Gravity and acceleration are equivalent?

[Qfwfq]

If I were to take a huge cylinder with the mass of the earth and stand on end of it, then my plumb-bobs would show as being absolutely equal.

Nope, but they would if you were standing on the surface of a layer of homogenous density and thickness extending infinitely from all directions around your feet. More in general, it would be enough for there to be uniform mass density along each surface parallel to that on which you are standing.

 

Kayra, your point is true but isn't a problem in general relativity because this is based on differential geometry and supposes, as an axiom, the principle of equivalence in differential terms. If you don't want mathematical explanations, that's a bit like saying that for each point on a curved line (or surface) there will be some straight line (or plane) which is tangent.

 

Actually, although not many people are aware of it, the first to state the principle was Newton. Corollary VI of the three axioms if I'm remembering right, in Philosophiae Naturalis Principia Mathematica.