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Is E = Δmc 2 mathematically derived or speculated in Einstein's September 1905 paper?

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In his paper, Einstein derived ΔL = Δmc 2 (light energy‐mass equation). It has not been completely studied; it is only valid under special conditions of the parameters involved, e.g., number of light waves, magnitude of light energy, angles at which waves are emitted and relative velocity v. Einstein considered just two light waves of equal energy, emitted in opposite directions and the relative velocity v uniform. There are numerous possibilities for the parameters which were not considered in Einstein's derivation. ΔE = Δmc 2 is obtained from ΔL = Δmc 2 by simply replacing L by E (all energy) without derivation. Fadner [Am. J. Phys. 56, 144 (1988)] correctly pointed out that Einstein neither mentioned E or ΔE = Δmc 2 in the derivation. Herein additional results are critically analyzed, taking all possible variables into account. Under some valid conditions of parameters, ΔL = Δmc 2 is not obtained, e.g., sometimes the result is M a = M b or no equation is derivable. If all values of valid parameters are taken into account, then the same derivation also gives L Δmc 2 or L = A Δmc 2, where A is a coefficient of proportionality. Thus, Einstein's derivation under valid parameters also predicts that energy emitted may be less than or more than ΔL = Δmc 2.
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Keywords: 1905 Derivation; Einstein; Inter-Conversion of Mass and Energy; Limitation of ΔL = ΔMc2 derivation; September; ΔL = Δmc2

Document Type: Research Article

Publication date: December 30, 2013

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  • Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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