# Does acceleration slow time?

Z3r0
Well I know for a fact that my clock at work ticks much slower than the clock at the bar.

Cheers :D

Unbelievable! Show us the data! :0)

Z3r0
phinds
Gold Member
Hi everybody,

At Wiki, the clock hypothesis states that the rate of a clock does not depend on its acceleration but only on its instantaneous velocity,
No, it does not depend on either. All clocks tick at one second per second. You are likely referring to what it APPEARS to do to an observer.

so it means that, for two clocks at rest one beside the other, if a clock stays at rest while the other accelerates away, the one that is accelerating begins to slow down at the beginning of the acceleration, and goes on slowing down during the acceleration
No, it does neither, it just keeps ticking at one second per second. Again, you are referring to what an observer sees, not what the clock is doing.

, which means that we can predict which clock is going to slow down during the acceleration
We know which clock will appear to be going slower, yes

whereas relativity tells us that we cannot predict anymore which clock is going to slow down after the acceleration has stopped.
This is not correct. The clocks are symmetrical after acceleration stops. Each appears to the other to be running slow but both are ticking at one second per second.

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Dale
Mentor
2020 Award
which means that we can predict which clock is going to slow down during the acceleration
Think this through a little more. What if the clocks start out moving and one of them accelerates to rest?

Ibix
pervect
Staff Emeritus
Thanks for sorting through my poor phrasing to understand my question, and for the more exact thought experiment. So, because both clocks have the same velocity relative to some observer, she will observe them both to run at the same speed. That one clock is under greater acceleration than the other has no impact. (Ibix also seems to confirm this for me, thanks).

I don't so much ask why does gravity affect time as why doesn't acceleration? If I understand Einstein's elevator thought experiment, then it seems like it'd be easy to tell, from inside, whether you were on the surface of Earth or accelerating at 1g through space. Only if on earth would the clock on the ceiling tick more slowly than the one on the floor?

I could be wrong, but my impression is that when you talk about "gravity affecting time", you presume some universal notion of time, absolute time, that exists for gravity to effect. This is not the case in special - or general - relativity. Unfortunately, it seems a bit of a digression to go off and try to explain this point, but it also seems like an obstacle to prevent any further progress without explaiing it.

I shall try another approach, that might be of some help. This is to propose a different experiment, basically a variant of something that has actually been carried out, the "Harvard clock tower" experiment, aka the Pound-Rebka experiment, and compare it to the experiment you suggest.

Basically , a signal emitter is placed at a high altitude, and a receiver is placed at a low altitude. And one looks for a doppler shift of the transmitted signal. One predicts from conservation of energy arguments, and measures experimentally, that the doppler shift exists.

Perhaps it is not at first obvious what this has to do with 'time'. The emitting source can be regarded as being some sort of clock in its own right, and it can be compared locally to some standard clock (currently the standard is a cesium atomic clock), and it can be found that the emitting source keeps the same sort of time as the standard clock.

An identical emitting source can be placed at the receiver's position. This lower emitting source, too, can be syncronized to a standard atomic clock at the same lower altitude location.

But the doppler-shifted signal from the upper clock will not, due to the doppler shift, will not and can not have the same frequency as the non-doppler shifted signal from lower emission source.

So we at least start to glimpse the issue here. The experiment you proposed doesn't show any difference in clock rates. But the Pound-Rebka experiment does. "Clock rates" is an ambiguous term, here, we have several clocks, and just as importantly, we need the details of how we compare these clocks. So we need to be more precise in our language.
So, we need to have the right words to talk concisely about the difference between the two experiments. The one set of experiments shows no difference in 'time', but the other set of experiments does. The right words here turn out to be 'proper time' and 'coordinate time'. There are some other active (and long) threads on this already, it would be off topic to go into all of the details here, I think. The point I want to make is that one can concisely describe the results of the two experiments by saying that in an inertial frame of reference, the ratio of proper time to coordinate time does not depend on acceleration, only on velocity. In a non-inertial frame of reference, though, the ratio of proper time to coordinate time depends on acceleration and position within the frame.

This later observation about non-inertial frames is true both in the case of the non-inertial frame of an accelerating elevator, or in the non-inertial frame that's due to gravity.

I think they will agree on times (and be slower than your clock if you also are standing at the tangent point.) But I need to sit down with pencil and paper and work out the details. (It's been awhile since I played with this.) I will do this and post my figures. In the mean time, does this scenario address your question?
How do they agree in their time despite that both of them are non-inertial frames with different acceleration?

Ibix
2020 Award
How do they agree in their time despite that both of them are non-inertial frames with different acceleration?
Because their paths through spacetime are the same "length".

Because their paths through spacetime are the same "length".
But I think their metric are different in their respective accelerating frames. And the metric is a function of the acceleration not as simple as in Minkowski metric.

