PART III ANALYSIS AND DATA
last updated: 05/14/2003
INFERENCES RESPECTING KINETIC ENERGY
The principle of relative velocity requires that the law of the conservation of energy should hold with respect to a co-ordinate system K, and also with respect to every co-ordinate system K' which is in a uniform motion of translation relative to K. The aforementioned requirement in conjunction with Planck's quantum equation for the energy of a photon, E = h f, suggest the subsequent conclusions.
A photon wave propagating with velocity c, which encounters a body K' moving relative to the wave's source at velocity v, exhibits to K' an alteration in frequency (delta f) equal to f (-v/c), so that as a consequence thereof, there is a change in angular kinetic energy of the photon wave. So that where
delta K. E. = K. E.d - K. E.
then
h (delta f) = h fd - h f
or
h f (-v/c) = h fd - h f
Moreover, the resulting angular kinetic energy of the altered photon wave becomes (see note 1),
h fd = h f + h f (-v/c)
or
h fd = h [f + f (-v/c)]
or
K. E.d = h [f + f (-v/c)].
Thus the Doppler (d) photon wave has the same angular kinetic energy as a wave with the frequency of
[f + f (-v/c)].
Hence we can say: If a photon wave absorbs (dissipates) an amount of angular kinetic energy (delta K. E.) when encountering a body K', moving at velocity v relative to its source, then the body K' (subject to the law of the conservation of energy) will dissipate (absorb) an equal amount of kinetic energy.
The Doppler (d) wave's frequency [f + f (-v/c)] and hence its angular kinetic energy h [f + f (-v/c)] is a function of K' 's velocity v. The the limit of the K' 's relative velocity v when encountering the wave can be regarded as the limit of the change in the photon wave's frequency (delta f) and therefore also as the limit of the change in the photon wave's angular kinetic energy.
Briefly then, the law of the conservation of energy gives rise to an exchange of kinetic energy between a photon wave and any body it encounters. This exchange is affected by the relative velocity v that exists between the photon wave's source and the body. The Doppler effect change in the photon wave's frequency and hence angular kinetic energy (delta K. E.) results from and is proportional to this relative velocity.
Note 1. The wave is considered altered to the extent that the Doppler (d) wave as experienced by K' differs from an associated standard wave as would be experienced by K.