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 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 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 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.
Is the wave-function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the quantum mechanics (QM) assume different answers to this question. It is shown in this article that the assumption that the wave-function is a real wave entails a contradiction with the predictions of the QM, when the special relativity is invoked. Therefore, this text concentrates on interpretations that conjecture that the reality that moves in our apparatuses is particles, and they move under the constraints of the wave-function. The de Broglie-Bohm interpretation, which matches this picture, assumes that the particle travels along a continuous trajectory. However, the idea of continuous trajectories was proved to lead to a contradiction with the quantum predictions. Therefore this interpretation is not considered here. S. Gao conjectured that the particle is in a permanent random and discontinuous motion (RDM). As it jumps all the time from place to place, the total set of occupied positions at a certain time is given by the absolute square of the wave-function. As motivation for his idea, Gao argued that if a charged particle were simultaneously in two or more locations at the same time, the copies of the particle would repel one another, destroying the wave-function. It is proved here that the quantum formalism renders this motivation wrong. Although refuting this motivation, the RDM interpretation is examined here. A couple of problems of this interpretation are examined and it is proved that they don’t lead to any observable contradictions with the QM predictions, except one problem which seems to have no solution. In all, it appears that none of the wide-spread interpretations of the QM is free of contradictions.
The measurement problem in quantum mechanics has been a cause of much puzzlement over the years. The very idea of having two different versions of reality for the same system has been a cause for much debate. Often quantum mechanics textbooks follow the ‘shut up and calculate’ paradigm. This denies the opportunity for the common student to understand the consequence of one of the most elegant and beautiful aspects of science. The state of the art textbooks give a purely algebraic, perfunctory and monotonous approach where the real consequence of the system is not fully appreciated. A good reason for this is the considerable deviation of the quantum mechanical process from the commonsensical idea of truth, reality and reason. We tend to look at the world in a materialistic, deterministic, causal and objectivistic way. We tend not to accept a world of contradictions. A quantum measurement is essentially an amalgamation of contradictions, mystery and duality. It encompasses an implicit dependence on subjectivity and contradicts with causality as we know it. We look at the world as in the present. But a quantum mechanical measurement is a prediction of the future influenced by the observer or the measurer. This offers a philosophical and pedagogical conundrum. It poses a challenge on not just how our perception of the world might change in addition to providing a big challenge on how to make it compatible with the other successful theories of physics. The most common text book interpretation of quantum mechanics has been the Copenhagen Interpretation suggests the ‘collapse of the wave function’ as a mechanism of transition between duality. But a more bizarre yet elegant theory, extending quantum formalism to the classical domain, called the Many Worlds Interpretation has been catching up very quickly; it stands for the split of the universe when we make a quantum mechanical measurement. Consequently, reality as we is redefined as a universal wave function which is a superposition of several outcomes, which is incompatible with many of the successful concepts of physics and has several problems like the correct idea about probability or basis. We adapt the idea of the universal wave function, but instead suggest a continuum interpretation of quantum mechanics where the universal wave function represents the entire singular universe and the concept of atoms or electrons as conceptually a continuous part of it rather than a distinct separate entity. Such an interpretation could be compatible with other continuum theories like the Superfluid vacuum theory or the Higgs Field.
In this work we attempt to confront the orthodox widespread claim present in the foundational literature of Quantum Mechanics (QM) according to which 'superpositions are never actually observed in the lab'. In order to do so, we begin by providing a critical analysis of the famous measurement problem which, we will argue, was originated by the strict application of the empirical-positivist requirements to subsume the quantum formalism under their specific understanding of 'theory'. In this context, the ad hoc introduction of the projection postulate (or measurement rule) can be understood as a necessary requirement coming from a naive empiricist standpoint which presupposes that observations are self evident givens of "common sense" experience --independent of metaphysical (categorical) presuppositions. We then turn our attention to two "non-collapse" interpretations of QM --namely, modal and many worlds-- which even though deny that the "collapse" is a real physical process anyhow retain the measurement rule as a necessary element of the theory. In contraposition, following Einstein's claim according to which "it is only the theory which decides what can be observed", we propose a return to the realist representational understanding of 'physical theories' in which 'observation' is considered as derived from theoretical presuppositions. It is from this standpoint that we discuss a new non-classical conceptual representation which allows us to understand quantum phenomena in an intuitive (anschaulicht) manner. Leaving behind the projection postulate, we discuss the general physical conditions for measuring and observing quantum superpositions.
The problem of measurement in quantum mechanics is that the quantum particle in the course of evolution, as described by the linear Schrodinger equation, exists in all of its possible states, but in measuring, the particle is always detected in only one of its states. This property is called the "collapse of the wave function" and was formulated by Von Neumann as one of the postulates of quantum mechanics. However, it remains unclear at what point in time and under what laws this transition occurs. This article demonstrates that the collapse of the wave function may be due to the creation or annihilation of particles (quasi-particles). The processes of the creation or annihilation of particles play a key role in the measurements and are described on the basis of quantum field theory. The system of equations of quantum field theory of particles and fields is non-linear; as a result, the principle of superposition does not hold for the theory. The collapse of the wave function is a consequence of this non-linearity and occurs at the moment of creation (annihilation) of a particle. This result demonstrates that the wave function collapse can occur in both microscopic and macroscopic systems. Understanding the mechanisms of the collapse of the wave function can lead to the creation of microscopic devices involved in the calculations based on quantum computing.