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Which Proof We Have against Continuous Trajectories for Particles?

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Journal of Modern Physics 2017年第1期8卷 68-81页

作者： sofia wechsler Kyriat Motzkin Israel

It is in general accepted that the concept of continuous trajectories for particles is at odds with the relativistic quantum mechanics. Namely, when examining the evolution of entangled quantum objects according to frames of coordinates in relative move-ment, one gets contradictory trajectories. Such a situation is typically derived from the famous “Hardy’s paradox”. However, it is argued here that if the rationale ignores the principle of quantum contextuality, as happens typically when using Hardy’s thought-experiment, the conclusion—rejection of the assumption of trajectories—is questionable. The issue is exemplified by an additional example: the 101 property of spin 1 bosons implies conflicting trajectories when the singlet state of two such bosons is examined according to frames in relative movement. It is concluded here that in the absence of a rationale which doesn’t violate the quantum contextuality, there are no sufficient arguments for refuting the possibility of a substructure of the quantum mechanics, consisting in particles following continuous trajectories.

关键词： 101 Property Bosonic Singlet Continuous Trajectories Nonlocality Relativity Theory

How Travels a Bohmian Particle?

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Journal of Modern Physics 2012年第12期3卷 1842-1848页

作者： sofia wechsler Israel Institute of Technology Haifa Israel

Bohm’s mechanics was built for explaining individual results in measurements, and mainly for getting rid of the enigmatic reduction postulate. Its main idea is that particles have at any time definite positions and velocities. An additional axiom is that particles follow continuous trajectories that admit the first derivative in time, the velocity. In the quantum theory, if the position of a quantum object is well-defined at some time, a Δt time later the object may be found anywhere in space, so, the velocity defined as Δx/Δt is completely undefined. This incompatibility is regarded in standard quantum theory as nature’s property. The disagreement between quantum and Bohm’s mechanics is particularly strong in wave-like phenomena, e.g. interference. For a particle traveling through an interference fringe, Bohm’s velocity formula shows a dependence of the time-of-flight on the fringe length. Such a dependence is not supported by the quantum theory. Thus, for deciding which prediction is correct one has to measure times-of-flight. But this is a problem. If one detects a particle at two positions and records the detection times, the time difference is meaningless, because the first position measurement disturbs the particle’s Bohm velocity (if exists). This text suggests a way around: instead of measuring positions and times, the particles are raised to an excited, unstable level, by passing them through a laser beam. The unstable level will decay in time, s.t. the density of probability of the excited atoms will indicate the time elapsed since excitation. For comparing the Bohmian and quantum predictions, this text proposes in continuation to send the beam of excited particle upon a mirror. Bohm’s velocity leads to anomalies in the reflected wave.

关键词： Bohmian Particle Bohmian Velocity Bohmian Trajectory Group Velocity Interference Time-of-Flight

About the Nature of the Quantum System—An Examination of the Random Discontinuous Motion Interpretation of the Quantum Mechanics

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Journal of Quantum Information Science 2021年第3期11卷 99-111页

作者： sofia D. wechsler Kiryat Motzkin Israel

What is the quantum system? Consider the wave-function of the electron—what we call “single particle wave-function”—and assume that it contains N wave-packets. If we pass all the wave-packets through an electric field, all are deflected, as if each one of them contains an electron. However, if we bring any two wave-packets to travel close to one another, they don’t repel one another, as if at least one of them contains no charge. In trying to solve the measurement problem of the quantum mechanics (QM), different interpretations were proposed, each one coming with a particular ontology. However, only one interpretation paid explicit attention to the contradiction mentioned above. This interpretation was proposed by S. Gao who named it “random discontinuous motion” (RDM), because it assumes the existence of a particle that jumps from place to place at random. The particle carries all the physical properties of the respective type of particle, mass, charge, magnetic momentum, etc. It jumps under the control of an “instantaneous condition” about which Gao did not give details so far. Along with presenting problems of the QM that this interpretation solves, this text reveals difficulties vis-à-vis entanglements and the special relativity.

关键词： Quantum Mechanics Quantum Particle Ontology Self-Interaction Instantaneous Condition

In Praise and in Criticism of the Model of Continuous Spontaneous Localization of the Wave-Function

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Journal of Quantum Information Science 2020年第4期10卷 73-103页

作者： sofia D. wechsler Kiryat Motzkin Israel

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.

关键词： Quantum Mechanics Collapse

What Was in the Apparatus before the Click of the Detector?

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Journal of Quantum Information Science 2021年第4期11卷 125-134页

作者： sofia D. wechsler Kiryat Motzkin Israel

When a quantum system is described by a superposition of wave-packets, each wave-packet traveling on a separate path, a commonly asked question is why only one of the wave-packets is able to trigger a click in a detector. In the second half of the last century many scientists considered the possibility that not all these wave-packets are identical. Namely, that there exist “full waves” and “empty waves”. The two types of waves were supposed to be identical only in the sense that they are able to produce interference when crossing one another, however, the full wave was supposed to be able to trigger a click in a detector, while the empty wave was supposed to leave the detector silent. The present text describes an experiment in which, for explaining the results, it seems necessary to admit the existence of full and empty waves.

关键词： Two-Particle Interference Coherence Length Full Waves Empty Waves

The Wave Function Cannot Be a Real Wave—Then, Can We Speak of an Ontology of Particles?

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Journal of Quantum Information Science 2022年第4期12卷 99-110页

作者： sofia D. wechsler Independent Researcher Kiryat Motzkin Israel

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.

关键词： Quantum Mechanics Quantum Particle Ontology Self-Interaction Instantaneous Condition Special Relativity

The Quantum Mechanics <i>Needs</i>the Principle of Wave-Function Collapse—But This Principle Shouldn’t Be <i>Misunderstood</i>

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Journal of Quantum Information Science 2021年第1期11卷 42-63页

作者： sofia D. wechsler Kiryat Motzkin Israel

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.

关键词： Quantum Mechanics Wave-Function Collapse Interpretations Elements of Reality

A Non-Relativistic Argument against Continuous Trajectories of Particles

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Journal of Quantum Information Science 2022年第2期12卷 29-36页

作者： sofia D. wechsler Kiryat Motzkin Israel

A thought-experiment is described and the probability of a particular type of results is predicted according to the quantum formalism. Then, the assumption is made that there exists a particle that travels from the source to one of the detectors, along a continuous trajectory. A contradiction appears: for agreeing with the quantum prediction, the particle has to land at once on two space-separated detectors. Therefore, the trajectory of the particle—if it exists—cannot be continuous.

关键词： Quantum Formalism de Broglie-Bohm Particle 3-Waves Joint Detection Three-Particle Interference

The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization?

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Journal of Quantum Information Science 2019年第3期9卷 155-170页

作者： sofia D. wechsler Kiryat Motzkin Israel

The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.

关键词： Quantum Mechanics Wave-Particle Duality Empty Waves First Quantization Second Quantization