Time Dilation: A & B's Age Difference

[jha192001]

This is a gendenke experiment.

You(A) and your friend (B) are on earth. Now your friend sits on a spaceship that can fly at speed of 0.1c. He flies for 5 year straight ahead(away from earth) and then returns back slowly.
The answer that i get is B would have aged. Assuming this answer is right i want to put a question.
B goes. away from A and returns. But in reference frame of B, A goes away at 0.1c and returns so according to him A would have aged more. But when they meet who would have aged more? If no one, then how could wr say speed even has a effect called Time Dilation.
Thanks For Your Time.[emoji1]

 

[Ibix]

Both would have aged, but B will be younger than A by about nine days.

B felt acceleration. A did not, remaining inertial for the whole experiment. Thus B cannot use naive time dilation results which are based on the use of inertial frames, since B was not at rest in an inertial frame for the whole experiment.

The one who felt acceleration will be younger. This is not a direct consequence of acceleration, by the way. Edit: see the article linked by Grinkle in the next post for details.

 

[Grinkle]

Read this -

https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/

 

[Nugatory]

And also http://physicsfaq.co.uk/Relativity/SR/TwinParadox/twin_paradox.html

 

[jha192001]

Both would have aged, but B will be younger than A by about nine days.

B felt acceleration. A did not, remaining inertial for the whole experiment. Thus B cannot use naive time dilation results which are based on the use of inertial frames, since B was not at rest in an inertial frame for the whole experiment.

The one who felt acceleration will be younger. This is not a direct consequence of acceleration, by the way. Edit: see the article linked by Grinkle in the next post for details.

Sir,
B is in noninertial frame but as A is on Earth he himself is in one too..Then on what basis "B is youner" can be said.
P.s: I am reading about lorentz rn

 

[Ibix]

Sir,
B is in noninertial frame but as A is on Earth he himself is in one too..Then on what basis "B is youner" can be said.
P.s: I am reading about lorentz rn

The Earth's surface rest frame is close enough to inertial that the error from treating it as inertial (Edit: or, more precisely, using the Sun-centred inertial frame and pretending that A is at rest in this frame) is tiny - about one part in 10⁸, if I've done my mental arithmetic right. As to why B is younger, it doesn't really have anything to do with being inertial or not. It's just you can't naively apply standard SR time dilation formulae to non-inertial frames, which you were trying to do. Did you read the article Grinkle linked? It explains the age difference quite well.

 

[Grinkle]

B is in noninertial frame but as A is on Earth he himself is in one too

If A were not on Earth but inertial, the age difference when he met up with B would be slightly more, as @Ibix noted.

If you are thinking that whether or not a frame is accelerating is frame dependent, this is incorrect. B felt acceleration according to B, and B felt acceleration according to A. They agree on this. A felt a much much smaller acceleration (being on Earth) according to A, and also according to B - they agree on that as well.

 

[PeterDonis]

B is in noninertial frame but as A is on Earth he himself is in one too..Then on what basis "B is youner" can be said.

It has nothing to do with frames. It has to do with their different paths through spacetime. The twin paradox FAQ that @Nugatory linked to goes into all this. Please read it.