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At 05:29 PM 2/17/00 -0600, Cliff Parker asked a bunch of questions about
the mass and momentum of photons.
I found a nicely-written article on the subject at
http://ftp.corepower.com/pub/relfaq/physics/light_mass.html
Just to underline one of the points it makes: Einstein wrote
E = m c^2 (1)
where m is what we nowadays call the "relativistic mass" which is a concept
that is best _avoided_. To be explicit:
E = relmass c^2 (2)
or equivalently
E^2 = relmass^2 c^4 (3)
Nowadays, we write
E^2 - p^2 c^2 = m^2 c^4 (4)
where nowadays m is the rest mass and p is the ordinary 3-vector
momentum. To be explicit,
E^2 - p^2 c^2 = restmass^2 c^4 (5)
which is distinctly different from equation (3).
We note in passing that the rest mass is the invariant length of the (E,p)
four-vector.
Because of the change in convention (m now conventionally stands for
restmass, not relmass) the most famous formula of 20th century physics (E =
m c^2) is no longer something we would conventionally write. Given changes
like that, it's a miracle that we can communicate with each other.
Photons always have relmass. Relmass is just energy measured in funny
units. In contrast, photons in free space have zero rest mass.
Photons in a box, or in a waveguide, do contribute to the rest mass of the========== >>
system. In fact, as I have said before, the waveguide equation is an
excellent way to see the connection between the dynamics of massive
particles and massless particles. The cutoff frequency corresponds to the
rest mass.