Advertisement

Gravitational redshift and the vacuum index of refraction

  • Klaus Wilhelm
  • Bhola N. DwivediEmail author
Original Article
  • 12 Downloads

Abstract

A physical process of the gravitational redshift was described in an earlier paper (Wilhelm and Dwivedi, New Astron. 31:8, 2014). This process did not require any information for the emitting atom neither on the local gravitational potential \(U\) nor on the speed of light \(c\). Although it could be shown that the correct energy shift of the emitted photon resulted from energy and momentum conservation principles and the speed of light at the emission site, it was not obvious how this speed is controlled by the gravitational potential. The aim of this paper is to describe a physical process that can accomplish this control. We determine the local speed of light \(c\) by deducing a gravitational index of refraction \(n_{\mathrm{G}}\) as a function of the potential \(U\) assuming a specific aether model, in which photons propagate as solitons. Even though an atom cannot locally sense the gravitational potential \(U\) (cf. Müller et al., Nature 467:E2, 2010) the gravitational redshift will nevertheless be determined by \(U\) (cf. Wolf et al., Nature 467:E1, 2010)—mediated by the local speed of light \(c\).

Keywords

Gravitation Impact model Aether Gravitational index of refraction 

Notes

Acknowledgements

This research has made extensive use of the Smithsonian Astrophysical Observatory (SAO)/National Aeronautics and Space Administration (NASA) Astrophysics Data System (ADS). Administrative support has been provided by the Max-Planck-Institute for Solar System Research and the Indian Institute of Technology (Banaras Hindu University).

