Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy
Keywords: refraction, Planck's equation, Snell's law, mass and energy conservation, photon, particle, relativistic spacetime, wavelength, self-interference, Heisenberg uncertainty principle
By direct substitution from E = mc2 and = h(mv)−1, energy becomes E = hc2(v)−1. This reduces to Planck's equation if, and only if, v = c. It follows from Snell's law that a photon undergoing refraction will gain energy E = hc2[(v)−1 − (0C)−1], where 0 is its wavelength in vacuo. This very small energy gain arises from work done on the photon's mass by the refracting medium in decelerating the photon from c to v. The medium therefore looses internal energy while the photon is passing through, regaining it when the photon leaves to resume speed c. Photon momentum is a linear, monotone-increasing function of speed, p = hc(0v)−1. The reason photons do not have rest mass is because they cannot rest in space (v = 0) for the same reason massive particles cannot rest in time (v = c): In either case the energy would be infinite. EPR-type paradoxes can be resolved by replacing the notion of self-interference with recognition of the fact that x is the extent of the x-axis that is instantaneously occupied by a particle.