The Twin Paradox: Exploring Aging Differences

[DaTario]

Hi All,

Regarding the twin paradox, is it true that if both twins had traveled in opposite directions and turned back, both would be still with the same age?

Tell me if it is right to think like this:
The central points in "aging faster" are 1)the non simmetric set up and 2) the fact that one of them has felt slower time because of being subjected to an acceleration (equivalent to gravitational) field.

And the last one:
Tell me if it makes sense to propose a problem where one of the twins (A) goes to a trip of one year (thus acquiring physical reasons to age slower) while the other (B) stays at the Earth, and the problem asks you to calculate the amount of mass that would have to be added to the Earth when A has left in order to compensate in B the difference in aging between them.


Best Regards,

DaTario

 

[Ich]

1) true
2) true in flat spacetime (you could change your speed aided by a gravitational field, where you would not feel any acceleration)

It makes sense: According to GR, clocks in a gravitational potential run slow. You could increase gravitation by adding a certain amount of mass to have B´s time running at the same rate as A´s time.

 

[yogi]

First Q - yes - if they both were given the same acceleration and acquired the same velocity relative to their starting point - so that everything is symmetrical about the point where the were initially located.

Second Q - depends upon how you interpret what is significant about the acceleration - it is not the acceleration per se that causes the difference in times - although some authors will claim this is so - but most texts take the view that once the Twin's clocks are brought to sync in the same reference fame - the acceleration is only incidental to calculating which twin aged the most - acceleration itself does not change the clock rate - the difference in times accumulated by the traveling twin and the stay at home twin depend upon the relative crusing velocity and the length of the journey.

Third Q invokes GR - but the Q re the addition of new mass may be misleading - GR deals with clocks that are subjected to different gravitational potentials - not different gravitational field strengths

 

[DaTario]

Second Q - depends upon how you interpret what is significant about the acceleration - it is not the acceleration per se that causes the difference in times - although some authors will claim this is so - but most texts take the view that once the Twin's clocks are brought to sync in the same reference fame - the acceleration is only incidental to calculating which twin aged the most - acceleration itself does not change the clock rate - the difference in times accumulated by the traveling twin and the stay at home twin depend upon the relative crusing velocity and the length of the journey.

So there must be several different ways of traveling to a 10 light-years distant position and coming back 40 years latter, so that each one yields a different traveller twin's age in relations to the twin that have stood on Earth. Is it correct ?

Third Q invokes GR - but the Q re the addition of new mass may be misleading - GR deals with clocks that are subjected to different gravitational potentials - not different gravitational field strengths

[/QUOTE]

But as you start modifying the gravitational field strengh, aren't you modifying also the gravitational potential ?

A book in a bookshelf wil be able of doing more work in the falling process if the mass of the Earth increases, isn't it correct?

 

[yogi]

Yes - there are an infinite number of paths that could be taken to a distant place - once the traveler gets up to speed after a short acceleration - he might follow a straight line and then stop - turn around - and accelerate back to Earth - or the traveler might follow a large circular path - for example first heading outward at right anges to his ultimate destination, but following a circular curved path then leads past his ultimate target and then back to his starting point - so he at no time makes any abrupt velocity changes nor directional changes - Einstein says that the total time lapsed between the twin on Earth and the traveler will depend only upon the length of the trip and the velocity.

As far as modifying the gravitational potential by adding mass - yes, but you need to know just how the field will vary wrt to the clock that is used for comparison - if the comparison clock is at infinity - then adding mass will allow you to make a comparison between the time dilation due to velocity and the time dilation due to gravitational potential - the relationship is curiously straightforward - the velocity that corresponds to a given time dilation is the same as the acceleration potential that results when a clock is centrifuged such that its tangential velocity is equal to the relative velocity between two frames in SR that yields the same time dilation. (I don't know if I said that very well).

 

[DaTario]

I think what you said is partially clear to me. I agree with that point in which you describe a clock at infinity as being a non gravitationally disturbed clock.

Thank you


Best Regards

DaTario