Re: massless or massive photon?

Juan R. González-Álvarez wrote:
The usual argument for massless photons uses the Hamiltonian [...]
H = pc

You notion of "usual" and mine differ ENORMOUSLY.

First, I cannot see how such a Lagrangian gives photons at all -- for that one needs a QUANTUM Lagrangian, as photons are inherently quantum objects. If your theory does not have any photons, how can you sensibly ask questions about their mass?

Second, given a proper quantum Lagrangian (and the corresponding Hamiltonian if you wish), there's no general theoretical argument that requires photons to be massless.

The REAL argument for massless photons is that when one treats the mass of the photon as a free parameter and fits the theory to experimental observations, one finds that the mass must be an INCREDIBLY small value, and is consistent with zero. The PDG lists the current upper bound on the photon mass as 6*10^-17 eV/c^2.

To put that in perspective, the lightest other particle
known (except neutrinos whose masses are not known) is the
electron. If an electron were scaled up to have the mass
of the earth, then the upper bound on the photon mass would
be scaled up to the mass of a half cubic meter of water.


If alternatively we start assuming (v = c) in the transformation, the
result is
H = pc - L = pc (2)
where no assumption was taken about the mass.
Is this Hamiltonian (2) representing some kind of massive photon (somewhat
as in Proca theory [#]) or is really the same that (1)?

The same objections apply. But on the question of this being different from (1), ask yourself: what changes in the meanings of symbols have occurred? If none, then these are obviously the same. But that is a subtle question, in particular: what is the meaning of "c"?


Well, I already remarked that theories with massive photon are giving the same experimental answers that classical electrodynamics in the corresponding limit.
And also pointed to one example of quantum theory with massive photon gives the same scattering amplitudes that computed using Feynman diagrams for QED

But that it not how one tests theories! To do that, one goes to the PDG website, looks up the experiments that they used to establish their limit on the photon mass, and one fits the theory with a massive photon to the experimental data, leaving mass as a free parameter in the theory. But, of course, that is essentially what those experimenters and the PDG already did to obtain their limit.


Tom Roberts
.

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