Skip to main content
SpringerLink
Log in

The Isotopic Field-Charge Assumption Applied to the Electromagnetic Interaction

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

“I dreamed that I used to be two cats, who played with each other.”

(Frigyes Karinthy, Hungarian writer and humorist, 1887–1938)

Motto

Abstract

This paper applies the isotopic field-charge spin theory (Darvas in Int. J. Theor. Phys. 50(10):2961–2991, 2011) to the electromagnetic interaction. First, a modified Dirac equation in the presence of a velocity dependent gauge field and isotopic field charges (namely Coulomb and Lorentz type electric charges, as well as gravitational and inertial masses) is derived. This equation is compared with the classical Dirac equation. It is shown that, since the presence of isotopic field-charges would distort the Lorentz invariance of the equation, there is a transformation, which together with the Lorenz transformation restores the invariance of the equation, in accordance with the conservation of the isotopic field-charge spin (Darvas in Concepts Phys. VI 1:3–16, 2009). The paper discusses conclusions derived from the extensions of the Dirac equation. It is shown that in semi-classical approximation the model returns the original Dirac equation, and at significantly relativistic velocities it approaches the Schrödinger equation. Among other conclusions, the clue gives physical meaning to the electric moment. The closing section summarises a few further conclusions and shows a few developments to be discussed in detail in a subsequent paper (Darvas in Int. J. Theor. Phys., 2013).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Electromagnetic field theories were related with anisotropic geometries in, at least, two terms. First, the Dirac matrices, introduced in QED [27] (1928) follow the rules of hypercomplex numbers (as shown, among others, by [1] Achiezer and Berestetskii, p. 90). An octonomial extension was studied recently in [9]. Something similar has been introduced by the help of Clifford algebras in [35]. Later Dirac published two essential extensions to his QED theory [28–31]. At second, he introduced a curvilinear co-ordinate system in [31]. So, he defined an auxiliary co-ordinate system y Λ, “which is kept fixed during the variation process and use the functions y Λ(x) to describe the x co-ordinate system in terms of the y co-ordinate system.” He defines the y system “so that the metric for the x system” be \(g_{\mu\nu}=y_{\varLambda,\mu}y^{\varLambda}_{,\nu}\). This metric, which then appears in the Hamiltonian of the electromagnetic interaction, was the first step to a later Finsler extension. Some consequences have been discussed in [8, 44, 47] and [40]. Concerning the parallel presence of a scalar and a kinetic gauge field, authors of [42] enlarge the configuration space by including a scalar field additionally, and taking anisotropic models into account too.

  2. This expression is very close to the approach applied by Dirac [29]. The roots are, however, much elder. To see the origins, I must mention a few other historical steps. Following the Symmetry Festival 2003, when I first discussed the basic ideas—developed in detail in my coming book [16]—with Yuval Ne’eman, there appeared a few publications with a similar approach. Starting from the fundamental equation by Dirac [29] ∂ μ J μ A ν=0, de Haas, E.P.J. in his PIRT paper [23], for example, derives similar (but not the same) conclusions like we, for QED and the SM, according to which physical real quantities can be derived by the distinction of the (spatially localised) electric potential and the Dirac velocity field. Although, in contrary to Dirac, our theory does not need to assume an ether, we can refer to Dirac’s statement [30] where he defines the velocity field through the electromagnetic four-potential: “We have now the velocity at all points of space-time, playing a fundamental part in electrodynamics. It is natural to regard this as the velocity of some real physical thing.” While Dirac identifies this “real physical thing” with an ether, our work is an attempt to identify these ‘things’ with the quanta of a gauge-field, ‘localised’ in that velocity field [22]. For I received objections since I first communicated the essence of the theory presented later in detail in [14], which objections stated that the assumption of a velocity dependent gauge contradicts localisation, I advise to keep in mind the cited words by Dirac (in addition to my main argument, namely the original formulation of Noether’s second theorem [39]). De Haas assumes an analogy between Mie’s [37] non-gauge invariant stress-energy tensor, and the stress-energy tensor in Dirac’s 1951 theory in a four-velocity field. The analogy works only partially (in my opinion), but the acknowledgement of the role of the velocity field in defining the stress-energy tensor is worth attention as it partially confirms my approach, and leads to the same derivation of the Lorentz transformation of the electromagnetic field components, as I have interpreted it [22]. As de Haas [25] refers to it, the stress-energy tensor by M. von Laue [48] can be written as T μν =J μ A ν , where

    $$A_{\nu}= \left [\begin{array}{c} \mathbf{A}\\ \frac{i}{c}\varPhi \end{array} \right ] \quad \mbox{and} \quad J_{\mu}= \left [ \begin{array}{c} \mathbf{J}\\ i c \rho \end{array} \right ] $$

