Solution to Rotating Coin Paradox

Most people believe that the answer will be once and are therefore surprised to discover that the truth is in fact twice...

...Or is it? Think about it.

From Earth we always see the same same face of the moon, but looking at it form Mars we would see it spinning. So, does the moon rotate, or doesn't it?

It could be argued that relative to a fixed point on the stationary coin, the moving coin only rotates once. How many times the coin rotates would seem to depend on the frame of referrence of the observer.

So, does the moon rotate about its own axis?
A Foucault pendulum can be used to detect the inertial effects caused by the rotation of astronomical bodies. If this pendulum were placed on the moon it would indicate that the moon does indeed rotate as it circles the earth.

However, this does not put an end to the argument. If the moon did not rotate, but instead the universe rotated about the moon, the pendulum would still act in exactly the same way. General realtivity shows that the gravity fields created by a rotating universe about a non-rotating moon would produce the same effects as the inertia fields which are generated if the moon rotates in a fixed universe.

It would therefore seem that in order to get to grips with this problem one needs to think in terms of relative motion.

Confused? Interested to know more? curiouser.co.uk recommends "Simply Einstein: Relativity Demystified" by Richard Wolfson; an excellent introduction to Einstein's Theory of Relativity for the lay reader.

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This problem was first published in Scientific American.