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The Various Equations of Variation of Mass with Velocity


  • Fundamental Physics Society, His Mercy Enclave, Post Box 107 GPO Shimla – 171001, Himachal Pradesh, India


Objectives: The origin of various equations involving variation of mass with velocity is discussed and new exponential equation is derived. At lower velocity this equation and Lorentz equation both give same results. Methods/Statistical Analysis: The various references right from inception of concept of variation of mass with velocity are discussed. The basic common point in various equations is that invalid operation division by zero is involved. Initially such equation was initiated by Thomson, and used by following scientists. Thus aspects are theoretically discussed. Findings: A newly derived equation is exponential in nature and is interpreted in view of existing experimental observations. It does not involve division by zero, hence never predicts that mass becomes infinite when velocity of body, v =c. Lorentz has given equation for transverse mass mT = ε 􀟛 mrest , where is undetermined factor or coefficient differing from unity by quantity of the order v2/c2. Lorentz’s equation (relativistic mass) is experimentally verified by with reasonable accuracy up to velocity 0.75c. Thus Lorentz’s equation is confirmed in limited region. In LHC the protons have energy 13TeV move with velocity at about 0.9999 99990c, at this velocity the relativistic mass of proton must be experimentally measured and compared. Then it must be confirmed up to which extent Lorentz’s equation is obeyed. New theory of variability of speed of light implies that speed of light was more in the early universe. It supports exponential equation which allows superluminal velocity. Applications/ Improvements: The exponential equation is the first equation which provides extension in the Lorentz equation in conceptual and mathematical way. It stresses superluminal velocities at some stages of formation of universe. The exponential equation can be checked in experiments in LHC which involve velocities tending to that of light and other experiments.


Einstein, Exponential Equation, Lorentz, Relativistic Mass, Transverse Mass

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  • Stokes GG. On some cases of fluid motion on Internet Archive.Transactions of the Cambridge Philosophical Society. 1843; 8(1):105–37.
  • Thomson JJ. On the electric and magnetic effects produced by the motion of electrified bodies. Philosophical Magazine. 1881; 11(68):229–49. Crossref
  • Heaviside O. On the electromagnetic effects due to the motion of electrification through a dielectric. Philosophical Magazine Series 5. 1889; 27(167):324–39.
  • Thomson JJ. Notes on recent researches in electricity and magnetism on Internet Archive. Oxford: The Clarendon Press; 1893. p. 21.
  • Searle GG. On the steady motion of an electrified ellipsoid. Philosophical Magazine. 1897; 44(269):329–41. Crossref
  • Abraham M. Prinzipien der Dynamik des Elektrons, Annalen der Physik. 1903; 315(1):105–79. Crossref
  • Lorentz HA. Simplified theory of electrical and optical phenomena in moving systems. Proceedings of the Royal Netherlands Academy of Arts and Sciences. 1899; 1:427–42.
  • Electromagnetic mass [Internet]. [cited 2017 Apr 17]. Available from: Crossref
  • Lorentz HA. Electromagnetic phenomena in a system moving with any velocity smaller than that of light. Proceedings of the Royal Netherlands Academy of Arts and Sciences. 1904; 6:809–31.
  • Okun LB. The concept of mass physics today. Institute of Theoretical and Experimental Physics, Moscow, USSR.1989; 42(6):31–6.
  • Okun LB. Mass versus relativistic and rest masses. American Journal of Physics. 2009; 77(5):430. Crossref12. Arons AB. A guide to introductory physics teaching. New York, John Wiley and Sons; 1990. p. 263.
  • Einstein A. Ann. der Phys. 1905; 17:891-921.
  • Bucherer A. H Mathematische Einführung in die Elektronentheorie. Leipzig, Teubner; 1904. p. 11–30.
  • Gamow G. My world line. Viking, New York; 1970. p. 44.
  • Rogers MM. A determination of the masses and velocities of three radium B beta-particles. Physical Review. 1940; 57:379–83. Crossref
  • Staley R. Einstein’s Generation. Chicago, University Press. 2008, pp. 242-244.
  • Large Hadron Collider [Internet]. [cited 2017 Apr 23].Available from: Crossref
  • LHC. How fast do these protons go? [Internet]. Available from: Crossref
  • Auffray C. In private communication to query by Cern Control Centre dated; 2016 Jan. p. 1–13.
  • Logan RK. The poetry of physics and physics of poetry.World Scientific Publishing Company; 2010. p. 117–18.Crossref
  • Poincaré H. The measure of time. The Foundations of Science (The Value of Science), New York: Science Press; 1913.p. 222–34.
  • Afshordi N , Magueijo J Phys. Rev. D 94, 101301(R). 2016.
  • Beiser A. Concepts of modern physics. McGraw Hill Book Company Fourth Edition, New York, Singapore; 1987. p.423–8.


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