Spontaneous radiation of free electrons in a nonrelativistic collapse model

Abstract

One way to solve the long-standing ``measurement''problem in quantum mechanics is to modify Schr\"odinger's equation so that the collapse of a state vector is the result of some intrinsic physical dynamics. The introduction of such collapse dynamics often results in energy nonconservation. In this paper, we first derive a general expression for the rate of change in the expectation value of energy in a general collapse model that supports a linear evolution of the density matrix. In particular, we show, under certain plausible assumptions, that energy nonconservation is an inevitable consequence of collapse. We then work with a specific model, namely, the nonrelativistic continuous spontaneous localization (CSL) model, to derive further consequences of collapse. In CSL, in a nonunitary evolution, a particle interacts with a fluctuating scalar field, leading to the collapse of the state vector. One consequence of this interaction is that a free electron can radiate spontaneously. We calculate the spectrum of this radiation. The result is then compared with the observed upper bound on spontaneous radiation in Ge and a constraint on the parameters of CSL is obtained.