Objective-collapse theories, also known as spontaneous collapse models or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes, not a superposition of them as predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases. In collapse theories, the Schrödinger equation is supplemented with additional nonlinear and stochastic terms (spontaneous collapses) which localize the wave function in space. The resulting dynamics is such that for microscopic isolated systems, the new terms have a negligible effect; therefore, the usual quantum properties are recovered, apart from very tiny deviations. Such deviations can potentially be detected in dedicated experiments, and efforts are increasing worldwide towards testing them. An inbuilt amplification mechanism makes sure that for macroscopic systems consisting of many particles, the collapse becomes stronger than the quantum dynamics. Then their wave function is always well-localized in space, so well-localized that it behaves, for all practical purposes, like a point moving in space according to Newton's laws. In this sense, collapse models provide a unified description of microscopic and macroscopic systems, avoiding the conceptual problems associated to measurements in quantum theory. The most well-known examples of such theories are:
Ghirardi–Rimini–Weber (GRW) model Continuous spontaneous localization (CSL) model Diósi–Penrose (DP) model Collapse theories stand in opposition to many-worlds interpretation theories, in that they hold that a process of wave function collapse curtails the branching of the wave function and removes unobserved behaviour.
History of collapse theories Philip Pearle's 1976 paper pioneered the quantum nonlinear stochastic equations to model the collapse of the wave function in a dynamical way; this formalism was later used for the CSL model. However, these models lacked the character of "universality" of the dynamics, i.e. its applicability to an arbitrary physical system (at least at the non-relativistic level), a necessary condition for any model to become a viable option. The next major advance came in 1986, when Ghirardi, Rimini and Weber published the paper with the meaningful title "Unified dynamics for microscopic and macroscopic systems", where they presented what is now known as the GRW model, after the initials of the authors. The model has two guiding principles:
The position basis states are used in the dynamic state reduction (the "preferred basis" is position); The modification must reduce superpositions for macroscopic objects without altering the microscopic predictions. In 1990 the efforts for the GRW group on one side, and of P. Pearle on the other side, were brought together in formulating the Continuous Spontaneous Localization (CSL) model, where the Schrödinger dynamics and a randomly fluctuating classical field produce collapse into spatially localized eigenstates. In the late 1980s and 1990s, Diosi and Penrose and others independently formulated the idea that the wave function collapse is related to gravity. The dynamical equation is structurally similar to the CSL equation.
Most popular models Three models are most widely discussed in the literature:
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