Can Photons travel faster than c?

[bhobba]

Where? Please give a reference. And if it isn't a textbook or peer-reviewed paper, be prepared to be told that it isn't a valid reference and you should look at textbooks or peer-reviewed papers.

I think its a confusion even I had a few years ago, but was corrected by Orodruin and I felt utterly silly I didn't see it.

In the path integral you have to include even paths that travel faster then light (off shell). I thought the fact that nothing can travel FTL meant they weren't really included - but of course they must be. It doesn't mean anything is actually traveling FTL - but it must be included in the calculations. Not making such a distinction can lead to confusion and perhaps that's what the OP is getting at:
https://en.wikipedia.org/wiki/On_shell_and_off_shell

Its part of the virtual particle thing that confuses many. To the OP there are a number of myths in QM and its wise to become acquainted with them - this virtual particle thing is one of the most insidious:
https://arxiv.org/pdf/quant-ph/0609163.pdf

Thanks
Bill

 

[Demystifier]

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.

This is explained very well in Padmanabhan's QFT textbook
https://www.amazon.com/dp/3319281712/?tag=pfamazon01-20
Sec. 1.5.2. The field operator can be split into a "particle" part and an "antiparticle" part. If you consider the commutator of the particle part only (or the antiparticle part only), then the commutator is small but non-zero at space-like distances. However, if you consider the commutator of the full field operator, then it vanishes exactly at space-like distances. This demonstrates that only the full field, not its "particle" and "antiparticle" parts, is a physical observable. In other words, some auxiliary mathematical objects of QFT can "travel" faster than light, but no physical observable of QFT can do that.

 

[vanhees71]

Yes, and that's the reason, why there must be always a particle and an antiparticle part in the field operator. At the same time only with both parts you get a local realization of the proper orthochronous Poincare group in the "canonical" way and, when obeying the spin-statistics theorem, an energy bounded from below. So locality, microcausality, and stability (existence of a ground state) all together lead to the idea of local field operators and the necessity of antiparticles in addition to particles (of course with the option that particles and antiparticles are the same).

 

[ISamson]

There is no such thing as a proof in physics. That's for math. You can only ask is there any observational evidence for ... and is there any observational evidence against ...

No. Experiments can't "prove" anything. But they can give evidence for it. The evidence is extremely strong that no particle can travel faster than the speed of light in a vacuum. That's the best you're going to get.

Evidence FOR something does not prove it

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.
Or is there just strong evidence (what do you mean by evidence, @PeterDonis ??) for something that you just assume there can't be anything else?
Thank you, please forgive my misunderstanding.

 

[vanhees71]

A proof in the scientific sense can only be given within mathematics, starting from a system of axioms and then using the rules of logic to prove theorems, lemmas, and however the mathematicians call their results. Mathematics in this sense is a set of rules of our mind. It's not a priori referring to anything in Nature.

With the discovery of the natural sciences in the 17th century (I'd say Kepler, Galileo, and Newton were the first famous figures in the history of modern natural sciences) it has turned out that mathematics is the only adequate language to make precise statements about objective "reality", where I understand "reality" as the objectively observable and quantifiable entities investigated by the natural sciences.

Of course, already much earlier, e.g., in ancient Egypt and Greece, one has used mathematics for practical purposes, most importantly geometry and arithmethics to organize daily life.

That math is such a successful tool in various branches of sciences (reaching from the natural sciences over engineering to economy and sociology) is in my opinion understandable by the fact that many mathematical subjects have been invented using everyday experience and thus are related to "reality" in the above understood sense. E.g., Euclidean geometry has been abstracted from our everyday experience of how bodies around us relate and how distances and directions can be quantified. This holds true even for more abstract subjects like functional analysis which has to a large extent been invented by the mathematicians to make sense of some ideas reaching back to Heaviside in electromagnetic theory ("operator calculus") and Dirac et al in developing modern quantum theory (theory of generalized functions, aka distributions, eigenvalue problems leading to the work by Hilbert, von Neumann, Schwartz et al).

In other cases math was first in inventing very useful theories for application to the natural sciences. E.g., a purely mathematical problem of interest in the 19th century came up when the mathemticians were asking themselves, whether one can prove the axiom of parallels of Euclidean geometry (which itself has undergone a revision by Hilbert et al, making the hidden assumptions on "the continuum" used without being mentioned by the ancient Greeks), leading to the development of non-Euclidean geometry and later on differential geometry and Riemann spaces, later useful for Einstein (after he had been tutored by his old friend Grossmann about this math ;-)) in the devolopment of the General theory of Relativity.

Now the natural sciences are distinct from math already by the fact that the natural sciences aim at describing objective reality or, put more carefully, our observations of objective reality using our senses and technical devices to extent our senses to the utmost small (atomic and subatomic scales) and the utmost large (astrophysical and even cosmological scales) and making everything quantitative and thus precisely analyzable by mathematical means. A physical model thus can never ever be proven in the strict sense a mathematical theorem is proven within a given axiomatic system, but one can test it at higher and higher accuracy by making progress in the development in ever more precise ways to observe and measure phenomena. So, if a physicist is telling you, "one has proven that and that model or theory", it means that so far even the most precise measurements confirmed the predictions of the model. Of course, within a given theory you can have mathematical proofs (like the Heisenberg uncertainty principle from the basic postulates of quantum theory), but this is not a "proof" that the underlying postulates concerning the physics are correct. Instead, the mathematical facts of a physical theory of this kind, may inspire some experimental physicist to new experimental/observational tests of the theory, and the outcome of such new tests always can be that we discover where our contemporary theories fail to explain an observed and measured phenomenon. Then the theoreticians have new work to get even better models, and they have to understand why the old models worked within their range of applicability (e.g., Newtonian mechanics can be understood as an approximately valid limit of relativistic mechanics).

 

[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