Abstract This chapter introduces the problem (that the wave function of standard quantum theory (SQT) cannot correspond to reality in nature) and its resolution (change Schrodinger’s equation). The chapter begins by citing Schrodinger’s argument as to how the collapse postulate of SQT leads to the cited problem. It then presents a resolution embodied in the continuous spontaneous localization (CSL) theory‘s altered Schrodinger equation. The chapter shows how the “Gambler’s Ruin” game, where two gamblers bet on a coin toss until one wins all the money, is a precise and intuitively appealing analogy to the needed collapse behavior for a superposition of two states evolving under random influence to one or another of those states. Following this, the chapter ends by presenting the structure of the book. The first seven chapters show how CSL works, discusses experimentally testable and already tested predictions, and covers interpretive features of CSL. The purpose of the remaining eleven chapters, called “Supplementary,” is summarized as well.
Abstract This chapter introduces the problem (that the wave function of standard quantum theory (SQT) cannot correspond to reality in nature) and its resolution (change Schrodinger’s equation). The chapter begins by citing Schrodinger’s argument as to how the collapse postulate of SQT leads to the cited problem. It then presents a resolution embodied in the continuous spontaneous localization (CSL) theory‘s altered Schrodinger equation. The chapter shows how the “Gambler’s Ruin” game, where two gamblers bet on a coin toss until one wins all the money, is a precise and intuitively appealing analogy to the needed collapse behavior for a superposition of two states evolving under random influence to one or another of those states. Following this, the chapter ends by presenting the structure of the book. The first seven chapters show how CSL works, discusses experimentally testable and already tested predictions, and covers interpretive features of CSL. The purpose of the remaining eleven chapters, called “Supplementary,” is summarized as well.
Abstract This book describes one approach to resolving the ‘measurement problem’ of standard quantum theory (SQT), by changing the Schrodinger equation’s evolution of the wave function. The wave function of SQT does not describe reality. For example, the wave function corresponding to a completed experiment is the sum of terms describing the different experimental outcomes whereas one of these outcomes is what appears in Nature, The rules of SQT respond to this deficiency by imposing an ill-defined ‘collapse postulate.’ The prior smooth evolution of the wave function according to Schrodinger’s equation is replaced by an abrupt ‘jump’ to one of the outcomes. When, why, how are unanswered questions. I have added a term to Schrodinger’s equation, obtaining a theory (which I named the ‘Continuous Spontaneous Localization’ theory, or CSL) that answers these questions. The term has a random field in it: each field makes the sum of terms evolve to one of the terms. The collection of all possible fields produces the (Born rule) probabilistic predictions of SQT. Thus, CSL does something SQT does not: it describes the occurrence of events. But, it is a different theory than SQT, so it predicts different results for some carefully crafted experiments. CSL has now existed for over three decades. While no experiment as yet has proven CSL true, no experiment has conflicted with it either. In this book I have aimed to give a clear exposition of CSL and its consequences, accessible to anyone who has studied SQT.
Abstract This chapter introduces the two equations that completely define CSL, for the simplest case, that is, a state vector in a two-dimensional Hilbert space. One equation is the modified evolution equation for the state vector which depends upon a Brownian motion function of time, B(t), a Hermitian operator A called the “collapse-generating operator,” and a collapse rate parameter λ. The state vector evolution is linear, but not unitary, so its norm changes with time. The second equation is called the probability rule. It says the probability a particular B(t) occurs in Nature is proportional to the squared norm of the state vector, that is, high norm state vectors are most likely to occur. The chapter shows how an initial state vector that is a superposition of the eigenstates of A evolves to one eigenstate, with the Born probability, as predicted by standard quantum theory. Finally, it discusses the density matrix description of the ensemble of evolutions under all possible B(t).
Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.
This is the first single volume about the collapse theories of quantum mechanics, which is becoming a very active field of research in both physics and philosophy. In standard quantum mechanics, it is postulated that when the wave function of a quantum system is measured, it no longer follows the Schrödinger equation, but instantaneously and randomly collapses to one of the wave functions that correspond to definite measurement results. However, why and how a definite measurement result appears is unknown. A promising solution to this problem are collapse theories in which the collapse of the wave function is spontaneous and dynamical. Chapters written by distinguished physicists and philosophers of physics discuss the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse. This is an invaluable resource for students and researchers interested in the philosophy of physics and foundations of quantum mechanics.
We emphasize that standard quantum theory (SQT) is incomplete because it doesn't describe what is experimentally observed, namely events, nor does it satisfactorily define the circumstances under which events may occur. Simple models are given (all of which have the same density matrix evolution) to illustrate schemes which claim to complete SQT. It is shown how the model based upon the Continuous Spontaneous Localization (CSL) theory, in which an individual statevector undergoes "True Collapse," gives a satisfactory description of events. It is argued that various "decoherence" based approaches, illustrated by models in which a density matrix undergoes "False Collapse," do not satisfactorily resolve these problems of SQT.
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.