Understanding Time Dilation: Exploring Special & General Relativity

[Tachyonie]

I am trying to get through Special & General Relativity on my own. However I seem to reach a problem.

Imagine person A standing on Earth and person B flying around Earth close to speed of light (it doesn't have to be close to speed of light, I just want to make the effects of relativity obvious). Now person A ages by 50 years and person B only by couple of minutes. However what's stopping the Person B from claiming that HE is at rest and person A is moving near the speed of light and thus HE should be the one with gray hair and grand children?

I tried to research it and I found that that of course, nothing stops him from saying that, and he would be also right to state it, but I don't seem to get the reason why is that? Clearly one is young and one is old at the end of the flight but how is that possible? Shouldnt they both be young and old at the same time?

 

[MeJennifer]

I am trying to get through Special & General Relativity on my own. However I seem to reach a problem.

Imagine person A standing on Earth and person B flying around Earth close to speed of light (it doesn't have to be close to speed of light, I just want to make the effects of relativity obvious). Now person A ages by 50 years and person B only by couple of minutes. However what's stopping the Person B from claiming that HE is at rest and person A is moving near the speed of light and thus HE should be the one with gray hair and grand children?

I tried to research it and I found that that of course, nothing stops him from saying that, and he would be also right to state it, but I don't seem to get the reason why is that? Clearly one is young and one is old at the end of the flight but how is that possible? Shouldnt they both be young and old at the same time?

Since B's path included acceleration and A's path did not (ignoring A's small effect on acceleration by standing on earth) B's accumulated proper time during the trip is less than that of A.

 

[Tachyonie]

So B cannot say that he's the one who stays at rest and A is the one moving because B had to accelerate at the beggining of his voyage?

 

[Ich]

So B cannot say that he's the one who stays at rest and A is the one moving because B had to accelerate at the beggining of his voyage?

No, because he has to accelerate to get back to the starting point.

 

[michael879]

So B cannot say that he's the one who stays at rest and A is the one moving because B had to accelerate at the beggining of his voyage?

You said he's orbiting Earth at a speed close to c. That means he's experiencing a very high constant acceleration during his orbit.

 

[Tachyonie]

I wanted to mention that he's not accelerating (orbiting) but traveling at straight line. Guess I should have included meh.

 

[bockerse]

Answer

Hi, my disclaimer as always is that I'm no physicist, but the acceleration of the ship refers to the TURNING AROUND to return to the starting point. The crew of the ship experiences forces that throw 'em to the walls, and the forces produce acceleration (F=ma). This ain't no paradox.

-Gerrit

 

[MeJennifer]

I wanted to mention that he's not accelerating (orbiting) but traveling at straight line. Guess I should have included meh.

Actually if he is orbiting he is not accelerating but in free fall. But obviously he has to enter and leave orbit to meet A and for that B needs to accelerate.

 

[MeJennifer]

You said he's orbiting Earth at a speed close to c. That means he's experiencing a very high constant acceleration during his orbit.

No, if he is orbiting, then regardless of relative speed, he is in free fall and not accelerating.

 

[Tachyonie]

How does the relative short time of acceleration change everything? Shouldnt they still be both able to say that they are the one at rest (except when turning, etc.)?

 

[MeJennifer]

How does the relative short time of acceleration change everything? Shouldnt they still be both able to say that they are the one at rest (except when turning, etc.)?

An objects that accelerates changes its orientation in spacetime with respect to other objects, a consequence of this is that the rate of accumulation of proper time changes from that moment on.

 

[phyti]

An object released from a height, accelerates, in free fall toward the Earth's center, until it's interrupted by the ground.
A satellite does the same thing, but with the proper horizontal velocity to avoid meeting the ground.
The satellite's direction of motion is changed by something!

 

[MeJennifer]

An object released from a height, accelerates, in free fall toward the Earth's center, until it's interrupted by the ground.

No, an object relased from a hight, free falls towards the Earth's center and starts to accelerate away from it when it reaches the surface of the earth.

The reason free falling objects approach each other is not due to acceleration but is due to the curvature of spacetime.

 

[GregStacey]

Hi Tachyonie - what you describe is a version of the Twin Paradox. It's described (and solved) in detail on wikipedia: just type "twin paradox" and you'll be on your way.

 

[Tachyonie]

Cheers mate! Thanks everybody, very helpful.