this debate would have been avoided.

 

[bhobba]

Is it possible to prove something in physics using mathematical proof and concepts, yes or no?

It depends on what you mean by proof.

Take Euclidean Geometry. If you accept its axioms then you have proved its conclusions. Everyday experience shows its axioms to a high degree of accuracy are correct - but very accurate measurements show they are wrong. But for surveyors etc the differences are so small for all practical purposes you have proved it.

What do you call that situation - beats me - I just call it science:


Thanks
Bill