Re: GPS falsifies H&K experimental claims


Paul B. Andersen wrote:
mluttgens@xxxxxxxxxx wrote:
Paul B. Andersen wrote:
mluttgens@xxxxxxxxxx wrote:
I received an E-mail from somebody I don't know. I tried to send him
(her)
a reponse, but the address seemed to be false.

Here are my comments :

You are perfectly right. If the ground clocks and the satellite clocks
emit the same frequency Nu1, the received signal from the satellite
clocks will be Nu2<>Nu1, unless the satellites clocks are "adjusted
*once* pre-launch for the predicted relativity effects" (leaving aside
small periodic adjustments). Then Nu2=Nu1, an quasi-permanent equality.

The classical explanation is indeed that "the satellite clocks speed up
because they are higher in the Earth's gravitational field, and slow
down because they are moving faster than objects on the Earth's
surface". One could as well consider that the moving clocks and
the Earth clocks keep ticking at the same rate, but the frequency of
the signals emitted by the satellite clocks are *observed* to be
blue-shifted by a gain of potential energy, and red-shifted by the
longer
path travelled by the signal when observed from Earth. The pre-launch
adjustment of the frequency of the satellite signals cancel the net
effect for the Earth observer.

You are rather confused.
The (1+4.4647*10^-10) frequency shift is NOT what is observed by
a stationary observer on the ground. If you measure the frequency
of the received signal from a satellite passing over your head,
this signal will be blue shifted by ca.(1+5*10^-7) as it rises above
the horizon, and will be red shifted by ca.(1-5*10^-7) right before it
goes below the horizon on the other side. Due to this Doppler shift
which is a thousand times bigger than the relativistic effect, it
is practically impossible to measure the latter by frequency
measurements on the ground.

I am not confused, contrary to you.
The 4.4647*10^-10 shift (not (1+4.4647*10^-10) is what is corrected by
the orbiting clock adjustment.
> Otherwise the shift would lead to
significative
errors in the GPS localizations.

Don't be such a blatant idiot. Think while you are reading.
Due to the relativistic effects the frequency is shifted by
the factor (1+4.4647*10^-10) regardless of what the emitted
frequency is.

The point I explained above is that this shift is so small
that it is practically impossible to measure it by direct
frequency measurements on the ground, because the Doppler
shift due to the motion of the satellite is vastly bigger.

Think just a little bit, and there is no way you can fail
to understand that this is true.

I will in the following assume that the satellite clock is
NOT "GR-corrected". That is, it runs at its normal, proper, intrinsic
rate. (Like the very first GPS-satellite did before the correction
was switched on.)

Assume rather that the clocks are "corrected".

Shut up and read!
I am explaining how the frequency shift you are talking about
actually was measured in the very first GPS satellite,
which was NOT corrected for the first 40 orbits.

The rate of the satellite clock is compared to the rate of
the ground clock like this:
The satellite clock counts the "ticks" from the frequency standard
(like any clock does). At a certain position on its orbit, it transmits
the satellite clock time to the ground. This is repeated at a later
time, after a number of orbits. (The only uncorrected satellite clock
was running for 20 days and 40 orbits).
The observer on the ground has then the proper time measured by
the satellite to go the 40 orbits, and can compare this proper time
to the proper time measured by the ground clock.

So what's clear and proven is:
The proper time measured by the satellite between two specific
events is longer than than the proper time measured by a ground
clock between the same two events by the factor (1+4.4647*10^-10).

This is the crux of the matter.
But you are ignoring it, aren't you?

The point is that what actually is measured is how much proper
time the satellite clock ticks out per orbit.
This time is proven to be longer than the proper time ticked
out by the ground clock per orbit.

Don't you see the consequence?


The GR explanation for this is that the satellite's world line
between the events is longer than the world line of the ground
lock between the same two events. The reason for that is the curvature
of space-time (and the motion of the satellites and the rotation of the Earth.)

(This is really a slight simplification because it is not really the same
two events, but two pair of events which are simultaneous in
the GPS-frame of reference.)

Note that two proper times are measured and compared,
and the "observed rate difference" is calculated as a necessary
consequence of the different proper times.