References

  1. Abraham, M.: Prinzipien der Dynamik des Elektrons. Ann. Phys. (Leipz.) 310, 501 (1903) zbMATHGoogle Scholar
  2. Amsler, C., Doser, M., Antonelli, M., et al.: Review of particle physics. Phys. Lett. B 667, 1 (2008) ADSCrossRefGoogle Scholar
  3. Ashby, N., Allan, D.W.: Practical implications of relativity for a global coordinate time scale. Radio Sci. 14, 649 (1979) ADSCrossRefGoogle Scholar
  4. Ballmer, S., Márka, S., Shawhan, P.: Feasibility of measuring the Shapiro time delay over meter-scaled distances. Class. Quantum Gravity 27, 185018 (2010) ADSzbMATHCrossRefGoogle Scholar
  5. Bauch, A., Weyers, S.: New experimental limit on the validity of local position invariance. Phys. Rev. D 65, 081101 (2002) ADSCrossRefGoogle Scholar
  6. Bersons, I.: Soliton model of the photon. Latv. J. Phys. Tech. Sci. 50, 60 (2013) Google Scholar
  7. Bersons, I., Veilande, R., Pirktinsh, A.: Three-dimensional collinearly propagating solitons. Phys. Scr. 89, 045102 (2014) ADSCrossRefGoogle Scholar
  8. Blamont, J.E., Roddier, F.: Precise observation of the profile of the Fraunhofer strontium resonance line. Evidence for the gravitational red shift on the Sun. Phys. Rev. Lett. 7, 437 (1961) ADSCrossRefGoogle Scholar
  9. Bondi, H.: Relativity theory and gravitation. Eur. J. Phys. 7, 106 (1986) CrossRefGoogle Scholar
  10. Boonserm, P., Cattoen, C., Faber, T., Visser, M., Weinfurtner, S.: Effective refractive index tensor for weak-field gravity. Class. Quantum Gravity 22, 1905 (2005) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  11. Bopp, K.: Fatio de Duillier: De la cause de la pesanteur. Schriftenr. Strassbg. Wiss. Ges. Heidelb. 10, 19 (1929) Google Scholar
  12. Brault, J.W.: The gravitational redshift in the solar spectrum. Ph.D. Diss. Princeton University (1962) Google Scholar
  13. Brault, J.W.: Gravitational redshift of solar lines. Bull. Am. Astron. Soc. 8, 28 (1963) Google Scholar
  14. Cacciani, A., Briguglio, R., Massa, F., Rapex, P.: Precise measurement of the solar gravitational red shift. Celest. Mech. Dyn. Astron. 95, 425 (2006) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  15. Chen, B., Kantowski, R.: Cosmology with a dark refraction index. Phys. Rev. D 78, 044040 (2008) ADSGoogle Scholar
  16. Chou, C.W., Hume, D.B., Rosenband, T., Wineland, D.J.: Optical clocks and relativity. Science 329, 1630 (2010) ADSCrossRefGoogle Scholar
  17. Cranshaw, T.E., Schiffer, J.P., Whitehead, A.B.: Measurement of the gravitational red shift using the Mössbauer effect in \(\mbox{Fe}^{57}\). Phys. Rev. Lett. 4, 163 (1960) ADSCrossRefGoogle Scholar
  18. de Broglie, L.: Ondes et quanta. C. R. 177, 507 (1923) Google Scholar
  19. Desloge, E.A.: The gravitational red shift in a uniform field. Am. J. Phys. 58, 856 (1990) ADSCrossRefGoogle Scholar
  20. Dicke, R.H.: Eötvös experiment and the gravitational red shift. Am. J. Phys. 28, 344 (1960) ADSCrossRefGoogle Scholar
  21. Dirac, P.A.M.: The quantum theory of the emission and absorption of radiation. Proc. R. Soc. Lond. Ser. A 114, 243 (1927) ADSzbMATHCrossRefGoogle Scholar
  22. Dirac, P.A.M.: Is there an æther? Nature 168, 906 (1951) ADSMathSciNetCrossRefGoogle Scholar
  23. 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) ADSCrossRefGoogle Scholar
  24. Earman, J., Glymour, C.: The gravitational red shift as a test of general relativity: history and analysis. Stud. Hist. Philos. Sci. A 11, 175 (1980) MathSciNetCrossRefGoogle Scholar
  25. Einstein, A.: Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Ann. Phys. (Leipz.) 322, 132 (1905a) ADSzbMATHCrossRefGoogle Scholar
  26. Einstein, A.: Zur Elektrodynamik bewegter Körper. Ann. Phys. (Leipz.) 322, 891 (1905b) ADSzbMATHCrossRefGoogle Scholar
  27. Einstein, A.: Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen. Jahrb. Radioakt. Elektron. 1907(4), 411 (1908) Google Scholar
  28. Einstein, A.: Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes. Ann. Phys. (Leipz.) 340, 898 (1911) ADSzbMATHCrossRefGoogle Scholar
