Twins paradox and ageing

ThomasT

Thanks. Reference?

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.
It's not the clock that changed, it's the relative motion between the clock and reference frame that changed. A clock runs slow relative to a frame in which it is in motion whether the clock accelerated or not.

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.

Another analogy is kinetic energy. The kinetic energy of an object is different in different reference frames. Would you ask for the "mechanics of the change" to explain how the object gained or lost kinetic energy simply because we switched reference frames? Of course not, because, like the rate of a clock in SR, kinetic energy is frame dependent.

edpell

A person on earth "observes" the flashes [let us say the clock on the ship emits a light flash every one second ship time] at a lower frequency due to the, distortion caused by the, finite speed of propagation of light. Versus if we have [this is a thought experiment] a signal that propagates at say 10^100 times c would the observer on earth see the flashes at a rate of one per earth clock second?

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?

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?

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.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.

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?

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."

Al68

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.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.

ThomasT

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.

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.

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.

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.

matheinste

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.

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.

matheinste

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.

edpell

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.

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.

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.

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.

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.

matheinste

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.

matheinste

Point taken.

Matheinste.