Re: The GPS GR Correction, put to Rest.

From: Bennett Standeven (berry_at_pop.networkusa.net)
Date: 10/04/04 

Date: 4 Oct 2004 10:38:57 -0700

H@..(Henri Wilson) wrote in message news:<v309l0dkpgs6p60j0igcbuum8oihvotjcd@4ax.com>...
> On Fri, 24 Sep 2004 13:29:24 +0200, "Paul B. Andersen" <paul.b.andersen@hia.no>
> wrote:
>
> >
> >"Henri Wilson" <H@..> skrev i melding news:vre6l0tu5m13q91031bpac7hl5erjrucmk@4ax.com...
> >> As you know, a 'GR correction' is applied to GPS clocks in order to make their
> >> rates in orbit the same as they were on the ground. The correction itself
> >> involves two terms, one supposedly to accommodate gravity differences and the
> >> other for relative velocity. Without the velocity term, the correction would be
> >> 20% out.
> >
> >Indeed it would.
> >But since it isn't even 0.1% out,
> >the prediction of GR is proven correct
> >within the precision of the clocks.
> >
> >> This simple experiment, which is a modification of my previous one, shows that
> >> no such velocity component exists.
> >
> >You have made no experiment.
> >However, a lot of experiments ARE made, all confirming GR.
> >No experiment has falsified GR.
> >
> >I will however address your attempt to show SR inconsistent
> >through a thought experiment.
> >
> >But first I will point out a common misconception, namely
> >that the GPS satellite clocks are made to run synchronously
> >in the frame of reference of a clock on the ground
> >(or "relative to a clock on the ground").
> >They are not.
> >"GPS-time" is a defined coordinate time of a specific non-rotating
> >coordinate system which I will call the "GPS coordinate system"
> >or "GPS-frame". Note that this frame is NOT rotating with the Earth.
> > Both the orbiting clocks AND clocks on the geoid are brought to
> >run synchronously to this coordinate time, that is, all the GPS clocks
> >(orbiting and ground clocks) show at any instant the coordinate time
> >of the spatial point where they are at that instant.
> >The "rate" of this coordinate time is defined such that normal
> >"SI-clocks" on the geoid will stay in synch to GPS-time.
> >(Ground clocks are moving in the GPS-frame and are thus
> >"running slow" compared to clocks stationary in the GPS-frame.)
> >The rate of the orbiting clocks are adjusted (the so called GR-correction)
> >to run synchronously to the GPS time.
> >Bottom line:
> >Both satellite clocks and ground clocks in the GPS run synchronously
> >to the GPS-time IN THE GPS-frame.
>
> yes Paul. Quite correct. The GPS frame is NOT rotating with the Earth. All GPS
> clocks must be in close ABSOLUTE synch with eachother.
>
>
> >
> >
> >> The experiment involves a large and perfectly spherical planet that is not
> >> rotating. Three observers A, B and G, with identical clocks are positioned
> >> together on the surface, where there clocks are synchronized.
> >>
> >> A and B are subsequently launched into orbit in opposite directions, 1 metre
> >> from the surface. G climbs onto a 1 metre high tower. The velocities and orbits
> >> of A and B are adjusted so that they always meet at the instant they pass G.
> >> Thus, the three can compare their readings each time they pass. A and B can
> >> also compare readings as they pass each other on the opposite side of the
> >> planet. Assume A and B are rotating once per orbit so that they are in tidal
> >> lock with the planet.
> >>
> >> According to SR, both A and B will appear to run slow in G's frame.
> >
> >Right.
> >But let's use unambiguous expressions stating what
> >actually can be observed in your scenario.
> >According to GR:
> >When A and B pass G, A and B's clocks will read the same,
> >but less than what G reads.
> >Or::
> > A and B will measure the same proper time
> >between two consecutive passings of G, while G will measure
> >a longer proper time between the same events.
>
> That's what your religion claims.
>
> >
> >> According to some SRians and not others, A will run slow in B's frame and B
> >> will run slow in A's frame. (another 'twins paradox')
> >> However, it is obvious from the symmetry of the setup that A and B will always
> >> be in synch with each other.
> >
> >Unambiguously put:
> >A and B will always read the same when they pass each other.
>
> ....and, just for the record, the same would apply if B's orbit was angled at
> 55 degres to A's. Correct?
>
> >
> >> During the experiment, the planet is given a rotational acceleration until its
> >> angular speed is exactly that of B's and B is permanently adjacent to G.
> >> The three clock are now in identical gravitational potential and free fall.
> >>
> >> Next, G synchs his clock with B's clock, knowing that this makes it also in
> >> synch with A's.
> >
> >Unambiguously put:
> >All three clocks will always read the same when they pass each other.
>
> Even more unambiguously put, the three clocks are now in absolute synch.
>
> >
> >> In G's frame, A is seen to revolve in a circle at a frequency double that of
> >> its orbit around the planet.
> >>
> >> We now have a configuration analogous to that of a GPS clock orbiting an
> >> observer on the Earth's surface.
> >>
> >> SR insists that a GPS clock runs slow due to its relative movement with the
> >> ground.
> >
> >No.
> >GR insists that if we compare a GPS clock in orbit to a _stationary_
> >clock in the GPS-frame at the same altitude, then the orbiting clock
> >will measure shorter proper time between two consecutive meetings
> >than the stationary clock will.
> >The same will be the case if we compare a clock on the ground
> >to a stationary clock in the GPS-frame at ground level.
> >But since the speed in the GPS-frame is much higher for the orbiting
> >clock than for the ground clock, the difference in proper times
> >will be bigger in the former case than in the latter.
>
> Stick to my experiment please Paul. It eliminates different gravity effects and
> speeds.
>
> >
> >> My experiment, having eliminated gravity, shows that clocks A and G are always
> >> in synch. The relative movement of A wrt G does NOT make A appear to run slow.
> >
> >Unambiguously put:
> >A, B and G will all measure the same proper time between consecutive
> >meetings, and will thus always read the same when they meet each other.
> >
> >Are you claiming that GR (or SR) predicts otherwise?
> >
> >If you insist that SR predicts that any of the clocks will
> >measure different proper time between the events than any
> >of the other clocks, you better show it.
>
> Paul, you are now well and truly trapped. Instead of initially setting A and B
> in opposite directions, we will separate their orbits by 55 degrees. That
> changes none of the previous logic.
> We then rotate the planet in the direction of B as before.
>
> We now have exactly the GPS configuration for a planet with the geostationary
> orbit 1 metre above its surface.

No; since G is the _ground_ clock, it should be on the ground, no?

[...]

> You insist that clock A will run slow in B and G's frame.

No. Clocks A and B will both run slow in clock G's frame, because
clock G is on the ground, and doesn't move as fast. (I ignore the
gravity of the planet, and its effects on the clock rates.)

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