Abstract
The work analyzes the compatibility between the classical freedom, the local relativistic causality and the non-local behavior of quantum mechanics in the frame of the stochastic approach of the quantum hydrodynamic analogy (SQHA). The work describes the role of the quantum potential in generating the quantum non-local dynamics in a fluctuating environment. The analysis shows that it is possible to maintain the concept of classical freedom between far away weakly bounded systems (moderate non-locality) as well as to make compatible the uncertainty principle with the relativistic postulate of invariance of light speed. The work shows that the paradox of instantaneous quantum non local behavior at infinite distances of the standard formalism is an artifact due to the non-relativistic non-stochastic ambit of such theory where the light speed is infinite and the non-local interaction owns an infinite range of action. The work envisages that the SQHA can possibly lead to a fully theoretically self-standing quantum mechanics where the wave function collapse, during a measurement process, can be described by the theory itself without empirical postulates. Under this light the paper discusses the need of searching for (both local and non-local) hidden variables quantum mechanics as well as the need of superluminal communications in quantum experiments. The analysis shows that all these hypotheses are attempts of interpreting the outputs of quantum measurements that cannot be fully explained by the semi-empirical formalism of quantum mechanics, based on the statistical postulates of the measuring process as well as the existence of a classical observer. A two photon experiment is discussed to the light of the SQHA approach. Key words: Quantum non-locality, superluminal transmission of quantum information, classical freedom, local relativistic causality, Einstein, Podolsky, and Rosen (EPR) paradox, macroscopic quantum decoherence, Bell’s inequalities, quantum hydrodynamic analogy.
Highlights
The work analyzes the compatibility between the classical freedom, the local relativistic causality and the non-local behavior of quantum mechanics in the frame of the stochastic approach of the quantum hydrodynamic analogy (SQHA)
The work analyzes the non-local property of quantum mechanics in the frame of the stochastic QHA model and shows that it can have a finite range of action, allowing in weakly bounded systems the realization of the classical mechanics on large scale limit
The analysis shows that it is possible to maintain the concept of freedom of the classical reality between far away systems beyond the range of interaction of quantum potential as well as to make compatible the local relativistic causality with the uncertainty principle, one of the most relevant manifestations of the non-local behavior of the quantum mechanics
Summary
The conflict between the quantum non-locality and the local character of the classical macroscopic experience is one of the most intriguing problems of the modern physics (Schrödinger, 1935; Einstein et al, 1935; Bell, 1964; Greenberger et al, 1990). In the SQHA, the wave-function collapse to an eigenstate (due to the interaction with a large scale apparatus in a classical fluctuating environment) can descend by the irreversible dynamics of the stochastic motion equations as a kinetic process to a stationary state (eigenstate) This fact leads to a quantum theory with the conceptual property of a complete theory (that does not need additional postulates) able to describe the quantum evolution even during irreversible quantum processes such as the measurements. We have to define the kind and the characteristics of such an interaction and its “mechanics” since it is not contained in the quantum one
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