JohnD: I will post something about such a case (equally massive binary planets in locked rotation), but first there are a few points I wish to get off my chest.
In
Bad Astronomy the BA addresses the paradox that somehow the Moon's gravity causes the far side of the Earth to bulge
away from the Moon. Common sense tells us that an attractive force can't repel something. So how can this be? In fact, there is really no paradox. Pioneer 10 is leaving the solar system even though the resultant gravitational force acting on it is in the opposite direction. But Pioneer 10 is travelling at 50,000 kph (or whatever it is) and that's why it's able to climb up out of the Sun's gravity well. If you were God and you reached out and stopped it in its tracks, it would slide back into the inner solar system.
Similarly, every part of the Earth is moving, and so does not necessarily fall towards the Moon. This, I thought, was the basis of your theory.
Sawicki and the BA explain tides using the old Newtonian sense of gravity as a force. This works well as far as the mathematics is concerned, but Newton's forces are fictitious. The Sun does not really pull on the Earth. It bends space, and the moving Earth is deflected by the curvature of spacetime.
You are probably familiar with the old adage:
Quote:
Matter tells space how to bend.
Space tells matter how to move.
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This means that in explaining a tidal bulge you can't cavalierly ignore the Earth's rotation. The point on the Earth's surface furthest from the Moon (ignoring the Sun for the moment) is moving through the spacetime continuum in a certain direction and at a certain speed. It should make no difference whether this movement is caused by the Earth's motion through space or its rotation on its axis.