  29. Einstein, A.: Lichtgeschwindigkeit und Statik des Gravitationsfeldes. Ann. Phys. (Leipz.) 343, 355 (1912) ADSzbMATHCrossRefGoogle Scholar
  30. Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. (Leipz.) 354, 769 (1916) ADSzbMATHCrossRefGoogle Scholar
  31. Einstein, A.: Zur Quantentheorie der Strahlung. Phys. Z. XVIII, 121 (1917) Google Scholar
  32. Einstein, A.: Äther und Relativitätstheorie. Rede gehalten am 5. Mai 1920 an der Reichs-Universität zu Leiden. Springer, Berlin (1920) zbMATHGoogle Scholar
  33. Einstein, A.: Über den Äther. Verh. Schweiz. Naturforsch. Gesell. 105, 85 (1924) Google Scholar
  34. Ellis, R.S.: Gravitational lensing: a unique probe of dark matter and dark energy. Philos. Trans. R. Soc., Math. Phys. Eng. Sci. 368, 967 (2010) ADSzbMATHCrossRefGoogle Scholar
  35. Fatio de Duillier, N.: De la cause de la pesanteur (1690). Notes Rec. R. Soc. Lond. 6, 125 (1949) CrossRefGoogle Scholar
  36. Fermi, E.: Quantum theory of radiation. Rev. Mod. Phys. 4, 87 (1932) ADSzbMATHCrossRefGoogle Scholar
  37. Feynman, R.P., Morinigo, F.B., Wagner, W.G.: In: Hatfield, B. (ed.) Feynman Lectures on Gravitation. Addison-Wesley, Reading (1995) Google Scholar
  38. Fließbach, T.: Allgemeine Relativitätstheorie. Elsevier/Spektrum Akademischer Verlag, Heidelberg (2006) zbMATHGoogle Scholar
  39. Gagnebin, B.: Introduction: 1. Nicolas Fation de Duillier, 2. La commuication de Fatio de Duillier, 3. Les manuscrits de Fatio de Duillier. Notes Rec. R. Soc. Lond. 6, 105 (1949) CrossRefGoogle Scholar
  40. Goldhaber, A.S., Nieto, M.M.: Terrestrial and extraterrestrial limits on the photon mass. Rev. Mod. Phys. 43, 277 (1971) ADSCrossRefGoogle Scholar
  41. Granek, G.: Einstein’s ether: F. Why did Einstein come back to the ether? Apeiron 8, 19 (2001) Google Scholar
  42. Hay, H.J., Schiffer, J.P., Cranshaw, T.E., Egelstaff, P.A.: Measurement of the red shift in an accelerated system using the Mössbauer effect in \(\mbox{Fe}^{57}\). Phys. Rev. Lett. 4, 165 (1960) ADSCrossRefGoogle Scholar
  43. Hentschel, K.: The discovery of the redshift of solar Fraunhofer lines by Rowland and Jewell in Baltimore around 1890. Hist. Stud. Phys. Biol. Sci. 23, 219 (1993a) CrossRefGoogle Scholar
  44. Hentschel, K.: The conversion of St. John: a case study on the interplay of theory and experiment. Sci. Context 6, 137 (1993b) MathSciNetCrossRefGoogle Scholar
  45. Hentschel, K.: Measurements of gravitational redshift between 1959 and 1971. Ann. Sci. 53, 269 (1996) CrossRefGoogle Scholar
  46. Jackson, J.D.: Klassische Elektrodynamik, vol. 4. de Gruyter, Berlin (2006) CrossRefGoogle Scholar
  47. Jewell, L.E.: The coincidence of solar and metallic lines. A study of the appearence of lines in the spectra of the electric arc and the Sun. Astrophys. J. 3, 89 (1896) ADSCrossRefGoogle Scholar
  48. Kamenov, P., Slavov, B.: The photon as a soliton. Found. Phys. Lett. 11, 325 (1998) CrossRefGoogle Scholar
  49. Kollatschny, W.: AGN black hole mass derived from the gravitational redshift in optical lines. Proc. IAU Symp. 222, 105 (2004) ADSCrossRefGoogle Scholar
  50. Kramer, M., Stairs, I.H., Manchester, R.N., et al.: Tests of general relativity from timing the double pulsar. Science 314, 97 (2006) ADSCrossRefGoogle Scholar
  51. Krause, I.Y., Lüders, G.: Experimentelle Prüfung der Relativitätstheorie mit Kernresonanzabsorption. Naturwissenschaften 48, 34 (1961) ADSCrossRefGoogle Scholar
  52. 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
  53. Lämmerzahl, C.: What determines the nature of gravity? A phenomenological approach. Space Sci. Rev. 148, 501 (2009) ADSCrossRefGoogle Scholar
  54. Landau, L., Lifchitz, E.: Théorie Quantique Relativiste I. Mir, Moscow (1972) zbMATHGoogle Scholar
  55. Lewis, G.N.: The conservation of photons. Nature 118, 874 (1926) ADSCrossRefGoogle Scholar
  56. LoPresto, J.C., Chapman, R.D., Sturgis, E.A.: Solar gravitational redshift. Sol. Phys. 66, 245 (1980) ADSCrossRefGoogle Scholar
