Relativity of Mass: Mass Can Decrease with Velocity

Authors

  • Asutosh Kumar Department of Physics, KSS College, Lakhisarai 811311, India. P.G. Department of Physics, Munger University, Munger 811201, India. Vaidic and Modern Physics Research Centre, Bhagal Bhim, Bhinmal, Jalore 343029, India. https://orcid.org/0000-0001-9569-7450

DOI:

https://doi.org/10.22105/kmisj.v3i1.109

Keywords:

Relativity of mass, Velocity-dependent mass, Mass can decrease with velocity, Superluminal signaling, Photon mass, Rest mass vs intrinsic mass

Abstract

We present a simple approach for deriving velocity-dependent masses using the principle of relativity. Our analysis reveals that the transformations associated with Galilean, Lorentz, and other space-time frameworks between two inertial reference frames are fundamentally equivalent in the context of the relativity of mass. Consequently, the notion of velocity-dependent mass is not the exclusive characteristic of Special Relativity (Lorentz transformation). Among the notable conclusions drawn from our formalism are: mass can both increase and decrease with velocity, a particle can never be completely at rest, and superluminal signaling is in principle feasible. Furthermore, we discuss on the nature of mass and argue that a photon is not massless.

References

Newton, I. (1833). Philosophiae naturalis principia mathematica. George Brookman. https://openli-

brary.org/books/OL2669888M/Philosophiae_naturalis_principia_mathematica

Michelson, A. A., & Morley, E. W. (1887). On the relative motion of the earth and the luminiferous Ether. American journal of sci-

ence, 3(203), 333–345. https://history.aip.org/exhibits/gap/PDF/michelson.pdf

Lorentz, H. A. (1937). Electromagnetic phenomena in a system moving with any velocity smaller than that of light. In

Collected papers: Volume v (pp. 172-197). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-015-3445-1_5

Trageser, W. (2016). Zur elektrodynamik bewegter körper. In Das relativitätsprinzip (pp. 57–78). Springer Spektrum.

https://doi.org/10.1007/978-3-662-48039-7_4

Einstein, A., & Minkowski, H. (1920). The principle of relativity: Original papers. Manipal University, Jaipur.

http://localhost:8080/jspui/handle/123456789/1996

Bergmann, P. G. (1976). Introduction to the theory of relativity. Courier Corporation. https://books.google.com/books?

id=3cE9jXr_QhwC&printsec=frontcover#v=onepage&q&f=false

Resnick, R. (1991). Introduction to special relativity. John Wiley & Sons. https://www.wiley.com/en-us/shop/general-

physics/introduction-to-special-relativity-p-9780471717256

Goy, F. (1997). A derivation of three-dimensional inertial transformations. Foundations of physics letters, 10(4), 329-346.

https://doi.org/10.1007/BF02764104

Chen, H., Sha, W. E., Dai, X., & Yu, Y. (2022). On the low speed limits of Lorentz's transformation.

https://doi.org/10.48550/arXiv.2202.10242

Cushing, J. T. (1981). Electromagnetic mass, relativity, and the Kaufmann experiments (AAPT). American journal of

physics, 49, 1133- 1149. https://doi.org/10.1119/1.12561

Planck, M. (1906). Das prinzip der relativität und die grundgleichungen der mechanik. Verhandlungen der deutschen

physikalischen gesellschaft, 8, 136–141. https://cir.nii.ac.jp/crid/1573105975293111168

Beiser, A. (1987). Perspectives of modern physics. McGraw-Hill Book Company, Singapore. https://openli-

brary.org/works/OL3481327W/Perspectives_of_modern_physics

Feynman, R. P., Leighton, R. B., & Sands, M. (1989). The feynman lectures on physics. Narosa Publishing House, New

Delhi. https://www.academia.edu/79025714/The_Feynman_Lectures_on_Physics_Volume_1

