Do tidal forces mean the Equivalence Principle is BS?

[my_wan]

This "restriction" is what I and the OP have a problem with. I'd rather deal with what logicians call "universals".

It seems evident that the Equivalence Principle sits somewhere between a "singular existential statement" and a "universal statement". This is not settling for those who see the "unlearning" previous teachings as an obstruction against their ability to learn. This is bad pedagogy in my opinion.

They are falling at the same rate, just not in the same direction because separate points in the same object are trying to go to the same point at the center of the planetary mass. Hence they bump into each other and often even break in the process.

 

[Phrak]

Well, the whole point in this exercise is the that gravitational field is constant, and in the same direction, which isn't the case for a spherical body. Take a body of uniform density and carve a spherical cavity in it. Now you have a uniform gravitational field in the weak field limit. Where are the objections to this model?

Really, Einstein's notion of equivalence is something he latter tries to clarify, calling it general covariance. This notion is better solidified mathematically as diffeomorphism invariance which is a scary way to say that things like vectors and stuff are independent of the coordinate system in which they are, or can be expressed. So if you go from Cartesian to polar coordinates, say, the vector you have doesn't get longer or shorter or change direction.

 

[atyy]

The two ingredients of the EP within GR are:

1) the gravitational field is the metric field - this geometrical notion ensures that when the metric is curved, things are still everywhere "locally" flat -where "local" means we don't look at curvature.
2) matter, conceived as all non-gravitational fields, is universally and minimally coupled to the metric - this means that there are laws of physics that are "local" and don't "directly" probe the curvature of the metric.

Curvature is non-local in the sense that it is defined using second derivatives of the metric, and higher order derivatives are more non-local than lower order ones, since they involve more differences between spacetime separated quantities (technically, derivatives are local since they are limits and exist at a point, but I'm not using that jargon). The EP does fail for experiments that are non-local.

http://www.pma.caltech.edu/Courses/ph136/yr2006/text.html, section 24.7