The role of equivalence in Quantum Mechanics

Abstract

On applying Quantum Mechanics to the problem of a particle bound in an external gravitational potential, we find the following results, which violate one's classical conception of the principle of weak equivalence: radii, frequencies, etc., depend on the mass of the bound particle; the binding energy has the wrong mass dependence; inertial forces do not look like gravitational forces; and there are mass-dependent interference effects. These inconsistencies disappear in the classical limit, which must be approached in a particular manner. The conclusion is reached that the classical statements one can make using weak equivalence have no direct quantum analog and thus the principle is somewhat irrelevant in discussing low-lying quantum states. © 1968.