Landau, L. D., & Lifshitz, E. M. (1971). The classical theory of fields. Pergamon Press (Oxford). https://openli-

brary.org/search?q=The+Classical+Theory+of+Fields+Landau+Lifshitz

Dikshit, B. (2015). A new approach in the derivation of relativistic variation of mass with speed. European journal of

physics, 36(3), 035005. https://doi.org/10.1088/0143-0807/36/3/035005

Hill, J. M., & Cox, B. J. (2016). Generalised Einstein mass-variation formulae: I subluminal relative frame velocities. Re-

sults in physics, 6, 112-121. https://doi.org/10.1016/j.rinp.2015.11.006

Hill, J. M., & Cox, B. J. (2016). Generalised Einstein mass-variation formulae: II superluminal relative frame velocities. Results

in physics, 6, 122-130. https://doi.org/10.1016/j.rinp.2016.02.002

Sharma, A. (2017). The various equations of variation of mass with velocity. Indian journal of science and technology, 10

(21), 1-10. https://doi.org/10.17485/ijst/2017/v10i21/96640

Beckmann, P. (1987). Einstein plus two. Golem Press, Boulder, Colorado. https://www.sciepub.com/reference/78069

McCausland, I. (2005). The persistent problem of special relativity. Physics essays, 18(4), 530.

https://doi.org/10.4006/1.3025766

Hatch, R. R. (1992). Escape from Einstein. Kneat Kompany. https://www.amazon.nl/-/en/Ronald-R-Hatch/dp/0963211307

Selleri, F. (1998). Open questions in relativistic physics. Open Questions in Relativistic Physics. https://openli-

brary.org/works/OL4495050W/Open_Questions_in_Relativistic_Physics

Dingle, H. (1972). Science at the crossroads. Martin Brian & O’Keeffe, London. https://www.ilglifo.it/pubblicazioni/Dingle_-

Science_at_the_Crossroads_Anteprima.pdf

Monti, R. A. (1996). Theory of relativity: A critical analysis. Physics essays, 9, 238-260. https://docslib.org/down-

load/4375428/theory-of-relativity-a-critical-analysis

Kelly, A. (2005). Challenging modern physics: Questioning Einstein's relativity theories. Universal-Publishers.

https://bookpump.com/bwp/pdf-b/1124376b.pdf

Marmet, P. (2006). The overlooked phenomena in the Michelson-Morley experiment. Galilean electrodynamics, 17(4), 63.

https://www.mahag.com/download/Marmet_Michelson.pdf

Perez, I. (2010). The physics surrounding the Michelson-Morley experiment and a new {AE} ther theory.

https://doi.org/10.48550/arXiv.1004.0716

Consoli, M., & Pluchino, A. (2023). Michelson–Morley experiments: At the crossroads of relativity, cosmology and Quantum

physics. International journal of modern physics a, 38(35n36), 2330017. https://doi.org/10.1142/S0217751X2330017X

Maggiore, M. (2011). Zero-point Quantum fluctuations and dark energy. Physical review D—Particles, fields, gravitation, and cos-

mology, 83(6), 063514. https://doi.org/10.1103/PhysRevD.83.063514

Clerk, A. (2012). Seeing the “Quantum” in Quantum zero-point fluctuations. Physics, 5, 8. https://physics.aps.org/articles/v5/8

Magueijo, J. (2003). New varying speed of light theories. Reports on progress in physics, 66(11), 2025-2068.

https://doi.org/10.1088/0034-4885/66/11/R04

Von Ignatowsky, W. (1911). Das relativitätsprinzip. Archiv der mathematik und physik, 3(17), 1-24. https://de.wik-

isource.org/wiki/Das_Relativit%C3%A4tsprinzip_%28Ignatowski%29

Weinstock, R. (1965). New approach to special relativity. American journal of physics, 33(8), 640-645.

https://doi.org/10.1119/1.1972047

Mitvalský, V. (1966). Special relativity without the postulate of constancy of light. American journal of physics, 34(9), 825-825.

https://doi.org/10.1119/1.1973524

Berzi, V., & Gorini, V. (1969). Reciprocity principle and the Lorentz transformations. Journal of mathematical physics, 10(8),