    so

    $$T_{\mu\nu}= \left [ \begin{array}{c} \mathbf{J}\\ i c \rho \end{array} \right ] \left [\begin{array}{c} \mathbf{A}\\ \frac{i}{c}\varPhi \end{array} \right ] = \left [ \begin{array}{c@{\quad}c} \mathbf{J} \otimes \mathbf{A} & \frac{i}{c}\varPhi\mathbf{J} \\ i c \rho \mathbf{A} & -\rho\varPhi \end{array} \right ] $$

    what demonstrates an analogy with our formula derived in [22] based on the findings in this paper. Note also that the potential (Coulomb) charges behave like corpuscles, while the kinetic (Lorentz type) charges like waves [16]. This complementary double behaviour (formulated first by Bohr in 1927, then discussed in 1937 [5]) became subject of studies again (cf., [41]).

  3. Later, Dirac [29] considered that the classical theories of electromagnetic field are approximate and are valid only if the accelerations of the electrons are small. He stated that the earlier problems of QED resulted not in quantization, rather in the incompleteness of the classical theory of electrons, and one must try to improve it. For this reason, he proposed to replace the application of the Lorentz condition with a gauge theory. He emphasised also the Hamiltonian approach instead of the Lagrangian one. He introduced a function λ (which was different from the quantity introduced by Feynman [34]) and got a current \(j_{\mu}=-\lambda(\partial S/\partial x^{\mu}+A^{*}_{\mu})\) where S was a gauge function attributed to A, and λ could be chosen to be an arbitrary infinitesimal at one instant of time, while its value at other times was then fixed by the conservation law ∂j μ /∂x μ=0. This method resulted in the conclusion that the theory (as expected) involves only the ratio e/m, not e and m separately. This [29] theory did not introduce the interaction of the electron with the electromagnetic field as a perturbation, like in the 1929–1932 Dirac-Fermi-Breit theories. The electron of that new theory could not be considered apart from its interaction with the electromagnetic field. As Dirac mentioned: “The theory of the present paper is put forward as a basis for a passage to a quantum theory of electrons… one can hope that its correct solution will lead to the quantization of electric charge…” and “…questions of the interaction of the electron with itself no longer arise.” Then, a further model by Dirac [31] p. 64) provided a possible solution for eliminating the runaway motions of the electron.

    Dirac’s [29] paper was an attempt to exclude approximations by perturbation in either direction. It was in harmony with the aim of Bethe and Fermi [4] to show the equivalence of the perturbations applied by Breit [6, 7] and Møller [38]. In this respect Dirac’s models were kin to the present attempt, in which, instead of a perturbation, we acknowledge the asymmetric roles of the interacting charged particles (as it can be read originally in [38]) and apply a gauge theory that has led us to a quantised theory. Certain ideas are borrowed here from [43]. The theory applied in this paper to QED and having been proposed in a general form in [14] eliminates the runaway motions of the electron too, although in an alternative way.

  4. At the end of their paper Bethe and Fermi ([4] p. 306) showed that the formula introduced by Møller holds also when one of the interacting particles is in bound state. They consider also the option that the two interacting particles emit two quanta, but they reject it, because (for symmetry consideration for the momentums of the two quanta) they take into account only identical type quanta to be emitted and absorbed. (Although, the emission of one quantum painted another asymmetry in the picture, in which they aimed at eliminating the asymmetry caused by Møller’s scattering matrix.) This conclusion by Bethe and Fermi is a result of their artificial symmetrisation of the potentials, and does not arise in the theory set forth, among others, in this paper. For those, who are interested in the problem of identity and non-identity of particles, as well as symmetrisation, more detailed analyses are recommended in [16, 26].

  5. The fact is, that Dirac ([27] p. 619) could not do anything with the electric moment, and so did all but most textbooks following him. The appearance of the kinetic field D made possible to calculate the full electric moment.

References

  1. Achiezer, A.I., Berestetskii, V.B.: Kvantovaya Elektrodynamika, 3rd modified edn., p. 623. Nauka, Moskva (1969) (in Russian)

    Google Scholar 

  2. Akhmedov, E.K., Smirnov, A.Y.: Neutrino oscillations: entanglement, energy-momentum conservation and QFT. Found. Phys. 41(8), 1279–1306 (2011). doi:10.1007/s10701-011-9545-4

    Article  ADS  MATH  Google Scholar 

  3. Barletta, E., Dragomir, S.: Gravity as a Finslerian metric phenomenon. Found. Phys. 42(3), 436–453 (2012). doi:10.1007/s10701-011-9614-8

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Bethe, H., Fermi, E.: Über die Wechselwirkung von zwei elektronen. Z. Phys. 77(5–6), 296–306 (1932)

