GPS Satellites & the Twin Paradox: Time Dilation Explored

[alvaros]

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, don't use the word "time", because I don't 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]

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.

[edit]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.

 

[alvaros]

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, I've seen it several times in the few days I've been reading this forum.

Thanks