-1524. https://doi.org/10.1063/1.1665000

Lee, A. R., & Kalotas, T. M. (1975). Lorentz transformations from the first postulate. American journal of physics, 43(5), 434-

https://doi.org/10.1119/1.9807

Lévy-Leblond, J. M. (1976). One more derivation of the Lorentz transformation. American journal of physics, 44(3), 271-277.

https://doi.org/10.1119/1.10490

Srivastava, A. M. (1981). Invariant speed in special relativity. American journal of physics, 49(5), 504-505.

https://doi.org/10.1119/1.12498

Mermin, N. D. (1984). Relativity without light. American journal of physics, 52(2), 119-124. https://doi.org/10.1119/1.13917

Schwartz, H. M. (1984). Deduction of the general Lorentz transformations from a set of necessary assumptions. American journal

of physics, 52(4), 346-350. https://doi.org/10.1119/1.13666

Schwartz, H. M. (1985). A simple new approach to the deduction of the Lorentz transformations. American journal of physics, 53

(10), 1007-1008. https://doi.org/10.1119/1.13989

Singh, S. (1986). Lorentz transformations in Mermin’s relativity without light. American journal of physics, 54(2), 183-184.

https://doi.org/10.1119/1.14689

Sen, A. (1994). How Galileo could have derived the special theory of relativity. American journal of physics, 62(2), 157-162.

https://doi.org/10.1119/1.17636

Pal, P. B. (2003). Nothing but relativity. European journal of physics, 24(3), 315-319. https://doi.org/10.1088/0143-

/24/3/312

Shen, J. Q. (2005). Lorentz, Edwards transformations and the principle of permutation invariance.

https://doi.org/10.48550/arXiv.physics/0509012

Feigenbaum, M. J. (2008). The theory of relativity-Galileo's child. https://doi.org/10.48550/arXiv.0806.1234

Tangherlini, F. R. (2014). Galilean-like transformation allowed by general covariance and consistent with special relativity.

Journal of modern physics, 5(5), 230-243. https://doi.org/10.4236/jmp.2014.55033

Pelissetto, A., & Testa, M. (2015). Getting the Lorentz transformations without requiring an invariant speed. American journal

of physics, 83(4), 338-340. https://doi.org/10.1119/1.4901453

Galiautdinov, A. (2017). Derivation of the Lorentz transformation without the use of Einstein's second postulate.

https://doi.org/10.48550/arXiv.1701.00270

Guo, H. (2021). A new paradox and the reconciliation of Lorentz and Galilean transformations. Synthese, 199(3), 8113-8142.

https://doi.org/10.1007/s11229-021-03155-y

Datta, S. (2022). A revisit to Lorentz transformation without light. https://doi.org/10.48550/arXiv.2212.03706

Redžić, D. V. (2026). Relativity with or without light and Maxwell. Time and space, 2(2), 4. https://doi.org/10.3390/times-

pace2020004

Kassir, R. M. (2014). The critical error in the formulation of the special relativity. International journal of physics, 2(6), 197-201.

https://doi.org/10.12691/ijp-2-6-3

Buenker, R. J. (2022). Proof that the Lorentz transformation is incompatible with the law of causality. East African scholars

journal of engineering and computer sciences, 5(4), 53-54. https://doi.org/10.36349/easjecs.2022.v05i04.002

Asokan, S. P. (2021). Special relativity sans Lorentz transformation (OR) perceptional relativity. https://doi.org/10.21203/rs.3.rs-

/v3

Voigt, W. (1887). Ueber das doppler’sche princip. Nachr ges wiss, 41(2), 41-51. https://hodge-podge.narod.ru/Relativ-

ity/Voigt.pdf

Heras, R. (2014). A review of Voigt's transformations in the framework of special relativity.

https://doi.org/10.48550/arXiv.1411.2559

Selleri, F. (1996). Noninvariant one-way velocity of light. Foundations of physics, 26(5), 641-664.

