Time Dilation: A & B's Age Difference

In summary, B felt acceleration while A did not, and according to B, this made him younger. However, according to A, this made him older.
  • #1
jha192001
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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]
 
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  • #2
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.
 
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  • #5
Ibix said:
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
 
  • #6
jha192001 said:
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.
 
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  • #7
jha192001 said:
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.
 
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  • #8
jha192001 said:
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.
 
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What is time dilation?

Time dilation is a phenomenon in which time appears to pass at a slower rate for an object or person who is moving at a high velocity compared to a stationary observer. This is one of the key principles of Einstein's theory of relativity.

How does time dilation affect the age difference between two people?

If two people, A and B, are moving at different velocities, then time dilation will cause their ages to differ. The person who is moving at a higher velocity will age slower, resulting in a smaller age difference between A and B over time.

What factors contribute to time dilation?

Time dilation is affected by an object's velocity and gravitational potential. The faster an object moves, or the closer it is to a massive object, the greater the time dilation effect will be.

Is time dilation a proven theory?

Yes, time dilation has been proven numerous times through experiments and observations. It is a fundamental principle of modern physics and has been validated by various experiments, including the famous Hafele-Keating experiment.

Can time dilation be experienced on Earth?

Yes, time dilation can be observed on Earth, but it is extremely small due to the relatively low speeds and weak gravitational forces. However, it is still a crucial factor in modern technologies such as GPS, which must account for time dilation effects in order to function accurately.

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