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.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.
From "http://en.wikipedia.org/wiki/Polaris" [Broken]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!
I just want to know if you, all people who master relativity, agree whith the statement of jtbell.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.
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.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 ??