The GR explanation can as well be replaced by my explanation, i.e.
the orbiting clocks keep ticking at the same rate as the ground clocks.

Stop right there.
The GR explanation IS that the clocks are ticking at the same proper,
intrinsic rate as the ground clocks (we are still talking about unadjusted
clocks).

But when YOU say:
"the orbiting clocks keep ticking at the same rate as the ground clocks",
I interpret it to mean that the clocks really ticks out the same amount
of time per orbit, but that the frequency is _observed_ to be increased
when it is measured from the ground.

This is wrong by two different reasons:

1. It is a _fact_ that the satellite clock advances more
than the ground clock per orbit, and that the difference
is t_satelite/t_ground = (1+4.4647*10^-10)

2. It is a blatant self-contradiction.
If the satellite clock ticks N+n cycles per orbit,
and every tick is observed from the ground, and
the ground clock ticks N cycles per orbit, then
the observed frequency shift must be (N+n)/N.
Isn't that obvious even to you?
There is no way both clocks can tick out the same
number of ticks per orbit, and that a frequency shift
can still be observed.

I repeat:
The relativistic frequency shift is never directly measured.
It is the proper times in 1. above that are measured.
The frequency shift is inferred from the reasoning explained in 2.
The relativistic frequency shift MUST be
(N+n)/N = t_satellite/t_ground = (1+4.4647*10^-10)

It is well known that accelerations, even enormous, don't affect the
tick rate of clocks. So, why should the small Earth's gravitational
field affect it. This seems to me a contradiction.
The Earth's gravitational field affects the curvature of space-time.


According to GR. But why such curvature should affect the rate of the
orbiting clocks, whereas accelerations don't?

The curvature doesn't affect the rate of the clocks,
and neither does acceleration. All clocks are always
running at their proper, intrinsic rate unless they
are malfunctioning.

Due to the curvature of space-time, the proper time of
the satellite's world line is simply longer that the proper
time of the ground clock's world line.

Consequently, contrarily to what they claimed, Hafele & Keating could
not observe significative time differences between the flying and
ground clocks after the former ones were brought back to the ground.
Needless to add that their experiment had a lot of experimental and
even systematic errors sources (They said themselves that "the number
of
measured values is too small for a good statistical analysis", whatever
"good" means. Perhaps that their analysis could not be considered
as good?).
Consequently, the gravitational field of the Earth, the motion
of the planes, and the rotation of the Earth will affect the lengths
of the different world lines in question.

My formula obtained from potential energy + geometical considerations
is the same as the GR formula, but excudes the possibility that the
orbiting and ground clocks tick at different rates.

..which means that you are talking nonsense.

But why care so much about the H&K experiment?

Simply because the clocks were brought back to Earth.

Several other experiments are done showing the same effect
with much better precision.
GPS, of course, and then there are the Alley experiment,
the Vessot (gravity probe A) and the flight experiments
described here:
http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf
see chapter 5.


In which other experiments were time differences observed on
clocks brought back on Earth?

Alley's plane landed where it started, and so did the planes
in the flight tests in the reference I gave above.

But I still don't get your point in the subject line.
The "H&K claims" are what GR predicts.
GPS clocks behaves as predicted by GR.
So how can a confirmed GR prediction falsify a GR prediction?

Your theoretical exposition is doubtless interesting, but could
you use it and solve the following problem?

Let's assume that GPS clocks can be put instantaneously into their
GPS orbits or brought back to Earth from those orbits.

1) Two GPS clocks A and B are synchronized on Earth. Clock B
is sent to its orbit at time 0 and brought back to Earth
after 1 day (you can use 86163 s or 86400 s).
What will be then the time difference between clocks A and B,
assuming that the only effect on clock B is due to the difference
in gravitational potential and its orbital velocity.


2) Just before launch, the frequency of GPS clock B is adjusted
downward by 4.4647 parts in 10^10 relatively to clock A.
After 1 day, clock B is brought back to Earth.
What will be then the time difference between clocks A and B,
assuming that the only effect on clock B is due to the difference
in gravitational potential and its orbital velocity.

Marcel Luttgens


How confused can you get?

Paul

.

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