[Paper Review] A unification scheme for classical and quantum mechanics at all velocities

John Johansson, Pär I. Johansson|ArXiv.org|Dec 27, 2004

Relativity and Gravitational Theory5 references5 citations

TL;DR

This paper proposes a unified framework that derives quantum mechanics from classical Newtonian and Maxwellian mechanics by modeling particles as stable configurations of electromagnetic waves in a structured vacuum. It shows that de Broglie waves, Schrödinger's equation, and wave-particle duality emerge naturally from mechanical wave disturbances of a bare charge in a Dirac-like vacuum medium, achieving convergence between classical and quantum mechanics across all velocities.

ABSTRACT

From a Newtonian-Maxwellian solution for a perturbed vacuum with a physical structure constructed based on pivotal experimental observations, we have achieved a general scheme for the formation of basic material particles. A basic particle, which may be e.g. an electron, is composed of a tiny free aether-pole (a bare charge) and the mechanical wave disturbances -- identifying with electromagnetic waves -- generated by it in the medium. When in motion, as a result of a first kind source effect, this particle wave exhibits all of wave and dynamic properties known for a de Broglie wave, and is here called a Newton- de Broglie (NdB) particle wave. In a confined space, the Newtonian solution for the NdB particle wave is equivalent to that given by Schrodinger's quantum mechanics. Through this general scheme we have accomplished a basic task of the unification of the classical- and the quantum- mechanics, both in terms of the deduction of the latter from the former, and the convergence of the latter into the former at high velocities. Through completing the task, we unfold the origins of a series of phenomena including the electromagnetic waves, the electromagnetic radiation and absorption, atomic and thermal excitations, the inertial mass, the Schrodinger's wavefunction and de Broglie wave, the Heisenberg's uncertainty relation, the de Broglie relations, the simultaneous existence of electron and positron or generally of particles and their anti-particles, the (rest) mass-energy equivalence relation, etc. The general scheme facilitates also a Theory of Relative Motion which we present in a separate paper, II; a series of followed studies are planned. (An original report of the scheme with a Preface remarking on the changes in later publications.)

Motivation & Objective

• To resolve the foundational gap between classical and quantum mechanics by deriving quantum phenomena from classical wave mechanics and vacuum structure.
• To explain the origin of particle mass, wave-particle duality, and the de Broglie relation through a mechanical model of electromagnetic wave disturbances.
• To unify the behavior of particles at all velocities, showing quantum mechanics as a limiting case of classical wave dynamics in a structured vacuum.
• To provide a physical mechanism for electromagnetic radiation, absorption, and thermal excitation based on wave mode interactions in the vacuum medium.
• To establish a consistent foundation for inertial mass, the uncertainty principle, and particle-antiparticle symmetry from wave interference and vacuum dynamics.

Proposed method

• Models a material particle as a stable configuration of a bare charge and its self-generated electromagnetic wave disturbances in a Dirac-type vacuum medium.
• Applies Newtonian mechanics to solve wave propagation in a structured vacuum, identifying the resulting wave solutions as Newton-de Broglie (NdB) waves.
• Derives the particle mass from the energy of the standing wave pattern formed by the oscillatory charge and its wave field.
• Shows that the NdB wave solution in a confined space matches the solutions of Schrödinger's equation, thus unifying quantum mechanics with classical wave mechanics.
• Uses wave mode addition (e.g., Kd) to model thermal excitation and de-excitation, with radiation and absorption processes described as reversible wave emission and reabsorption.
• Introduces the concept of 'vaculeons' and 'vacuuons' as bound states of oscillatory charge poles, providing a physical basis for particle-antiparticle pairs and mass-energy equivalence.

Experimental results

Research questions

• RQ1 How can quantum mechanical phenomena such as wave-particle duality and the de Broglie relation emerge from classical wave mechanics in a structured vacuum?
• RQ2 What is the physical origin of inertial mass and the Schrödinger wavefunction in terms of electromagnetic wave interference and vacuum structure?
• RQ3 How do electromagnetic radiation and absorption arise from mechanical wave disturbances in a vacuum medium?
• RQ4 Can the uncertainty principle and particle-antiparticle symmetry be derived from wave dynamics and vacuum polarization?
• RQ5 How does the proposed model achieve convergence between classical and quantum mechanics at all velocities, including relativistic regimes?

Key findings

• The Newton-de Broglie (NdB) wave solution for a confined particle in the vacuum medium exactly matches the solutions of Schrödinger's equation, demonstrating that quantum mechanics emerges from classical wave dynamics.
• The particle mass is derived as a function of the wave number and amplitude of the self-consistent electromagnetic wave field, providing a mechanical origin for mass.
• Thermal excitation and de-excitation are explained as the addition and release of wave mode disturbances (Kd) to the intrinsic wave field, with radiation and absorption described as reversible wave emission processes.
• The model predicts the existence of stable bound states of opposite-sign oscillatory charges (vacuuons), which account for the simultaneous existence of particles and antiparticles.
• The Heisenberg uncertainty principle is shown to arise naturally from the wave-packet localization and momentum spread in the NdB wave solution.
• The framework provides a physical basis for Einstein's mass-energy equivalence, as the rest energy of the particle is identified with the total energy of the self-sustained wave field in the vacuum medium.