Is E = Δmc 2 mathematically derived or speculated in Einstein's September 1905 paper?
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
2 or L = A
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
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Document Type: Research Article
Publication date: December 30, 2013
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