Relative motion and accumulated time dilation

In summary: I'll bite. If we want to figure out what one of the watches observes, we would need GR to figure out what the other watch is observing.
  • #1
coktail
118
1
I have a few questions about time dilation and how it accumulates.

1a. Say you have a situation where you have two clocks that move away from each other with symmetrical acceleration and relative motion. From what I understand, each clock would appear to have slowed down relative to the other, and this is not a paradox because each is in their own reference frame. Then the two clocks move back towards each other with symmetrical acceleration and relative motion. How would they compare to each other once they were back in the same reference frame?

1b. Same question as above, but assume there is instant acceleration.

1c. What if instead of moving back towards each other, they were teleported back together?


2. Though time dilation at earthly speeds is negligible in our every day lives, it still occurs. How is it that it does not accumulate over time and lead to small differences in our watches and such? Or, does it, but it is so small as to be unnoticeable? This applies to both gravitational and velocity-based time dilation, but I'm mostly interested in velocity for the sake of this question.

Thanks!
 
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  • #2
1a.
Not an expert on General Relativity, but since this situation is perfectly symmetric, they'll have the same time. General Relativity is required if you want to see how one observes the other over the course of the experiment.

1b.
Same.

1c.
Invalid, one cannot teleport and time travel would necessarily follow from being able to teleport, which raises some paradoxes. This also raises some issues with Relativity of Simultaneity.

2.
Yes, it does lead to tiny differences, but they are so phenomenally tiny that they're unnoticeable.

Also, the differences are small enough that they're within the improbability range of Quantum Mechanics, so you've got some problems there. And before anyone gets mad at me for trying to combine Quantum Mechanics and General Relativity, note that I'm combining Quantum Mechanics with Special Relativity, which has been done and is very well done.
 
  • #3
coktail said:
I have a few questions about time dilation and how it accumulates.

1a. Say you have a situation where you have two clocks that move away from each other with symmetrical acceleration and relative motion. From what I understand, each clock would appear to have slowed down relative to the other, and this is not a paradox because each is in their own reference frame. Then the two clocks move back towards each other with symmetrical acceleration and relative motion. How would they compare to each other once they were back in the same reference frame?
If the paths are symmetrical in an inertial frame, the accumulated times will be same.

coktail said:
1b. Same question as above, but assume there is instant acceleration.
Same

coktail said:
1c. What if instead of moving back towards each other, they were teleported back together?
Depends on the teleporter specifications.

coktail said:
it is so small as to be unnoticeable?
Yes.
 
  • #4
A.T. said:
If the paths are symmetrical in an inertial frame, the accumulated times will be same.

Does this mean that they will both dilate, but by the same amount (relative to a third stationary clock, say), or that neither will dilate? Will they dilate on the way away from each other, and then contract on the way back towards each other?

Thanks for your responses!
 
  • #5
coktail said:
Does this mean that they will both dilate, but by the same amount (relative to a third stationary clock, say), or that neither will dilate? Will they dilate on the way away from each other, and then contract on the way back towards each other?

Thanks for your responses!

I think it means that both will dilate, but by the same amount, and they'll both dilate both ways. Then again, a perfect explanation requires GR, which I'm no expert at.
 
  • #6
coktail, the reading on a clock between two events can be calculated from the proper time of the clocks worldline between the events. And, most importantly, this time is the same in any frame. It is absolutely invariant. Time dilation is a coordinate effect and is not directly observable, whereas the proper time is ( you can look at the reading on any clock) and is invariant.

Whovian said:
Then again, a perfect explanation requires GR, which I'm no expert at.
No it does not. It is not helpful to bring GR into this. Differential ageing is completely explained by the proper time as I've stated above.
 
  • #7
Mentz114 said:
coktail, the reading on a clock between two events can be calculated from the proper length of the clocks worldline between the events. And, most importantly, this time is the same in any frame. It is absolutely invariant.


No it does not. It is not helpful to bring GR into this. Differential ageing is completely explained by the proper time as I've stated above.

True, but what if we want to figure out what one of the watches observes? This is a change of reference frames ... which is only valid with *gasps* GR, I thought? Or probably my brain isn't working at its best at the moment.
 
  • #9
Mentz114 said:
Time dilation is a coordinate effect and is not directly observable, whereas the proper time is ( you can look at the reading on any clock) and is invariant.

I was under the impression that time dilation was observable, but only from an external reference frame. For example, for clocks observe (if they have eyes or an observer sitting on top of them) each other dilating, but to each clock its own time remains unchanged.
 
  • #10
Whovian said:
True, but what if we want to figure out what one of the watches observes? This is a change of reference frames ... which is only valid with *gasps* GR, I thought? Or probably my brain isn't working at its best at the moment.
A change of coordinates does not require GR. A Lorentz transformation in SR is just a change of coordinates from one frame to another.

The accumulated time on any clock between events is easy to calculate using the line element of Minowski spacetime

c22 = c2dt2 - dx2 - dy2 - dz2
 
  • #11
coktail said:
I was under the impression that time dilation was observable, but only from an external reference frame. For example, for clocks observe (if they have eyes or an observer sitting on top of them) each other dilating, but to each clock its own time remains unchanged.

Under no acceleration, yes.

