Wave function collapse has been a contentious concept in quantum mechanics for a considerable time. Here we show examples of how the concept can be used to advantage in predicting the statistical results of three experiments in atomic physics and quantum optics: photon antibunching, single-photon phase difference states and interrupted single-atom fluorescence. We examine the question of whether or not collapse is 'really' a physical process, and discuss the consequences of simply omitting it but including the observer as a part of the overall system governed by the laws of quantum mechanics. The resulting entangled world does not appear to be inconsistent with experience.
Wave function collapse has been a contentious concept in quantum mechanics for a considerable time. Here we show examples of how the concept can be used to advantage in predicting the statistical results of three experiments in atomic physics and quantum optics: photon antibunching, single-photon phase difference states and interrupted single-atom fluorescence. We examine the question of whether or not collapse is 'really' a physical process, and discuss the consequences of simply omitting it but including the observer as a part of the overall system governed by the laws of quantum mechanics. The resulting entangled world does not appear to be inconsistent with experience.
The postulate of the collapse of the wave-function stands between the microscopic, quantum world, and the macroscopic world. Because of this intermediate position, the collapse process cannot be examined with the formalism of the quantum mechanics (QM), neither with that of classical mechanics. This fact makes some physicists propose interpretations of QM, which avoid this postulate. However, the common procedure used in that is making assumptions incompatible with the QM formalism. The present work discusses the most popular interpretations. It is shown that because of such assumptions those interpretations fail, i.e. predict for some experiments results which differ from the QM predictions. Despite that, special attention is called to a proposal of S. Gao, the only one which addresses and tries to solve an obvious and major contradiction. A couple of theorems are proved for showing that the collapse postulate is necessary in the QM. Although non-explainable with the quantum formalism, this postulate cannot be denied, otherwise one comes to conclusions which disagree with the QM. It is also proved here that the idea of “collapse at a distance” is problematic especially in relativistic cases, and is a misunderstanding. Namely, in an entanglement of two quantum systems, assuming that the measurement of one of the systems (accompanied by collapse of that system on one of its states) collapses the other systems, too without the second system being measured, which leads to a contradiction.
The postulate of the collapse of the wave function stands between the microscopic, quantum world, and the macroscopic world. Because of this intermediate position, the collapse process cannot be examined with the formalism of the quantum mechanics (QM), neither with that of classical mechanics. This fact makes some physicists to propose interpretations of QM, which avoid this postulate. However, the common procedure used in that, is making assumptions incompatible with the QM formalism. The present work discusses the most popular interpretations. It is shown that because of such assumptions those interpretations fail, i.e. predict for some experiments results which differ from the QM predictions. Despite of that, special attention is called to a proposal of S. Gao, the only one which addresses and tries to solve an obvious and major contradiction. A couple of theorems are proved for showing that the collapse postulate is necessary in the QM. Although nonexplainable with the quantum formalism this postulate cannot be denied, otherwise one comes to conclusions which disagree with the QM. It is also proved here that the idea of collapse at a distance is problematic especially in relativistic cases, and is a misunderstanding. Namely, in an entanglement of two quantum systems, assuming that the measurement of one of the systems (accompanied by collapse of that system on one of its states) collapses the other system too without the second system being measured, leads to a contradiction.
The collapse postulate in quantum mechanics is problematic due to the measurement problem. The problem lies not with collapse per se, but with the appeal to measurement; a theory that could underwrite the collapse process without ineliminable reference to measurement would constitute a solution to the measurement problem. This is the strategy pursued by dynamical (or spontaneous) collapse theories. But dynamical collapse theories face a number of challenges. First, they make different empirical predictions from standard quantum mechanics, and hence are potentially empirically refutable. Second, there are difficulties reconciling the dynamical collapse mechanism with special relativity. Third, the post-collapse state is not the same as the post-measurement state of standard quantum mechanics, raising the possibility that dynamical collapse theories do not solve the measurement problem after all. Assuming that these challenges can be met, dynamical collapse theories can lay claim to being serious contenders for the correct description of the quantum world. And the description they provide has a number of interesting consequences. First, it makes indeterminism an irreducible fact about the physical world. It has been argued that this has important consequences for the foundations of statistical mechanics, for free will, and for consciousness. Second, many dynamical collapse theories can be taken to imply that the quantum wave function is fundamental, giving rise to a new kind of vagueness, since a wave can be fuzzy around the edges in a way that a particle cannot. Furthermore, the quantum wave function is defined over a high-dimensional space, not the three-dimensional space of experience, suggesting to some that three-dimensionality is an illusion.
A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the alternatives is to assume that one or the other is correct and attempt to draw physical, observable consequences which then could be empirically verified or ruled out. As a working hypothesis, we propose simple models of collapse as a real physical process for direct binary symmetric measurements made on one particle. This allows one to construct irreversible unstable Schrödinger equations capable of describing continuously the process of collapse induced by the interaction of the quantum system with the measuring device. Due to unknown initial conditions the collapse outcome remains unpredictable so no contradictions with quantum mechanics arise. Our theoretical framework predicts a finite time-scale of the collapse and links with experiment. Sensitive probes of the collapse dynamics could be done using Bose-Einstein condensates, ultracold neutrons or ultrafast optics. If confirmed, the formulation could be relevant to the transition from quantum fluctuations to classical inhomogeneities in early cosmology and to establishing the ultimate limits on the speed of quantum computation and information processing.
Collapse theories are versions of quantum mechanics according to which the collapse of the wave function is a real physical process. They propose precise mathematical laws to govern this process and to replace the vague conventional prescription that a collapse occurs whenever an "observer" makes a "measurement." The "primitive ontology" of a theory (more or less what Bell called the "local beables") are the variables in the theory that represent matter in space-time. There is no consensus about whether collapse theories need to introduce a primitive ontology as part of their definition. I make some remarks on this question and point out that certain paradoxes about collapse theories are absent if a primitive ontology is introduced.
Whether the wave function collapses or not is a major remaining question in the theory of quantum measurement. This difficulty stems from the following two facts. First, it has not been recognized that single-particle quantum mechanics and many-particle quantum mechanics must be treated separately. Second, quantum jump (QJ) and wave function collapse (WFC) need clearer definitions. We define a QJ as a process of selecting a set of system eigenvalues (SEVs) of an observable and a WFC as a process of determining the probability distribution (PD) of SEVs, both from a single measurement. The goal of quantum observation is to obtain the PD, which is determined from an ensemble of SEVs. The wave function becomes an observable when the PD is determined. In single-particle quantum mechanics, a single measurement results in only one set of SEVs, and the PD is not observable. Therefore, the WFC does not happen. In many-particle quantum mechanics, we focus on the occupation number of a single quantum state. The wave function does not collapse in general, but there are exceptions. The occupation number can be huge and macroscopic for photons or for Bose-Einstein condensates. In such a case, the PD is determined from a single measurement of a real ensemble, and the WFC occurs. We call it a macroscopic quantum jump, which effectively is a measurement of a classical observable.