How does the direction of rotation impact time dilation on a rotating object?

[Jorrie]

I am sure the rotating disc has been discussed on this forum over and over, but I could not find a thread. (Maybe I'm using the search function wrongly.)

If someone could perhaps point me to a thread. I have read http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

This pdf is the best fairly balanced view I could find on the web.
www.smcm.edu/nsm/physics/SMP03S/KeatingB.doc.pdf[/URL]

Any newer/better links?

 

[pervect]

The FAQ:

http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

my favorite treatment:
http://arxiv.org/abs/gr-qc/9805089

Quoting the abstract:

It is often taken for granted that on board a rotating disk it is possible to operate a \QTR{it}{global}3+1 splitting of space-time, such that both lengths and time intervals are \QTR{it}{uniquely} defined in terms of measurements performed by real rods and real clocks at rest on the platform. This paper shows that this assumption, although widespread and apparently trivial, leads to an anisotropy of the velocity of two light beams traveling in opposite directions along the rim of the disk; which in turn implies some recently pointed out paradoxical consequences undermining the self-consistency of the Special Theory of Relativity (SRT). A correct application of the SRT solves the problem and recovers complete internal consistency for the theory. As an immediate consequence, it is shown that the Sagnac effect only depends on the non homogeneity of time on the platform and has nothing to do with any anisotropy of the speed of light along the rim of the disk, contrary to an incorrect but widely supported idea.

What it means in practice.

If you take a clock on a trip around the rotating disk (including for example the rotating Earth as a specific example if you don't mind the fact that it's a sphere rather than a disk), no matter how slowly you do it, you will find that it is not synchornized with a clock that remains "at rest" (in the rotating frame) when the traveling clock returns. Circulating in one direction, slowly, it gains time. In another, it loses time. For low velocities the time lost/gained is constant per round trip.

One has to make a choice between using a general coordinate system, which does not attempt to use Einstein clock synchronization, or introduce a discontinuity in the coordinate system, a bit like the "international dateline" to deal with this behavior of moving clocks.

For timekeeping on the Earth, the usual coordinate time (TAI time) does not incorporate such a discontinuous line, which means that Einstein's clock synchronization was not used. This means that if one wants to measure the speed of light on the Earth and get correct answers, one needsd to use Einstein's original method to synchronize clocks, and not synchronize them by using TAI time.

This implies "do not use GPS time to synchronize your clocks when measuring the speed of light" as GPS time is derived from (the same as?) TAI time.

Various people have tried to make a big deal out of all this.

 

[Jorrie]

Thanks pervect. Both my favorite: www.smcm.edu/nsm/physics/SMP03S/KeatingB.doc.pdf[/url] and yours: [url]http://arxiv.org/abs/gr-qc/9805089[/URL] are very enlightening!

 

[cesiumfrog]

Circulating in one direction, slowly, it gains time. In another, it loses time.

So you're saying centripetal acceleration only dilates time if the rotation is .. anticlockwise?

 

[Jorrie]

Circulating in one direction, slowly, it gains time. In another, it loses time.

So you're saying centripetal acceleration only dilates time if the rotation is .. anticlockwise?

I understood pervect's statement in the context of the synchronization of clocks on a rotating disk or sphere. There it does depend on which direction you move a clock relative to the rotating object. The desynchronisation of clocks causes the Sagnag and other rotating body effects.

And BTW, I do not think centripetal acceleration per se has anything to do with time dilation, but let's ask pervect.

Jorrie

 

[pervect]

So you're saying centripetal acceleration only dilates time if the rotation is .. anticlockwise?

The Earth rotates anti-clockwise (unless I got it backwards?) when viewed from the North pole. Of course, if you view it from the South pole, I guess it rotates the other way :-).

So when you travel in the same direction that the Earth is rotating (which I guess would be "anti-clockwise"?) you get "more time dilation".

I don't view this an acceleration effect, however. I tend to think about the situation from an Earth-Centered-Inertial-Frame. From this POV, it's the velocity that causes time dilation, and not the acceleration. Offhand I can't think of any viewpoint in which centripetal acceleration causes time dilation.

The only two things that matter are one's velocity, and the metric coefficient of the clock (which I usually imagine as being on the equator).
The Earth is pretty round (modulo some nitpicking about tidal bulges, etc.) so the metric coefficient will be essentially the same everywhere on the equator. Thus velocity is the only really important variable.