Are photons definitely massless?

[LightningInAJar]

TL;DR

Are photons for sure massless? And if not, what are the implications?

Recently saw this video.


"Why No One Knows If Photons Really Are Massless: What if they Aren't?"
Arvin Ash

He says photons need not be massless, but they must be quite light nonetheless. He separates speed of light from speed of causality. Is it true that we can't know its mass below a certain level of sensitivity and we just kind of presumed it had no mass?

 

[PeterDonis]

Recently saw this video.

This is not a valid reference. Pop science videos are not good sources to learn actual science.

Is it true that we can't know its mass below a certain level of sensitivity

Any actual experiment will have a finite sensitivity, so yes, an actual experiment cannot tell you with infinite precision that the photon's mass is exactly zero. The best we can do with an actual experiment is to set an upper bound on the photon's mass. I believe the current upper bound is something like $10^{-24}$ times the electron mass.

we just kind of presumed it had no mass?

Not at all. We have mountains of evidence that are consistent with photons having zero mass, and no evidence at all that rules it out. So we are not just "presuming" it has zero mass; we are using the best model consistent with all of the available evidence.

 

[Meir Achuz]

I believe that a limit on the mass of the photon is measured by the 1/r dependence of the Coulomb potential, calculated by the exchange of one photon. If the photon had a mass, however small, QED could not be considered a gauge theory, and special relativity would be an approximation.

 

[hutchphd]

TL;DR Summary: Are photons for sure massless? And if not, what are the implications?

"Why No One Knows If Photons Really Are Massless: What if they Aren't?"

Perhaps pigs really can fly: what if they do???......breathless anticipation......

With respect you need to select your inspiration with much more care. .

 

[ohwilleke]

According to the Particle Data Group, the experimental upper bound on the mass of the photon is 10^-18 eV.

But, this isn't the end of the story. Particles with zero rest mass have qualitatively different properties than particles with tiny, non-zero rest mass. On this basis, there is every indication that photons have zero mass. Gravitational lensing, the infinite range of the electromagnetic force, and special relativity, for example, are all consistent with zero rest mass for photons. A physics article published in a peer reviewed article published in 2004 marshals many other kinds of relevant evidence.

 

[robphy]

https://www.google.com/search?q="lectures+on+gravitation"+feynman+"photon+has+no+rest+mass"&tbm=bks (search on Google Books)

Feynman Lectures On Gravitation (2.2 Difficulties of Speculative Theories)

...
In this connection I would like to relate an anecdote, something from a conversation after a cocktail
party in Paris some years ago. There was a time at which all the ladies mysteriously disappeared, and I
was left facing a famous professor, solemnly seated in an armchair, surrounded by his students. He
asked, “Tell me, Professor Feynman, how sure are you that the photon has no rest mass?” I answered
“Well, it depends on the mass; evidently if the mass is infinitesimally small, so that it would have no
effect whatsoever, I could not disprove its existence, but I would be glad to discuss the possibility that
the mass is not of a certain definite size. The condition is that after I give you arguments against such
mass, it should be against the rules to change the mass.” The professor then chose a mass of 10^{-6} of an
electron mass.

My answer was that, if we agreed that the mass of the photon was related to the frequency as
\omega=\sqrt{k^2+m^2}, photons of different wavelengths would travel with different velocities. Then in observing
an eclipsing double star, which was sufficiently far away, we would observe the eclipse in blue light and
red light at different times. Since nothing like this is observed, we can put an upper limit on the mass,
which, if you do the numbers, turns out to be of the order of 10^{-9} electron masses. The answer was
translated to the professor. Then he wanted to know what I would have said if he had said 10^{-12}
electron masses. The translating student was embarrassed by the question, and I protested that this was
against the rules, but I agreed to try again.

...

"The Mass of the Photon"
Alfred Scharff Goldhaber, Michael Martin Nieto
Scientific American, Vol. 234, No. 5 (May 1976), pp. 86-97 (12 pages)
https://www.jstor.org/stable/24950353

"Photon and Graviton Mass Limits"
Alfred Scharff Goldhaber, Michael Martin Nieto
Rev.Mod.Phys.82:939-979,2010 ( https://doi.org/10.1103/RevModPhys.82.939 )
https://arxiv.org/abs/0809.1003

Special Relativity deals with a finite maximum speed of causality.
If it turned out that the photon had a nonzero rest mass,
then we should call "c" in special relativity (say) "the speed of causality" or "maximum signal speed" instead of "the speed of light".

https://en.wikipedia.org/wiki/Proca_action
can be used to write a set of equations like the Maxwell Equations (Gauss and Ampere would get extra terms... see pg 6 in Goldhaber & Nieto).

UPDATE: The first 8 minutes of the video in the OP seems fine... making some of the points I listed above. (I didn't watch the rest of it, which might also be fine.)

 

[Nugatory]

If the photon had a mass, however small, QED could not be considered a gauge theory, and special relativity would be an approximation.

Would a non-zero photon mass necessarily imply that special relativity is not exact? There is the possibility that SR remains exact and the speed of light is less than the invariant speed of SR.

(Of course the metrologists would be annoyed)

 

[Vanadium 50]

The first 8 minutes of the video in the OP seems fine... making some of the points I listed above. (I didn't watch the rest of it)

An interesting, but unknowable, question is whether the OP watched it as well.

Would a non-zero photon mass necessarily imply that special relativity is not exact?

No, it would merely mean light travels incrementally slower than c, which would still be a constant of nature.

Particles with zero rest mass have qualitatively different properties than particles with tiny, non-zero rest mass.

