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I don't think Feynman would agree with you there at all. Physicists often shift reference frames in doing calculations.
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I know, and I hadn't fully grasped in my head what the problem was and so I expressed it badly. You do get a negative force relative to the centre of the Earth, but this does not explain why the far side of the Earth moves away from the moon, this is what I had meant by a negative force, and I admit this was careless use of language (plus the fact I had't realy thought about the tidal effect on a falling body).
The way I read the argument was a man at the top of the tower feels less force from the Earth than a man in the middle of the tower. So relative to the man at the middle of the tower the man at the bottom feels a negative force, so the man at the top moves away from the man in the middle and from the Earth.
Now if the tower disapeared I accept that the man at the top will move away from the man in the middle. You have to explain if the man at the middle doesn't move, why does the man at the top get further away, both from the man in the middle and the Earth. (The far side of the Earth moves away from both the Centre of the Earth and the moon)
I am going to be away from computers for the next few days, so I will not be able to contribute again until next week.
Simon