https://doi.org/10.1007/BF02058237

Selleri, F. (1997). Inertial transformations: A review. In The present status of the Quantum theory of light (pp. 379–407). Springer.

https://doi.org/10.1007/978-94-011-5682-0_40

Edwards, W. F. (1963). Special relativity in anisotropic space. American journal of physics, 31(7), 482–489.

https://doi.org/10.1119/1.1969607

Edwards, W. F. (1963). Special relativity in anisotropic space. American journal of physics, 31(7), 482–489.

https://doi.org/10.1119/1.1969607

Adler, C. G. (1987). Does mass really depend on velocity, dad? American journal of physics, 55(8), 739-743.

https://doi.org/10.1119/1.15314

Whitney, C. (2005). Does mass really increase. Galilean electrodynamics, 16, 57-58. https://physics.stackexchange.com/ques-

tions/358325/does-the-mass-of-object-really-increase

Okun, L. B. (2008). The Einstein formula: E 0= mc 2." Isn't the Lord laughing?". Physics-uspekhi, 51(5), 513-527.

https://doi.org/10.1070/PU2008v051n05ABEH006538

Einstein, A. (1935). Elementary derivation of the equivalence of mass and energy. Bulletin American mathematical society, 41(4),

-230. https://doi.org/10.1090/S0002-9904-1935-06046-X

Steck, D. J., & Rioux, F. (1983). An elementary development of mass–energy equivalence. American journal of physics, 51(5),

–462. https://doi.org/10.1119/1.13238

Rohrlich, F. (1990). An elementary derivation of E= mc 2. American journal of physics, 58(4), 348-349.

https://doi.org/10.1119/1.16168

Peliti, L. (2016). Elementary derivation of the expressions of momentum and energy in special relativity. Revista brasileira de en-

sino de física, 38(2), e2312. https://doi.org/10.1590/1806-9126-rbef-2015-0029

Nenashev, A. V., Baranovskii, S. D., & Gebhard, F. (2023). A pedestrian approach to Einstein's formula $ E= mc^ 2$ with an appli-

cation to photon dynamics. https://doi.org/10.48550/arXiv.2308.02612

Sharma, A. (2004). The origin of the generalized mass-energy equation ΔE= Ac²ΔM and its applications in general physics and

cosmology. Physics essays, 17(2), 195. https://doi.org/10.4006/1.3025675

Sabarish, V. M. (2020). Apparent weight of a photon box: Revisiting mass-energy equivalence. Resonance, 25(7), 911-914.

https://doi.org/10.1007/s12045-020-1008-9

Weinberg, S. (1995). The Quantum theory of fields. Volume 1: Foundations. Cambridge University Press. https://pierre.ag.ger-

ard.web.ulb.be/textbooks/books/The_Quantum_Theory_of_Fields_1.pdf

Matsko, A. B., Rostovtsev, Y., Welch, G. R., Zibrov, A. S., & Scully, M. O. (2001). Slow, ultraslow, stored, and frozen light. In

Advances in atomic, molecular, and optical physics (Vol. 46, pp. 191-242). Academic Press. https://doi.org/10.1016/S1049-250X (01)80064-1

Khurgin, J. B. (2010). Slow light in various media: A tutorial. Advances in optics and photonics, 2(3), 287-318.

https://doi.org/10.1364/AOP.2.000287

Georgescu, I. (2012). Frozen light switch. Nature physics, 8(4), 252-252. https://doi.org/10.1038/nphys2290

Fleischhauer, M., & Juzeliūnas, G. (2016). Slow, stored and stationary light. In Optics in our time (pp. 359-383). Cham: Springer

International Publishing. https://doi.org/10.1007/978-3-319-31903-2_15

Trypogeorgos, D., Gianfrate, A., Landini, M., Nigro, D., Gerace, D., Carusotto, I., ... & Sanvitto, D. (2025). Emerging superso-

lidity in photonic-crystal polariton condensates. Nature, 639(8054), 337-341. https://doi.org/10.1038/s41586-025-08616-9

