Does a photon have "resting" mass?

The photon mass is zero and it is not very correct to talk about a photon rest mass as they cannot be at rest. For massive particles, rest mass is what physicists normally refer to when they say "mass". The term "relativistic mass" is not used much and you will have a hard time finding a physicist who refers to it as just "mass".

 

In almost all the cases, the photons are massless.. Only under certain conditions, you can give them an effective mass.
They are massless (rest mass =0 ) because they don't interact with Higgs, but ... we knew before Higgs that they should be massless, for many reasons- one of which is that they travel at [itex]c[/itex], or that Coulomb's law make the force have infinite range, etc...

 

Since photons have zero rest mass, the gravitational lensing effect must prove the existence of the photon's effective mass, when traveling at c.

 

Ah. Thanks.

 

Heh,... and I really wish we would always say "invariant mass" instead of "rest mass".

 

Well, in the forum I talk about "invariant mass". In daily life, I just say mass, because nobody in my environment would misunderstand it to be some strange old-fashioned quantity known as the "relativistic mass" ;-)).

 

Photon has no rest mass. In solid material where you have spontaneous breaking of phase symmetry (Anderson-Higgs phenomenon, condensed matter version of Higgs mechanism), it would acquire a mass. In which case it becomes dispersive and group velocity would be different from c.

I am guessing the 'mass' you are referring to is possibly the relativistic mass. It is related to energy, which is not an invariant quantity. General relativistic gravitation is related to the energy-momentum density; in that sense, for a photon gas, there would be frame involving energy density and pressure and this energy density might have an effective gravitating mass density (you still have to take the gravitational effect of pressure relativistically though).

 

As stated before in relativistic theory for decades one uses the word mass only for "invariant mass". Only very rarely you find proponents of the old-fashioned idea of "relativistic mass", which were invented in the very early days of relativity (they even had two kindes of "relativistic mass", a transverse and longitudinal one). In my opinion, this notions were obsolete with Minkowski's famous talk on the mathematical structure of (special) relativistic spacetime.

The invariant mass of a free photon is 0. In a medium you can define the retarded photon propagator and a spectral function from it (in thermal equilibrium it's either the analytic continuation of the in-medium Matsubara propagator to real time or equivalently the corresponding matrix element of the Schwinger-Keldysh contour propagator). If this spectral function is sharply peaked enough, you can use a quasi-particle description and define an invariant mass of the photon through the corresponding dispersion relation, otherwise this doesn't make sense und you have to use the broad spectral distribution to describe the corresponding plasmon excitations.