FUNDAMENTAL CONSTANTS AND THE PROBLEM OF TIME

We point out that for a large class of parametrized theories there is a constant in the constrained Hamiltonian which drops out of the class ical equations of motion in configuration space. Examples include the mass of a relativistic particle in free fall, the tension of the Nambu string, and Newton's constant for the case of pure gravity uncoupled to matter or other fields. In the general case, the classically irrele vant constant is proportional to the ratio of the kinetic and potentia l terms in the Hamiltonian. It is shown that this ratio can be reinter preted as an unconstrained Hamiltonian, which generates the usual clas sical equations of motion. At the quantum level, this immediately sugg ests a resolution of the ''problem of time'' in quantum gravity. We th en make contact with a recently proposed transfer matrix formulation o f quantum gravity and discuss the semiclassical limit. In this formula tion, it is argued that a physical state can obey a (generalized) Poin care algebra of constraints, and still be an approximate eigenstate of three-geometry. Solutions of the quantum evolution equations for cert ain minisuperspace examples are presented. An implication of our propo sal is the existence of a small, inherent uncertainty in the phenomeno logical value of Planck's constant.