Relative motion and accumulated time dilation

coktail

Thank you, George.
Given this, would clock and A and B detect discrepancies between their times as they travel, but they would resolved themselves by the time they reunited, or would they stay "in sync" the entire time?

Mentz114

Any oscillatory process is subject to the Doppler effect, including clocks ticking.

coktail

But the relativistic Doppler effect just affects the perceived frequency of the light (e.g. red/blue shift), not the time dilation itself, correct?

yuiop

As they accelerate away from each other, they will each see light from the other as red shifted. As soon as they turn around to return, they will each see the red shift of light from the other transition to an increasing blue shift, with the maximum blue shift occurring after they see the the other turn around. (There is a delay between their own turn around and seeing the other turn around, because of light travel times.) If they allow for the classical Doppler effect, they will conclude that the total elapsed time on the others clock is the same as on their own clock. When they return to their starting point they will see equal time has elapsed on their clocks, but more time has elapsed on a clock that remained at the starting point the whole time. In short, they do not see each other as remaining in sync the whole time but the differences resolve after the round trips. An inertial observer that remains at the starting point will see A and B as being in sync the whole time.

yuiop

Yes, that is sort of correct. The relativistic Doppler effect includes the classical Doppler effect and time dilation. If you can measure the velocity of an object you can calculate the classical Doppler shift and after allowing for this, deduce the time dilation from the observed relativistic Doppler shift.

[EDIT]It is worth adding that if the clocks send out one second signals, they will be subject to relativistic Doppler shift, but the number of one second signals received will agree with the number of seconds elapsed on the other clock when they are back alongside each other again. In the classical and asymmetrical twins paradox, the stay at home twin receives less time signals than the travelling twin, agreeing with the fact the travelling twin experiences less elapsed time.

Mentz114

The perceived rate of a clock will also be affected. The formula for the Doppler shift includes the factor γ (the time dilation).

ghwellsjr

I think your questions have already been answered by others but let me summarize it this way. If each clock (observer) took a video of the other ones clock, assuming, of course, some great telescopic equipment, or if each clock were sending out a radio signal announcing its current time that could be detected by a receiver traveling with the other clock and the information from that signal could be recorded, then each traveler would record exactly the same "program" through their entire trip and when they reunite, they could play them side by side and they would look identical.

I want to also make clear that Relativistic Doppler affects not just the red/blue shift of the frequency of the light, it also affects the actual images such that if you could see the hands move on an analog clock or the numbers displayed on a digital clock, you would see them progressing slower while traveling away and faster while returning. But it involves the motion of both the source and the receiver with the time delay determined by their distance apart.

coktail

So the relativistic doppler effect *includes* time dilation, and is not a separate cause for seeing the image of the clock slow down/speed up? I just want to make sure I understand that point correctly.

Mentz114

Yes.

coktail

Awesome.

ghwellsjr

Relativistic Doppler describes what you actually see. It is independent of any particular theory or any particular Frame of Reference. Think about your experience of hearing an emergency vehicle with the sound of the siren changing pitch as it goes by you. It doesn't matter how you analyze or theorize why that happens as it won't change what is happening, will it? This effect has been call Doppler shift and is dependent on both the velocity of the source through the medium and the velocity of the receiver through the medium and is "caused" by the ever-increasing (or decreasing) propagation delay of the signal from source to receiver.

However, in the case of light, the Doppler shift is not dependent on the two velocities with respect to a medium but only on the relative velocity between the source and the receiver. Now we need a good theory to explain how this can happen and that is what the Special Relativity provides. In that theory, we establish an arbitrary Frame of Reference and then any object/clock that is moving in that frame has its clock running slow which means it sends out its timing signals at a slower rate and any timing signals that it receives will be perceived as coming in at a higher rate. So these effects, plus the normal Doppler effect combine in such a way as to make the Relativistic Doppler be symmetrical between the two objects/clocks. Of course, in some Reference Frames, all the time dilation can be assigned to just one object/clock but still, the perception will be symmetrical. If the objects/clocks accelerate symmetrically as describe before, then the actual time dilations can also be non-symmetrical but the perception of the Doppler shift will be symmetrical. It's no different than the velocities being different in different frames but the perception or measurement of the velocities continues to be symmetrical.

As I said before, you really need to learn about how a Frame of Reference is constructed and what events are and how to use the Lorentz Tranformation to see how the co-ordinates of these events change from one frame to another in order to really grasp how time dilation, length contraction and simultaneity all work together to provide a meaningful explanation of what different observers perceive.

feynmanisbest

1a. They would both be on the same time.
1b. Ditto.
1c. Teleportation is impossible according to General Relativity since it assumes that the objects move faster than the speed of light.
2. It does accumulate, but it is unnoticeable, like you said. If you get on a fast airplane and circle the planet, and then come back to your twin, you will be younger than her and the change will be permanent. Sadly the difference is on the order of nanoseconds, so it's not that interesting.