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arXiv:physics/0310050

Model conception of quantum phenomena: logical structure and investigation methods

Yuri A. Rylov

Published Oct 13, 2003• 8 citations
arXivHTMLPDF

Abstract

One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to thermodynamics. Such a possibility is based on a new conception of geometry, which admits one to construct such a deterministic space-time geometry, where motion of free particles is primordially stochastic. The space-time geometry can be chosen in such a way that statistical description of random particle motion coincides with the quantum description. Transition from ACQP to MCQP is a result of correction of some mistakes in the foundation of ACQP. Methods of MCQP in investigation of quantum phenomena appear to be more subtle and effective than, that of ACQP. For instance, investigation of the free Dirac equation in framework of MCQP shows that the Dirac particle is in reality a rotator, i.e. two particles rotating around their common center of inertia. In the framework of MCQP one can discover the force field, responsible for pair production, that is impossible in the framework of ACQP.

DOI
10.48550/arxiv.physics/0310050

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One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to thermodynamics. Such a possibility is based on a new conception of geometry, which admits one to construct such a deterministic space-time geometry, where motion of free particles is primordially stochastic. The space-time geometry can be chosen in such a way that statistical description of random particle motion coincides with the quantum description. Transition from ACQP to MCQP is a result of correction of some mistakes in the foundation of ACQP. Methods of MCQP in investigation of quantum phenomena appear to be more subtle and effective than, that of ACQP. For instance, investigation of the free Dirac equation in framework of MCQP shows that the Dirac particle is in reality a rotator, i.e. two particles rotating around their common center of inertia. In the framework of MCQP one can discover the force field, responsible for pair production, that is impossible in the framework of ACQP.
One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to thermodynamics. Such a possibility is based on a new conception of geometry, which admits one to construct such a deterministic space-time geometry, where motion of free particles is primordially stochastic. The space-time geometry can be chosen in such a way that statistical description of random particle motion coincides with the quantum description. Methods of MCQP in investigation of quantum phenomena appear to be more subtle and effective than, that of ACQP. For instance, investigation of the free Dirac equation in framework of MCQP shows that the Dirac particle is in reality a rotator, i.e. two particles rotating around their common center of inertia. In the framework of MCQP one can discover the force field, responsible for pair production, that is impossible in the framework of ACQP.
Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on a possibility of the event space modification and on a possibility of stochastic (Brownian) motion of free particles. One considers the space-time modification, based on a new conception of geometry. In the framework of this conception any geometry is obtained as a result of the proper Euclidean geometry deformation. In the framework of this conception it is possible such a space-time geometry, where the free particle motion appears to be stochastic, although the geometry in itself remains to be deterministic. The stochasticity intensity depends on the particle mass. It is small for particle of a large mass, and it is essential for the particle of a small mass. The space-time geometry may be chosen in such a way, that the statistical description of random world lines of particles be equivalent to the quantum description (the Schrödinger equation). At such a description the quantum principles are not used. They can be obtained as a corollaries of the statistical description of nonrelativistic stochastic particles. The nonrelativistic quantum principles may not be used for description of relativistic phenomena.
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special concepts, and this procedure cannot be repeated. In the model conception of quantum phenomena (MCQP) the quantum particle is a partial case of a stochastic particle, and the quantum dynamics is a special case of the stochastic particle dynamics. In MCQP the quantization is a dynamical procedure, where a special quantum term is added to the Lagrangian of the statistical ensemble of (classical) particles. This procedure can be repeated many times, because it is not accompanied by introduction of new concepts. It is very convenient from the formal viewpoint, because the set of dynamic quantizations forms a one-parameter group, which allows one to separate the dynamical and statistical (stochastic) properties.
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and ensembles, clarifies the logical relations and operations for them, and shows how they give rise to dynamics and probabilities. States are identified with maximal consistent sets of weak equalities in the algebra of observables (instead of, as usual, with the rays in a Hilbert space). This leads to a concise foundation of quantum mechanics, free of undefined terms, separating in a clear way the deterministic and the stochastic features of quantum physics. The traditional postulates of quantum mechanics are derived from well-motivated axiomatic assumptions. No special quantum logic is needed to handle the peculiarities of quantum mechanics. Foundational problems associated with the measurement process, such as the reduction of the state vector, disappear. The new interpretation of quantum mechanics contains `elements of physical reality' without the need to introduce a classical framework with hidden variables. In particular, one may talk about the state of the universe without the need of an external observer and without the need to assume the existence of multiple universes.
One uses the investigation strategy: ”Find a mistake in foundation of physics and correct it”. Two fundamental defects are corrected: (1) nonrelativistic concept of the particle state, (2) inadequacy of the differential geometry formalism at the metric approach to geometry. Usage of relativistic concept of the particle state admits one to create united formalism for description of deterministic and stochastic particles motion. The quantum mechanics is founded as a statistical description of the stochastic particles motion. Stochasticity of the quantum particles motion is explained by multivariance of the space-time geometry, which leads to the world lines wobbling of elementary particles. Relativistic concept of the particle state and the metric approach to the space-time geometry admit one to construct the skeleton conception of elementary particles. The skeleton conception admits one to investigate the arrangement of elementary particles (but not only to systamatize them, ascribing quantum numbers to them).
By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws ofmore » motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle.« less