Re: GPS falsifies H&K experimental claims
- From: mluttgens@xxxxxxxxxx
- Date: 2 Jul 2006 04:02:18 -0700
Henri Wilson wrote:
On 29 Jun 2006 03:30:01 -0700, mluttgens@xxxxxxxxxx wrote:
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.
I've been pointing this out for a year but they cannot understand let alone
accept it.
The interesting thing is that GPS works largely on phase relationships between
signals, which means that the Newtonian correction is just as effective as the
GR one.
Of course, their claim that the clocks actually speed up by exactly the GR
prediction has never been accurately verified and would be purely coincidental
if approximately true.
Formulae very easily obtained from the "mass" and potential energy
of photons are identical to corresponding GR formulae.
Some GRists claim that the energy and frequency of photons do not
change with height, but that clocks run faster when they are situated
higher in the gravitational potential.
Other GRists claim that satellite clocks "are measuring the
duration of an orbit to be longer, than the clocks on the ground
measure the duration of an orbit to be." (for instance, Paul B.
Andersen).
Tom Roberts is more eclectic. According to him (see
http://groups.google.fr/group/sci.physics.relativity/browse_frm/thread/1ac904c7cf440d3d/bcc966485405a82b?lnk=st&q=GR+frequency+shift+formula&rnum=1&hl=en#bcc966485405a82b
Fri, Apr 14 2006), there are three possible GR explanations:
1) Clocks run the faster the higher they are located in the potential,
whereas the energy and frequency of the propagating photon do not
change with height. The light thus appears to be redshifted relative
to the frequency of the clock.
2) Photons lose energy when they overcome the gravitational attraction
of a massive body or gain energy when they are "attracted" by
a massive body, and the clock position in the gravitational well
plays no role.
3) Both the clock rates vary and the energy/frequency of the light
vary.]
He adds that "GR itself is independent of coordinate choice, but
clock rate, energy, and frequency are not. These interpretations are
based on different choices of coordinates, that's all."
As for me, "flying" clocks are *observed* from the ground to advance
more than ground clocks.
Only experiments where clocks are brought back to Earth can support
the view that the flying clocks ticked faster than the ground clocks.
Till now, this has been done only once, it was the H&K experiment,
but "An analysis of the real data shows that no credence can be
given to the conclusions of Hafele and Keating.", see
http://www.cartesio-episteme.net/H&KPaper.htm .
In other experiments cited by GRists, the clocks crashed in the
ocean (http://en.wikipedia.org/wiki/Scout_rocket_experiment).
Clocks were compared on the plane and on the ground by EM signals
( http://www.exo.net/~pauld/physics/relativity/relativitytimefly.htm ).
In other words, they were simply *observed* to tick faster.
Gravity Probe B
(http://einstein.stanford.edu/content/faqs/faqs.html#publish )
whose results are expected in April 2007, is attempting to test
Einstein's theory of General Relativity. If it is found wrong, the
potential energy explanation will be indirectly supported.
Marcel Luttgens
Marcel Luttgens
- Randy
HW.
www.users.bigpond.com/hewn/index.htm
Appropriate message snipping is considerate and painless.
.
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