[Paper Review] Investigation methods in model conception of quantum phenomena

Yuri A. Rylov|ArXiv.org|Feb 7, 2003

Quantum Mechanics and Applications17 references3 citations

TL;DR

This paper proposes a model conception of quantum phenomena (MCQP) as a deterministic geometric foundation for quantum mechanics, where quantum behavior emerges from stochastic particle motion in a modified space-time geometry (T-geometry). By replacing quantum principles with geometric constraints—particularly a non-Riemannian, asymmetric world function—MCQP reproduces quantum statistics and reveals new physical insights, such as the Dirac particle as a rotating system and a geometric origin for pair production.

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. 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.

Motivation & Objective

• To develop a model conception of quantum phenomena (MCQP) that explains quantum behavior as a statistical outcome of stochastic particle motion in a deterministic space-time geometry.
• To overcome the limitations of axiomatic quantum mechanics (ACQP) by replacing rigid quantum principles with flexible geometric parameters.
• To construct a new geometric framework (T-geometry) where particle motion is inherently stochastic, yet the underlying geometry remains deterministic.
• To demonstrate that quantum mechanics arises as a statistical description of this stochastic motion, analogous to how thermodynamics emerges from statistical mechanics.
• To identify and resolve three key obstacles: inadequate geometry, flawed statistical description of world lines, and improper integration of wave functions into fluid-like dynamics.

Proposed method

• Introduce T-geometry—a non-Riemannian space-time geometry with a world function that incorporates the quantum constant ℏ as a fundamental geometric correction.
• Use an asymmetric world function σ(x,x′) = σᵢ(x′)ηⁱ + ½σᵢₖ(x′)ηⁱηᵏ + ⅙σᵢₖₗ(x′)ηⁱηᵏηˡ + … to describe geometric fields, including a vector field (σᵢ), tensor field (σᵢₖ), and third-rank tensor field (σᵢₖₗ).
• Model particle motion as stochastic trajectories in this geometry, where the statistical distribution of world lines reproduces the quantum wave function ψ via the relation jᵏ = −(iℏ/2)(ψ*∂ᵏψ − ∂ᵏψ*·ψ).
• Derive quantum-like equations (e.g., Dirac equation) from the geometric dynamics of stochastic world lines, showing that the Dirac particle behaves as a two-body rotator.
• Apply fluid-dynamic analogies to the statistical ensemble of world lines, transforming the wave function into a current density jᵏ, enabling derivation of quantum behavior from geometric constraints.
• Modify the world function to include curvature and asymmetric fields, allowing for the emergence of new physical fields (e.g., a third-rank tensor field potentially linked to dark matter).

Experimental results

Research questions

• RQ1 Can quantum phenomena be derived as a statistical consequence of stochastic particle motion in a deterministic geometric space-time?
• RQ2 What geometric structure allows for primordial stochasticity in particle motion while preserving deterministic intervals?
• RQ3 How can the wave function and spinor structure of quantum mechanics emerge from a geometric description of world lines?
• RQ4 Can the Dirac equation and the behavior of the Dirac particle as a rotator be derived from geometric dynamics in T-geometry?
• RQ5 What role do asymmetric world functions and higher-order geometric fields play in explaining phenomena like pair production and dark matter?

Key findings

• The model conception of quantum phenomena (MCQP) successfully reproduces quantum mechanics as a statistical description of stochastic particle motion in a deterministic T-geometry, with ℏ emerging from geometric corrections.
• In MCQP, the Dirac particle is not a point particle but a system of two particles rotating around their common center of inertia, explaining its intrinsic spin and mass.
• The theory reveals a geometric origin for pair production through the asymmetric world function σᵢ(x′), which introduces a vector field effective at short distances and not accessible in standard ACQP.
• The expansion of the asymmetric world function reveals three independent geometric fields: a vector field (σᵢ), a tensor field (σᵢₖ) for gravity, and a third-rank tensor field (σᵢₖₗ), potentially explaining astrophysical anomalies like dark matter.
• MCQP allows for continuous, dynamical modification of the world function without altering its foundational structure, enabling systematic exploration of new physical regimes.
• By removing unjustified constraints from standard geometry and statistical description, MCQP provides a more flexible and logically coherent foundation than ACQP, which relies on disconnected principles and ad hoc postulates.