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arXiv:1505.02393

Quantum jump mechanics

Alexey Yur'evich Samarin

Published May 10, 2015• 2 citations
arXivHTMLPDF

Abstract

The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is the integral wave equation with kernel in the form of a path integral. It is shown, that wave function collapse is the specific transformation which is fundamentally differ from Shrödinger's evolution. Specifically, a formal cause of the collapse is a local time derivative (infinite large) of the potential energy. Such transformation can not be described using mathematical apparatus of conventional quantum mechanics.

DOI
10.48550/arxiv.1505.02393

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The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is the integral wave equation with kernel in the form of a path integral. It is shown, that wave function collapse is the specific transformation which is fundamentally differ from Shrödinger's evolution. Specifically, a formal cause of the collapse is a local time derivative (infinite large) of the potential energy. Such transformation can not be described using mathematical apparatus of conventional quantum mechanics.
It is shown, that in addition to the evolution quantum object motion wave equation in the integral form can describe the wave function reduction as a physical process. Such description is represented for the space localization process, taking place when the space coordinate is measured, and it is shown, that collapse arises, as the result of the quantum particle and corresponding measuring instrument interaction. This physical phenomenon mathematical image looks like the instantaneous transformation of the virtual paths set to the subset, determined by the measuring process conditions, when the macroscopic changes appears in the measuring instrument.In conventional quantum mechanics such Hilbert space collapse itself corresponds to such reduction phenomenon.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.
Quantum measurement problem is still unconsensus since it has existed many years and inspired a large of literature in physics and philosophy. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is showing that the stochastic and instantaneous collapse of the quantum measurement is due to the "potential noise" of the apparatus or environment and "inner correlation" of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.
The wave function transformation of the quantum particle considered as a continuous medium was described by the evolution operator with the kernel in the form of path integral. It is shown that this approach allows considering not only Schrodinger evolution, but and the collapse phenomenon. The collapse entity is the nonlocal transformation of the quantum particle internal structure and it is not connected with its mechanical motion. Probably this fact allows the instantaneous signalling using the collapse without violating relativistic requirements.
Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the “potential noise" of the apparatus or environment and “inner correlation" of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for this investigation. A derivation of reduction from quantum mechanics is proposed on a specific example, using standard methods of statistical physics. Although these methods are valid only "for all practical purposes", arguments are given to ascribe an emerging status to reduction (or the uniqueness of physical reality), similar to the status of classical physics. Examination of measurements of the particles in an EPR pair by two space-like separated apparatuses shows that the model is consistent with the non-separable character of quantum mechanics, although both measurements are local. Quantitative estimates are given.