Do Centrifugal Forces Affect Clock Time Dilation?

[sigurdW]

We have two clocks within a laboratory.
We put one on the table and the other in a centrifuge made of glass so we can observe both clocks existence simultaneously.
Now observe the clocks throughout the experiment. And now stop centrifuging the clock. Check the time of both clocks.

My first simple question is: For how long time have the clocks been in the lab during the experiment?
Suppose the stationary clock says for one hour and the spinning clock says fiftynine minutes:

1 Has the spinning clock really been only 59 minutes in the laboratory?

2 Is the experiment the twin paradox with a difference?

 

[ghwellsjr]

We have two clocks within a laboratory.
We put one on the table and the other in a centrifuge made of glass so we can observe both clocks existence simultaneously.
Now observe the clocks throughout the experiment. And now stop centrifuging the clock. Check the time of both clocks.

My first simple question is: For how long time have the clocks been in the lab during the experiment?
Suppose the stationary clock says for one hour and the spinning clock says fiftynine minutes:

1 Has the spinning clock really been only 59 minutes in the laboratory?

2 Is the experiment the twin paradox with a difference?

Both clocks have been in the laboratory rest frame for 60 minutes. The stationary one had a gamma of 1 so its Proper Time is the same as the Coordinate Time of the laboratory. The spinning clock had a gamma of a little more than one because of its speed in the laboratory frame and so it experienced Time Dilation meaning that the Coordinate Time was longer than its Proper Time with a ratio of gamma.

 

[sigurdW]

I agree. Next question:
1 Can the orientation of the Earth rotational axis be decided from within the lab?

To simplify matters, let's film both clocks continuosly, sending the information to a computer presenting the time in the clocks in any convenient form on a screen.Making continuos observation and comparison possible.

2 Just a note because there has been no comments on the nature of this experiment:
As in the traditional twin expeiment it can in principle be determined that the clocks differ, seen as termodynamical systems: though they have existed for equally long time one is "younger" than the other.

 

[ghwellsjr]

I agree. Next question:
Can the orientation of the Earth rotational axis be decided from within the lab?
To simplify matters, let's film both clocks continuosly, sending the information to a computer presenting the time in the clocks in any convenient form on a screen.Making continuos observation and comparison possible.

If you are asking if it is possible to do an experiment with two ideal clocks to determine the rotational axis of the Earth, the answer is yes, if you can move the lab around. (We are assuming also an ideal Earth with no gravitational influences to worry about.) Also, I don't see why you would want one of them to be in a centrifuge.

All you have to do is position the two clocks at each end of a long trailer and see what the difference in their tick rates is. Then rotate the trailer until you find the orientation that maximizes the difference. When you find it move the trailer in that direction and see if the difference gets greater. If it does, keep moving in that direction, otherwise go in the opposite direction. Keep comparing while traveling until the difference starts getting smaller, in other words you want to find the place on the Earth where the difference is maximum and the clock that is ticking faster will be at one of the poles.

If you want to do it in a localized lab with a centrifuge, you need to specify where that lab is (on the equator, at a pole, somewhere in between) or you need to specify that you would like a solution anywhere and you need to specify the orientation of the centrifuge (horizontal or vertical) or if you are allowed to change its orientation. I really haven't thought about this enough to determine if it would be possible but it seems like an added complication to me to use a centrifuge.

 

[pervect]

I agree. Next question:
1 Can the orientation of the Earth rotational axis be decided from within the lab?

To simplify matters, let's film both clocks continuosly, sending the information to a computer presenting the time in the clocks in any convenient form on a screen.Making continuos observation and comparison possible.

2 Just a note because there has been no comments on the nature of this experiment:
As in the traditional twin expeiment it can in principle be determined that the clocks differ, seen as termodynamical systems: though they have existed for equally long time one is "younger" than the other.

The Earth is not a sphere. This turns out to be important to the experiment, because while the Earth's rotatioal velocity does affect clocks on its surface as viewed from a earth-centered inertia frame of reference, the change in altitude and gravitational potential due to Earth's shape ALSO affects the rate at which clocks tick due to "gravitational time dilation".

The net result is that all clocks on the geoid (roughly speaking, at sea level) tick at the same rate.

One reference for this: http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=articlese3.html

To account for the fact that reference clocks for the GPS are not at infinity, I shall consider the rates of atomic clocks at rest on the earth’s geoid. These clocks move because of the earth’s spin; also, they are at varying distances from the earth’s center of mass since the Earth is slightly oblate. I

...

Thus, the very useful result has emerged, that ideal clocks at rest on the geoid of the rotating Earth all beat at the same rate. This is reasonable since the earth’s surface is a gravitational equipotential surface in the rotating frame. (It is true for the actual geoid whereas I have constructed a model.) Considering clocks at two different latitudes, the one further north will be closer to the earth’s center because of the flattening – it will therefore be more redshifted. However, it is also closer to the axis of rotation, and going more slowly, so it suffers less second-order Doppler shift. The earth’s oblateness gives rise to an important quadrupole correction. This combination of effects cancels exactly on the reference surface.

There is of course a fairly simple way to determine the Earth's rotatioal axis through physical experiments. This is to operate a series of Focault pendulums. The ones at the poles will rotate once per day, the ones at the equator won't rotate at all.

It's not directly related to the rates at which clocks tick, though one might be able to apply Hamilton's principle - the idea that objects follow the paths that extremize proper time - to come up with some arrangement of high precision clocks that peforms the same function. It's easier to use the pendulii, though, I think.

 

[pervect]

[add]One other experiment that can be done isn't a "laboratory" experiment, but the Hafele-Keating experiment. It directly shows the time dilation due to the Earth's rotation by comparing two clocks flown around the world in different directions.http://en.wikipedia.org/w/index.php?title=Hafele–Keating_experiment&oldid=551242565

[add#2]
A ring laser gyro will also do the trick