Understanding Time Dilation in Accelerating Frames and the Equivalence Principle

[alexbib]

1. The time distortion due to relative velocity does not cause any "real" loss if time in itself,loss of time only happens with acceleration, right? How can I predict the amount of time that has been lost relative to an inertial point of view(if I know the value for the other variables)?

2. Is the gravitational field created by an object relative? ie: does the m in the formula vary with 1/(1-sqrt(v^2/c^2))?

3. c is the limit of the velocity an object can have. Is there a limit to the acceleration an object can have (I am speaking only of instantaneous acceleration here)?

 

[lethe]

Originally posted by alexbib
1. The time distortion due to relative velocity does not cause any "real" loss if time in itself,loss of time only happens with acceleration, right? How can I predict the amount of time that has been lost relative to an inertial point of view(if I know the value for the other variables)?

i m not sure what it means for time to be "lost". time runs slower in one frame relative to another, if the frame is in motion. time a frame with a stronger gravitational field runs slower relative to an inertial frame as well, since, by the equivalence principle, that frame is accelerating.

2. Is the gravitational field created by an object relative? ie: does the m in the formula vary with 1/(1-sqrt(v^2/c^2))?

yes, the motion of the particle effects the gravitational field, although it is not so simple as just multiplication by gamma. there are gravito-magnetic effects.

3. c is the limit of the velocity an object can have. Is there a limit to the acceleration an object can have (I am speaking only of instantaneous acceleration here)?

no limit to the acceleration a particle can have, in its rest frame, as far as i know.

 

[alexbib]

" m not sure what it means for time to be lost" I mean that if you speed up your watch to .95c and then turn it around and make it comeback to its original position it will be behind a clock that has not moved by a certain amount of time. When you compare them, the rate at which they count time should be equal, but the clock that has moved will be behind the other.

 

[alexbib]

false. By hasn't moved, I meant that has not accelerated. I use this clock as reference frame. When the other clock comes back from the trip, it will be lagging behind (not in counting rate, but in the hour shown). This has even been proven experimentally. Once they are back at the same place, and are at relative rest, the clock that has accelerated is late. At this moment, from any reference frame, clock that has accelerated IS late.

Edit: sorry, I misread your last post, we are in fact agreeing on this. But obviously, the fact that less time has passed on the clock that made the trip depends on acceleration, not relative speed. What depends on relative speed at any moment is the rate at which they count the time from each other's prespective.

 

[alexbib]

but if you have two clocks that move with relative velocity v, wihtout accelerating (or rather, let's say that they are in orbit around a planet, so they undergo the same acceleration), and they come back to the same initial position, after completing a turn in opposite directions, their clocks will agree (the question here is: do they agree, in the hour they display, acording to the observers traveling with the clocks, or do theym only agree to a "neutral" observer that we use as a reference frame?), even though each one sees the other running slow.

If they only agree according to a neutral observer, then you are right and the fact that they disagree in the situation where one of them accelerates is only due to the fact that the observers share the reference frame of the inertial watch

 

[alexbib]

yeah, I get what you mean. but we agree that in the situation where one of the clocks is accelerating and then coming back at rest(relative to the other clock) at its initial position, once they are at the same position and at relative rest, their reference frames become one and the same. So they both agree that the inertial clock has counted more time? How can you explain that, from the point of view of the clock that has accelerated, the other clock must have actually been running faster, even though it had a relative velocity? By your method, from the point of view of the clock that has accelerated, it is the inertial clock that should be late, while in reality (and in experiement), they both agree that the accelerating clock is late.

 

[alexbib]

So you're saying that from the point of view of the accelerating clock, at every moment, it sees the other clock running slow, but in the end it sees it displaying more elapsed time? And even if it is so, the only difference between clock A and B is that B has accelerated, and it displays less elapsed time. Then the acceleration should be the cause of the "missing" time on it. Because, as we have seen with symmetrical situations, relative velocity alone does not cause a difference in elapsed time.

Thanks for the link, I'll take a look!

 

[Janus]

Originally posted by alexbib
How can you explain that, from the point of view of the clock that has accelerated, the other clock must have actually been running faster, even though it had a relative velocity? By your method, from the point of view of the clock that has accelerated, it is the inertial clock that should be late, while in reality (and in experiement), they both agree that the accelerating clock is late.

If you break the trip down by stages, this is what the accelerating clock measures:

1. Accelerating away.
Inertial clock changes from in sync to running slow.

2. Coasting away.
Inertial clock running slow.

3. decelerating to a stop relative to the inertial clock.
Inertial clock running fast.

4. Accelerating towards inertial clock.
Inertial clock running fast.

5. Coasting towards inertial clock.
Inertial clock runs slow.

6. Decelerating to a stop next to inertial clock.
Inertial clock goes from running slow to being in sync.

After all these combined effects are taken into account, the accelerating clock will have found that less time has past for it.

Meanwhile, the inertial clock will just see the accelerating clock run slow the whole time just due to relative velocity.

(One point. during phases 3 and 4, the accelerating clock will see two effects operating on the inertial clock: the tendency to run fast due to the acceleration, and the tendency to run slow due to relative velocity. Which one dominates at any given time depends on the distance form the inertial clock, the relative velocity and the acceleration. The total measured elasped time for the inertial clock will always end up as more for these periods.)

 

[alexbib]

Thx, good explanation!

"the tendency to run fast due to the acceleration"

how does the acceleration cause this?

 

[alexbib]

No, I think Janus is right, the inertial clock actually running faster has to be due to acceleration. Go read the GR explanation from the link you provided.

 

[alexbib]

I get your point. As you say, it depends only on the velocity, and the best way to calculate it is to do it with time distortion relative to the inertial frame.
However, I also think it is important to understand why you still get more elapsed time on the inertial clock from the non-inertial clock's point of view, which is (in my opinion) explained pretty well on the link you posted.

Thanks a lot for your answers guys.

 

[GijXiXj]

This is all so terribly confusing ...

... http://gijxixj.home.att.net/Relativity/GrSrTpSatExplns.htm ?

I'm very dubious about accelerations not being a factor, or at least an easily discountable one.

Question: If you accelerate, does the Principle of Equivalence not include the idea that your time slows down as if you were in a gravitational field? I know (foggy memory) that at least your not supposed to be able to tell if your falling (gravity) or accelerating, at least by any 'internal' experiment.