# Twins paradox and ageing

by adw73uk
Tags: ageing, paradox, twins
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P: 1,414
 Quote by Al68 The clock will run slow relative to an observer's rest frame if the relative velocity between the clock and observer changes, but it makes no difference whether the clock or observer accelerated.
Yes, but when we know which clock was accelerated, then doesn't that allow us to infer that its changes in velocity had a real, physical effect on its tick rate?

 Quote by Al68 For example a clock on a "moving" spaceship will run at the same rate as the watch of a co-moving observer on the ship, both keeping proper time. But if that observer decides to leave the ship on a shuttle and decelerate to come to rest with earth, then the ship's clock will then run slow relative to him. Nothing happened to the clock at all. There are no "mechanics of the change" because there was no physical change of the clock.
What about the watch that went to the earth?

The way I interpret the experiments that I've read is that the tick rates of clocks (ie. the periods of oscillators) are affected by velocity changes. Do you think this is wrong?
P: 801
 Quote by ThomasT Yes, but when we know which clock was accelerated, then doesn't that allow us to infer that its changes in velocity had a real, physical effect on its tick rate?
No, because the exact same effect occurs anytime there is a change in the relative velocity between clock and observer. An effect that occurs whether the clock accelerates or not can't be attributed to its acceleration.
 What about the watch that went to the earth? The way I interpret the experiments that I've read is that the tick rates of clocks (ie. the periods of oscillators) are affected by velocity changes. Do you think this is wrong?
They aren't "affected" by a change in velocity of the clock, they depend on the relative velocity between clock and reference frame. That's a subtle but crucial difference.

The tick rate of a valid clock is 1 sec per second of proper time in its rest frame, regardless of its motion or acceleration. It's the ratio between proper time in the rest frame of the clock and coordinate time in the observer's rest frame that "changes" with a change in the relative velocity between clock and observer, not anything physical about the clock itself.
P: 1,414
 Quote by Al68 No, because the exact same effect occurs anytime there is a change in the relative velocity between clock and observer. An effect that occurs whether the clock accelerates or not can't be attributed to its acceleration.
Keep two identical clocks side by side at a constant velocity and they display the same times.
Now accelerate one clock, then bring it back aside the other again and they display different times. Doesn't it make sense to attribute this difference to the acceleration?

 Quote by Al68 They aren't "affected" by a change in velocity of the clock, they depend on the relative velocity between clock and reference frame. That's a subtle but crucial difference. The tick rate of a valid clock is 1 sec per second of proper time in its rest frame, regardless of its motion or acceleration. It's the ratio between proper time in the rest frame of the clock and coordinate time in the observer's rest frame that "changes" with a change in the relative velocity between clock and observer, not anything physical about the clock itself.
And yet, when we reunite the clocks and compare their times, they're significantly (physically) different.

In light of the evidence, I don't understand how one can say that a different tick accumulation (associated with an acceleration) isn't "anything physical about the clock itself."
P: 801
 Quote by ThomasT Keep two identical clocks side by side at a constant velocity and they display the same times. Now accelerate one clock, then bring it back aside the other again and they display different times. Doesn't it make sense to attribute this difference to the acceleration?
Sure. But a difference in elapsed time between events is very different from the previous issue of a clock running slow relative to a different frame.
 And yet, when we reunite the clocks and compare their times, they're significantly (physically) different. In light of the evidence, I don't understand how one can say that a different tick accumulation (associated with an acceleration) isn't "anything physical about the clock itself."
It's physical in the sense that one clock physically had a path through specetime with less elapsed time than the other path. Each clock shows 1 second for each second of time elapsed along their path.

In other words, one path between two events has less elapsed proper time than the other path between those events. Each clock keeps good proper time. The difference in clock readings is due to a difference in elapsed proper time, not a difference in the clocks.
P: 1,414
 Quote by Al68 It's physical in the sense that one clock physically had a path through spacetime with less elapsed time than the other path.
This is one way of representing it. But I don't think that this is the sense in which it's physical.

We know that the two clocks have counted a different number of ticks, and that one clock was accelerated and the other not. So, we agree that we can attribute the difference to the acceleration intervals.

 Quote by Al68 The difference in clock readings is due to a difference in elapsed proper time, not a difference in the clocks.
There's a difference in the clock readings of the twins, while there's no difference in the visual count of the number of years from takeoff to landing for any and all observers. So, we know that the trip took, say, 20 years, but the traveller's clock only counted, say, 5 years and he only aged 5 years.

