# B Does acceleration slow time?

1. Jul 7, 2017

### Chris Miller

I understand that time slows with increased velocity and gravity, but even after reading this (article http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html) I'm a little confused as to whether or not acceleration alone, as in independent of (i.e., in addition to) velocity slows time.

E.g., consider a clock in a centrifuge out in space passed by another non-accelerating clock whose relative velocity is momentarily 0 (i.e., equal to the centrifuge clock's tangential velocity). Are they running at the same rate?

E.g., During the instant I smash into a brick wall (go from say 150 mph to 0), is my car's clock running faster or slower than before the collision?

2. Jul 7, 2017

### phinds

No, it does not. It APPEARS to an observer to run slower but locally it does not slow. Consider this; right now as you read this you are MASSIVELY time dilated and traveling at near light speed relative to a particle in the CERN accelerator. You are also traveling fast and mildly time dilated according to a passing asteroid. You are also stationary and not time dilated at all relative to the chair you are sitting in. Does your clock reflect any of this? Of course not.

3. Jul 7, 2017

### Bartolomeo

The both (rotating and tangential) clocks will measure, that clock in the center of the circumference is ticking $\gamma$ times faster. The clock in the center will measure, that the both rotating and tangential clock dilate $\gamma$ times.

4. Jul 7, 2017

### jambaugh

Your questions are a bit ill posed due to some implicit assumptions. Like "have you stopped beating your wife?" it is hard to answer directly. But here's a go.

Firstly when you say "time slows" there is the begged question "relative to what?" It is well to pay attention to Einstein's oft quoted definition of time. "Time is what a clock reads". So time as measured by a given clock never slows relative to that clock. To formulate your question better let's then just talk about moving clocks and accelerating clocks and what they will read as predicted by Einstein's theories. Lets also be very very careful not to take a "God's eye view" and imagine we can peek at all the clocks "at the same time" because that is not well defined without a.) consulting another clock and b.) explaining how to communicate time information between distant points.

I will mention that by the equivalence principle: gravity = acceleration so both should have equivalent effects (including formations of stationary event horizons).
To compare two moving clocks we need to bring them into very close proximity so that a signal between them takes effectively no time (as seen by all observers)
or to bring them into a co-moving inertial frame with 0 relative velocity so that they can pass singles back and forth enough to synchronize.

So let me propose an explanatory thought experiment which, I hope, will clarify the issue for you. Imagine two clocks traveling on circular tracks at the same tangential velocity (one circle inside the other but touching at a point.)

Let the clocks start clockwise around these circles with the same speed as measured by you who are free floating and see the circles as stationary.
The inner circling clock will experience a stronger acceleration than the outer one but both are traveling at the same speed in your frame and according to each other when they happen to come together at the tangent point. Let's also make the the big circle's circumference a rational multiple of smaller's so that after the inner clock makes n turns and the outer clock makes m turns they will both be at the tangent point at the same time (though each may measure that time as a different value). The question then is what will the two clocks read at this point? Different values or the same value?

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?

5. Jul 7, 2017

### jambaugh

I should have recalled but yes they will agree. In this scenario the differential time rates will only depend on their speeds relative to the stationary observer and since they travel at the same speed for the same amount of time they will have the same proper times.

$$d\tau^2 = dt^2 - dx^2 \to d \tau/dt = \sqrt{1-v^2}$$
in c=1 units.

Then you may ask "why do clocks slow when inside a gravity well?" That situation is more akin to comparing the clocks going around the circle to the clock of the stationary observer at the tangent point. Do note that again it is tricky to speak about comparing two clocks when they are separated in space and you can't have different gravity for different objects at the same location. But this is a more classic question and I refer you to the texts on the matter.

6. Jul 7, 2017

### Ibix

You have to be a bit careful with your definitions here. In an inertial reference frame, the speed of the clock as measured in that frame is the only thing that you need to determine its tick rate. The only way acceleration enters into it is that it can affect speed.

What the tick rate is at the instant of a car crash isn't a well-posed question. It's assuming a discontinuity in the speed of the car, a time where speed isn't actually defined, and asking "what is the value of something that depends on the speed that isn't defined". In practice a car cannot be perfectly rigid and there will be a velocity profile to its deceleration; the velocity profile in some frame defines the clock rate in that frame.

