Time Dilation Exp: Answers to Questions on A & B's Experiences

[Guilherme Mesquita]

Hello everyone,

The questions I am about to ask have probably been explained already, but even after everything I've read I still cannot understand how this experiment would play out and how to answer these questions. So without further ado here is the experiment:

Imagine you have person A standing still while person B is riding a train in a small circular route around him (they can see each other) at near the speed of light.
For B, he has been traveling for 1 year. Let's consider (if we can) that the ratio of time dilation is: 1 year for B corresponds to 50 years for A.

Questions:
1) How much time does A think has passed?
2) If the answer is 50 years, then B must have seen A aging very quickly no? Which is to say, would B see the life of A like in fast forward motion?
3) Would A see the clock on the train in slow motion?
4) If the answer is yes, is the train also in slow motion (doesn't make much sense)?

I apologize for the ignorance, and I appreciate the time and answers!

 

[PeroK]

1) 50 years.

2) Yes. Yes.

3) Yes.

4) No.

 

[Guilherme Mesquita]

1) 50 years.

2) Yes. Yes.

3) Yes.

4) No.

Thank you for the answer, but it is a bit confusing that the speed of the train slows the mechanical process of the clock being seen by A but not the train itself. Could you explain why?

 

[PeroK]

Thank you for the answer, but it is a bit confusing that the speed of the train slows the mechanical process of the clock being seen by A but not the train itself. Could you explain why?

The speed of the train is given. That is what A observes/measures. That is the defining factor of the problem. The speed of the train can't cause the speed of the train to reduce. That would make no sense.

Do you understand the concept of time dilation?

 

[Guilherme Mesquita]

The speed of the train is given. That is what A observes/measures. That is the defining factor of the problem. The speed of the train can't cause the speed of the train to reduce. That would make no sense.

Do you understand the concept of time dilation?

I do know (maybe not understand) what the concept is and I'm somewhat clarified by a few experiments that show, in conjunction with the equation of c x time = distance, how, for example, from observing B shooting a light beam to a mirror and back to him, A would measure a greater distance traveled by light from her point of view, due to B being in movement. Correct me if I'm wrong, but with c (speed of light) being constant, if c was 1 (i know it isnt) and distance for B was 4 and for A was 5, that only leads to unknown variable T, which leads to being higher to one and lower to the other (4 and 5), therefore proving time dilation?

 

[PeroK]

I do know (maybe not understand) what the concept is and I'm somewhat clarified by a few experiments that show, in conjunction with the equation of c x time = distance, how, for example, from observing B shooting a light beam to a mirror and back to him, A would measure a greater distance traveled by light from her point of view, due to B being in movement. Correct me if I'm wrong, but with c (speed of light) being constant, if c was 1 (i know it isnt) and distance for B was 4 and for A was 5, that only leads to unknown variable T, which leads to being higher to one and lower to the other (4 and 5), therefore proving time dilation?

That's more or less the idea.

In your scenario we could assume A is in an inertial reference frame and B is moving at constant speed in a circle. For A, therefore, B's time is dilated.

Everything else follows from the fact that the distance between A and B is constant.

As B is in a rotating, hence non-inertial, reference frame it is more difficult to analyse things from B's frame. There are, in fact, some recent threads about this problem if you search for them.

I'm going offline now, but I'm sure others will help if you have more questions.

 

[Guilherme Mesquita]

That's more or less the idea.

In your scenario we could assume A is in an inertial reference frame and B is moving at constant speed in a circle. For A, therefore, B's time is dilated.

Everything else follows from the fact that the distance between A and B is constant.

As B is in a rotating, hence non-inertial, reference frame it is more difficult to analyse things from B's frame. There are, in fact, some recent threads about this problem if you search for them.

I'm going offline now, but I'm sure others will help if you have more questions.

Thank you very much for the information. It is indeed the point of reference of B that has caught my attention the most since what I've read usually only tells how A perceives B's time to slow down which, eventhough is a strange idea, I've grown "accustomed" to it, while the fact that B would see A's life going fast forward is a bit more mind-boggling for me now.

 

[Ibix]

The "I see you go slow, you see me go slow" phenomenon follows from Einstein's postulate that the laws of physics are the same in all inertial frames. We're both in inertial frames, so we must both see the same effects in the other from symmetry.

But the situation you have here is not symmetric. The person on the train is not in an inertial frame, and will rapidly notice that they are splattered all over the "outside" wall of the train. So there can't be a requirement of symmetry. In this case, it turns out that the situation matches the naive "I see you go slow, you see me go fast" that people wrongly expect of relativity.

 

[Mister T]

Thank you for the answer, but it is a bit confusing that the speed of the train slows the mechanical process of the clock being seen by A but not the train itself. Could you explain why?

Do you mean why, if a clock is in motion relative to a person, that the person will observe the clock running slow?

One way for you to understand this is to ask yourself why you'd expect the clock to not run slow. What Einstein showed was that if the clock doesn't run slow then the speed of light will have to depend on the speed of the light source. Experiments have shown the speed of light does not depend on the speed of the source, and that the clock does run slow.