Q & A: How can photons have energy if they have no mass?

How can light/photons have energy if they have no mass? Also if light is the universal speed limit because it has no resistance in the theoretical Higgs field, then how can light have a faster speed in a vacuum then in water? Aren't particles at colliders going faster then light in water?
- Sean (age 16)
Wisconsin

The special theory of relativity says that the total energy of a particle is given by the following:  E² = (m_oc²)² + (pc)²  where E is the total energy, m_o is the rest mass, and p is the momentum. This equation has been verified by many, many experiments and as far as we know is correct. The fact that momentum carries energy is even true in classical E & M where electromagnetic fields are involved.  Since photons have zero rest mass then their energy is simply  E = pc. The fact that light carries momentum is also verified by experiment.

The other issue you raise, the fact that the apparent velocity of light is less in a dielectric medium, has to do with the interaction of light within the medium.  The reason is that the light is continually being absorbed and then re-emitted in a coherent way by the atoms in the medium.   The net result is that the effective re-radiated light has an apparent slower speed than c.  There is a curious effect, the Cherenkov Effect, that happens when a relativistic charged particle travels though a dielectric medium.  The electric fields get 'confused' by the fact the particle is traveling faster than c and so the medium compensates by emitting this Cherenkov radiation.
See:  http://en.wikipedia.org/wiki/Cherenkov_radiation  for some information.

LeeH

(published on 12/29/2009)