Paradoxes and Dilemmas

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Would you agree that uniqueness theorem for the force/potential relation does not stand?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I don't immediately see the relevance (if any) to physical models. For informed comments, you should ask someone more current in related areas of math research than I am. -|Tom|-

Can I dumb this down and ask about the slowing of clocks due to gravity on the north pole? TVF said clocks on the np slowed down and I want to know what the "correct" clock's(the one not slowed) position is so some base can be established from where the other effects can be explained.

Rereading the TVF statement I see GPS clocks are also slow running. What is the the "correct" clock in this case? And where is it located?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Rereading the TVF statement I see GPS clocks are also slow running. What is the the "correct" clock in this case? And where is it located?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The gravitational potential is GM/R, where R is the distance from mass M. The effect therefore goes to zero only at infinity. But we can correct the rate of any clock to remove the effect of gravitational potential on its rate.

Because the length of one second is an arbitrary, human-chosen length anyway (not an interval provided by nature), there is no need to make such corrections. The speed and potential effects all over Earth's surface cancel, so everywhere at sea level, atomic clocks tick at the internationally agreed rate of roughly 9 billion transitions of cesium that define one second. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>If GPS clocks run faster away from earth then time is correct at infinity where the potential becomes zero. What would the correction factor at infinity be?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

From GPS altitude to infinity is a correction of 14,400 ns/day, as given previously. From Earth's surface to infinity, it is 60,300 ns/day, as given previously (in this forum and at the link I provided).

Because the length of the second is arbitrary, we define one "international second" (SI) to be the length at Earth's surface, not the length it would be for a clock at infinity. Nothing in nature cares how long one second is, as long as we are consistent. To be consistent, we must change the rates of GPS clocks before launch so that, after launch, they will tick at the same rate as ground clocks.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>In other words, if we assume that earth and sat were the only objects in the universe and if the sat had an orbit of infinite radius around earth, in that case, what would be the rate in GPS clock as opposed to earth?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The GPS clock would tick 60,300 ns/day faster than clocks at Earth's surface if the rate is not corrected. It would tick at the same rate as clocks on Earth's surface if the rate is corrected before launch. Note that all clocks tick off approximately 10^14 ns/day, so these are very tiny corrections.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>I start getting a feeling that something is is wrong here. I think Jim is along the same lines.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

? -|Tom|-

The difference in the time of all these clocks is only ~1sec/70yr and that is a small effect. None the less it is interesting that the shape of Earth and its spin speed interact and exactly cancel each other so that a clock anywhere on Earth is running at the same rate. The only thing is if clocks are running slow on the north pole then every clock on Earth is also running slow-I guess?