Re: GPS CLOCK PARADOX

"The Ghost In The Machine" <ewill@xxxxxxxxxxxxxxxxxxxxxxx> wrote in message
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In sci.physics.relativity, Jeckyl
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on Thu, 31 Jan 2008 09:28:55 +1100
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In sci.physics.relativity, Jeckyl
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"snapdragon31" <snapdragon31@xxxxxxxxx> wrote in message
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On Jan 29, 8:54 pm, Randy Poe <poespam-t...@xxxxxxxxx> wrote:
On Jan 29, 8:14 pm, HW@....(Dr. Henri Wilson) wrote:

According to relativists, GPS clocks GAIN 38us per day on the
ground
clock.
That is due to two components, 45us for gravity and -7us for
relative
speed.

Accordingly, an observer (OO) in GPS orbit would see the GC LOSING
52us
per
day.

After one year, the OO would calculate that the OC was about 19ms
ahead
of the
GC.
However, the GO would calculate that his GC was only 13ms behind.

What happens when the clocks are reunited?
Who is right?

Two people drive different routes from city A to
city B. When they are reunited, one odometer reads
220 km and the other reads 230 km. Which one is
right?

- Randy

| According to relativity, both odometer readings are wrong. They do
| not represent the true distance of the routes travelled because of
the
| length contraction effect.
| According to Newton's law, both odometer readings are right.

| The GPS clock paradox is a variation of the twin paradox, so no
valid
| solution.

The paradox resides in the third postulate.

Androcles .. we've told you .. there is no third postulate

Yes there is; it's not usually expressed as a postulate, but
it is a simple one:

- If a TWLS be conducted between a source and a moving mirror,
then the time taken (as observed by the source) of the
light beam from source to mirror and back to source is
exactly twice that of the time taken from source to
mirror. In other words, t_AB = t_BA.

That follows from the second postulate, that says the speed of light is c
..
as the distances are the same ,the time must be the same. Why do you
need
another postulate forthat?

An interesting subpoint, that; I am not certain now. However, it's
clear that three events in A's space occur, and A can only observe
two of them.

These are, of course;

(0,0)_A
(L,L/c)_A
(0,2L/c)_A

for some value L. A cannot observe the second one directly.

Yeup .. that's the whole point of having a definition of what it means for
clocks to be synchronised at two remote position in an intertial frame.

[snip]
If B is not at rest, it does raise some issue in determining the distance
AB
without some definition of simultaneity.
It's not *that* difficult, though you're right; one can
get tied into semantical knots if one's not careful.
But given that A is motionless and B moves v away from A,
one can simply calculate that L, the distance the beam
travels from A to B, is such that
(0,t0)_A => (L,t0+L/c)_A = (gL-gv(t0+L/c), gL0+gL/c-gvL/c^2)_B
using the Lorentz.

Yes .. but that assumes one already has Lorentz transforms derived or
postulated .. Einstein's definition for synchronisation for remote clocks in
a given frame of reference (ie that clock B shows the 1/2 the time for
A-to-B that clock A shows for A-to-B-to-A) was set up before his derivation
of Lorentz


.

Relevant Pages

  • Re: GPS CLOCK PARADOX
    ... | According to relativity, ... | The GPS clock paradox is a variation of the twin paradox, ... The paradox resides in the third postulate. ... If B is not at rest, it does raise some issue in determining the distance AB ...
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  • Re: GPS CLOCK PARADOX
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    (sci.physics.relativity)
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