All measurable phenomena in physics are irreducibly particle like and the wave picture of physical systems only arises when explaining a statistically relevant set of measurements of individual systems as an average. The wave picture arises in the effects of interference which can always be explained in the context of the state description of the interfering system, interference necessitates that the measurement outcomes be calculated by squaring the amplitudes after adding and non-interference is calculated by squaring before adding. Even though the calculation for each is independently valid, the change in the statistics when one modulates between interference and noninterference, as in the quantum eraser, requires a violation of the law of conservation of energy. There is no “driving force ” in the change of statistics. It is always a change in preparation that leads to the change of interference statistics, whilst in the calculation there is only a change in the state description. The irreducibly particle like nature of the quanta requires that there be a causal “driving force ” in the change in statistics and a mere change in description is an insufficient explanation by the standards of energy conservation. We present the argument that indeed this has already all been proven in the historic 1991 study of the ZWM papers of quantum coherence. Wave Particle Duality by Statistical Correspondence The first conceptual argument to arise in the history of quantum mechanics is that which questions how the
All measurable phenomena in physics are irreducibly particle like and the wave picture of physical systems only arises when explaining a statistically relevant set of measurements of individual systems as an average. The wave picture arises in the effects of interference which can always be explained in the context of the state description of the interfering system, interference necessitates that the measurement outcomes be calculated by squaring the amplitudes after adding and non-interference is calculated by squaring before adding. Even though the calculation for each is independently valid, the change in the statistics when one modulates between interference and noninterference, as in the quantum eraser, requires a violation of the law of conservation of energy. There is no “driving force ” in the change of statistics. It is always a change in preparation that leads to the change of interference statistics, whilst in the calculation there is only a change in the state description. The irreducibly particle like nature of the quanta requires that there be a causal “driving force ” in the change in statistics and a mere change in description is an insufficient explanation by the standards of energy conservation. We present the argument that indeed this has already all been proven in the historic 1991 study of the ZWM papers of quantum coherence. Wave Particle Duality by Statistical Correspondence The first conceptual argument to arise in the history of quantum mechanics is that which questions how the
e1921529118 (2021)], it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/nonconservation in individual cases. Specifically, in the above paper, an experiment was presented in which it can be proven that in some individual cases, energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome and that something must be wrong if there are individual instances in which conservation does not hold, even though this is not required by the standard conservation law. Here, we revisit that experiment and show that although its results are correct, there is a way to circumvent them and ensure individual case conservation in that situation. The solution is however quite unusual, challenging one of the basic assumptions of quantum mechanics, namely that any quantum state can be prepared, and it involves a time-holistic, double nonconservation effect. Our results bring light on the role of the preparation stage of the initial state of a particle and on the interplay of conservation laws and frames of reference. We also conjecture that when such a full analysis of any conservation experiment is performed, conservation is obeyed in every individual case.
Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.
The measurement problem of quantum mechanics was probably born in 1926: ‘Thus Schrödinger’s quantum mechanics gives a very definite answer to the question of the outcome of a collision; however, this does not involve any causal relationship. One obtains no answer to the question “what is the state after the collision,” but only to the question “how probable is a specific outcome of the collision” (in which the quantum-mechanical law of [conservation of] energy must of course be satisfied). This raises the entire problem of determinism. From the standpoint of our quantum mechanics, there is no quantity that could causally establish the outcome of a collision in each individual case; however, so far we are not aware of any experimental clue to the effect that there are internal properties of atoms that enforce some particular outcome. Should we hope to discover such properties that determine individual outcomes later (perhaps phases of the internal atomic motions)? Or should we believe that the agreement between theory and experiment concerning our inability to give conditions for a causal course of events is some pre-established harmony that is based on the non-existence of such conditions? I myself tend to relinquish determinism in the atomic world. But this is [also] a philosophical question, for which physical arguments alone are not decisive.’ (Born, 1926a, p. 866; translation by the author) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
In quantum mechanics, conservation laws are usually understood only statistically and only in the context of unitary evolution: during such evolution, if an observable commutes with the Hamiltonian, its expectation value and Born-rule probability distribution remain unchanged. Individual measurement outcomes, however, disrupt even this weak form of statistical conservation. Recently, though, it has been argued that a stronger, non-statistical form of conservation, valid at the level of individual measurement outcomes, can be recovered. The proposal relies on the claim that any superposition of eigenstates of a conserved quantity must ultimately be prepared relative to another physical system, which serves as the relevant reference frame and remains correlated with the system being prepared. On this enlarged description, the change observed in the measured system is claimed to be exactly compensated by an opposite change in the preparer, thereby restoring conservation at the level of individual measurement outcomes. We analyze this proposal and argue that it faces significant conceptual difficulties. We show that the proposed mechanism is not adequately justified and, moreover, does not establish conservation in individual measurement outcomes as claimed.
After eighty years of Quantum Mechanics (QM) we have learned to live with wave functions without worrying about their physical nature. This attitude is certainly justifled by the extraordinary success of the theory in predicting and explaining not only all the phenomena encountered in the domain of microphysics, but also some spectacular nonclassical macroscopic behaviors of matter. Nevertheless one cannot ignore that the wave{particle duality of quantum objects not only still raises conceptual problems among the members of the small community of physicists who are still interested in the foundations of our basic theory of matter, but also induces thousands and thousands of physics students all around the world to ask each year, at their flrst impact with Quantum Mechanics, embarrassing questions to their teachers without receiving really convincing answers. Remember that Feynman once said \It is fair to say that nobody understands
Abstract Moving to more subtle experiments, we consider how the standard formulation of quantum mechanics predicts and explains interference phenomena. Tracking the conditions under which one observes interference phenomena leads to the notion of quantum decoherence. We see why one must sharply distinguish between collapse phenomena and decoherence phenomena on the standard formulation of quantum mechanics. While collapses explain determinate measurement records, environmental decoherence just produces more complex, entangled states where the physical systems involved lack ordinary physical properties. We characterize the quantum-mechanical wave function as both an element of a Hilbert space and a complex-valued function over a configuration space. We also discuss how the wave function is interpreted in the standard theory.