Research Article | | Peer-Reviewed

A Proposal for the Reaction Force in the Emission of Electromagnetic Radiation

Received: 3 October 2025     Accepted: 17 January 2026     Published: 24 April 2026
Views:       Downloads:
Abstract

An equation for the radiation reaction force is proposed that does not violate causality and produces fairly intuitive results. The equivalence principle is solved. The radiating charge appears to be in an excited state. This may seem strange, but the Compton effect seems to confirm this assumption. Applications are made to the most relevant cases of electromagnetic radiation emission. The results appear to confirm the correctness of the assumptions made. Motion with a constant electric field yields results that are as one would expect. Motion under the action of a constant magnetic field occurs with the same frequency obtained previously, and the approximation required due to the complexity of the calculations yields the spiral motion already obtained in a previous publication starting from different assumptions. Free motion without external forces is discussed, and in addition to uniform rectilinear motion, there is a motion that brings the charge to rest, as one would expect. A simple numerical application is suggested for experimental verification. The key point is that, compared to classical electromagnetism, used by all previous authors, an axiom has been added that solves the problem. Evidently, the axioms of classical electromagnetism are not sufficient to derive an expression for the reaction force, for which one must rely on experience. The Compton effect seems to confirm the hypotheses assumed. Before emission, the electron is off-shell, in a virtual state in which it has the extra energy required by the formula we used. Therefore, the additional energy required is not pure fantasy, or an assumption to be verified, one of the mysteries and wonders of quantum mechanics.

Published in American Journal of Zoology (Volume 9, Issue 2)
DOI 10.11648/j.ajz.20260902.11
Page(s) 33-40
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Radiation Reaction Force, Violation of Causality, Euler Spiral, Incompleteness of Theoretical Principles, Axiom’s, Clothoid, Compton Effect, Off-shell, Virtual Particle

