# Can photons have mass?

1. Apr 12, 2013

### medgalis

Me and my teacher have been arguing, whether photons have or don't have mass. I say that it's impossible for photons to have mass, but my teacher says that we can calculate the photons mass. So my question is, can photons have mass?

2. Apr 12, 2013

### psmt

Not in a vacuum. I would be interested to know what your teacher says "the photon's mass" is, if it can be calculated.

In a superconductor, photons acquire mass, via the famous Higgs mechanism:
http://en.wikipedia.org/wiki/Higgs_mechanism#Examples
... but it doesn't sound like this is what your teacher had in mind.

3. Apr 12, 2013

### Staff: Mentor

Photons in some system with other stuff contribute to the total energy of that system in the center of energy frame, which can be translated into a mass. That does not mean that photons have mass (on their own).
Photons are massless in theory, and experiments were able to set http://pdglive.lbl.gov/Rsummary.brl?nodein=S000 [Broken] (less than 10-23) times the electron mass) on any possible photon mass.

Last edited by a moderator: May 6, 2017
4. Apr 12, 2013

### bhobba

Its impossible to have REST mass otherwise it could not move at the speed of light. By definition it can have relativistic mass but many people, myself included, believe its not really a concept that's particularly useful.

Thanks
Bill

5. Apr 12, 2013

### medgalis

She says it can be calculated with E=mc^2.

6. Apr 12, 2013

### Staff: Mentor

That would correspond to the concept of relativistic mass. This concept is not used any more in physics, it just remains in old textbooks and bad TV documentations.

7. Apr 12, 2013

### medgalis

But she still teaches this kind of a thing she believes it and i don't know how can she still believe it. And she says that a moving photon has mass.

8. Apr 12, 2013

### bhobba

Its true - by definition it has relativistic mass. Its just that these days its not a particularly useful concept. You might like to ask for relativistic mass with a particle that has a rest mass if it has the same effective mass regardless of what direction a force is applied (it doesn't) and if that is a property you normally associate with the concept of mass?

John Baez gives a nice explanation:
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Thanks
Bill

Last edited: Apr 12, 2013
9. Apr 12, 2013

### vanhees71

I'm strictly against the use of what has been known as "relativistic" mass in the early days of special relativity. Then it was even worse: They introduced also two kinds of relativstic mass, called transverse and longitudinal mass. All this makes a clear subject, namely the special relativity very confusing, and as soon as you go even further to general relativity it's impossible to get anything clear with such non-covariant concepts.

In modern language thus mass refers to the invariant mass of a system. This clarifies a lot of confusing issues of the early days, particularly when it comes to really non-trivial concepts like the renormalization of mass of charged bodies/particles in classical and quantum electrodynamics or even more complicated quantum field theories as the complete standard model, etc.

That said, the photon mass in free space is, within the standard model, 0. There is, however, no first principle telling us that it must be 0, because you can give even a "naive" mass to a renormalizable Abelian gauge-field theory without spoiling gauge invariance and renormalizability (Stückelberg formalism for Abelian massive gauge fields). Thus, we have to consider the masslessness of the photon a pretty precisely measured empirical input into the standard model.

Of course, there is not only free space but also macroscopic bodies, and there the whole issue becomes even more involved. There you also have contributions to the mass from the interaction of the photons with the medium. The funny thing in the context of the photon mass here are superconductors. Effectively superconductors can be described as a "Higgsed QED", i.e., the electromagnetic gauge symmetry is "spontaneously broken" in the sense of the Higgs mechanism. This has been deduced by Anderson some time before Higgs's famous paper on the Higgs mechanism in electroweak theory! Thus, in a superconductor photons acquire a mass through this Anderson-Higgs mechanism.

10. Apr 12, 2013

### DrZoidberg

As far as I understand it relativistic mass is just a synonym for energy. E = mc2 is just an equation for converting one unit of energy into another (i.e. kg to J).
In particle physics the mass of a particle is defined as the energy that particle possesses at rest. So if photons can never be at rest how can they have mass?

11. Apr 13, 2013

### Staff: Mentor

To do that, you need an atom nearby, an isolated electron cannot do that. The whole atom is participating in that process, even if the change for the electron is the most interesting part.
The electron mass (="rest mass") of roughly 511 keV does not change, however. Not even a tiny bit. The total energy of the atom changes.

12. Apr 13, 2013

### medgalis

Oh. Well i didn't know that.