TIME DILATION. WHY do clocks that are

[ThomasT]

Except that it has been shown experimentally that acceleration has no effect on time measurement.

Differences in speed have an effect on time measurement. So it follows that changes in speed have an effect on time measurement.

But let me try to think through this out loud.

The general form of the Lorentz Factor, γ = (1 - v²)^-1/2, remains unchanged wrt acceleration.

The value of the Lorentz Factor is directly affected only by the speed at which an oscillator is moving.

So we can say that the period of an oscillator is directly affected only by the speed at which the oscillator is moving. The faster(slower) an oscillator is moving, the greater(lesser) its period, and the lesser(greater) its frequency.

However, the speed at which an oscillator is moving is a direct effect of the oscillator's most recent acceleraton (assuming that the oscillator's speed hasn't remained constant throughout its entire history). That is, when the speed of an oscillator has changed during a certain interval, then we call the rate of change during that interval an acceleration. (Although an oscillator can presumably be accelerated, by changing its direction of motion, without in any way changing its speed, we're only concerned with the component of velocity that has to do with the oscillator's speed. And, a change in speed refers to, by definition, an acceleration.)

By varying the angular velocity and length of the centrifuge arm, you can set the experiment up so that the sample travels at different speeds but experiences the same acceleration or travels at the same speed but experiences different accelerations.

The speed of the sample is proportional to the rotational radius (r), the distance of the sample from the rotational axis (roughly the length of the centrifuge arm), times the RPM's of the sample. Increase(decrease) r while keeping RPM's the same and the speed of the sample increases(decreases). Increase(decrease) RPM's while keeping r the same and the speed of the sample increases(decreases).

I'm assuming that changes in either the rotational radius of the samples, or the RPMs of the samples isn't done on the fly. Otherwise, there are obvious accelerations involved. (Ie., if the arm is extended/retracted while keeping the RPMs constant, or if the RPMs are varied while keeping the rotational radius constant.)

I agree that the experiments you mentioned do show that the general form of the Lorentz Factor is unaffected by acceleration.

What I'm wondering about (with the understanding that the quantity of differential aging is a function of the time during which an oscillator is propagating at a certain speed), is when the change occurs wrt an oscillator whose frequency has been altered -- as it seems obvious that it can't be occurring while the oscillator is propagating at a constant speed. It follows that the changes in oscillator frequency must be occurring during intervals of acceleration.

Which means that speed accelerations/decelerations do directly affect (produce changes in) the periods of oscillators.

Thus, acceleration (involving variations in speed) affects time measurement.

 

[Dale]

Differences in speed have an effect on time measurement. So it follows that changes in speed have an effect on time measurement.

Yes, but acceleration is a change in velocity, not a change in speed. The whole point of using uniform circular motion is to have high acceleration without a change in speed. When you do that you find that acceleration does not cause time dilation, at least not up to about 10^18 g.

However, the speed at which an oscillator is moving is a direct effect of the oscillator's most recent acceleraton (assuming that the oscillator's speed hasn't remained constant throughout its entire history).

As you mention, it also depends on the initial velocity. Furthermore, if the most recent acceleration was centripetal then the speed does not depend on it. Your statement is not true in general.

 

[ThomasT]

Yes, but acceleration is a change in velocity, not a change in speed.

Speed is the magnitude component of velocity. While an acceleration doesn't necessarily involve a change in speed, a change in speed is, by definition, called an acceleration.

Wrt differential time measurement, it's the accelerations that involve changes in speed that we're concerned with.

The whole point of using uniform circular motion is to have high acceleration without a change in speed. When you do that you find that acceleration does not cause time dilation, at least not up to about 10^18 g.

I agree. As the experiments show, time measurement depends only on the speed component of velocity. So, to say that time measurement is unaffected by acceleration because it's unaffected by the directional component of velocity is sort of misleading.

