Re: GPS 'GR Correction' Myth.
- From: The Ghost In The Machine <ewill@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 29 Jul 2005 05:00:03 GMT
In sci.physics.relativity, H@..(Henri Wilson)
<H@>
wrote
on Thu, 28 Jul 2005 11:56:51 GMT
<9rhhe19rbqfe14p2d7pudumoo9fj8aauck@xxxxxxx>:
> On Thu, 28 Jul 2005 05:00:10 GMT, The Ghost In The Machine
> <ewill@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
>
>>In sci.physics.relativity, H@..(Henri Wilson)
>><H@>
>> wrote
>>on Wed, 27 Jul 2005 23:55:08 GMT
>><dl7ge159os435ht9jkp67vi24ee8lep9n4@xxxxxxx>:
>>> On Wed, 27 Jul 2005 21:18:27 +0200, Kim B <spamfree@xxxxxxx> wrote:
>>>
>>>>On Sun, 24 Jul 2005 11:14:03 GMT, H@..(Henri Wilson) wrote:
>>>>
>>>>>On Sun, 24 Jul 2005 02:29:45 +0000 (UTC), bz <bz+sp@xxxxxxxxxxxxxxxxxxxx>
>>>>>wrote:
>>>>>
>>>>>>On earth, the test clock is again compared to the ground control clock.
>>>>>>They are now keeping time at the same rate. The test clock seems to have
>>>>>>gained time while in orbit.
>>>>>
>>>>>Correct. It ran fast for all the time it was up there.
>>>>>GR says it will read the same when it returns to Earth.
>>>>>
>>>>
>>>>No, that's not what GR says.
>>>
>>> Please tell us, in your wisdom, precisely what GR DOES say.
>>> Nobody seems to know....
>>
>>You do have a point. Of course, in order to properly answer
>>that question one has to know precisely what the clock is doing.
>>In short:
>>
>>[1] what's the path to orbit?
>>[2] how long it stays in orbit (what's the path during orbit)?
>>[3] what's the path to deorbit?
>
> Ghost, most of the time your massages are pe\retty rational.
>
> But every now and then you come ouit with the most outrageous comments.
>
> GR apparetly has a theory about why clocks should change rates when in
> different gravity potentials.
> I want a relativist to tell me exactly what that theory is.
To boil it down as cryptically as possible, GTR postulates
that G = T. Or, if one wants a slightly more long-winded
explanation, one can refer to John Baez's General Relativity
tutorial, located conveniently at
http://math.ucr.edu/home/baez/gr/gr.html
where he defines G as the Einstein tensor, and T as the
stress-energy tensor.
Most people, of course, will use more useful forms of these
equations -- I'd have to find a usable copy of Hafele-Keating,
for example, or one might refer to
http://relativity.livingreviews.org/Articles/lrr-2003-1/node2.html
which works through an inertial-to-rotating Minkowskian reference
frame transformation, or
http://relativity.livingreviews.org/Articles/lrr-2003-1/node5.html
which has a lot of hairy math but comes up with the result
-4.4647*10^-10 (eq #35), which means that the orbital observer
will see the ground clock as being too slow, or, equivalently,
that the ground observer will see the orbiting clock as running fast.
The math looks vaguely reasonable but I've not schlogged through it
in detail.
--
#191, ewill3@xxxxxxxxxxxxx
It's still legal to go .sigless.
.
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