Environmental and spontaneous localization

The dynamical elimination or reduction of macroscopic superpositions has long been of interest, particularly with regard to the quantum theory of measurement. A number of models have demonstrated this for the reduced density matrix of a system interacting with an environment. Alternatively, Ghirardi, Rhimini, and Weber [Phys. Rev. D 34, 470 (1986)] have proposed a fundamental modification of the Schrödinger equation, quantum mechanics with spontaneous localization (QMSL), which provides a master equation similar in mathematical form. In this paper we consider an isotropic environment that is elastically scattered by the system of interest with negligible momentum transfer, extending a previous result of Joos and Zeh [Z. Phys. B. 59, 223 (1985)] from small length scales to all length scales. We discuss the physical nature and relevance of the differences between our result and similar open systems calculations. We describe the mathematical similarity between our extended environmental model and the QMSL dynamics determining the QMSL parameters that allow calculations using QMSL to be used as a model for the effect of the environment. That gives us access to a number of interesting results obtained for the QMSL master equation. Finally, we discuss some experimental considerations for the purposes of detecting effective nonunitary evolution of this form.