As you mention, it also depends on the initial velocity. Furthermore, if the most recent acceleration was centripetal then the speed does not depend on it.

If the speed remains constant, and the rate of time measurement remains constant, then this shows that the rate of time measurement doesn't depend on accelerations that don't involve changes in speed.

But, again, a change in speed is, by definition, an acceleration. And time measurement depends on speed. Therefore it's incorrect to say that changes in the rate of time measurement don't depend on acceleration. It's just a semantic thing that needs clarification.

Your statement is not true in general.

How about this? Changes in time measurement are a function of accelerations that involve changes in speed.

By the way, thanks also for your feedback on my previous concern. Since I don't have a mechanistic theory of relativistic differential time measurement to refer to (the extant ether theories aren't quite what I had in mind), then I'm left with the geometric account.

 

[ghwellsjr]

Speed is the magnitude component of velocity. While an acceleration doesn't necessarily involve a change in speed, a change in speed is, by definition, called an acceleration.

Wrt differential time measurement, it's the accelerations that involve changes in speed that we're concerned with.

I agree. As the experiments show, time measurement depends only on the speed component of velocity. So, to say that time measurement is unaffected by acceleration because it's unaffected by the directional component of velocity is sort of misleading.

If the speed remains constant, and the rate of time measurement remains constant, then this shows that the rate of time measurement doesn't depend on accelerations that don't involve changes in speed.

But, again, a change in speed is, by definition, an acceleration. And time measurement depends on speed. Therefore it's incorrect to say that changes in the rate of time measurement don't depend on acceleration. It's just a semantic thing that needs clarification.

How about this? Changes in time measurement are a function of accelerations that involve changes in speed.

By the way, thanks also for your feedback on my previous concern. Since I don't have a mechanistic theory of relativistic differential time measurement to refer to (the extant ether theories aren't quite what I had in mind), then I'm left with the geometric account.

The point is, when discussing the Twin Paradox, that although, if one twin remains inertial and the other one experiences acceleration, we can identify that twin as the one that will have elapsed less time than the inertial one upon their reuniting, but we don't say that it is his acceleration that causes the change in age rate. It is his difference in speed over a period of time that causes it. Of course, the acceleration can cause a change in his speed which will then cause a change in his aging rate, but that by itself won't cause a change in his age when they reunite. He has to accumulate time at the different aging rate to acumulate a difference in age.

Consider a traveling twin that doesn't just decelerate to a stop at the turn-around point and then accelerate back to the home twin but rather maintains a constant speed and makes a loop back to turn around. Now he has never changed speed but he has accelerated.

Or consider Einstein's original introduction of the Twin Paradox in his 1905 paper in which one clock takes a circular path away from the inertial clock and every time it comes back, it has accumulated less time on it.

 

[Jocko Homo]

ghwellsjr, I'd like to give you credit for the explanations you gave in this topic.
Earlier I said that the change of direction is not of any importance for the difference in the observations.
I see now that I was wrong.
Thank You :)

I second this. Thank you ghwellsfr for your illuminating examples and your great patience with some of the posters in this thread. I just wanted to make sure you understand that your efforts are appreciated!

 

[Dale]

How about this? Changes in time measurement are a function of accelerations that involve changes in speed.

That is OK as long as you add "and the initial speed". Although it will cause you communication problems for the following reason:

Do you know the difference between a partial derivative and a total derivative? When scientists say "X doesn't depend on Y" what they generally mean is $\frac{\partial X}{\partial Y}=0$. Basically, this means that X does not change if you change Y without changing anything else. So if X is a function of Y and Z then the partial derivative of X wrt Y is obtained by keeping Z fixed.

So, the type of centrifuge experiment described by Janus above is exactly the kind of experiment that would be used to investigate this type of dependence. That way you could change accelerations without changing speed and obtain $\frac{\partial \gamma}{\partial a}=0$ indicating that time dilation does not depend on acceleration, in the meaning intended by scientists.