Twins Paradox - but with a different spin

[jartsa]

Do we know the relative velocity that a spinning twin sees, when looking at the other twin?

There is a formula into which we can plug the velocity, and then the formula produces the rate of a clock that is seen by a twin looking at the other twin's clock.

Relativistic Doppler shift is the name of the formula.

 

[plbeale]

Here is an article about an experiment that shows the time shift between two atomic clocks, one stationary and one flown around the world, that were reunited at the stationary lab and compared.

http://www.npl.co.uk/news/time-flies

According to this article, and others I have found, the relative speed causes the traveling clock to run slower and the difference in gravity causes the stationary clock to run slower, because gravity is stonger on the ground. The net effect is that the traveling clock has gained time relative to the stationary clock on the ground, because the effect of gravity, in this experiment, is more pronounced than the effect due to the speed.