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Gravity, massive particles, photons and Shapiro delay

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Abstract

An impact model of gravity designed to emulate Newton’s law of gravitation is applied to particles with relative motions at slow and relativistic speeds. Based on this model, a gravitational interaction mode is then conceived between photons and massive particles. This implies a deflection perpendicular to the propagation direction of a photon twice as large as expected from the mass-energy relation of photons—in accordance with observations and the General Theory of Relativity. The longitudinal interaction is compatible with the energy and momentum conservation principles applied to massless entities, and the results are consistent with the observed Shapiro delay.

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Notes

  1. With the help of the integral formulae taken from Bronstein and Semendjajew (1985) and the definitions Σ=b 2+ξ 2 and ϒ=arctanξ/b they are—without integration constants:

  2. The same decrease in the speed of light has been obtained by Gupta et al. (2010) with fundamentally different arguments.

References

  • Amsler, C., Doser, M., Antonelli, M., Particle Data Group: Review of particle physics. Phys. Lett. B 667, 1 (2008)

    Article  ADS  Google Scholar 

  • Ballmer, S., Márka, S., Shawhan, P.: Feasibility of measuring the Shapiro time delay over meter-scaled distances. Class. Quantum Gravity 27, 185018-1 (2010)

    Article  ADS  Google Scholar 

  • Bopp, K.: Fatio de Duillier: De la cause de la pesanteur. Schriften der Straßburger Wiss. Ges. Heidelberg 10, 19 (1929)

    Google Scholar 

  • Bronstein, I.N., Semendjajew, K.A.: Taschenbuch der Mathematik, Aufl. 22. Harri Deutsch, Thun (1985)

    Google Scholar 

  • Drude, P.: Ueber Fernewirkungen. Ann. Phys. (Leipz.) 268(12), 1 (1897)

    Google Scholar 

  • Dyson, F.W., Eddington, A.S., Davidson, C.: A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of May 29, 1919. Philos. Trans. R. Astron. Soc. Lond. A 220, 291 (1920)

    Article  ADS  Google Scholar 

  • Einstein, A.: Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Ann. Phys. (Leipz.) 322, 132 (1905a)

    Article  ADS  Google Scholar 

  • Einstein, A.: Zur Elektrodynamik bewegter Körper. Ann. Phys. (Leipz.) 322, 891 (1905b)

    Article  ADS  Google Scholar 

  • Einstein, A.: Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes. Ann. Phys. (Leipz.) 340, 898 (1911)

    Article  ADS  Google Scholar 

  • Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. (Leipz.) 354, 769 (1916)

    Article  ADS  Google Scholar 

  • Fermi, E.: Quantum theory of radiation. Rev. Mod. Phys. 4, 87 (1932)

    Article  ADS  Google Scholar 

  • Goldhaber, A.S., Nieto, M.M.: Terrestrial and extraterrestrial limits on the photon mass. Rev. Mod. Phys. 43, 277 (1971)

    Article  ADS  Google Scholar 

  • Gupta, R.C.: Gravity as the second-order relativistic-manifestation of electrostatic-force (2005). arXiv:physics/0505194v1

  • Gupta, R.C., Pradhan, A., Gupta, S.: Refraction-based alternative explanation for: bending of light near a star, gravitational red/blue shift and black-hole (2010). arXiv:1004.1467v1

  • Heaviside, O.: On the forces, stresses, and fluxes of energy in the electromagnetic field. Philos. Trans. R. Soc. Lond. A 183, 423 (1892)

    Article  ADS  MATH  Google Scholar 

  • Hestenes, D.: The Zitterbewegung interpretation of quantum mechanics. Found. Phys. 20, 1213 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  • Hund, F.: Theoretische Physik. Bd. 1, 4. Aufl. Teubner, Stuttgart (1956)

    Google Scholar 

  • Jaffe, J., Shapiro, I.I.: Lightlike behavior of particles in a Schwarzschild field. Phys. Rev. D 6, 405 (1972)

    Article  ADS  Google Scholar 

  • Koltun, D.S.: Gravitational deflection of fast particles and of light. Am. J. Phys. 50, 527 (1982)

    Article  ADS  Google Scholar 

  • Kutschera, M., Zajiczek, W.: Shapiro effect for relativistic particles–testing general relativity in a new window. Acta Phys. Pol. B 41, 1237 (2010)

    Google Scholar 

  • Landau, L., Lifchitz, E.: Théorie quantique relativiste I. Mir, Moscou (1972)

    Google Scholar 

  • Laplace, P.-S.: Système du Monde, vol. II, Paris, p. 305 (1795)

  • Michell, J.: On the means of discovering the distance, magnitude, etc. of the fixed stars. Philos. Trans. R. Soc. 74, 35 (1784)

    Article  Google Scholar 

  • Mikhailov, A.A.: The deflection of light by the gravitational field of the sun. Mon. Not. R. Astron. Soc. 119, 593 (1959)

    ADS  Google Scholar 

  • Okun, L.B.: The concept of mass. Phys. Today 42(6), 31 (1989)

    Article  Google Scholar 

  • Okun, L.B.: Photons and static gravity. Mod. Phys. Lett. A 15, 1941 (2000)

    Article  ADS  Google Scholar 

  • Schiff, L.I.: On experimental tests of the general theory of relativity. Am. J. Phys. 28, 340 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  • Shapiro, I.I.: Fourth test of general relativity. Phys. Rev. Lett. 13, 789 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  • Shapiro, I.I., Ash, M.E., Ingalls, R.P., Smith, W.B., Campbell, D.B., Dyce, R.B., Jurgens, R.F., Pettengill, G.H.: Fourth test of general relativity: new radar result. Phys. Rev. Lett. 26, 1132 (1971)

    Article  ADS  Google Scholar 

  • Soldner, J.: Ueber die Ablenkung eines Lichtstrals von seiner geradlinigen Bewegung durch die Attraktion eines Weltkörpers, an welchem er nahe vorbei geht. Berliner Astron. Jahrb. 161 (1804)

  • Sommerfeld, A.: Optik. Harri Deutsch, Thun (1978)

    Google Scholar 

  • Wilhelm, K., Wilhelm, H., Dwivedi, B.N.: An impact model of Newton’s law of gravitation. Astrophys. Space Sci. (2012, in press)

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Acknowledgements

We thank an anonymous referee for constructive comments, and discussions with Harry Kohl, Kristian Schlegel, Eckart Marsch, Luca Teriaca, Udo Schühle and Horst Wilhelm on some aspects of this paper are gratefully acknowledged. This research has made extensive use of the Astrophysics Data System (ADS).

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Authors and Affiliations

  1. Max-Planck-Institut für Sonnensystemforschung (MPS), 37191, Katlenburg-Lindau, Germany

    Klaus Wilhelm

  2. Dept. of Applied Physics, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005, India

    Bhola N. Dwivedi

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  1. Klaus Wilhelm
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  2. Bhola N. Dwivedi
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Correspondence to Bhola N. Dwivedi.

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Wilhelm, K., Dwivedi, B.N. Gravity, massive particles, photons and Shapiro delay. Astrophys Space Sci 343, 145–151 (2013). https://doi.org/10.1007/s10509-012-1207-2

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