M Theory Model of a Big Crunch/Big Bang Transition

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant non-relativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that $p$-brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational back-reaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in {\it inverse} powers of $\alpha'$. We argue that interactions should be well-behaved because the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.