[Paper Review] Nonpotential Solution of the Electron Problem

Alexander Ivanchin|arXiv (Cornell University)|Feb 8, 2009

Statistical Mechanics and Entropy6 references3 citations

TL;DR

This paper proposes a nonpotential solution to the electron problem by introducing a linearly independent, non-potential vector field solution to the electron's field equation, distinct from the classical potential solution. It derives a nonpotential force and interaction energy dependent on angular orientation, explaining neutron-antineutron duality, annihilation selection rules, and proton-neutron similarity through the nonpotential nature of the electric field.

ABSTRACT

Modern physics makes wide use of the equation for which only a potential solution is sought. The probability that this equation has a nonpotential solution is omitted from consideration automatically without any explanation. In this paper, using the electron problem as an example, an exact nonpotential solution linearly independent of the classical one is found. A solution with minimum potential energy is chosen as a physically feasible solution. The force acting on an electron with a nonpotential field in a homogeneous electric field and the interaction energy of two electrons with a nonpotential field is determined. The interaction energy depends on three angles responsible for mutual orientation of the electrons. Taking into account a nonpotential solution explains why there exist two types of neutrons: a neutron and an antineutron, why annihilation of the antineutron - proton is possible whereas that of the proton - neutron is impossible, why neutrons behave similar to protons. All the above properties result from the nonpotential character of an electric field.

Motivation & Objective

• To investigate the existence of nonpotential solutions to the electron field equation, overlooked in standard physics.
• To explore the physical implications of a nonpotential vector field in the context of electron behavior and interactions.
• To explain the existence of two neutron types (neutron and antineutron) and their annihilation behavior using nonpotential field theory.
• To demonstrate that the nonpotential character of the electric field accounts for the observed similarity between neutrons and protons.
• To provide a physically feasible solution by selecting the minimum potential energy configuration among nonpotential solutions.

Proposed method

• Derives an exact nonpotential solution to the electron field equation that is linearly independent of the classical potential solution.
• Applies the principle of minimum potential energy to select a physically feasible nonpotential solution from the solution space.
• Calculates the force acting on an electron in a homogeneous electric field using the nonpotential field configuration.
• Determines the interaction energy between two electrons with nonpotential fields, showing dependence on three mutual orientation angles.
• Uses the nonpotential field structure to model neutron and antineutron states as distinct field configurations.
• Analyzes the implications of angular dependence in interaction energy for particle stability and annihilation processes.

Experimental results

Research questions

• RQ1 Can a nonpotential solution exist for the electron field equation, and is it physically viable?
• RQ2 How does a nonpotential field modify the force on an electron in a homogeneous electric field?
• RQ3 What is the form of the interaction energy between two electrons when their fields are nonpotential and orientation-dependent?
• RQ4 Why do neutrons and antineutrons exist as distinct states, and why is only antineutron-proton annihilation allowed?
• RQ5 How does the nonpotential character of the electric field explain the observed similarity between neutrons and protons?

Key findings

• A nonpotential solution to the electron problem is found that is linearly independent of the classical potential solution.
• The interaction energy between two electrons with nonpotential fields depends on three angles, indicating orientation-dependent forces.
• The nonpotential field configuration explains the existence of two distinct neutron states: neutron and antineutron.
• Annihilation is possible between antineutron and proton but not between neutron and proton, due to the nonpotential field structure.
• The nonpotential nature of the electric field accounts for the observed similarity in behavior between neutrons and protons.