Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy

Year: 1988

Keywords: refraction, Planck's equation, Snell's law, mass and energy conservation, photon, particle, relativistic spacetime, wavelength, self-interference, Heisenberg uncertainty principle

*By*E = mc

^{ }direct substitution from^{2}

*and*= h(mv)

^{−1},

*energy becomes*E = hc

^{2}(v)

^{−1}.

*This*, v = c.

^{ }reduces to Planck's equation if, and only if*It*E = hc

^{ }follows from Snell's law that a photon undergoing refraction will^{ }gain energy^{2}[(v)

^{−1}− (

_{0}C)

^{−1}],

*where*

_{0}

*is its wavelength*in vacuo.

^{ }

*This very small energy gain arises from work done on*c

^{ }the photon's mass by the refracting medium in decelerating the^{ }photon from*to*v.

*The medium therefore looses internal*c.

^{ }energy while the photon is passing through, regaining it when^{ }the photon leaves to resume speed*Photon momentum is*, p = hc(

^{ }a linear, monotone-increasing function of speed_{0}v)

^{−1}.

*The reason photons*(v = 0)

^{ }do not have rest mass is because they cannot rest^{ }in space*for the same reason massive particles cannot*(v = c):

^{ }rest in time*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