Two Spheres, Two Humans: Who is Older?

[aritrasasmal]

Let there be two spheres in free space. Also there are two humans on each of them.
Now the spheres move apart and come together again(like a harmonic oscillator),
When they move apart , wrt one human the other is moving into lesser grav field and when he comes back he should have aged less than him. But to the other the observations are the same. So ehen they come together how will they agree on who is older? Will they?

 

[Polyrhythmic]

The situation is symmetric, when they come back together, they should've aged at the same rate.

 

[aritrasasmal]

The situation is symmetric, when they come back together, they should've aged at the same rate.

Please elaborate on your answer. Note we are looking from the point of view of each individual.

 

[PAllen]

Please elaborate on your answer. Note we are looking from the point of view of each individual.

You're confusing SR inertial frame principles with GR non-inertial frames. Also, you have gravitational time dilation backwards - moving to lower gravity leads to faster aging, not slower.

Anyway, as they move apart, each experiences less gravity (strength due to combined masses), thus faster aging, then slower, completely symmetric. Each observes the other's clock moving the *same* as theirs, at all times.

 

[martinbn]

It seems that he moves into a lesser grav field compare to the field before the move, not lesser than the field where the stationary man is, no?

 

[bcrowell]

What role do the spheres play in the example?

As Polyrhythmic said, it's a symmetric situation, so of course they'll agree.

When they move apart , wrt one human the other is moving into lesser grav field and when he comes back he should have aged less than him.

I think this must be where you're running into trouble. I assume you're talking about flat spacetime here. In a static spacetime, which this is, gravitational time dilation can be determined from the gravitational potential (not the field). In a flat spacetime, there is a constant gravitational potential, so there's no gravitational time dilation.