It appears I've made a serious error in my prior attempts
to calculate the energy of a photon using Newtonian methods
(for these purposes a photon is a ball of just the right
mass moving at lightspeed); I am going to reattempt these
calculations and see what I come up with. Bear in mind
this won't refute SR in any fashion, as there are many
other effects that are not accounted for here -- many
of them easily observable in particle accelerators and
stellar phenomena.
First, we need to determine the photon's mass. Given that
the photon has total energy E, it is naive to think that
this is all kinetic energy or potential energy; a logical
alternative is that m = kE/c^2, where k is some constant.
Since the momentum of a photon is E/c = 2E/v = mv, where
v = c, then k = 1/2, and the photon is half kinetic energy
(KE), half indeterminate energy (IE).
We now drop this photon from a height, and measure the
ratio of energies.
At time 0 and height h, the photon has velocity -c,
since we're assuming up is positive in this experiment.
At time t, the photon has velocity -c-tg and is at the
point h-ct - 1/2gt^2.
The ground is at 0 so h-ct-1/2gt^2=0, or 1/2gt^2+ct-h=0,
or t=-c/g+sqrt(c^2+2gh)/g = c*(sqrt(1+2gh/c^2)-1)/g.
The KE of the photon is 1/2 m (c+tg)^2
= 1/2 m (1+2gh/c^2). The IE, presumably, hasn't changed;
therefore the total energy is 1/2 m (2+2gh/c^2) = m(1+gh/c^2).
Therefore E/E_0 = 1+gh/c^2, the same as predicted by GR,
and it's far from clear that Pound-Rebka can distinguish
between the two by solely using energy unless second-order
effects are involved.
A pity, admittedly.
--
#191,
It's still legal to go .sigless.
.
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