Mail Time: Does light have mass?

Michael Herrin writes in:

A student asked me, “Does light have mass? If it has mass, this implies it is matter.  If that is so, what state of matter is it?”

My answer, though I freely admit that any area of physics in which experiments cannot be set up in the classroom is outside my expertise:

Light does NOT have mass.  Light carries momentum, but the equation for momentum of a photon is p=h/λ.  Light carries energy, but the equation for energy of a photon is hc/λ.  No experiment or theory that I'm aware of has ever shown or postulated massive photons.

Michael follows up:

That’s what I thought, as well but wanted to make sure I got it right.  I explained that yes, we can take mass and convert it to energy (mass defect, e=mc^2, etc) but to my knowledge, we haven’t done the reverse, although Einstein showed that it is theoretically possible.

Oh, but "we" have, or at least the universe has.  It's called "pair production": Some energy, say after a huge collision between particles, is converted to mass of a positron-electron pair, or some other pair that conserves charge, mass-energy, etc.  In fact, the energy-time uncertainty principle insists that such pairs be produced all the time, they just re-annihilate back into energy before we have, um, time to see them.

I always appreciate questions via email... Thanks, Michael!

GCJ