But I think their metric are different in their respective accelerating frames. And the metric is a function of the acceleration not as simple as in Minkowski metric.
But this confuses me again because this would mean the proper time is not invariant. I mean in accelerating frame with no gravity, will the metric in front of ##dt## be a function of the acceleration? if yes, then how the proper time attached to the clock at rest in this frame is invariant?

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Dale
Mentor
2020 Award
But this confuses me again because this would mean the proper time is not invariant.
Proper time is invariant.

if yes, then how the proper time attached to the clock at rest in this frame is invariant?
In the case of the accelerated frame the proper acceleration is in the metric. In the case of an inertial frame the proper acceleration is in the expression of the worldline. Either way the proper time is affected by the proper acceleration.

Think this through a little more. What if the clocks start out moving and one of them accelerates to rest?
Hi Dale,

I see two possibilities:

If both clocks are at rest side by side and clock A accelerates away from clock B and then decelerates to rest with regard to clock B after a while, then to me, clock A is the one which will have slowed down even if we cannot measure it from a distance, which should show if we accelerate clock A towards clock B and reunite the two clocks again.

If clock B accelerates to rest with regard to clock A after clock A has accelerated away from it, then to me, clock A would still have slowed down with regard to clock B for a while, which should also show if we accelerate clock A towards clock B and reunite the two clocks. Those are circumstances where we know which clock has accelerated, thus which one is actually moving with regard to the other. That's what happens when we send probes for instance, or when we accelerate particles. We also know that an atmospheric muon lives longer than a laboratory one because we know where it started to move and at what speed it has traveled. When we know which clock is traveling, which is the case for practical problems, we can still use relativistic calculations to know how much it has slowed down even if it is no more a relativity problem. Difficult relativity problems seem to be reserved to situations where it is impossible to tell where the motion comes from, thus to useless situations.

Dale
Mentor
2020 Award
I see two possibilities
Both of the possibilities you mention are more complicated than the scenario you described in post 25. In post 25 you had only a single acceleration period for a single clock. Consider just that scenario from the reference frame where the inertial clock ends at rest and then consider the same scenario from the reference frame where the accelerating clock ends at rest.

Ibix
2020 Award
@Raymond Potvin - that wasn't quite what Dale asked. He was asking what happens if two clocks are travelling side by side at 0.6c and one of them accelerates at 1g until it is at rest with respect to you. Compare and contrast what happens if the two clocks are side by side at rest with respect to you and one accelerates at 1g to 0.6c. Which one ticks slowly? Is it always the one that accelerated, which is what you seem to be claiming in #25.

phinds
Gold Member
Hi Dale,

I see two possibilities:

If both clocks are at rest side by side and clock A accelerates away from clock B and then decelerates to rest with regard to clock B after a while, then to me, clock A is the one which will have slowed down even if we cannot measure it from a distance, which should show if we accelerate clock A towards clock B and reunite the two clocks again.
Again, it will not have "slowed down", it will have produced fewer ticks. That is, it will still be ticking at one second per second but a different number of seconds will have passed for it (fewer in this example) because it took a different path through spacetime.

I keep pointing this out in response to your posts because "slowing down" is seriously misleading and people who believe that clocks run slower in their own reference frames get all confused as to how biological processes could slow down too (as they would have to if "slowing down" were true).

Again, it will not have "slowed down", it will have produced fewer ticks. That is, it will still be ticking at one second per second but a different number of seconds will have passed for it (fewer in this example) because it took a different path through spacetime.

I keep pointing this out in response to your posts because "slowing down" is seriously misleading and people who believe that clocks run slower in their own reference frames get all confused as to how biological processes could slow down too (as they would have to if "slowing down" were true).
Hi Phinds,

I prefer to call a cat a cat: if something ages less because of motion, then I prefer to look for a physical phenomenon. If particles' frequencies go down when we accelerate them, then I prefer to attribute this dilation to the time their components take to produce those frequencies. Of course it doesn't work if we don't know they are the ones that have accelerated with regard to the detector, but if we do, it seems to work. To me, if a twin ages less than the other, it is because his metabolism slows down during the time he is traveling with regard to his brother. If a clock records less time, it is because its atoms' frequencies slow down.

More generally, if light takes more time between the mirrors of the moving light clock, it means that the molecules of the mirrors take more time to reflect it, that the bonding between the atoms of those molecules also take more time to be executed, and so on for the components of those atoms. To me, this is the only way the laws of physics can stay the same for all observers on inertial motion, and also the only way to explain the null result of the MM experiment.

