The 4-Dimensional Dirac Equation in Relativistic Field Theory

  • Wim Vegt Department of Physics Eindhoven University of Technology 5600-MB Eindhoven The Netherlands.
Keywords: General Relativity; Quantum Physics; Dirac Equation; Gravitational-Electromagnetic Interaction; Black Holes; Gravitational-Electromagnetic Confinement; Electromagnetism; Quantum Optics


An important milestone in quantum physics has been reached
by the publication of the Relativistic Quantum Mechanical
Dirac Equation in 1928. However, the Dirac equation
represents a 1-Dimensional quantum mechanical equation
which is unable to describe the 4-Dimensional Physical
In this article the 4-Dimensional Relativistic Quantum
Mechanical Dirac Equation expressed in the vector
probability functions  and the complex conjugated vector
probability function  *will be published. To realize this, the
classical boundaries of physics has to be changed. It is
necessary to go back in time 300 years ago. More than 200
years ago before the Dirac Equation had been published.
A Return to the Inception of Physics. The time of Isaac
Newton who published in 1687 in the “Philosophiae
Naturalis Principia Mathematica” a Universal Fundamental
Principle in Physics which was in Harmony with Science and
Religion. The Universal Path, the Leitmotiv, the Universal
Concept in Physics. Newton found the concept of “Universal
Equilibrium” which he formulated in his famous third
equation Action = - Reaction. This article presents a New

Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity.
The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason these material waves in Schrödinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function.
In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined

Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values.


(1) Oki Gunawana and Yudistira Virgus; The one-dimensional camelback potential in the parallel dipole line trap: Stability conditions and finite size effect; Journal of Applied Physics 121, 133902 (2017);

(2) IBM Blog Research; A new effect in electromagnetism discovered – 150 years later;

(3) J. W. Vegt, A Continuous Model of Matter based on AEONs, Physics Essays ,1995, Volume 8, Number 2, 201-224 A Continuous model of Matter ( )

(4) Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Gutiérrez-Jáuregui, R.J. Schoelkopf, N. Mirrahimi, H.J. Carmichael and M. H. Devoret; To catch and reverse a quantum jump mid-flight; Nature; 03 June 2019 equilibrium beyond Einstein 4-Dimensional, Kaluza-Klein 5-Dimensional and Superstring 10- and 11 Dimensional Curved Hyperspaces.

(5) A. S. Stodolna, A. Rouzée, F. Lépine, S. Cohen, F. Robicheaux, A. Gijsbertsen, J. H. Jungmann, C. Bordas, and M. J. J. Vrakking. Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure of Stark States. Phys. Rev. Lett. 110, 213001 – Published 20 May 2013
How to Cite
Vegt, W. (2021). The 4-Dimensional Dirac Equation in Relativistic Field Theory. European Journal of Applied Sciences, 9(1), 35-93.