Again, thanks Steve, it is in your wheelhouse. So if you and others wish to play with it, the empirical values in computation were as follows:
c = 2.997925^10 cm/sec
h = 6.626196^-27 erg/sec^-1
Boltzmann = 1.380648^-16 erg/Kelvin*
e generated by algebraic OS of calculator; key ( 1, INV, lnx, =, store)
Water trickles towards towards a floor drain on a well laid concrete floor because the drain is about 3cm lower than at the sidewall 5m away. A bowling ball placed near the wall will slowly roll toward the drain so gently it could nudge an egg out of its path. But Putt a golf ball across the same surface and it would splatter the egg. Momentum (p) is the sum over path intervals of the cosine transformation of rapidity of change of slope of a waveform of EMR decelerating from midpoint of wave length to rest moment. So the photon rest energy can exceed the value of Planck's Constant in wavelengths longer than a benchmark spherical waveform having progressively lower amplitudes. Given that the 21cm microwave frequency is paramount in CMB surveys, suggests that a real spherical waveform might be in the vicinity of 10^-2 to 10^2 cm. And ALL rest energy quantities of the EM spectrum would be less than what would have a proportionate upper density bound equal to or greater than the theoretical specific Kinetic (inelastic) Density.
"Roll a ball, a ball a penny a pitch." as an old, old song goes. :) jrc