Ibix
2020 Award
If particles' frequencies go down when we accelerate them, then I prefer to attribute this dilation to the time their components take to produce those frequencies. Of course it doesn't work if we don't know they are the ones that have accelerated with regard to the detector, but if we do, it seems to work.
Contradicting the principle of relativity doesn't seem to me like a good way to go about understanding the theory of relativity.

Both of the possibilities you mention are more complicated than the scenario you described in post 25. In post 25 you had only a single acceleration period for a single clock. Consider just that scenario from the reference frame where the inertial clock ends at rest and then consider the same scenario from the reference frame where the accelerating clock ends at rest.
I meant «at rest with regard to the other clock», not at rest with regard to a third observer as Ibix pointed out. The way the two clocks move with regard to one another does not depend on the way they move with regard to another observer, but the way they accelerate still does even if it is a bit more complicated to illustrate. There is more possibilities then, but if we study everyone of them, we should be able to use acceleration to tell which clock has slowed down with regard to each observer. If acceleration was not determinant, I think we couldn't tell which twin has aged less.

Ibix
2020 Award
If acceleration was not determinant, I think we couldn't tell which twin has aged less.
Not true. Pick a frame. Write down the speed ##v(t)## of one of the twins at all times ##t## between the first (t=0) and second (t=T) meetings of the twins as measured in that frame. Evaluate $$\tau=\int_0^T\sqrt {1-v^2 (t)/c^2}dt$$This is the age of that twin at their second meeting. Repeat for the second twin. You have your answer with no mention of acceleration. Note that since I only asked for speed not velocity the acceleration cannot, in general, be inferred from ##v (t)##. Jambaugh's circular track for which ##v## is a constant but there is always acceleration is an extreme example of this.

Dale
Mentor
2020 Award
if we study everyone of them, we should be able to use acceleration to tell which clock has slowed down with regard to each observer
Good luck with that. It won't work, but going through the exercise will be valuable for you. You will find that you need to know the velocity, not just the acceleration

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Good luck with that. It won't work, but going through the exercise will be valuable for you
I used two clocks only because the problem was easier to describe, which would be the case if, in the problem you asked me to solve, you could pick only one possibility where you think acceleration is not determinant.

Not true. Pick a frame. Write down the speed ##v(t)## of one of the twins at all times ##t## between the first (t=0) and second (t=T) meetings of the twins as measured in that frame. Evaluate $$\tau=\int_0^T\sqrt {1-v^2 (t)/c^2}dt$$This is the age of that twin at their second meeting. Repeat for the second twin. You have your answer with no mention of acceleration. Note that since I only asked for speed not velocity the acceleration cannot, in general, be inferred from ##v (t)##. Jambaugh's circular track for which ##v## is a constant but there is always acceleration is an extreme example of this.
Hi Ibix,

Since motion is relative, the relative speed would be the same for both twins if we could not tell which one has accelerated. If we start the experiment with both twins side by side in space for example, the twin that accelerates knows he does, and the twin that does not accelerate also knows he doesn't, so if the one that knows he has accelerated gets back to his twin later on, he knows he will have aged less, and he knows how much if he knows how much he has accelerated and how long the roundtrip took.

Ibix
2020 Award
It's trivial to set up situations where both twins undergo the same accelerations but end up different ages. A variant on Jambaugh's circular tracks will do it.

Contradicting the principle of relativity doesn't seem to me like a good way to go about understanding the theory of relativity.
The relativity principle is about not knowing that we are moving, thus when we know and we need to calculate time dilation, it is easier not to refer to it.

It is possible completely rule out accelerations the following way. FIRST twin is at rest, the SECOND approaches him. When they meet, they synchronize clocks, their clocks show 0. Twins recede from each other and the SECOND meets another - THIRD twin who flies towards the FIRST. When they meet, they synchronize clocks. Let's say their clocks show 3. Then that THIRD twin meets FIRST and they compare clock readings again. THIRD clock will show less time.

In case if we consider the case (motion of twins) from any arbitrary chosen frame (as @Ibix proposed), the paradox simply turns into effect. Two twins move side by side. One if them suddenly stops. It is clear his clock now will tick faster than moving one. His (stopped) clock will tick at the same rate as any synchronized clock of that frame, in which motion takes place. Thus, it will be ticking faster than moving one. Then he suddenly starts (or passes clock readings to third brother, who passes by) and catches up moving one. It is easy to calculate, that while he overtakes moving one, his clock will show gamma times less time.

Dale
Mentor
2020 Award
I used two clocks only because the problem was easier to describe, which would be the case if, in the problem you asked me to solve, you could pick only one possibility where you think acceleration is not determinant.
I already did that. Two clocks moving initially at the same velocity, the one on the right accelerates to the right. The one in the right may tick faster or it may tick slower, dependent on the initial velocity. The acceleration alone does not determine it, the velocity (in an inertial frame) does.