[Paper Review] Quantum mechanics as electrodynamics of curvilinear waves

Alexander G. Kyriakos|ArXiv.org|Sep 2, 2002

Quantum Mechanics and Applications8 references3 citations

TL;DR

This paper proposes a novel interpretation of quantum mechanics as the electrodynamics of closed, non-linear, curvilinear waves, suggesting that quantum phenomena emerge from the behavior of such waves in a geometric framework. It claims to reproduce key results of quantum field theory and provide a unified classical foundation for quantum mechanics through wave curvature and self-consistent field interactions.

ABSTRACT

The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.

Motivation & Objective

• To reformulate quantum mechanics as a classical electrodynamics of closed, non-linear, curvilinear waves.
• To explain quantum phenomena—such as superposition and entanglement—through the geometric and dynamic properties of these waves.
• To provide a classical underpinning for quantum field theory results using wave curvature and self-consistent field equations.
• To unify quantum behavior with classical wave mechanics by introducing a non-linear, closed-wave model.
• To challenge the standard interpretation of QM by proposing a deterministic, geometric alternative rooted in wave topology.

Proposed method

• Model quantum systems as closed, non-linear, curvilinear waves propagating in a geometric space.
• Apply electrodynamics principles to these waves, treating their curvature as the source of field interactions.
• Derive effective field equations from wave continuity and energy-momentum conservation in curved wave geometries.
• Use topological constraints to enforce quantization conditions via wave closure and phase coherence.
• Introduce a self-consistent field model where wave curvature generates and sustains electromagnetic-like fields.
• Demonstrate that the resulting wave dynamics reproduce standard quantum mechanical predictions, such as energy levels and probability distributions.

Experimental results

Research questions

• RQ1 Can quantum mechanical behavior emerge from the electrodynamics of closed, non-linear, curvilinear waves?
• RQ2 How do wave curvature and topology enforce quantization in a classical wave framework?
• RQ3 To what extent can quantum field theory results be reproduced using only classical wave dynamics and geometric constraints?
• RQ4 What is the role of self-consistent field interactions in generating quantum-like phenomena?
• RQ5 Can a deterministic, geometric wave model replace the probabilistic interpretation of standard quantum mechanics?

Key findings

• The theory reproduces key quantum mechanical results, such as discrete energy levels, through the topological constraints of closed, non-linear waves.
• Wave curvature generates self-consistent field interactions that mimic electromagnetic and quantum potential effects.
• The model explains wave-particle duality as a consequence of the closed, non-linear nature of the wave structure.
• Quantization arises naturally from the requirement of phase coherence and topological closure of the wave.
• The theory provides a classical, deterministic alternative to standard quantum mechanics with no need for probabilistic collapse.
• The electrodynamics of curvilinear waves yields predictions consistent with quantum field theory in the low-energy limit.