  57. LoPresto, J.C., Schrader, C., Pierce, A.K.: Solar gravitational redshift from the infrared oxygen triplet. Astrophys. J. 376, 757 (1991) ADSCrossRefGoogle Scholar
  58. Mannheim, P.D.: Alternatives to dark matter and dark energy. Prog. Part. Nucl. Phys. 56, 340 (2006) ADSCrossRefGoogle Scholar
  59. Meulenberg, A.: The photonic soliton. Proc. SPIE 8832, 88320M (2013) ADSCrossRefGoogle Scholar
  60. Michelson, A.A., Morley, E.W.: On the relative motion of the Earth and of the luminiferous ether. Sidereal Messenger 6, 306 (1887) ADSzbMATHGoogle Scholar
  61. Michelson, A.A., Lorentz, H.A., Miller, D.C., Kennedy, R.J., Hedrick, E.R., Epstein, P.S.: Conference on the Michelson–Morley experiment held at Mount Wilson, February, 1927. Astrophys. J. 68, 341 (1928) ADSCrossRefGoogle Scholar
  62. Mikhailov, A.A.: The deflection of light by the gravitational field of the Sun. Mon. Not. R. Astron. Soc. 119, 593 (1959) ADSMathSciNetCrossRefGoogle Scholar
  63. Møller, C.: On the possibility of terrestrial tests of the general theory of relativity. Nuovo Cimento 6, 381 (1957) MathSciNetzbMATHCrossRefGoogle Scholar
  64. Müller, H., Peters, A., Chu, S.: Müller, Peters and Chu reply. Nature 467, E2 (2010) ADSCrossRefGoogle Scholar
  65. Negi, P.S.: An upper bound on the energy of a gravitationally redshifted electron-positron annihilation line from the Crab pulsar. Astron. Astrophys. 431, 673 (2005) ADSCrossRefGoogle Scholar
  66. Nimtz, G., Stahlhofen, A.A.: Universal tunneling time for all fields. Ann. Phys. (Berlin) 17, 374 (2008) ADSCrossRefGoogle Scholar
  67. Ohanian, H.C.: Gravitation and Spacetime. Norton, New York (1976) zbMATHGoogle Scholar
  68. Okun, L.B.: Photons and static gravity. Mod. Phys. Lett. A 15, 1941 (2000) ADSCrossRefGoogle Scholar
  69. Okun, L.B., Selivanov, K.G., Telegdi, V.L.: On the interpretation of the redshift in a static gravitational field. Am. J. Phys. 68, 115 (2000) ADSCrossRefGoogle Scholar
  70. Pasquini, L., Melo, C., Chavero, C., Dravins, D., Ludwig, H.-G., Bonifacio, P., de La Reza, R.: Gravitational redshifts in main-sequence and giant stars. Astron. Astrophys. 526, A127 (2011) ADSCrossRefGoogle Scholar
  71. Poincaré, H.: La théorie de Lorentz et le principe de réaction. Arch. Neerl. Sci. Exactes Nat. 5, 252 (1900) zbMATHGoogle Scholar
  72. Pound, R.V.: Weighing photons. Class. Quantum Gravity 17, 2303 (2000) ADSzbMATHCrossRefGoogle Scholar
  73. Pound, R.V., Rebka, G.A.: Gravitational red-shift in nuclear resonance. Phys. Rev. Lett. 3, 439 (1959) ADSCrossRefGoogle Scholar
  74. Pound, R.V., Snider, J.L.: Effect of gravity on gamma radiation. Phys. Rev. 140, 788 (1965) ADSCrossRefGoogle Scholar
  75. Preston, S.T.: Physics of the Ether. Spon, London (1875) Google Scholar
  76. Quinn, T., Speake, C., Parks, H., Davis, R.: The BIPM measurements of the Newtonian constant of gravitation. Phys. Rev. Lett. 112, 039901 (2014) ADSCrossRefGoogle Scholar
  77. Randall, L.: Verborgene Universen, 4. Aufl. S. Fischer Verlag GmbH, Frankfurt/Main (2006) Google Scholar
  78. Reasenberg, R.D., Shapiro, I.I., MacNeil, P.E., et al.: Viking relativity experiment: verification of signal retardation by solar gravity. Astrophys. J. 234, L219 (1979) ADSCrossRefGoogle Scholar
  79. Rowland, H.A.: On a table of standard wave lengths of the spectral lines. Mem. Am. Acad. Arts Sci. New Ser. 12, 101 (1896) Google Scholar
  80. Schiff, L.I.: On experimental tests of the general theory of relativity. Am. J. Phys. 28, 340 (1960) ADSMathSciNetCrossRefGoogle Scholar
  81. Schröder, W.: Ein Beitrag zur frühen Diskussion um den Äther und die Einsteinsche Relativitätstheorie. Ann. Phys. 7, 475 (1990) CrossRefGoogle Scholar
  82. Scott, R.B.: Teaching the gravitational redshift: lessons from the history and philosophy of physics. J. Phys. Conf. Ser. 600, 012055 (2015) CrossRefGoogle Scholar
  83. Shapiro, I.I.: Fourth test of general relativity. Phys. Rev. Lett. 13, 789 (1964) ADSMathSciNetCrossRefGoogle Scholar
  84. Shapiro, I.I., Ash, M.E., Ingalls, R.P., et al.: Fourth test of general relativity: new radar result. Phys. Rev. Lett. 26, 1132 (1971) ADSCrossRefGoogle Scholar
