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arXiv:1308.3880

Nonlocal and relativistic behavior from a mutual physical base: a toy model

Artur Szczepański

Published Aug 18, 2013• 0 citations
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Abstract

Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of the nature of quantum objects has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could be reasonably revisited. The presented model indicates new issues which could result from exploring a specific kind of objects: topological defects in solids.

DOI
10.48550/arxiv.1308.3880

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Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of the nature of quantum objects has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could be reasonably revisited. The presented model indicates new issues which could result from exploring a specific kind of objects: topological defects in solids.
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of quantum objects nature has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could be reasonably revisited. The outlined model indicates new issues, which could result from following and exploring the canonical idea of Dirac. Topological defects in solids are considered as an example. The aim is helping to grasp the underlying pre-theoretical new intuitions, which should replace the old ones attached to the background of classical physics.
Ever since quantum theory was developed during the first quarter of the 20th century, we have lived with a strange division. Objects in our daily lives behave “normally” – they appear to obey classical physics – whereas microscopic objects can behave counter-intuitively and reveal intriguing features of quantum physics. But where exactly is the boundary between the quantum and classical worlds – if, indeed, there is one? If quantum physics is a universal theory, why is it respectable to talk about the quantum behaviour of electrons but not, say, of footballs?
Geometrical model for material Dirac wave field and for Maxwell electromagnetic field is suggested where above fields are considered as propagating regions of the space itself with distorted euclidean geometry. It is shown that equations for these fields can be considered as relations describing the space topological defects. These defects, being closed topological manifolds, are embedded in the outer five-dimensional space, and observable objects appear to be intersections of above defects with the physical space. This interpretation explains irrational properties of quantum objects such as wave-corpuscular duality, stochastic behavior, instantaneous nonlocal correlation in EPR-paradox, the light velocity invariance and so on. Wave-corpuscular properties arise as a result of the defect periodical movement in the outer space relative to its intersection with the physical space, and just this periodical movement attributes phase to the propagating object. Appearance of probabilities within the formalism is a consequence of uncertainty of the closed topological manifold shape, and ensemble of all possible shapes for the same object can be considered as an ensemble of hidden variables that leads to probabilistic description. Embedded in the outer space topological defects provide channels for nonlocal correlations between their intersections-- noninteracting particles in EPR-experiments, and this means that the proposed approach can be considered as a nonlocal model with hidden variables.
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This interpretation explains irrational properties of quantum objects such as wave-corpuscular duality, stochastic behavior, instantaneous nonlocal correlation in EPR-paradox, the light velocity invariance and so on. It is shown also that Dirac equation for hydrogen atom can be also considered as relation describing the space topological defect. Electromagnetic potentials appears within this approach as connectivities of the defect universal covering space and gauge invariance of electromagnetic field happens to be a natural consequence of topological interpretation. Proposed approach can be also considered as a nonlocal model with hidden variables. Preliminary results were published by parts early, and here they are presented completely.