the not-so-equivalent principle

I posted this puzzle a while ago on wbmh, but subsequently it got deleted and I think it is worth reposting it here. Please write a comment if you have an answer (or remember the discussion on wbmh) and win the famous golden llama award.

Perhaps you have seen the video clip of astronaut David Scott dropping a hammer and a feather on the surface of the moon, repeating Galileo's famous (thought)experiment.

But strictly speaking in a high precision experiment the two objects will in general not hit the moon at the exact same time.

Why is that?


Let me clarify a few things.

We assume that the shape of the objects makes no difference (we assume the spherical cow approximation is valid) and the surface of the moon is perfectly smooth. Further we assume that there is no trace of an atmosphere on the moon and no electrical charges (attached to the objects). We assume that the presence of the astronaut (and his gravitational field) can be neglected and we assume the sun, earth and the other planets are sufficiently far away. We ignore quantum theory and assume that the many-worlds interpretation and any other conspiracy theories can be neglected...

added later: Furthermore we assume that all objects and observers move slowly compared to the speed of light, so that we can use the standard St. Augustine definition of simultaneity.

update: Akshay Bhat is the proud winner of the famous golden llama award ...

... he will enjoy a free subscription to this blog for a whole year. Congratulations!

If you want to see my own solution to this puzzle click here.


Anon Ymous said...

In the theory of relativity the simultaneity of two events cannot be defined and a moving observer will not see the two objects hit at exactly the same time.

wolfgang said...

Good point, but relativity is not an issue in this puzzle.
I have modified the blog post to make this clear.


Because gravitational force depends upon mass of both objects. i.e. The moon and the hammer. Thus in a high precision experiment even moon will be attracted towards the hammer, while the attraction towards the feather will be lesser.

Thats my guess

wolfgang said...

Yes indeed. We have yet another proud winner of the golden llama award!