Spacetime path(s) notwithstanding, I think we're forced to conclude that the periods of the oscillator(s) of the traveller's clock and the traveller himself have been temporarily, physically altered during their accelerations.
P: 801
 Quote by ThomasT There's a difference in the clock readings of the twins, while there's no difference in the visual count of the number of years from takeoff to landing for any and all observers. So, we know that the trip took, say, 20 years, but the traveller's clock only counted, say, 5 years and he only aged 5 years.
Sure, but it's not like the traveler's clock counted 5 years while 20 years elapsed in that path. Only 5 years elapsed on that path.

Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different.

Acceleration affects the spacetime paths, which affects the proper time elapsed. The only reason SR predicts different clock readings for the twins is because it assumes that each clock accurately records the elapsed time for each twin.
P: 1,060
 Quote by Al68 Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different. Acceleration affects the spacetime paths, which affects the proper time elapsed. The only reason SR predicts different clock readings for the twins is because it assumes that each clock accurately records the elapsed time for each twin.
The above really says it all.

When talking of timelike intervals, which are the only type which can be traversed by a clock, the time recorded by an ideal clock while traversing this interval is said to be proper time whatever its motion or path through that interval. It is a measure of spacetime path length.

In a frame in which it is at rest the proper time recorded by the clock is the same as the coordinate time, that is the projection of the interval onto the time axis of that frame.

Since the coordinates in any inertial frame can be Lorentz transformed into coordinates in any other relatively moving inertial frame, the coordinates of a clock in any infinitessimal region of its travels can be transformed into those of a frame at which it as at rest in that infinitessimal region.

Since all inertial frames are equivalent in SR, each infinitessimal amount of coordinate time, which in each comoving rest frame is equal to proper time, can be summed, and, in the limit, as these infinitessimal regions are allowed to become smaller and smalle, so apprroaching zero, integrated over the path (timelike) of the clock to give the exact proper time, as a sum of coordinate times, for this path.

So there is nothing in this derivation of proper time which gives any clock any preference over any other clock as all proper times can be made equivalent to the sum of coordinate times of a clock in frames in which it is at rest.

In other words the time recorded by a clock can be viewed as the sum of coordinate times in inertial frames in which it is (for an infinitessimally small region) at rest, and since the use of all inertial frames is equally valid, all times so recorded are equally valid or "correct". So for a clock, any clock, the time it records, proper time, is for that clock THE time.

Matheinste.
 Mentor P: 17,322 I don't think that this is nearly as complicated as many of the posters have made this out to be. The reason that light clocks exhibit time dilation is the second postulate. The reason that all other clocks exhibit the same time dilation is the first postulate. There is no deeper reason than the postulates, they are fundamental. And the reason we accept the postulates is that they fit the data very well.
P: 1,060
 Quote by DaleSpam I don't think that this is nearly as complicated as many of the posters have made this out to be. The reason that light clocks exhibit time dilation is the second postulate. The reason that all other clocks exhibit the same time dilation is the first postulate. There is no deeper reason than the postulates, they are fundamental. And the reason we accept the postulates is that they fit the data very well.
What you say is true, but lots detailed explanation is often needed to explain something that may not be obvious to some. I have a little knowledge of SR now, but had I been given nothing more than the above in a textbook, although it is possible to derive all of SR from the postulates, I am one of the many who could not have done so without much help and detailed explanation.

Matheinste.
P: 451
 Quote by Al68 Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different.[/i]
I agree and add what makes this topic (movement at speeds comparable to c) counter-intuitive is that when you transform to any frame that is not your own local rest frame time and the spatial dimension (the one of three that is in the direction of travel) are not orthogonal any more.
P: 1,414
 Quote by Al68 Sure, but it's not like the traveler's clock counted 5 years while 20 years elapsed in that path. Only 5 years elapsed on that path.
Setting aside the spacetime interpretation for the moment, what's been altered is the traveller's clock and the traveller due to their accelerations. Nothing else in the scenario has been altered by their accelerations. The earth-sun system evolved 20 years, the earthbound twin aged 20 years and his clock ticked off 20 years, and every other observer inside or outside the solar system agrees that the trip took 20 years. The anomalies are the accelerated twin and his accelerated clock.

 Quote by Al68 Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different.
I agree. The traveller's clock actually ticked off 5 years and the earthbound clock actually ticked off 20 years, and the traveller actually aged 5 years and the earthbound twin actually aged 20 years, and they and all other observers actually counted 20 years wrt the earth-sun system.

 Quote by Al68 Acceleration affects the spacetime paths, which affects the proper time elapsed.
Yes, that's a valid statement. But to say something about the physical differences that are measured in the real world we can say: accelerations (velocity changes) change the periods of oscillators. Can't we?

Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry.
Mentor
P: 17,322
 Quote by matheinste What you say is true, but lots detailed explanation is often needed to explain something that may not be obvious to some.
This is very true. But in this case the OP already understands how time dilation for a light clock follows from the 2nd postulate and just doesn't understand how we go from that to biological aging. And that is what follows directly from the 1st postulate.
P: 1,060
 Quote by ThomasT Yes, that's a valid statement. But to say something about the physical differences that are measured in the real world we can say: accelerations (velocity changes) change the periods of oscillators. Can't we? Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry.
There's seems no point in repeating what others have said about acceleration not being the direct cause of differential ageing but it is worth pointing out that the invariance of the spacetime interval is fundamental to relativity.

Matheinste.
P: 1,060
 Quote by DaleSpam This is very true. But in this case the OP already understands how time dilation for a light clock follows from the 2nd postulate and just doesn't understand how we go from that to biological aging. And that is what follows directly from the 1st postulate.
Point taken.

Matheinste.
P: 801
 Quote by ThomasT Setting aside the spacetime interpretation for the moment, what's been altered is the traveller's clock and the traveller due to their accelerations. Nothing else in the scenario has been altered by their accelerations. The earth-sun system evolved 20 years, the earthbound twin aged 20 years and his clock ticked off 20 years, and every other observer inside or outside the solar system agrees that the trip took 20 years. The anomalies are the accelerated twin and his accelerated clock.
No they don't. They all agree that 20 years elapsed in earth's path and 5 years elapsed in the ship's path.
 I agree. The traveller's clock actually ticked off 5 years and the earthbound clock actually ticked off 20 years, and the traveller actually aged 5 years and the earthbound twin actually aged 20 years, and they and all other observers actually counted 20 years wrt the earth-sun system.
and they and all other observers actually counted 5 years elapsed wrt the ship's system. You only listed three of the four relevant facts.
 Yes, that's a valid statement. But to say something about the physical differences that are measured in the real world we can say: accelerations (velocity changes) change the periods of oscillators. Can't we?
Not really, since the exact same change in the period of an oscillator is observed when the observer changes velocity instead of the oscillator. The change in the period of the oscillator occurs because of a change in relative velocity between oscillator and reference frame, whether or not the oscillator accelerates.
 Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry.
It may be more intuitive, but it's conceptually wrong. Each twin ages 1 year per year of elapsed time. Again, it's time itself that "flows" differently in different frames, not a change in the operation of various devices used to measure it.

Conceptually, it's like saying that my bathroom scales read higher because I ate too much ice cream and cake last week. The scales read higher because I'm heavier, not because of any difference in the scales' operation. This is true of any measuring device: different results do not imply a difference in the measuring device itself.
P: 1,414
 Quote by Al68 No they don't. They all agree that 20 years elapsed in earth's path and 5 years elapsed in the ship's path.
Sorry for the delay in replying.

We're setting aside the spacetime interpretation for the moment.
 Quote by Al68 ... and they and all other observers actually counted 5 years elapsed wrt the ship's system.
Right. The travelling clock actually recorded fewer ticks than the earthbound clock.
 Quote by Al68 Not really, since the exact same change in the period of an oscillator is observed when the observer changes velocity instead of the oscillator.
No, the physical fact is that only one clock ran slow -- this is the point of including the visual tracking of the earth-sun system.
 Quote by Al68 The change in the period of the oscillator occurs because of a change in relative velocity between oscillator and reference frame, whether or not the oscillator accelerates.
No, the change in the period of an oscillator is due to the acceleration of that oscillator. What you're saying applies to situations where we don't have sufficient info regarding the acceleration histories (or we simply disregard it) of the two clocks being compared. But in the usual earthbound-travelling twin scenario, we do.
P: 451
 Quote by Al68 The change in the period of the oscillator occurs because of a change in relative velocity between oscillator and reference frame, [I]whether or not the oscillator accelerates.[I]
We have to be careful on the word here. You can not get velocity without acceleration.

Is it the velocity that alters that state of the clock or is it the acceleration that alters the state of the clock? What experiment can we do to measure which is responsible? Two things happen and a third is found to be correlated. If you can never separate the two things how will you ever be able to call one the cause and the other not the cause?
P: 1,414
 Quote by Al68 It may be more intuitive, but it's conceptually wrong. Each twin ages 1 year per year of elapsed time. Again, it's time itself that "flows" differently in different frames, not a change in the operation of various devices used to measure it.
Time itself ... flows differently??

The traveller, and all other observers, watched the earth-sun system rotate 20 times during the trip. Yet the traveller and his clock only ticked off 5 years.

We agree that difference in tick rate is due to difference in velocity, don't we? It seems clear to me from experiments that it isn't intervals of constant, uniform velocity that exhibit tick rate changes, but intervals of acceleration.

 Quote by Al68 ... different results do not imply a difference in the measuring device itself.
In this case they do.

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