Dynamical Wave Function Collapse: Could It Have Cosmological Consequences?

An interpretation of a theory may be defined as a set of rules for going from mathematical statements to statements about reality. In particular, given an initial state vector and the Hamiltonian governing its evolution, an interpretation of quantum theory should enable one to say which are the states which might be realized in nature, and their probabilities of realization. The famous so-called “measurement problem,” which I prefer to call the “reality problem,” is that no currently proposed interpretation of standard quantum theory is well-defined. The “Copenhagen Interpretation” rules rely upon the undefined notion of apparatus. The “Everett/Relative State/Many Worlds Interpretations” rules rely upon the undefined notion of observer or (in its most recent manifestation) the success of the Decoherent Histories program. This latter is not yet well-defined in that general rules for picking the projection operators and times of projection which its formalism requires are still lacking. Quantum theory has been around a long time, so one might reasonably suspect that it is incapable of supporting a well-defined interpretation. If a mathematical theory is not well-defined, that is obviously reason for improving it. The same should be true of a physical theory. This is the motivation for altering quantum theory so that it describes wave function collapse as a dynamical, physical, process. In the theory discussed here (called Continuous Spontaneous Localization, or CSL), an anti-Hermitian, operator is added to the Hamiltonian in Schrödinger’s equation. This operator is a randomly fluctuating scalar field w(x, t) coupled to the mass density of particles. The altered evolution evolves a state vector, expressed as a superposition of states of different mass density configurations, toward one of those states. The evolution is very slow if e.g., the states differ in the relative displacement of just a few particles, so that the usual quantum theory predictions of microscopic behavior are negligibly affected. The evolution is very rapid if e.g., the states differ in the relative displacement of a macroscopic object: thus, the state vector describes the macroscopic world we see around us instead of (what