References
[1] Jackson, Classical electrodynamics. J. Wiley, New York(1975)
[2] L. D. Landau - E. M. Lifsits, Teoria dei campi. Editori Riuniti, Roma (1981).
[3] K. Lechner, Campi elettromagnetici. it.scribd.com,
[4] Misne Thorn Wheeler, Gravitation. W. H. Freeman and Company, New York (1973).
[5] Benn-Tucker, An Introduction to Spinors and Geometry with Application in Physics. Adam Hilger (IOP Publishing Ltd) (1989).
[6] M. Bramanti, Esercitazioni di Analisi 2. Esculapio, Bologna (2012).
[7] Richard T. Hammond, Relativistic Particle Motion and Radiation Reaction in Electrodynamics, EJTP 7, No. 23,221 (2010).
[8] Fresnel integral. Wikipedia, the free encyclopedia,
[9] Clotoide. Wikipedia,
[10] Euler spiral. Wikipedia, the free encyclopedia,
[11] Paolo Tritella, A simplified trajectory for a radiating charge moving in a uniform magnetic field,
[12] W. E. Baylis and J. Huschilt, Problematic solutions to the Landau-Lifshitz equation,
[13] Paul McKenna, High Field QED Experiments with ELINP2x10PW Laser,
[14] F. Rohrlich, The Principle of equivalence, Ann. Phys. 22,169-191 (1963).
[15] George E. A. Matsas, Do inertial electric charges radiate with respect to uniformly accelerated observers?,
[16] Erik Eriksen and Oyvind Gron, On the energy and momentum of an accelerated charged particle and the sources of radiation, Eur. J. Phys. 28, 401-407(2007).
[17] Erik Eriksen, Electrodynamics of Hyperbolically Accelerated Charges, Ann. Phys. 297,243-294(2002).
[18] C. Leibovitz and A. Peres, Energy Balance of Uniformly Accelerated Charge, Ann. Phys. 25, 400-404 (1963).
[19] Fritz Rohrlich, The dynamics of a charged particle,
[20] F. Lenz, Gauge fields in accelerated frames,
[21] M. Ribaric and L. Sustersic, Improvement on the Lorentz-Abraham-Dirac equation,
[22] A. Elitzur, E. Cohen, P. Beniamini, Charge Acceleration and Field-Lines Curvature: A Fundamental Symmetry and Consequent Asymmetries,
[23] J. Franklin, D. Griffiths, The Fields of a Charged Particlein Hyperbolic Motion,
[24] Katarzyna Krajewska, Jerzy Z. Kaminski, Quest for MeV frequency combs – proposal for ELI experiments,
[25] H. P. A. M. Dirac, Proc. Roy. Soc. A, (London) A167,148 (1938).
[26] P. Kazinski, S. Lyakhovich, A. Sharapov, Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension,
[27] G. Ares de Parga, R. Mares and S. Dominguez, Landau-Lifshitz equation of motion for a charged particle revisited, Annales de la Fondation Louis de Broglie, Volume 30 no 3-4, (2005).
[28] Gal’tsov & Spirin, Radiation reaction reexamined: bound momentum and,
[29] P. O. Kazinski, S. L. Lyakhovich, A. A. Sharapov, Acomment on "Radiation reaction reexamined: bound momentum and Schott term” by D. V. Gal’tsov and P. Spirin,
[30] Camila de Almeida, the radiation of a uniformly accelerated charge is beyond the horizon: A simple derivation, Am. J. Phys. 74, 154 (2006).
[31] Oyvind Gron, Electrodynamics of Radiating Charges, Advances in Mathematical Physics Volume 2012 (2012), Article ID 528631, 29 pages.
[32] Gupta, Abhinav et al., Radiation from a charged particle and radiation reaction - revisited, Phys. Rev. D57, 7241(1998).
[33] A. Harpaz N. Soker, Radiation from a Uniformly Accelerated Charge, Gen. Relativ. Gravit. August1998, Volume 30, Issue 8, pp 1217-1227(1998).
[34] A. Harpaz N. Soker, Radiation from a Charge in a Gravitational Field,
[35] H. Spohn, The critical manifold of the Lorentz-Diracequation, EPL (Europhysics Letters), Volume 50, Number 3 (2000).
[36] E. Poisson, An introduction to the Lorentz-Diracequation,
[37] A. Singal, A uniformly accelerated charge and the question of Schott energy-momentum,
[38] G. Ares de Parga, R. Mares and S. Dominguez, Landau-Lifshitz equation of motion for a charged particle revisited, Annales de la Fondation Louis de Broglie, Volume 30 no 3-4, (2005).
[39] Dimiter L. Balabanski and the ELI-NP ScienceTeam, Future Experiments with Intense Laser Beams and Brilliant Gamma Beams at the ELI-NP Facility, J. Phys.: Conference Series 590, 012005 (2015).
[40] K. Mcdonald, Hawking-Unruh Radiation and Radiationof a Uniformly Accelerated Charge,
[41] Muharrem Kusku, The Free Maxwell Field in Curved Spacetime,
[42] Rick Bradford, Chapter 52 Does a Uniformly Accelerating Charge Radiate? Yes (I think) but not everyone can see it (perhaps).,
[43] Stephen Parrott, Comment on Phys. Rev. D 60 084017 "Classical self-force” by F. Rohrlich,
[44] Christos G Tsagas, Electromagnetic fields in curved spacetimes, Class. Quantum Grav. 22, 393-407 (2005).
[45] G. A. Scott, Electromagnetic radiation and the mechanical reactions arising from it,
[46] Matthias Lienert, Direct interaction along light cones at the quantum level,
[47] A. I. Nikishov, The Lorentz-Dirac equation in light of quantum theory, Zh. Eksp. Teor. Fiz. 110, 510-525 (August 1996).
[48] Matthias Lienert, Extreme Light Infrastructure – Nuclear Physics ELI-NP-CERN,
[49] E Eriksen and O Gron, Relativistic dynamics in uniformly accelerated reference frames with application to the clock paradox, 1990 Eur. J. Phys. 11, 39 (1990).
[50] ELI-NP, Extreme Landscape of Subatomic Physics with High Power Lasers and Gamma beams, University of Florida.
[51] Y. Friedman and T. Scarr, Making the Relativistic Dynamics Equation Covariant: Explicit Solutions for Motion under a Constant Force, Physica Scripta, 86, 065008 (2012).
[52] Ashok K Singal, Reply to comment on ’Poynting flux in the neighbourhood of a point charge in arbitrary motion and the radiative power losses, Eur. J. Phys. 39, 018002 (2018).
[53] V. Onoochin K. McDonald, Fields of a Uniformly Accelerated Charge,
[54] E A Seddon et al, Short-wavelength free-electron laser sources and science: a review, 2017 Rep. Prog. Phys. 80, 115901 (2017).
[55] Roberto De Pietri, Mutamenti nella Nozione di Vuoto, 2017 Rep. Prog. Phys. 80, 115901 (2017).
[56] F. Rohrlich, The self-force and radiation reaction, Am. J. Phys. 68, 1109 (2000).
[57] Timothy H. Boyer, Mass Renormalization and Radiation Damping for a Charged Particle in Uniform Circular Motion, Am. J. Phys. 68, 1109 (2000).
[58] Richard Sigal, Electromagnetic Radiation in Curved Spaces, Journal of Mathematical Physics 12, 2490 (1971).
[59] Jacques D. Templin, An approximate method for the direct calculation of radiation reaction, Am. J. Phys. 66, 403 (1998).
[60] Angel Prieto, On the electrodynamic group: The relativistic radiation reaction force, J. Math. Phys. 39,1478 (1998).
[61] Andrea Macchi, Intense Laser Sheds Light on Radiation Reaction,
[62] Angel Prieto et al., Experimental Evidence of Radiation Reaction in the Collision of a High-Intensity Laser Pulse with a Laser-Wakefield Accelerated Electron Beam, Phys. Rev. X 8, 011020 (2018).
[63] A. Singal, The equivalence principle and an electric charge in a gravitational field, Gen. Relativ. Gravit. 27, Issue 9, (1995) pp 953-967.
[64] R. Casalbuoni, Appunti per il corso di Elettrodinamica: (A.A.1993/94), Dipartimento di Fisica della Universita’ di Firenze, Firenze, pp 88-93.
Cite This Article
  • APA Style

