# Does acceleration slow time?

phinds
Gold Member
2019 Award
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.
Well, if you insist, as you clearly do, on being completely and totally wrong, then there's nothing else I can do for you.

Dale
Mentor
Since motion is relative, the relative speed would be the same for both twins if we could not tell which one has accelerated.
The v in @Ibix's formula (post 43) is the velocity relative to an inertial frame, not the relative speed. Your statement "motion is relative" is an incorrect statement of the first postulate.

Ibix
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.
Nevertheless, if the twins know their accelerations and the time spent between each of them, they also know how much they have aged since the beginning, so they can compare their calculations at the end to know which one is younger instead of looking at their clocks. All they need is a precise accelerometer and a precise clock.

Dale
Mentor
instead of looking at their clocks. All they need is a precise accelerometer and a precise clock
Hahaha!

Ibix
All they need is a precise accelerometer and a precise clock.
Really? If I've got clock readings from both, why do I need the accelerometer to calculate their age? Why not just use the clock reading?

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.
You did not say that the clocks were initially moving, so I didn't know you added a third observer. Now I know, and of course, the accelerating clock can either decelerate or accelerate with regard to that observer, whereas it can only accelerate away from the other clock. I'm afraid there is no way to solve that kind of problem, unless maybe we put your observer side by side with the clocks in the beginning, and we accelerate it away from the clocks. This way, we know that his clock will be suffering time dilation with regard to the two other clocks, so if one of those clocks accelerates until it gets at rest with regard to him, we know it will suffer time dilation with regard to its twin clock and no more time dilation with regard to the observer's one, whereas if it accelerates in the other direction, we know it will suffer less time dilation with regard to its twin clock than with regard to the observer's one. This way, it seems to work, but it means that the accelerations need to have the same origin in space, thus in time also. If you can provide a better answer, please do.

Ibix
That's just a really long-winded way of admitting that you need to know the velocity, not just the acceleration.

Dale
Hahaha!
Thanks for making me laughing! It's good for health! :0)

Ibix
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.
That'll go badly wrong if you try it in non-flat spacetime.

If you were saying that it's always possible to analyse any experiment in any frame, I'd agree with you. Sometimes it is easier to pick a frame and work entirely in its coordinates. But you're stating that as "knowing that you are moving", which is a really silly way to think of it when, by your own admission, you can't know that.

Moving in some reference frame you can know. Moving, you can't know. And thinking that you kind-of-can will come back to bite you if you approach GR like that.

That's just a really long-winded way of admitting that you need to know the velocity, not just the acceleration.
What I said is that knowing the velocity with regard to the third observer did not seem to help solve the problem, and I added that, to solve it, we may have to know where that velocity came from. It looks as if bodies' inertial motions could have a common origin even if we cannot identify it. We could almost consider that the actual motion of a body is a remnant of all the accelerations a body has suffered.

Dale
Mentor
You did not say that the clocks were initially moving,
Yes, I did. Post 29, second sentence.

Sure, the best answer is @Ibix's answer $$\tau=\int_0^T\sqrt {1-v^2 (t)/c^2}dt$$
I'm afraid there is no way to solve that kind of problem
With your method there is no way to solve it. The standard method works just fine.

Note that the reason your method appears to work in specific cases is because since you are implicitly assuming v(0)=0 you can then use a(t) to determine v(t) which then allows you to use the standard formula. When v(0) is unknown then your approach fails, precisely because a(t) is not sufficient.

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Ibix
Ibix
We could almost consider that the actual motion of a body is a remnant of all the accelerations a body has suffered.
The "almost" is the problem. You need an initial velocity. And that's because, as @Dale says, you have ##dv/dt## and you need to integrate to get ##v## to determine elapsed time. If it were acceleration that mattered you would not need to know that original velocity.

Yes, I did. Post 29, second sentence.
Sorry, I missed it!

Dale said:
Sure, the best answer is @Ibix's answer $$\tau=\int_0^T\sqrt {1-v^2 (t)/c^2}dt$$
With your method there is no way to solve it. The standard method works just fine.
That formula doesn't tell us the direction or the speed the clock that accelerates has with regard to the observer after it has accelerated, so I don't see how it can give a unique answer. Its dilation with regard to that observer depends on its speed with regard to it, which depends on the direction of its acceleration, which is not specified. It may as well get at rest with regard to the observer and suffer no more time dilation, or it may accelerate the other way and suffer more time dilation than before. Maybe I missed something again.

