Can I just chip in and say that the time dilation associated with GR and the GPS is not symmetrical like the twin's paradox time dilation associated with SR.

Can I just chip in and say that the time dilation associated with GR and the GPS is not symmetrical like the twin's paradox time dilation associated with SR.
Yes, it is true. The rates of clocks on the Earth surface and in space (all other things being equal) are different in an absolute sense. For all observers, clocks on the Earth surface (in a lower, or more negative, gravitational potential) tick slower than clocks in space (in a higher gravitational potential). There is no symmetry.

If the two ships have the same "acceleration profiles" then yes, their clocks will show the same amount of elapsed time when they return to Earth.
And during the journey, isnt there any time dilation due their relative velocity ?

How can you go North from the North pole or South from the South Pole? Did you mean "North Pole direction South" and "South Pole Direction North"? That would be ambiguous since from the North Pole every direction is South and from the South pole every direction is North!
From "http://en.wikipedia.org/wiki/Polaris" [Broken]

Polaris (α UMi / α Ursae Minoris / Alpha Ursae Minoris), more commonly known as The North Star or simply North Star, is the brightest star in the constellation Ursa Minor. It is very close to the north celestial pole (42′ away as of 2006), making it the current northern pole star.

Im shure you understood me.

Anyway, sorry for my poor english.

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If the two ships have the same "acceleration profiles" then yes, their clocks will show the same amount of elapsed time when they return to Earth.
I just want to know if you, all people who master relativity, agree whith the statement of jtbell.

If you give any further explanation, please, dont use the word "time", because I dont understand it, use "the reading on clock A".

And ( please again ) compare clocks when they are at the same place.

I understand that the clocks signal can be emitted ( by electromagnetic waves ) and received at another place where there is another clock, and the two clock signals can be compared ( yes, there will be a doppler effect ).

Thanks.

pervect
Staff Emeritus
So, if one twin takes off from North Pole direction North and the other takes off from South Pole direction South.
They accelerate at the same rate, until they spend the first tank of fuel (say one day )
They continue their voyage whit the engines off ( say one year, mesured by their own clock ).
They switch on their engines to return to earth, two days, two more tanks of fuel.
They continue their voyage towards earth whit the engines off .
They land on earth after another year, one day, another tank of fuel.

Their clocks have the same reading ??
As jtbell remarked, assuming you mean "celestial north" and "celestial south", the answer to this question is that both clocks on the spaceships will have the same reading (within experimental error) when the ships reunite.

It would actually be better if both ships took off in opposite directions perpendicular to the ecliptic plane of the solar system rather than to celestial north and south - you might get some very minor effects (depending on whether the launch was at solstice or equniox or somewhere in-between), but I don't think that's the point of the question.

I would think this would be obvious - it's a consequence of isotropy, the fact that neither "north" nor "south" is a preferred direction.

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pervect wrote:
"As jtbell remarked, assuming you mean "celestial north" and "celestial south", the answer to this question is that both clocks on the spaceships will have the same reading (within experimental error) when the ships reunite."

Ok, this is enough for me.

I suppose you all are tired of the same cuestion, Ive seen it several times in the few days Ive been reading this forum.

Thanks