    Tritella, P. (2026). A Proposal for the Reaction Force in the Emission of Electromagnetic Radiation. American Journal of Zoology, 9(2), 33-40. https://doi.org/10.11648/j.ajz.20260902.11

    Copy | Download

    ACS Style

    Tritella, P. A Proposal for the Reaction Force in the Emission of Electromagnetic Radiation. Am. J. Zool. 2026, 9(2), 33-40. doi: 10.11648/j.ajz.20260902.11

    Copy | Download

    AMA Style

    Tritella P. A Proposal for the Reaction Force in the Emission of Electromagnetic Radiation. Am J Zool. 2026;9(2):33-40. doi: 10.11648/j.ajz.20260902.11

    Copy | Download

  • @article{10.11648/j.ajz.20260902.11,
      author = {Paolo Tritella},
      title = {A Proposal for the Reaction Force in the Emission of Electromagnetic Radiation},
      journal = {American Journal of Zoology},
      volume = {9},
      number = {2},
      pages = {33-40},
      doi = {10.11648/j.ajz.20260902.11},
      url = {https://doi.org/10.11648/j.ajz.20260902.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajz.20260902.11},
      abstract = {An equation for the radiation reaction force is proposed that does not violate causality and produces fairly intuitive
    results. The equivalence principle is solved. The radiating charge appears to be in an excited state. This may seem strange,
    but the Compton effect seems to confirm this assumption. Applications are made to the most relevant cases of electromagnetic
    radiation emission. The results appear to confirm the correctness of the assumptions made. Motion with a constant electric field
    yields results that are as one would expect. Motion under the action of a constant magnetic field occurs with the same frequency
    obtained previously, and the approximation required due to the complexity of the calculations yields the spiral motion already
    obtained in a previous publication starting from different assumptions. Free motion without external forces is discussed, and in
    addition to uniform rectilinear motion, there is a motion that brings the charge to rest, as one would expect. A simple numerical
    application is suggested for experimental verification. The key point is that, compared to classical electromagnetism, used by
    all previous authors, an axiom has been added that solves the problem. Evidently, the axioms of classical electromagnetism are
    not sufficient to derive an expression for the reaction force, for which one must rely on experience. The Compton effect seems
    to confirm the hypotheses assumed. Before emission, the electron is off-shell, in a virtual state in which it has the extra energy
    required by the formula we used. Therefore, the additional energy required is not pure fantasy, or an assumption to be verified,
    one of the mysteries and wonders of quantum mechanics.},
     year = {2026}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - A Proposal for the Reaction Force in the Emission of Electromagnetic Radiation
    AU  - Paolo Tritella
    Y1  - 2026/04/24
    PY  - 2026
    N1  - https://doi.org/10.11648/j.ajz.20260902.11
    DO  - 10.11648/j.ajz.20260902.11
    T2  - American Journal of Zoology
    JF  - American Journal of Zoology
    JO  - American Journal of Zoology
    SP  - 33
    EP  - 40
    PB  - Science Publishing Group
    SN  - 2994-7413
    UR  - https://doi.org/10.11648/j.ajz.20260902.11
    AB  - An equation for the radiation reaction force is proposed that does not violate causality and produces fairly intuitive
    results. The equivalence principle is solved. The radiating charge appears to be in an excited state. This may seem strange,
    but the Compton effect seems to confirm this assumption. Applications are made to the most relevant cases of electromagnetic
    radiation emission. The results appear to confirm the correctness of the assumptions made. Motion with a constant electric field
    yields results that are as one would expect. Motion under the action of a constant magnetic field occurs with the same frequency
    obtained previously, and the approximation required due to the complexity of the calculations yields the spiral motion already
    obtained in a previous publication starting from different assumptions. Free motion without external forces is discussed, and in
    addition to uniform rectilinear motion, there is a motion that brings the charge to rest, as one would expect. A simple numerical
    application is suggested for experimental verification. The key point is that, compared to classical electromagnetism, used by
    all previous authors, an axiom has been added that solves the problem. Evidently, the axioms of classical electromagnetism are
    not sufficient to derive an expression for the reaction force, for which one must rely on experience. The Compton effect seems
    to confirm the hypotheses assumed. Before emission, the electron is off-shell, in a virtual state in which it has the extra energy
    required by the formula we used. Therefore, the additional energy required is not pure fantasy, or an assumption to be verified,
    one of the mysteries and wonders of quantum mechanics.
    VL  - 9
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Sections