Dale said:
Note that the reason your method appears to work in specific cases is because since you are implicitly assuming v(0)=0 you can then use a(t) to determine v(t) which then allows you to use the standard formula. When v(0) is unknown then your approach fails, precisely because a(t) is not sufficient.
If we don't know if it is the two clocks or the observer that is moving to begin with, then I don't see how the problem can be solved. If we know that it is the two clocks that have accelerated away from the observer, then we know it is the clocks that suffer time dilation. If one of them accelerates away from the observer again, then we know it will suffer more time dilation with regard to the observer than with regard to the other clock since that other clock is already suffering time dilation with regard to the same observer. If it accelerates toward the observer, then we know it will suffer less time dilation with regard to the observer than with regard to the other clock since that other clock is again already suffering time dilation with regard to the same observer. Am I missing something in the way you presented the problem?

timmdeeg
Gold Member
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.
Do you say his heartbeat slows down and he dies?

Do you say his heartbeat slows down and he dies?
:0) Hi Timmdeeg,

No he doesn't die, because his atoms also slow down their heartbeat, and without dying, so he won't even notice the difference. Maybe he will die from acceleration though, because at the end, his mass will have increased a lot, so it will take a lot of force to increase its speed, what could crush his heart, and he could bleed to death! :0)

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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).
I'm not sure how hard you need to stress this. For me, it's more a matter of sloppy writing than understanding. There is (in this 4D universe) no measurement for the rate of time passing. A second is always a second, etc. But your (frame's) second might not equal mine. I read where a clock just a few feet higher off the ground than another ticked slightly faster, that your feet age more slowly than your head. My original question asked whether acceleration alone would slow a clock relative to a non-accelerating observer's, and got the answer: no.

I know that if I'm deep in a gravity well, and you are not, then my clock will appear to you to run slower. Will your clock then appear to run faster to me? If so, the universe must look very strange with planets and galaxies spinning around > c.

phinds
Gold Member
2019 Award
I'm not sure how hard you need to stress this.
Well, how about for someone who has it totally wrong, as in:

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.

Chris Miller
Well, how about for someone who has it totally wrong, as in:
Stop pushing, my resistance to change has increased so much in that direction that my heart is about to bleed! :0)

phinds
Gold Member
2019 Award
Stop pushing, my resistance to change has increased so much in that direction that my heart is about to bleed! :0)
Well, you just need to travel faster so the bleeding slows down

Well, you just need to travel faster so the bleeding slows down
If I succeed, it's gonna slow down with regard to you, but not to me, and I will suffer more resistance to change, which might brake my heart definitively. :0)

jbriggs444
Homework Helper
2019 Award
I know that if I'm deep in a gravity well, and you are not, then my clock will appear to you to run slower. Will your clock then appear to run faster to me? If so, the universe must look very strange with planets and galaxies spinning around > c.
Yes, a clock higher in a gravitational field will appear to run fast. Gravitational time dilation is not symmetric.

In special relativity, the speed of light is a global limit. Spacetime is flat and velocities here can compared with velocities there unambiguously. The speed of light is what it is (as long as we are all using inertial frames).

In general relativity, the speed of light is a local limit. Spacetime is not flat and comparing velocities here to velocities there is ambiguous. There is no such thing as an global inertial frame and the velocity that you get when you measure something far away depends on the coordinate system you use.

As we speak, you are sitting in a gravitational potential well. Does the universe look strange to you?

Chris Miller
timmdeeg
Gold Member
No he doesn't die, because his atoms also slow down their heartbeat,
So if atoms slow down consequently molecules will slow down too. If water molecules slow down due to cooling the water freezes. So in case of our twin, the water in his glass will freeze, right? Not because of cooling in this case but because of the slowing down of the water molecules due to less aging.

jbriggs444
Homework Helper
2019 Award
So if atoms slow down consequently molecules will slow down too. If water molecules slow down due to cooling the water freezes. So in case of our twin, the water in his glass will freeze, right? Not because of cooling in this case but because of the slowing down of the water molecules due to less aging.
The fact that you are, right now, moving very rapidly in the rest frame of a particle in an accelerator at CERN does not cause your body to freeze instantly.

So if atoms slow down consequently molecules will slow down too. If water molecules slow down due to cooling the water freezes. So in case of our twin, the water in his glass will freeze, right? Not because of cooling in this case but because of the slowing down of the water molecules due to less aging.
If our own time dilation is unobservable, then any phenomenon that is happening inside us because of that is also unobservable. Length contraction is unobservable for instance, but without it, our data would be unexplainable. If our atoms' frequencies slow down with regard to an observer, then our molecules must slow down, our metabolism must slow down, everything we do must slow down. To me, that's the only way to explain relativistic aging anyway, otherwise we might as well invoke magic to explain the data.

The fact that you are, right now, moving very rapidly in the rest frame of a particle in an accelerator at CERN does not cause your body to freeze instantly.
Hi Jbriggs,

The fact that we know the particle is actually accelerating with regard to us means that we know it is actually getting speed with regard to us, and we know it is not us that is getting speed because we know we are not accelerating, so we also know that it is the particle that is suffering more and more time dilation.