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arXiv:1507.07202

Non-mechanical nature of the wave function collapse

Alexey Yur'evich Samarin

Published Jul 26, 2015• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1507.07202

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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.
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The meaning of the wave function and its evolution are investi-gated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A dis-crete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic expe-rience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity.
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schrodinger equation in quantum mechanics. This strongly implies what quantum mechanics describes is discontinuous motion of particles. Considering the fact that space-time may be essentially discrete when considering gravity, we further present a theory of discontinuous motion of particles in discrete space-time. We show that its evolution will naturally result in the dynamical collapse process of the wave function, and this collapse will bring about the appearance of continuous motion of objects in the macroscopic world.
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.
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies what quantum mechanics describes is discontinuous motion of particles. Considering the fact that space-time may be essentially discrete when considering gravity, we further present a theory of discontinuous motion of particles in discrete space-time. We show that its evolution will naturally result in the dynamical collapse process of the wave function, and this collapse will bring about the appearance of continuous motion of objects in the macroscopic world.
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies what quantum mechanics describes is discontinuous motion of particles. Considering the fact that space-time may be essentially discrete when considering gravity, we further present a theory of discontinuous motion of particles in discrete space-time. We show that its evolution may naturally result in the dynamical collapse process of the wave function, and this collapse will bring about the appearance of continuous motion of objects in the macroscopic world.