Mass-energy equivalence and the gravitational redshift: Does energy always have mass?

Ariticle ID: 525
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Keywords: special relativity; general relativity; mass-energy equivalence; gravitational frequency shift; conservation of energy; conservation of linear momentum; thought experiments


One of the most widespread interpretations of the mass-energy equivalence establishes that not only can mass be transformed into energy (e.g., through nuclear fission, fusion, or annihilation) but that every type of energy also has mass (via the mass-energy equivalence formula). Here, we show that this is not always the case. With the help a few thought experiments, we show that, for instance, the electric potential energy of a charged capacitor should not contribute to the capacitor’s gravitational rest mass (while still contributing to its linear momentum). That result is in agreement with the fact that light (ultimately, an electromagnetic phenomenon) has momentum but not rest mass.


[1] Einstein A. Is the inertia of a body dependent on its energy content (German)? Annalen der Physik. 1905; 323(13): 639-641. doi: 10.1002/andp.19053231314

[2] Planck M. On the dynamics of moving systems. Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, Berlin, Erster Halbband. 1907; 29: 542–570.

[3] Laue M. On the Dynamics of the Theory of Relativity. Annalen der Physik. 1911; 340 (8): 524–542.

[4] Klein F. On the Integral Form of the Conservation Laws and the Theory of the Spatially Closed World. Nachr. Königl. Gesells. Wissensch. Göttingen. 1918; 394–423.

[5] Einstein A. An Elementary Derivation of the Equivalence of Mass and Energy (1946). In: Out of My Later Years: The Scientist, Philosopher, and Man Portrayed Through His Own Words. Philosophical Library, New York; 1950.

[6] Ives Herbert E. 1952 Derivation of the mass-energy relation. J. Opt. Soc. Am. 1952; 42(8): 540–543.

[7] Jammer M. Concepts of Mass in Classical and Modern Physics. Dover; 1961.

[8] Stachel J, Torretti R. Einstein’s first derivation of mass-energy equivalence. Am. J. Phys. 1982; 50(8): 760–763. doi: 10.1119/1.12764

[9] Rohrlich F. An Elementary Derivation of E = mc2. Am. J. Phys. 1990; 58: 348–350. doi: 10.1119/1.16168

[10] Ohanian H. Did Einstein prove E = mc2? Studies in History and Philosophy of Science Part B 2009; 40(2): 167–173. doi: 10.1016/j.shpsb.2009.03.002

[11] Ohanian H. Einstein’s Mistakes: The Human Failings of Genius. W.W. Norton; 2009.

[12] Hecht E. How Einstein confirmed E = mc2. Am. J. Phys. 2011; 79(6): 591–600. doi: 10.1119/1.3549223

[13] D’Abramo G. Mass-energy connection without special relativity. Eur. J. Phys. 2020; 42(1): 015606. doi: 10.1088/1361-6404/abbca2

[14] The Equivalence of Mass and Energy, Stanford Encyclopedia of Philosophy. Available online: (accessed on 22 August 2023).

[15] D’Abramo G. Einstein’s 1905 derivation of the mass-energy equivalence: is it valid? Is energy always equal to mass and vice versa? Phys. Part. Nuclei 2023; 54(5): 966–971. doi: 10.1134/S1063779623050076

[16] Misner CW, Thorne KS, Wheeler JA. Gravitational Red Shift Derived From Energy Conservation. In: Gravitation. W.H. Freeman; 1973.

[17] D’Abramo G. Sound escapes any gravity well. Phys. Educ. 2024; 59(3): 035011. doi: 10.1088/1361-6552/ad2ffa

[18] Singal KA. Contribution of electric self-forces to electromagnetic momentum in a moving system. Available online: (accessed on 31 October 2023).

How to Cite
D’Abramo, G. (2024). Mass-energy equivalence and the gravitational redshift: Does energy always have mass?. Journal of AppliedMath, 2(2), 525.