Technically true, but highly, highly misleading. If the photon had a mass, the Coluomb force would not be exactly inverse square. (To take one example) But how big a deviation can we see? A part oer million? A part per trillion? The lower the photon mass, the closer to inverse square the force becomes. Eventually it dfrops below measurement error.

 

[vanhees71]

Would a non-zero photon mass necessarily imply that special relativity is not exact? There is the possibility that SR remains exact and the speed of light is less than the invariant speed of SR.

(Of course the metrologists would be annoyed)

This is also an urban myth. For the Abelian case you can have a gauge invariant realization of a massive vector field. That's known as the Stueckelberg description. It has the advantage that you can use any gauge also for massive vector bosons and thus you get manifestly renormalizable models.

Another way is of course the Higgs mechanism, which also works in the non-Abelian case.

Whether the real photon has a mass or not indeed doesn't affect special relativity at all. Of course, if the em. field were not massless than the "limiting speed" of special relativity were not "the speed of light in vacuum" anymore.

 

[Meir Achuz]

If you believe that light is composed of photons, then a massive photon would mean that the speed of light was different in different Lorentz frames. This should be checked over 100 years ago.

 

[Ibix]

If you believe that light is composed of photons, then a massive photon would mean that the speed of light was different in different Lorentz frames. This should be checked over 100 years ago.

But if the photon has an extremely low mass then the tiniest force on it for the tiniest time sets it zipping off at 0.9999....9c, and it's really hard to apply a force precisely enough to slow it down to a speed relative to us that is measurably different from c. It's therefore possible for a photon to have a tiny mass and a frame variant speed that is always indistinguishable from c in any circumstance we have so far tested. That's one way to set a bound on the possible mass of a photon - it cannot be very heavy or we'd have noticed one travelling much slower than c by now.

Other techniques are more sensitive and apply tighter bounds. Our failure to detect any deviation from Gauss' law, mentioned above, is one such.

 

[PeterDonis]

It's therefore possible for a photon to have a tiny mass and a frame variant speed that is always indistinguishable from c in any circumstance we have so far tested.

Note that this is precisely the position we are in with regard to neutrino masses: they are small enough that we can't directly observe any difference from $c$ in measurements of their speed. We have to resort to indirect methods to show that they have nonzero masses and to estimate those masses. And this is for masses many orders of magnitude larger than the current upper bound on the photon mass.

 

[Vanadium 50]

It's pretty clear we have put in 1000x as much effort into this than the OP did, which is pretty doggone annoying.

However, there are some replies that misuderstand "photon" and "vacuum:.

c is the speed of light in vacuum. Even outer space is not a perfect vacuum. A measurement that light is a little slow may mean the photon is massive, or it may mean that the medium has a non-trivial index of refraction. The limits today are comparable to what you would expect from the index of the ISM (but not the IGM).

A photon itself is an idealization. A photon starts at minus infinity, goes to plus infinity, and never interactions, neither to be created nor destroyed. If you actually create one and detect one, the equations for that are slightly and subtly different than the idealization of the last sentence. That mass can, in principle, be non-zero (but very small) so it doesn't really tell you what the idealization does.

A combination of the two - medium and boundary condition effects - happens in a superconductor, where the photon gains a substantial mass.

A photon is massless like the ratio of a circle's circumference to its diameter is π. The fact that there are no perfect circles in nature doesn't change this.

 

[vanhees71]

Another point of view is that $c$ has a priori nothing to do with the electromagnetic interaction of photons. You can derive the Minkowski space as a spacetime model from just assuming that Newton's 1st Law holds (i.e., the assumption that there's an inertial frame of reference) and that for an inertial observer space is a 3D Euclidean affine space (with its implied symmetries of homogeneity and isotropy) and also time is translation invariant. From that assumption you get that the spacetime model must either be Galilei-Newton spacetime (with no limiting speed) or Einstein-Minkowski spacetime (with a limiting speed, which we usually call $c$).

These spacetimes have the usual symmetry groups (Galilei or Poincare invariance, respectively), from which to a large extent the form of the general dynamical laws (for point-particle mechanics, field theories, quantum theories, etc.) can be derived.

Whether or not the electromagnetic field is "really massless" is then just an empirical question. There's no known deeper law that would imply that it must be massless. So it's up to measurement, whether it's massless or it may have a mass. There are only upper limits, $m_{\gamma}<10^{-18} \text{eV}/c^2$. There are no hints at all that $m_{\gamma} \neq 0$. So it's pretty safe to assume that $m_{\gamma}=0$, as already discussed at length above. For details on the experimental evidence, see the already quoted review by Goldhaber and Nieto.

 

[Pony]

No, there is no strong evidence that photons are massless. Photons having a small mass is consistent with every experiment and phenomenon we know of.

 

[Pony]

Particles with zero rest mass have qualitatively different properties than particles with tiny, non-zero rest mass.

This is true, but this doesn't mean that we should have observed them already.

Question: if photons have mass, can I have a lamp, that its light is slow and my shadow lags? I don't think that my eyes could see such a light, but maybe if I illuminate the wall and the objects, the reflected light turns out to be fast, and I can see it?

 

[Ibix]

Question: if photons have mass, can I have a lamp, that its light is slow and my shadow lags?

Sort of. Every lamp we know of emits light at a speed indistinguishable from $c$, but if photons have mass it is in principle possible to have a beam of light moving at walking pace, yes. In practice this certainly isn't possible with current technology, and may never be possible outside of tightly controlled lab conditions. Or may be outright impossible if photons are actually massless.