Is there a theory that physically explains the origin equivalence principle / explains gravity via acceleration?

I've been thinking about how gravity could arise from a 4th dimensional spinning cylinder with space-time that has pliability like rubber (which I think is a generally accepted analogy). The centrifugal force of matter on the inside of the cylinder would cause massive bodies to bend space-time, and other objects in the vicinity would fall into that curved area purely because of momentum.

Are there rigorous theories that explain gravity via that kind of geometry? If so, I'd also like to hear an explanation of the shape of such a geometry, and I'd like to know how such a geometry is consistent with the equivalence principle and relativity.

• What does it mean to you for a theory to "physically explain" a fact? Arguably that is exactly what all theories do and in particular what general relativity does. – dmckee Jan 23 '15 at 1:46
• Well, the way i'm used to hearing it, the equivalence principle is generally used as a premise. I guess what I mean is a theory that explains that fact without using that fact as a premise. – B T Jan 23 '15 at 1:52
• Here's the rub: only non-fundamental theories can be like that. All---all---fundamental facts in science have as their justification only their predictive power. That's more or less what we mean by describing an idea as "fundamental" in the first place. Ideas that can be explained as consequences of other ideas aren't fundamental. – dmckee Jan 23 '15 at 2:57
• @dmckee: I don't know how to answer OP's question, but consider the following analogy: In QM, the spin-statistics theorem must be introduced as a postulate. In QFT, the spin-statistics theorem may be derived from other postulates (Lorentz invariance, causality, etc.). In one theory it is fundamental, in another it is derived. – Ryan Unger Jan 23 '15 at 3:02
• @0celo7 Well, yes. The question of what is fundamental is a matter of context; spin statistics was for a while and now it is not. If the OP wants to know if GR is (currently) fundamental then we can answer that. If he's looking for a clockwork model of the equivalence principle he is (currently) out of luck. – dmckee Jan 23 '15 at 3:08