Question about time dilation.

cragar

Ok I have attached a picture of what I am talking about.
A, B, C, represent people with clocks. And A is at rest with respect to the middle of the planet.
A, B , C all synchronize their clocks . Then B and C start to orbit around the planet with the same speed but in opposite directions. then they will meet on the other side and then eventually meet back where A is. in A's frame wont B and C's clock be dilated the same amount. So A would see B and C's clock reading the same time. In B's frame wouldn't he see
C's clock to be running different than his. Ok now my question is when B and C go around the planet once and meet up back with A. If A see's B and C's clock to be the same, would B see C's clock to be different?

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bcrowell

It sounds like you're basically describing a variation of the Hafele-Keating experiment. Unless I'm missing something, the answer to your question is yes. At the end, B and C are at the same event, so they agree on simultaneity of that event. They can unambiguously compare their clocks, and must agree on whether the clocks match. By symmetry, the two clocks must match.

cragar

why would the clocks match if they are moving with respect to one another?

bcrowell

There is no general rule stating that clocks in motion relative to one another must disagree, regardless of what the motion is.

Mike Holland

The rotation around the Earh complicates the picture. Rather think about triplets, two of whom travel away from Earth in opposite directions, and then return to compare clocks. While they are in relative motion, each sees the other two time dilated and their clocks running slowly. As they return, the same applies. When they return, the travellers clocks will agree, but they will both be behind the stay-at-home triplet's clock. How come? Because the accelerations to reverse direction and return have a reverse effect on their clocks so that each sees the other clocks running fast during this period.

Your picture is complicated because they are accelerating all the time to counter Earth's gravity and to travel in an orbit. They are travelling away from each other and then towards each other every revolution. But when they stop to compare notes their deceleration balances the books and their clocks agree.

Mike

jbriggs444

That is a reasonable summary. However the deceleration when they stop to compare notes has absolutely no effect on the "books".

The effect of acceleration manifests as a changing standard of simultaneity. Multiply acceleration by separation and you get a rate of change of clock readings over there, "right now". If the separation is nil, the effect of acceleration is nil.

Mike Holland

OK, I stand corrected on that detail. I know that it is the acceleration that resolves the space-travelling twin paradox, and blithely assumed that the same appied in this case.
Thanks for the correction.
Mike

ghwellsjr

Acceleration only resolves which twin ages less if only one twin accelerates. But what do you do if both twins experience exactly the same acceleration? How do you resolve it then?

For example, suppose that some time after the first twin accelerates away, the second twin follows after the first one with exactly the same acceleration but then after a short time turns around and eventually decelerates to rest at the original starting point. Then the first twin turns around in the same way as the second one did and also decelerates identically to rest with the second twin. Now how do you resolve the age issue? Are they the same age since they accelerated identically?

Or suppose their accelerations are not identical but that the second twin takes off with a higher acceleration after the first one, then turns around more quickly and comes to rest with a higher deceleration than the first one will. Does that mean the second one will be younger? How does acceleration resolve the twin paradox in this situation?

GrammawSally

A++!

phyti

Imagine the earth moving in the direction of its polar axis. A moves at a constant rate along with the earth center. B & C move in a spiral path centered on the polar axis, but at a constant speed greater than that of A. Same path, same time, more time dilation for B & C.
Less time dilation for A.

ghwellsjr

Because of what you said here:
Two clocks traveling at the same speed in an inertial frame, no matter what their directions are or how their directions change, even if they are not symmetrical, will be time dilated by exactly the same amount so if they start out with synchronized clocks, they will remain synchronized and therefore will have the same time on them every time they meet up again. All other frames will agree that they will display the same time each time they meet but they may not agree that they display the same time when they are separated.

So, for example, in a non-inertial frame in which clock B is at rest, the time dilation of clock C will be fluctuating all over the place, even becoming time contraction during parts of the orbit but with the net result that every time they rejoin, their two clocks display the same time.

Now if two clocks that start out synchronized and travel at the same speed in one frame but never meet up again, then there are other frames in which their time dilations result in them remaining forever desynchronized, including each others rest frames.

ghwellsjr

I'm not sure you have this correct and I'm not talking about the deceleration when they stop. You state that while they are traveling away from Earth, "each sees the other two time dilated and their clocks running slowly" and when they are traveling toward the Earth, "each sees the other clocks running fast". Why didn't you also say during the return that "each sees the other two time dilated"? Why did you only say that about the outbound portion of the trip?

Mike Holland

Sorry, that's not correct. I did say that during the return trip, the same applies. In other words, as long as they are travelling at uniform speed relative to each other they will see each others clocks running slow/time dilated, irrespective of direction.

The only time they see each other's clocks running fast is during acceleration/deceleration. During departure and arrival, when they are close together, the effect is negligible. It is the turnaround when they are far apart that counts. As the stay-at-home guy does not experience accceleration, he does not see the other guy's clocks speed up, but they do see his and each other's clocks speed up.

Mike

ghwellsjr

Thanks for clarifying. But I would like to ask you what you mean by the word "see". Do you mean literally with their eyes or do you really mean something along the lines of "interpret" or "understand"?

rickylritter

This is really a simple issue. As long as both clocks are traveling at the same speed for the same amount of time (acceleration and deceleration are irrelevant) they will agree with one another. The clock that has not moved in relationship to the traveling twins will have not changed and thus in relationship to the twins the times will not agree. The reason being time progresses more slowly with change in relationship to position (motion). Thus the twins will have experienced less time in comparison to the stationary clock. The earth may have an effect on the motion; however, as long as the two objects travel the same distance and speed the effect is irrelevant in relationship to the two travelers. If the stationary object truly does not move in relationship to the two moving bodies then their will be no effect by the presence of the Earth. The Earth is irrelevant to the problem all together.

Mike Holland

It is much more complicated than that. They may be travelling at the same speed (relative to the stay-at-home guy, but if they have some velocity relative to each other then each will see the other's clock running slow, whether they are receding from each other or approaching. This is the relative part of Special Relativity.

George, I am thinking in terms of a space-time diagram that an observer would draw up, knowing SR and GR, to determine times and distances in his time-frame. Actual observations get more complicated because of the time light takes to travel.

Mike

rickylritter

If their motion over time or change relative position is the same (mirrored) then their clocks will be the same.