Re: I Owe Einstein an Apology. Sorry Albert!

From: The Ghost In The Machine (ewill_at_sirius.athghost7038suus.net)
Date: 12/13/04 

Date: Mon, 13 Dec 2004 17:01:28 GMT

In sci.physics.relativity, jahn
<susysewnshow@yahoo.com.au>
 wrote
on Mon, 13 Dec 2004 09:49:46 -0500
<325ohrF3igb86U1@individual.net>:
>
> "Paul B. Andersen" <paul.b.andersen@deletethishia.no> wrote in
> message news:cpk8u2$9l5$1@dolly.uninett.no...
>> Excuse me for butting in, but I find so much
>> confusion about the GPS in this thread that I
>> feel the need for clearing up a few misconceptions.

Feel free. :-)

>>
>>
>> jahn wrote:
>> > "The Ghost In The Machine" wrote:
>> >>jahn wrote:
>> >>>"The Ghost In The Machine" wrote:
>> >>>> jahn wrote:
>> >>>>>"The Ghost In The Machine" wrote:
>> >>>>>>If the clocks are moving then SR predicts they will not remain
>> >>>>>>synchronized.
>>
>> Clocks moving in a frame of reference will not
>> generally stay synchronous in that frame,
>> but they may do so in special cases.
>> For example, clocks moving in a circle with
>> the same speed will stay synchronous to each
>> other in the "stationary frame". They will
>> run slow compared to stationary clocks,
>> but they will stay in sync.
>> This is the case in the GPS.
>> All the GPS satellite clocks stay in sync
>> to each other in the ECI frame because
>> they all move in circular orbits with the
>> same speed and at the same gravitational potential.
>>
>> >>>>>SR predicts moving clocks can't keep good time?
>> >>>>>I have two garden hoses an egg timer and a bag
>> >>>>>of marbles that says they must be broken.
>> >>>>>http://www.boulder.nist.gov/timefreq/time/commonviewgps.htm
>> >>>>
>> >>>>The SR correction is t' = (t-vx/c^2) * gamma .
>> >>>
>> >>>>The vx/c^2 is merely a reflection that the two clocks are
>> >>>>communicating through speed-of-light (e.g., radio), but
>> >>>>the gamma is the killer; gamma = 1/sqrt(1-v^2/c^2).
>>
>> The vx/c^2 is a reflection of the simultaneity of relativity.
>> It has nothing to do with "communication through speed of light".
>>
>> >>>>It's a very slow killer, of course; the typical speed
>> >>>>of a spacecraft is on the order of 9 km/s = 3 * 10^-5 c, which
>> >>>>results in a gamma of about 4.5 * 10^-10. The GPS delta is
>> >>>>almost exactly this: 4.46 * 10^-10. However, this is at
>> >>>>best a very very rough estimate, just to give one the feel.
>> >>>>It's also the wrong sign. :-)
>>
>> Which should tell you something. :-)
>>
>> It is actually quite simple to make a first order
>> calculation of the rate of the GPS satellites.
>>
>> The relative difference in the rate of a clock in circular orbit
>> compared to a clock on the surface of the Earth is according to GR
>> to a first order approximation:
>> (Approximation of the Schwarzchild solution)
>>
>> (f2 - f1)/f1 =
>> (G*M/(c^2*r1) - G*M/(c^2*r2)) - (0.5*v2^2/c^2 - 0.5*v1^2/c^2)
>>
>> Where G = gravitational constant, M = mass of the Earth,
>> r1 = radius of the Earth, r2 = radius of the orbiting clock's orbit,
>> v1 = speed of the Earth clock in ECI frame,
>> v2 = speed of the orbiting clock in ECI frame
>>
>> Since we have G*M/r1^2 = g, acceleration at Earth's surface, we have:
>> (G*M/(c^2*r1) - G*M/(c^2*r2)) = (g/c^2)*r1*(1-r1/r2)
>>
>> Altitude of GPS satellites = 20200 km
>> Orbital period = half sidereal day
>> Radius of the Earth r1 = 6.37*10^6 m
>> Radius of GPS orbit r2 = 26.57*10^6 m
>> g = 9.81 m/s^2
>>
>> Inserting these numbers, we find that the rate difference
>> due to gravitation is: 5.28*10^-10 (+45.6 us/day)
>>
>> So to the speed part:
>> v1 = 40000km/(23h 56m) = 4*10^7/86160 = 464 m/s
>> v2 = 2*pi*r2/(11h 28m)= 3.87*10^3 m/s (-7.1 us/day)
>>
>> 0.5*v2^2/c^2 = 0.83*10^-10
>> 0.5*v1^2/c^2 = 1.2*10^-12
>> Thus the rate difference due to the speed will be: -0.82*10^-10
>>
>> The combined rate difference: (5.28-0.82)*10^-10 = 4.46*10^-10
>> Note that the orbiting clock runs _fast_.
>>
>> During one day, the difference in proper times will amount to:
>> 4.46*10^-10*86400 s = 38.5*10^-6 s = 38.5 us
>>
>> According to:
>> http://vishnu.nirvana.phys.psu.edu/mog/mog9/node9.html
>
> *****MORE BS ******
> While trying to retrieve the URL: http://vishnu.nirvana.phys.psu.edu/mog/mog9/node9.html
>
> The following error was encountered:
>
> Unable to determine IP address from host name for vishnu.nirvana.phys.psu.edu
> The dnsserver returned:
>
> Name Error: The domain name does not exist.
> This means that:
>
> The cache was not able to resolve the hostname presented in the URL.
> Check if the address is correct.
>
> Your cache administrator is root.
>

Looks like something moved. http://phys.psu.edu exists fine.

The math looks fine, too. :-)

[crunched] 

-- 
#191, ewill3@earthlink.net
It's still legal to go .sigless.
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