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AIP conference proceedings

Second entanglement and (re)Born wave functions in Stochastic Electrodynamics

Aloysius F. Kracklauer

Published Jan 1, 2006• 1 citation
Publisher

Abstract

The wave function in Quantum Mechanics has properties that render its physical interpretation unclear. On the one hand, its modulus squared is interpreted as a probability density, but, unlike conventional probabilities, it interacts with the material world. In addition, it is thought to have encapsulated nonlocal correlation and, according to modern thought, parallel information in a manner impossible according to classical physics. In this paper, an extended version of Stochastic Electrodynamics is presented which offers conventional models for these otherwise spooky features.

DOI
10.1063/1.2158739

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The wave function in Quantum Mechanics has properties that render its physical interpretation unclear. On the one hand, its modulus squared is interpreted as a probability density, but, unlike conventional probabilities, it interacts with the material world. In addition, it is thought to have encapsulated nonlocal correlation and, according to modern thought, parallel information in a manner impossible according to classical physics. In this paper, an extended version of Stochastic Electrodynamics is presented which offers conventional models for these otherwise spooky features.
I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction of a quantum system with an observer, and probabilities will not arise unless the observer is unable to access all the information available in the system's wave function. Quantum mechanics generally does not permit all the information to be obtained, even in principle, just as in relativity information from outside the past light cone cannot be obtained. But probabilities do not imply indeterminism. Instead, quantum mechanics is more deterministic than classical mechanics.
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement mechanism: entanglement effects do not originate from superpositions of wave functions, but result from the bilinear structure of density matrices. Quantum interference appears as a multiplicative phenomenon rather than an additive superposition mechanism. We propose two general requirements such that the bilinear representation of density matrices is given in terms of two uniquely defined, identically distributed, Markovian stochastic jump processes. These general ideas are illustrated for the Einstein-Podolsky-Rosen and double-slit experiments. The expression of the stochastic nature of quantum mechanics in terms of random variables rather than their probability distributions facilitates an ontological viewpoint and leads us to a bra-ket interpretation of quantum mechanics.
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields, interaction with a measuring apparatus inclusive, in a deterministic manner without any jumps. Quantum mechanics is an approximate theory because its equations follow from the above equations upon neglecting the self-field of the electron itself. Just this leads to paradoxes, seeming contradictions and jumps in quantum mechanics. The quantum mechanical wavefunction has a dual interpretation. In some problems the square of its modulus represents a real distribution of the electronic density while in others the same square determines the probability distribution of coordinates. It is shown why, given the different interpretations of the wavefunction, it satisfies one and the same Dirac or Schrödinger equation. Description of many-electron systems is also considered in the starting approach as well as in quantum mechanics. Neutrinos are discussed in brief.
Abstract The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement mechanism: entanglement effects do not originate from superpositions of wave functions, but they result from the bilinear structure of density matrices. Quantum interference appears as a multiplicative phenomenon rather than an additive superposition mechanism. We propose two general requirements such that the bilinear representation of density matrices is given in terms of two uniquely defined, identically distributed, Markovian stochastic jump processes. These general ideas are illustrated for the Einstein-Podolsky-Rosen and double-slit experiments. The expression of the stochastic nature of quantum mechanics in terms of random variables rather than their probability distributions facilitates an ontological viewpoint and leads us to a bra-ket interpretation of quantum mechanics.