Re: GPS falsifies H&K experimental claims


Randy Poe wrote:
Phineas T Puddleduck wrote:
In article <1151069215.451483.287750@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<mluttgens@xxxxxxxxxx> wrote:

Short form

Photon has gained gravitational potential energy

e = hf

If e has increased, f must also increase as h is constant

therefore blue shift.

Congratulation! There is no other sensible explanation!

Marcel Luttgens

Um gravitational shift (red/blue) of photons ... whats the issue?

That Marcel likes to say "gravitational potential energy of
a photon" is -GMm/r, where m = hf/c^2.

I'm not very knowledgeable about GR, but I don't believe
that's correct since it would imply that photons experience
a gravitational force equal to GMm/r^2, and that photon mass
experiments directly contradict that.

You are probably referring to a hypothetical photon rest mass.
One has to consider that photons move at c, and that their
energy corresponds to hf = mc^2, hence their mass is given by hf/c^2.

Otoh, the gravitational potential at a distance d from the
center of an object of mass M is gd = -GM/d^2. At the surface
of the object of radius R, one has gR = -GM/R^2.
A photon of mass m moving from d to R will gain a potential energy
Ep = m * gm * (d-R), where gm is the geometrical mean of gd and gR,
i.e. gm = GM/(d*R).
Thus, Ep = hf/c^2 * GM/(d*R) * (d-R)
= hf * GM/c^2 * (1/R - 1/d)
After having travelled the distance d-R the total energy of the photon
will be hf1 = hf + Ep
= hf + hf * GM/c^2 * (1/R - 1/d)
= hf * (1 + GM/c^2 * (1/R - 1/d))
Hence, f1/f = 1 + GM/c^2 * (1/R - 1/d), and the corresponding shift
is f1/f - 1 = GM/c^2 * (1/R - 1/d)

This last formula is identical to the GR formula for the gravitational
effect, for instance on a GPS satellite.

In such case, M is the Earth's mass Me, R is the Earth radius Re
and d is the distance of the satellite from the center of the Earth
The observed frequency shift of the satellite clock will be
GMe/c^2 * (1/Re - 1/d). By multiplying the shift by a sidereal day,
one gets about 45.6 microseconds.

Marcel Luttgens


- Randy

.

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