Regarding the centrifuge question, at the instant that the centrifuge clock is stationary with respect to the inertial clock they tick at the same rate (at least, there's a well-defined limit where that's true).

7. Jul 7, 2017

### Chris Miller

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?

8. Jul 7, 2017

### Chris Miller

I understand that my clock only appears slower to an observer on the asteroid or particle, just as theirs does to me. Sorry for the muddled phrasing.

9. Jul 7, 2017

### Chris Miller

Little confused by this. If only relative velocity, and not acceleration, is affecting time, then both the rotating and stationary clock should measure the other as running slower?

EDIT: Is it their different world lines?

10. Jul 7, 2017

### Bartolomeo

Not quite. Everything is very simple.
First: Look for Mossbauer rotor time dilation test - ONLY blueshift of frequency for rotating absorber, redshift of frequency if source rotates and absorber is in the center.
https://en.wikipedia.org/wiki/Ives–Stilwell_experiment
Second: look for transverse Doppler Effect - blueshift of frequency is observer moves in the reference frame of the source - "light received at closest approach in the receiver frame will be blueshifted relative to its source frequency"
https://en.wikipedia.org/wiki/Relativistic_Doppler_effect
Third: Look for Champeney and Moon time dilation test, when absorber and source placed on opposite sides of the rim - no shift of frequency, the both clock measure the same ticking rate.
http://iopscience.iop.org/article/10.1088/0370-1328/77/2/318/meta
Fourth:
https://www.researchgate.net/public...res_of_Time_Dilation_During_Circular_Movement

Also the last chapter
http://www.mathpages.com/home/kmath587/kmath587.htm

Last edited: Jul 7, 2017
11. Jul 7, 2017

### Hiero

Viewing things on the surface of the Earth is supposed to be (on a small scale) like viewing things in an accelerating room. If the floor clock and ceiling clock have no relative motion in an accelerating room, will they be moving relative to each other in the non-accelerating frame?

12. Jul 7, 2017

### Chris Miller

The clocks have a relative velocity of 0 in both scenarios. But on earth, the lower clock is deeper in the gravity well and should run slower. Actually... even if acceleration did affect time the way gravity does, all elevator clocks would still tick at the same rate.

13. Jul 7, 2017

### phinds

yes

yes

Well, sort of. Clocks in a gravity well (and you are positing for the moment that acceleration acts the same) tick LOCALLY at the same rate as all local clocks, but they are on a different world line than a clock higher up in the gravity well and if you were to bring them together the one lower in the gravity well would have ticked fewer times.

14. Jul 7, 2017

### Hiero

Wait, what? If I see a spaceship accelerating relative to me, and two clocks (say on the floor and ceiling of the spaceship) have no relative motion within the accelerating frame, will I not see the two clocks as moving towards each other? (Because the proper distance between the clocks is being contracted more and more as the speed between the frames increases...?)

15. Jul 7, 2017

### phinds

Yes, but I took his statement to be about the local relationship of the clocks not what we would perceive. As you just said, within the accelerating frame they have no relative motion. I see now that his response wasn't really a direct answer to the post he quoted and led me astray.

16. Jul 7, 2017

### Chris Miller

No, it was about the local relationship of the clocks, and being able to determine from inside the 1 g accelerating "elevator" that you were not on earth. No external observer.

17. Jul 7, 2017

### Chris Miller

Different topic/question. And no, I don't think you'd see the clocks moving toward each other as much as the scale changing. Else if a light year long train were to (somehow) accelerate to .85c in a few days, you'd measure the relative velocity of the engine and caboose to be way faster than c.

18. Jul 7, 2017

### Chris Miller

But wouldn't their world lines in an accelerating elevator (unlike in a gravity well) be parallel?

19. Jul 7, 2017

### Buzz Bloom

Hi Ibix:

Your statement above raises the following questions with respect to the two circle example in post #4.
When moving at a uniform speed in a circle, is the rotating reference frame inertial?
When moving at a uniform speed in a circle, is the non-rotating reference frame inertial?

Regards,
Buzz

20. Jul 7, 2017

### Ibix

When you are at rest in a frame, do you weigh anything? If yes, it is not an inertial frame. Whether or not the frame you are working in is inertial has no bearing on whether or not any other frame is inertial.

Someone at rest on a train circling either of those tracks will be plastered against the outside wall of the train.