    Article  ADS  Google Scholar 

  5. Bohr, N.: Philos. Sci. 4, 289 (1937)

    Article  Google Scholar 

  6. Breit, G.: Phys. Rev. 34, 553 (1929)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Breit, G.: Phys. Rev. 39, 616 (1932)

    Article  ADS  Google Scholar 

  8. Brinzei, N., Siparov, S.: Equations of electromagnetism in some special anisotropic spaces, 15 p. (2008). arXiv:0812.1513v1 [gr-qc]

  9. Chanyal, B.C., Bisht, P.S., Negi, O.P.S.: Generalized octonion electrodynamics. Int. J. Theor. Phys. 49(6), 1333–1343 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Darvas, G., Farkas, F.T.: An artist’s works through the eyes of a physicist: graphic illustration of particle symmetries. Leonardo 39(1), 51–57 (2006)

    Article  Google Scholar 

  11. Darvas, G., Farkas, F.T.: Quantum Scent Dynamics (QSD): a new composite model of physical particles, 21 p. (2008). arXiv:0803.2497v1 [hep-ph]

  12. Darvas, G.: Conserved Noether currents, Utiyama’s theory of invariant variation, and velocity dependence in local gauge invariance. Concepts Phys. VI 1, 3–16 (2009)

    Article  ADS  Google Scholar 

  13. Darvas, G.: GTR and the Isotopic field charge spin assumption. Paper presented to the Physical Interpretations of Relativity Theory—11 Conference, held in Moscow, 4–7 July 2011, 10 p. (2011)

  14. Darvas, G.: The isotopic field charge spin assumption. Int. J. Theor. Phys. 50(10), 2961–2991 (2011). doi:10.1007/s10773-011-0796-9

    Article  MathSciNet  MATH  Google Scholar 

  15. Darvas, G.: Isotopic field charge spin conservation in general relativity theory. In: Duffy, M.C., Gladyshev, V.O., Morozov, A.N., Rowlands, P. (eds.) Physical interpretations of relativity theory, Proceedings of the International Scientific Meeting PIRT-2011, Moscow, 4–7 July 2012, pp. 53–65. Bauman Moscow State Technical University, Moscow, Liverpool, Sunderland (2012), 347 pp

    Google Scholar 

  16. Darvas, G.: Another version of facts. On physical interactions 136 p. (2013, manuscript, under review)

  17. Darvas, G.: Finsler geometry in GTR in the presence of a velocity dependent gauge field. Bull. Transilvania Univ. Brasov, Ser. III, Math. Inf. Phys. 5(54), 2, 23–34 (2012)

    MathSciNet  Google Scholar 

  18. Darvas, G.: GTR and the isotopic field charge spin assumption. Hypercomplex Numbers Geom. Phys. 1(17), 9, 50–59 (2012)

    Google Scholar 

  19. Darvas, G.: Finsler geometry in the presence of isotopic field charges applied for gravity. In: Moskaliuk, S. (ed.) Proceedings of the Vth Petrov International Symposium, High Energy Physics, Cosmology and Gravity, pp. 17–42. TIMPANI, Kiev (2012), 299 pp

    Google Scholar 

  20. Darvas, G.: Finslerian approach to the electromagnetic interaction in the presence of isotopic field-charges and a kinetic field. Hypercomplex Numbers Geom. Phys. 2(18) 9, 1–19 (2012)

    Google Scholar 

  21. Darvas, G.: A few consequences of the isotopic field-charge spin conservation. In: Kamalov, T.F. (ed.) Theoretical Physics and Its Application. MSOU Press, Moscow (2012). ISBN 978-5-7045-1304-9

    Google Scholar 

  22. Darvas, G.: Electromagnetic interaction in the presence of isotopic field-charges and a kinetic field. Int. J. Theor. Phys. (2013, submitted for publication, under review)

  23. de Haas, E.P.J.: The combination of de Broglie’s harmony of the phases and Mie’s theory of gravity results in a principle of equivalence for quantum gravity. Ann. Fond. L. de Brioglie 29(4), 707–726 (2004)

    Google Scholar 

  24. de Haas, E.P.J.: A renewed theory of electrodynamics in the framework of a Dirac ether. In: Proc. P.I.R.T.-IX (London 2004), pp. 95–123. PD Publications, Liverpool (2004)

    Google Scholar 

  25. de Haas, E.P.J.: From Laue’s stress-energy tensor to Maxwell’s equations and the implications for Einstein’s GTR. In: Duffy, M.C., et al. (eds.) Proceedings of the Int. Conference “Physical Interpretation of Relativity Theory (PIRT-05)”. Bauman Univ. Press, Moscow (2005)

