# Time dilation due to changing the speed of rotation of the earth

1. Aug 27, 2014

### Eel13

I was wondering about how to speed up time because I was bored, so I considered rotating my body clockwise (in the northern hemisphere) in order to speed up the rotation of the earth by creating angular momentum opposite to that of the earth. I was thinking that this would then speed up the velocity of everyone on the earth and thus make time progress faster for them.

However, on further investigation into general relativity, I realized that I am not completely sure that a change in the rotational speed of the earth would have the intended effect, or any effect, on the time dilation on the earth relative to an observer outside of the earth's rotation and gravitational field.

I understand that these velocity changes and time dilations would be ridiculously small and negligible but I am just interested in the theoretical effects. Thanks!

Last edited: Aug 27, 2014
2. Aug 27, 2014

### Simon Bridge

If you stand at the pole, ignoring the other effects etc, you are at the axis of a rotating coordinate system.
Presumably if you rotate opposite the Earth's rotation at 1 rev per day then you are stationary and the Earth turns about you (well you are orbiting with the Earth but lets say).

Then everyone else is travelling at some speed in your reference frame - so their clocks run slow.
Note: they don't notice anything different - time does not run at a different speed for them.

3. Aug 27, 2014

### Eel13

I'm not really thinking about effects due to myself being stationary, but more about the effects on the surface of the earth due to its increased velocity and increased acceleration.

4. Aug 27, 2014

### Simon Bridge

Oh you mean that if you turn one way, conservation of angular momentum will change the rotation of the Earth a bit?

Makes no difference to the observation except that the time dilation factor is a tiny bit bigger.
Other people do not experience their time speeding or slowing. Clocks at rest with respect to you always tick off one second every second.

5. Aug 27, 2014

### Eel13

I was wondering about the time dilation relative to an observer outside the earths rotational acceleration, rotational velocity, and gravity.

6. Aug 27, 2014

### Staff: Mentor

If you slowed down the earth's rotation then, relative to an observer at rest at infinity, you would indeed speed up all of the clocks attached to the surface of the earth.

7. Aug 27, 2014

### Simon Bridge

OK - what do you want to know.

The trick with relativity questions is to be painfully precise about what you are describing.
Be very clear about what is happening and who is doing the observing.

You are asking about an observer outside Earth's gravity - what does this mean? Considering that gravity is an extremely long-range effect.

You are thinking, perhaps, of an observer so far away from the Earth that the effect on time dilation of the earth's gravity is much smaller than the time dilation effect due to someone standing on the north pole and twirling around quite fast?The effect of the twirling thing is very tiny indeed - so that would be a very long way away ... so far that the motion of someone standing not on the pole would be quite complicated... of course this also depends on the relative translational motion of the observer and the Earth.

Perhaps you want to set up more of a thought experiment along ideal lines.
Maybe have a clock on a turntable spinning fast and an observer on the ground with his own clock?
Variable speed turn-table.
That better?

But... what dalespam said.

Last edited: Aug 27, 2014
8. Aug 27, 2014

### willoughby

Please correct me if I am wrong. I can look at this from two different angles. One being that special relativity is specific to inertial reference frames and neither rotating along with the surface of the Earth nor standing at the pole spinning opposite the Earth's rotation are inertial reference frames. The second way I look at it is by noting that time dilation in this cased is caused by a difference in relative VELOCITY; not relative speed. If you were spinning opposite the Earth's rotation while standing at the poles, then you would observe everyone else's VELOCITY as constantly changing. I don't know how this would reconcile with time dilation - as if you started rotating with some 'fixed' person on Earth in a specific position, then proceeded to rotate 1 billion times (just arbitrary number), and stopped rotating with that same person in the same position, then their average velocity was zero. I guess what I am getting at is that I was under the impression that while motion is relative in special relativity, this only applies to inertial motion (not rotation), so assuming that there will be time dilation effects by spinning on Earth is akin to claiming that the vast majority of distant stars move faster than the speed of light relative to Earth. That's not the case because 'relative motion' only applies to inertial motion in special relativity.

Again - correct me if I am wrong. Thanks.

9. Aug 27, 2014

### pervect

Staff Emeritus
If we interpret "time progressing factor" as time relative to a static observer at infinity (or actually, any fixed location) then you'd want to stop or slow the rotation to speed up time, not increase it

Note that you wouldn't notice anything yourself, as far as you were concerned a second would still be a second

10. Aug 27, 2014

### Chronos

The 'effect' you are looking for would be absolutely trivial. You might age a fraction of a second less per thousand years [relative to nonrotating observers] with great dedication.

11. Aug 29, 2014

### Simon Bridge

In other words: does time dilation depend on the direction of the relative velocity?

In the usual derivation for the time-dilation equation, you are implicitly aligning one axis along the direction of the relative velocity. (In physics, the orientation of the axes is completely arbitrary - we can draw them however we like so we choose their position and orientation so the maths is easy.)

So in S, the moving clock has $\vec v = v\hat\imath$ and in S' the moving clock has $\vec v = -v\hat\imath$

Have you tried doing the derivation (for inertial frames) where $vec v$ in an arbitrary orientation wrt the coordinate axes?