Gravitational redshift explained as a Doppler Effect in uniformly accelerated frames

  • A. Sfarti CS Department, 387 Soda Hall, UC Berkeley, Berkeley, CA 94720, USA
Ariticle ID: 156
63 Views, 19 PDF Downloads
Keywords: Pound-Rebka, Gravitational Redshift, Tests of General Relativity, Einstein Equivalence Principle, Doppler Effect for uniformly accelerated motion, Error Analysis for Numerical Methods


Einstein predicted a change in the energy of photons in the proximity of a gravitational field, the change being directly proportional with the distance from the gravitational source. In the early 60’s Pound and Rebka have set to verify Einstein’s prediction. The experiment was reprised with even higher precision by Pound and Snider. Later, Vessot reprised the experiment in space at a much improved precision. The standard explanation of gravitational redshift falls out straight from the Schwarzschild solution of the Einstein Field Equations (EFE). In the following, we will present an approach to the experiment relying on the Einstein Equivalence Principle and on the recently derived expressions of Doppler Effect for uniformly accelerated motion of the source and the receiver. We will conclude with a chapter on the numerical limits of applicability of the described method.


[1] Pound RV, Rebka GA Jr. Resonant absorption of the 14.4-kev gamma Ray from 0.10-µsec Fe57. Physical Review Letters 1959; 3(12): 554. doi: 10.1103/PhysRevLett.3.554

[2] Pound RV, Snider JL. Effect of gravity on nuclear resonance. Physical Review Letters 1964; 13(18): 539–540. doi: 10.1103/physrevlett.13.539

[3] Vessot RFC, Levine MW, Mattison EM, et al. Test of relativistic gravitation with a space-borne hydrogen maser. Physical Review Letters 1980; 45(26): 2081–2084. doi: 10.1103/physrevlett.45.2081

[4] Einstein A. On the electrodynamics of moving bodies. Annalen der Physik 1905; 17: 891–921.

[5] Will CM. The confrontation between general relativity and experiment. Living Reviews in Relativity 2001; 4(1): 4. doi: 10.12942/lrr-2001-4

[6] Vessot RFC, Levine MW. A test of the equivalence principle using a space-borne clock. General Relativity and Gravitation 1979; 10(3): 181–204. doi: 10.1007/bf00759854

[7] Taylor JH. Astronomical and Space Experiments to Test Relativity. Cambridge University Press; 1987. pp. 209–222.

[8] Feynman RP, Wagner WG, Morinigo FB, et al. Feynman Lectures on Gravitation. Addison-Wesley; 1995.

[9] Misner CW, Thorne KS, Wheeler JA. Gravitation. W. H. Freeman and Company; 1973.

[10] Desloge EA. Nonequivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field. American Journal of Physics 1989; 57(12): 1121–1125. doi: 10.1119/1.15802

[11] Desloge EA. The gravitational red shift in a uniform field. American Journal of Physics 1990; 58(9): 856–858. doi: 10.1119/1.16349

[12] Dicke RH. New research on old gravitation. Science 1959; 129(3349): 621–624. doi: 10.1126/science.129.3349.621

[13] Dicke RH. Mach’s principle and equivalence. In: Møller C (editor). Evidence for Gravitational Theories: Proceedings of Course 20 of the International School of Physics “Enrico Fermi”. Academic Press; 1962.

[14] Einstein A. About the Principle of Relativity and the Conclusions Drawn from it (German). Jahrbuch der Radioaktivitaet und Elektronik; 1907.

[15] Einstein A. On the influence of gravity on the propagation of light. Annalen der Physik 1911; 340(10): 898–908. doi: 10.1002/andp.19113401005

[16] Brans CH. The roots of scalar-tensor theory: An approximate history. arXiv 2005; arXiv:gr-qc/0506063. doi: 10.48550/

[17] Ohanian HC, Ruffini R. Gravitation and Spacetime, 2nd ed. W. W. Norton & Company; 1994.

[18] Uzan JP. The fundamental constants and their variation: Observational and theoretical status. Reviews of Modern Physics 2003; 75(2): 403–455. doi: 10.1103/revmodphys.75.403

[19] Will CM. Theory and Experiment in Gravitational Physics. Cambridge University Press; 1993.

[20] Niebauer TM, Sasagawa GS, Faller JE, et al. A new generation of absolute gravimeters. Metrologia 1995; 32(3): 159–180. doi: 10.1088/0026-1394/32/3/004

[21] Peters A, Chung KY, Chu S. High-precision gravity measurements using atom interferometry. Metrologia 2001; 38(1): 25–61. doi: 10.1088/0026-1394/38/1/4

[22] Linet B, Teyssandier P. Time transfer and frequency shift to the order 1/c4 in the field of an axisymmetric rotating body. Physical Review D 2002; 66(2): 024045. doi: 10.1103/physrevd.66.024045

[23] Sfarti A. QED-based derivation of the general forms of the relativistic Doppler effect and of the relativistic aberration for uniformly rotating frames and for uniformly accelerated frames. Modern Physics Letters A 2022; 37: 37n38. doi: 10.1142/s0217732322502388

How to Cite
Sfarti, A. (2023). Gravitational redshift explained as a Doppler Effect in uniformly accelerated frames. Journal of AppliedMath, 1(2), 156.