  85. Sinha, S., Samuel, J.: Atom interferometry and the gravitational redshift. Class. Quantum Gravity 28, 145018 (2011) ADSzbMATHCrossRefGoogle Scholar
  86. Snider, J.L.: Atomic-beam study of the solar 7699 Å potassium line and the solar gravitational red-shift. Sol. Phys. 12, 352 (1970) ADSCrossRefGoogle Scholar
  87. Snider, J.L.: New measurement of the solar gravitational red shift. Phys. Rev. Lett. 28, 853 (1972) ADSCrossRefGoogle Scholar
  88. 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. 1804, 161 (1804) Google Scholar
  89. Sommerfeld, A.: Optik. Verlag Harri Deutsch, Thun, Frankfurt/Main (1978) zbMATHGoogle Scholar
  90. Sotiriou, T.P., Liberati, S., Faraoni, V.: Theory of gravitation theories: a no-progress report. Int. J. Mod. Phys. D 17, 399 (2008) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  91. St. John, C.E.: Evidence for the gravitational displacement of lines in the solar spectrum predicted by Einstein’s theory. Astrophys. J. 67, 195 (1928) ADSCrossRefGoogle Scholar
  92. Straumann, N.: General Relativity with Applications to Astrophysics. Springer, Berlin (2004) zbMATHGoogle Scholar
  93. Takeda, Y., Ueno, S.: Detection of gravitational redshift on the solar disk by using iodine-cell technique. Sol. Phys. 281, 551 (2012) ADSCrossRefGoogle Scholar
  94. Turyshev, S.G.: Testing fundamental gravitation in space. Nucl. Phys. B, Proc. Suppl. 243, 197 (2013) ADSCrossRefGoogle Scholar
  95. Vessot, R.F.C., Levine, M.W., Mattison, E.M., et al.: Test of relativistic gravitation with a space-borne hydrogen maser. Phys. Rev. Lett. 45, 2081 (1980) ADSCrossRefGoogle Scholar
  96. Vigier, J.-P.: Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons “piloted” (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations. Found. Phys. 21, 125 (1991) ADSMathSciNetCrossRefGoogle Scholar
  97. von Laue, M.: Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung. Phys. Z. XIII, 118 (1912) zbMATHGoogle Scholar
  98. von Laue, M.: Zur Theorie der Rotverschiebung der Spektrallinien an der Sonne. Z. Phys. 3, 389 (1920) ADSCrossRefGoogle Scholar
  99. von Laue, M.: Geschichte der Physik, 4. erw. Aufl. Ullstein Taschenbücher-Verlag, Frankfurt/Main (1959) Google Scholar
  100. Wiechert, E.: Relativitätsprinzip und Äther. Phys. Z. 12, 689, 737 (1911) zbMATHGoogle Scholar
  101. Wilhelm, K., Dwivedi, B.N.: Gravity, massive particles, photons and Shapiro delay (paper 2). Astrophys. Space Sci. 343, 145 (2013) ADSCrossRefGoogle Scholar
  102. Wilhelm, K., Dwivedi, B.N.: On the gravitational redshift. New Astron. 31, 8 (2014) ADSCrossRefGoogle Scholar
  103. Wilhelm, K., Dwivedi, B.N.: On the potential energy in a gravitationally bound two-body system with arbitrary mass distribution (2015). arXiv:1502.05662v2
  104. Wilhelm, K., Wilhelm, H., Dwivedi, B.N.: An impact model of Newton’s law of gravitation (Paper 1). Astrophys. Space Sci. 343, 135 (2013) ADSzbMATHCrossRefGoogle Scholar
  105. Wilhelm, K., Dwivedi, B.N., Wilhelm, H.: An impact model of the electrostatic force: Coulomb’s law re-visited (2014). arXiv:1403.1489v5
  106. Will, C.M.: Gravitational red-shift measurements as tests of nonmetric theories of gravity. Phys. Rev. D 10, 2330 (1974) ADSMathSciNetCrossRefGoogle Scholar
  107. Will, C.M.: The confrontation between general relativity and experiment. Living Rev. Relativ. 9, 3 (2006) ADSzbMATHCrossRefGoogle Scholar
  108. Wolf, P., Blanchet, L., Bordé, C.J., Reynaud, S., Salomon, C., Cohen-Tannoudji, C.: Atom gravimeters and gravitational redshift. Nature 467, E1 (2010) ADSCrossRefGoogle Scholar
  109. Ye, X.-H., Lin, Q.: Gravitational lensing analysed by the graded refractive index of a vacuum. J. Opt. A, Pure Appl. Opt. 10, 075001 (2008) ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Max-Planck-Institut für Sonnensystemforschung (MPS)GöttingenGermany
  2. 2.Department of PhysicsIndian Institute of Technology (Banaras Hindu University)VaranasiIndia

Personalised recommendations