Philosophical Implications of the GRW Theory of Wave Function Collapse

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

This is a research project in the foundations of quantum mechanics that focuses on the concept of spontaneous collapse of the wave function, and more specifically on a specific theory that characterizes the collapse that was first put forward by Ghirardi, Rimini, and Weber (GRW) in 1986. Although Quantum mechanics underlies most of modern physics, it is beset with foundational problems; it is very successful in predicting observable phenomena, ye it does not actually say what kind of microscopic events and mechanisms lead to these phenomena. Theories that attempt to complement quantum mechanics and close this gap are called "quantum theories without observers." They do so by replacing Schroedinger's equation by a stochastic time-evolution law for the wave function that implements the concept of collapse of the wave function in a precise way; more to the point, it also implies that macroscopic superpositions such as Schroedinger's cat quickly decay, while the Schroedinger equation remains an excellent approximation for any system comprising only a small number of particles. This project is an investigation into philosophical aspects of the GRW theory. The first goal, on which the PI and a graduate student will work together, is to mathematically prove statements like the following: It is impossible for inhabitants of a GRW universe to measure the number of collapses that occur in a given system in a given time interval, although, according to the GRW theory, this is a well-defined number. More generally, the statements studied describe limitations to what inhabitants can know about their world. The researchers in this project do epistemology by means of mathematical proofs. Another goal, on which the PI will work with collaborators from physics and philosophy, is to explore and explain the philosophical framework of the GRW theory, in particular in the light of a recent technical development in which the PI was involved: the derivation of an operator formalism, analogous but not identical to the operator formalism of quantum mechanics, encoding the empirical predictions of the GRW theory including small deviations from standard quantum mechanics. The topics to be discussed include the need for a precise ontology in space and time (such as the flash ontology) and the idealizations involved in both operator formalisms.