The Sage of Main Street
Gold Member
Freeze a Rainbow, and You Get a Jagged EdgeI just wrote this up I hope it helps.
Relativistic energy and momentum[edit]
See also: Photon energy and Special relativity
The cone shows possible values of wave 4-vector of a photon. The "time" axis gives the angular frequency (rad⋅s−1) and the "space" axis represents the angular wavenumber (rad⋅m−1). Green and indigo represent left and right polarization
In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[24]
�2=�2�2+�2�4 .
The energy and momentum of a photon depend only on its frequency (�) or inversely, its wavelength (λ):
�=ℏ�=ℎ�=ℎ���=ℏ� ,
where k is the wave vector, where
Since �
- k ≡ |k| = 2π /λ is the wave number, and
- ω ≡ 2 πν is the angular frequency, and
- ħ ≡ h/ 2π is the reduced Planck constant.[25]
points in the direction of the photon's propagation, the magnitude of its momentum is
�≡|�|=ℏ�=ℎ��=ℎ� .
If the photon moves in a wave and not a straight line, it can't move at its maximum velocity. Different color photons move on waves of different lengths, so they must not all arrive at the same time. But the difference is so small they appear to all come out together as white light.
There actual potential is c², but space is a substance that slows them down.