Albanay, Y. A. (2013). Special theory of relativity for photons. Soviet physics uspekhi, 11, 338–341.

https://doi.org/10.3367/UFNr.0095.196805i.0131

Franken, P. A., & Ampulski, G. W. (1971). Photon rest mass. Physical review letters, 26(2), 115. https://doi.org/10.1103/Phys-

RevLett.26.115

Okun, L. B. (1989). The concept of mass. Physics today, 42(6), 31-36. https://doi.org/10.1063/1.881171

Lakes, R. (1998). Experimental limits on the photon mass and cosmic magnetic vector potential. Physical review letters, 80(9),

https://doi.org/10.1103/PhysRevLett.80.1826

Tu, L. C., & Luo, J. (2004). Experimental tests of Coulomb's law and the photon rest mass. Metrologia, 41(5), S136-S146.

https://doi.org/10.1088/0026-1394/41/5/S04

Tu, L. C., Luo, J., & Gillies, G. T. (2005). The mass of the photon. Reports on progress in physics, 68(1), 77-130.

https://doi.org/10.1088/0034-4885/68/1/R02

Ryutov, D. D. (2007). Using plasma physics to weigh the photon. Plasma physics and controlled fusion, 49(12b), b429-b438.

https://doi.org/10.1088/0741-3335/49/12B/S40

Goldhaber, A. S., & Nieto, M. M. (2010). Photon and graviton mass limits. Reviews of modern physics, 82(1), 939-979.

https://doi.org/10.1103/RevModPhys.82.939

Goldhaber, A. S., & Nieto, M. M. (2010). Photon and graviton mass limits. Reviews of modern physics, 82(1), 939-979.

https://doi.org/10.1103/RevModPhys.82.939

Nyambuya, G. G. (2014). Are photons massless or massive. Journal of modern physics, 5(10), 1-35.

http://dx.doi.org/10.4236/jmp.2014.518207

Van der Mark, M. B. (2015). Light is heavy. https://doi.org/10.48550/arXiv.1508.06478

Marchal, C. (2019). LIGO: The hypothesis of photons with non-zero rest mass. Journal of physics: Conference series (Vol. 1251,

No. 1, p. 012034). IOP Publishing. https://doi.org/10.1088/1742-6596/1251/1/012034

Ahmed, A. M. K., Yousif, M. A. M., Kurawa, Z. M., Saad, Z. A. A. A., Makawy, S. S., Mohammed, M. I., ... & Mohammed, S.

A. E. (2020). Determination of Photon and elementary particles rest masses using Maxwell’s equations and generalized potential dependent special relativity. Natural science, 12(8), 588–598. https://doi.org/10.4236/ns.2020.128045

Friedman, Y., & Gofman, Y. (2002). Relativistic linear spacetime transformations based on symmetry. Foundations of physics, 32

(11), 1717–1736. https://doi.org/10.1023/A:1021450706566

Bars, I., & Kounnas, C. (1997). Theories with two times. Physics letters b, 402(1-2), 25-32. https://doi.org/10.1016/S0370-2693

(97)00452-8

Zahir, S. (2023). Extra time dimension: Deriving relativistic space-time transformations, kinematics, and example of dimen-

sional compactification using time-dependent non-relativistic Quantum mechanics. Journal of modern physics, 14(10), 1333-1354. https://doi.org/10.4236/jmp.2023.1410077

Kletetschka, G. (2025). Three-dimensional time: A mathematical framework for fundamental physics. Reports in advances of

physical sciences, 9, 2550004. https://doi.org/10.1142/S2424942425500045

Published

2026-06-17

How to Cite

Kumar, A. (2026). Relativity of Mass: Mass Can Decrease with Velocity. Karshi Multidisciplinary International Scientific Journal, 3(1), 1-12. https://doi.org/10.22105/kmisj.v3i1.109

Similar Articles

You may also start an advanced similarity search for this article.