Objective-collapse theory

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: where the Schrödinger dynamics and a randomly fluctuating classical field produce collapse into spatially localized eigenstates. 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: • Ghirardi–Rimini–Weber (GRW) model: which proves several important mathematical results regarding the collapse equations. In all models listed so far, the noise responsible for the collapse is Markovian (memoryless): either a Poisson process in the discrete GRW model, or a white noise in the continuous models. The models can be generalized to include arbitrary (colored) noises, possibly with a frequency cutoff: the CSL model has been extended to its colored version (cCSL), as well as the QMUPL model (cQMUPL). In these new models the collapse properties remain basically unaltered, but specific physical predictions can change significantly. In all collapse models, the noise effect must prevent quantum mechanical linearity and unitarity and thus cannot be described within quantum-mechanics. Because the noise responsible for the collapse induces Brownian motion on each constituent of a physical system, energy is not conserved. The kinetic energy increases at a constant rate. Such a feature can be modified, without altering the collapse properties, by including appropriate dissipative effects in the dynamics. This is achieved for the GRW, CSL, QMUPL and DP models, obtaining their dissipative counterparts (dGRW, dCSL, dQMUPL, DP (dcQMUPL model). == Tests of collapse models ==

Collapse models modify the Schrödinger equation; therefore, they make predictions that differ from standard quantum mechanical predictions. Although the deviations are difficult to detect, there is a growing number of experiments searching for spontaneous collapse effects. They can be classified in two groups: • Interferometric experiments. They are refined versions of the double-slit experiment, showing the wave nature of matter (and light). The modern versions are meant to increase the mass of the system, the time of flight, and/or the delocalization distance in order to create ever larger superpositions. The most prominent experiments of this kind are with atoms, molecules and phonons. • Non-interferometric experiments. They are based on the fact that the collapse noise, besides collapsing the wave function, also induces a diffusion on top of particles' motion, which acts always, also when the wave function is already localized. Experiments of this kind involve cold atoms, opto-mechanical systems, gravitational wave detectors, underground experiments. == Problems and criticisms to collapse theories ==

=== Violation of the principle of the conservation of energy === According to collapse theories, energy is not conserved, also for isolated particles. More precisely, in the GRW, CSL and DP models the kinetic energy increases at a constant rate, which is small but non-zero. This is often presented as an unavoidable consequence of Heisenberg's uncertainty principle: the collapse in position causes a larger uncertainty in momentum. This explanation is wrong; in collapse theories the collapse in position also determines a localization in momentum, driving the wave function to an almost minimum uncertainty state both in position and in momentum, that attempt to generalize in a relativistic sense the GRW and CSL models, but their status as relativistic theories is still unclear. The formulation of a proper Lorentz-covariant theory of continuous objective collapse is still a matter of research. Tails problem In all collapse theories, the wave function is never fully contained within one (small) region of space, because the Schrödinger term of the dynamics will always spread it outside. Therefore, wave functions always contain tails stretching out to infinity, although their "weight" is smaller in larger systems. Critics of collapse theories argue that it is not clear how to interpret these tails. Two distinct problems have been discussed in the literature. The first is the "bare" tails problem: it is not clear how to interpret these tails because they amount to the system never being really fully localized in space. A special case of this problem is known as the "counting anomaly". Supporters of collapse theories mostly dismiss this criticism as a misunderstanding of the theory, as in the context of dynamical collapse theories, the absolute square of the wave function is interpreted as an actual matter density. In this case, the tails merely represent an immeasurably small amount of smeared-out matter. This leads into the second problem, however, the so-called "structured tails problem": it is not clear how to interpret these tails because even though their "amount of matter" is small, that matter is structured like a perfectly legitimate world. Thus, after the box is opened and Schroedinger's cat has collapsed to the "alive" state, there still exists a tail of the wavefunction containing "low matter" entity structured like a dead cat. Collapse theorists have offered a range of possible solutions to the structured tails problem, but it remains an open problem. ==See also==