Thanks, DaleSpam, I heard accelerating reference frames are treatable under SR, but not necessarily in the same way. Probably got my information from a not so great source.
 
  • #12
Ah, so with acceleration clock A would see clock B slow down, while clock B would see clock A speed up? What if the acceleration is symmetrical?
 
  • #13
coktail said:
I was under the impression that time dilation was observable, but only from an external reference frame. For example, for clocks observe (if they have eyes or an observer sitting on top of them) each other dilating, but to each clock its own time remains unchanged.
I think if you watch a moving clock the Doppler effect takes over. You would see a receding clock ticking more slowly, and an approaching clock ticking faster.

Yes, an observer will see no change in his clock.

Please look at this page and the especially the section 'What it Looks Like'

http://en.wikipedia.org/wiki/Twin_paradox
 
  • #14
coktail said:
2. Though time dilation at earthly speeds is negligible in our every day lives, it still occurs. How is it that it does not accumulate over time and lead to small differences in our watches and such? Or, does it, but it is so small as to be unnoticeable? This applies to both gravitational and velocity-based time dilation, but I'm mostly interested in velocity for the sake of this question.
Although we don't notice any difference in the watches we carry around, time dilation, both gravitational and velocity-based, is noticed by the precise atomic clocks that are the international standards and for the GPS clocks in orbit around the earth. They all run at different rates depending mainly on their elevation. So, for purposes of knowing what time it is, we can't rely on our own precise atomic clocks, if we had them, but instead on a co-ordinated time source like GPS.
 
  • #15
Mentz114 said:
I think if you watch a moving clock the Doppler effect takes over

My impression was that since the speed of light is constant, the only thing the Doppler effect would cause is a red/blue shift...
 
  • #16
Also, in the Twin Paradox, I don't understand why a change in acceleration as the spaceship twin turns around sets off the asymmetry, but the initial acceleration of the spaceship doest not. Sorry for the side tangent.
 
  • #17
coktail said:
Ah, so with acceleration clock A would see clock B slow down, while clock B would see clock A speed up? What if the acceleration is symmetrical?
Even without gravity effects, if clock B is moving at a constant speed but remains a constant distance from clock A so that it is accelerating in a circle around clock A (think orbit), then clock A will observe clock B to be running at a slower rate and clock B will observe clock A to be running at a faster rate. But this is clearly a non-symmetrical acceleration because only clock A is accelerating.

If you are going to talk about a symmetrical acceleration such that the clocks start out together and follow the same acceleration/velocity profile except in opposite directions and they eventually reunite, then each one will view the other ones clock in the same way and they will end up with the same time on them.
 
  • #18
ghwellsjr said:
If you are going to talk about a symmetrical acceleration such that the clocks start out together and follow the same acceleration/velocity profile except in opposite directions and they eventually reunite, then each one will view the other ones clock in the same way and they will end up with the same time on them.

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?
 
  • #19
coktail said:
My impression was that since the speed of light is constant, the only thing the Doppler effect would cause is a red/blue shift...
Any oscillatory process is subject to the Doppler effect, including clocks ticking.
 
  • #20
Mentz114 said:
Any oscillatory process is subject to the Doppler effect, including clocks ticking.

But the relativistic Doppler effect just affects the perceived frequency of the light (e.g. red/blue shift), not the time dilation itself, correct?
 
  • #21
coktail said:
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?
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.
 
  • #22
coktail said:
But the relativistic Doppler effect just affects the perceived frequency of the light (e.g. red/blue shift), not the time dilation itself, correct?
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 traveling twin, agreeing with the fact the traveling twin experiences less elapsed time.
 
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  • #23
coktail said:
But the relativistic Doppler effect just affects the perceived frequency of the light (e.g. red/blue shift), not the time dilation itself, correct?
The perceived rate of a clock will also be affected. The formula for the Doppler shift includes the factor γ (the time dilation).
 
  • #24
coktail said:
ghwellsjr said:
If you are going to talk about a symmetrical acceleration such that the clocks start out together and follow the same acceleration/velocity profile except in opposite directions and they eventually reunite, then each one will view the other ones clock in the same way and they will end up with the same time on them.
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?
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.
 
  • #25
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.
 
  • #26
coktail said:
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.
Yes.
 
  • #27
Awesome.
 
  • #28
coktail said:
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.
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.
 
  • #29
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.
 

1. What is relative motion?

Relative motion refers to the movement of an object in relation to another object. It is described as the change in position of one object relative to another object.

2. How does relative motion affect time dilation?

Relative motion can cause time dilation, which is the difference in the passage of time between two objects due to their relative motion. The faster an object moves, the more time dilation occurs.

3. What is accumulated time dilation?

Accumulated time dilation is the total amount of time that has passed for an object traveling at high speeds compared to an object at rest. This is due to the effects of relative motion and time dilation.

4. How is accumulated time dilation measured?

Accumulated time dilation can be measured using special relativity equations, which take into account an object's velocity and the speed of light. It can also be measured using clocks that are synchronized on Earth and on a moving object.

5. How does accumulated time dilation impact space travel?

Accumulated time dilation has a significant impact on space travel. As objects travel at high speeds, time dilation causes time to pass more slowly for them, which means that astronauts on long space missions age slower than those on Earth. This must be taken into account for accurate navigation and communication in space missions.

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