Note on the quantum mechanics of M theory

Abstract

We observe that the existence of black holes limits the extent to which M Theory (or indeed any quantum theory of gravity) can be described by conventional quantum mechanics. Although there is no contradiction with the fundamental properties of quantum mechanics, one can prove that expectation values of Heisenberg operators at fixed times cannot exist in an ordinary asymptotic Lorentz frame. Only operators whose matrix elements between the vacuum and energy eigenstates with energy greater than the Planck scale are artificially cut off, can have conventional Green's functions. This implies a Planck scale cutoff on the possible localization of measurements in time. A similar behavior arises also in ``little string theories''. We argue that conventional quantum mechanics in light cone time is compatible with the properties of black holes if there are more than four non-compact flat dimensions, and also with the properties of ``little string theories''. We contrast these observations with what is known about M Theory in asymptotically Anti-de Sitter spacetimes.