    Google Scholar 

  26. Dieks, D., Lubberdink, A.: How classical particles emerge from the quantum world. Found. Phys. 41(6), 1051–1064 (2011). doi:10.1007/s10701-010-9515-2

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Dirac, P.A.M.: The quantum gravity of the electron. Proc. R. Soc. A, Math. Phys. Eng. Sci. 117(778), 610–624 (1928). doi:10.1098/rspa.1928.0023

    Article  ADS  MATH  Google Scholar 

  28. Dirac, P.A.M.: A theory of electrons and protons. Proc. R. Soc. Lond. 126(801), 360–365 (1929)

    Article  ADS  Google Scholar 

  29. Dirac, P.A.M.: A new classical theory of electrons. Proc. R. Soc. A, Math. Phys. Eng. Sci. 209, 291–296 (1951)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Dirac, P.A.M.: Nature 168, 906–907 (1951)

    Article  MathSciNet  ADS  Google Scholar 

  31. Dirac, P.A.M.: An extensible model of the electron. Proc. R. Soc. A, Math. Phys. Eng. Sci. 268, 57–67 (1962)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Duffy, M.C., Gladyshev, V.O., Morozov, A.-N., Rowlands, P. (eds.): Physical Interpretations of Relativity Theory. Proceedings of the International Scientific Meeting PIRT-2011, p. 347. Bauman Moscow State Technical University, Moscow, Liverpool, Sunderland (2012)

    Google Scholar 

  33. Fabbri, L.: A discussion on Dirac field theory, No-Go theorems and renormalizability. Int. J. Theor. Phys. 52(2), 634–643 (2013)

    Article  MATH  Google Scholar 

  34. Feynman, R.P.: Space-time approach to quantum electrodynamics. Phys. Rev. 76(6), 769–789 (1949)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Hiley, B.J., Callaghan, R.E.: Clifford algebras and the Dirac-Bohm quantum Hamilton-Jacobi equation. Found. Phys. 42(1), 192–208 (2012). doi:10.1007/s10701-011-9558-z

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. Landau, L.D., Lifshitz, E.M.: Teoriya Polya, p. 458. Nauka, Moskva (1967) (in Russian)

    Google Scholar 

  37. Mie, G.: Grundlagen einer theorie der materie. Ann. Phys. 37, 511–534 (1912)

    Article  MATH  Google Scholar 

  38. Møller, C.: Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte. Z. Phys. 70(11–12), 786–795 (1931)

    Article  ADS  MATH  Google Scholar 

  39. Noether, E.A.: Invariante Variationsprobleme. Nachrichten Königlichen Gesellschaft Wissenschaften Göttingen, Math.-Phys. Klasse, 235–257 (1918)

  40. Pons, J.M., Salisbury, D.C., Shepley, L.C.: Gauge transformations in Einstein-Yang-Mills theories. J. Math. Phys. (1999, submitted). arXiv:gr-qc/9912086v1

  41. Rabinowitz, M.: Challenges to Bohr’s wave-particle complementarity principle. Int. J. Theor. Phys. 52(2), 668–678 (2013)

    Article  MATH  Google Scholar 

  42. Sarkar, K., Sk, N., Debnath, S., Sanyal, A.K.: Viability of Noether symmetry of F(R) theory of gravity. Int. J. Theor. Phys. 52(4), 1194–1213 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  43. Schroer, B.: An alternative to the gauge theoretic setting. Found. Phys. 41(10), 1543–1568 (2011). doi:10.1007/s10701-011-9567-y

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. Siparov, S.: Introduction to the Anisotropic Geometrodynamics. World Scientific, Singapore (2012). 303 p.

    MATH  Google Scholar 

  45. ’t Hooft, G.: Introduction to General Relativity. Rinton Press, Princeton (2002)

    Google Scholar 

  46. ’t Hooft, G.: A class of elementary particle models without any adjustable real parameters. Found. Phys. 41(12), 1829–1856 (2011). doi:10.1007/s10701-011-9586-8

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. Voicu, N.: Equations of electromagnetism in some special anisotropic spaces, part 2. Hypercomplex Numbers Geom. Phys. 7(14), 61–72 (2010)

    Google Scholar 

  48. von Laue, M.: Ann. Phys. 35, 524–542 (1911)

    Article  MATH  Google Scholar 

  49. Weinberg, S.: A model of leptons. Phys. Rev. Lett. 19(21), 1264–1266 (1967)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Symmetrion, 29 Eötvös St., Budapest, 1067, Hungary

    György Darvas

Authors
  1. György Darvas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to György Darvas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Darvas, G. The Isotopic Field-Charge Assumption Applied to the Electromagnetic Interaction. Int J Theor Phys 52, 3853–3869 (2013). https://doi.org/10.1007/s10773-013-1693-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-013-1693-1

Keywords

Search

Navigation