The Long History of the Mass-Energy Relation
A guest article by Hartwig Thim – Abstract of a talk presented at the annual meeting of the Austrian Physical Society in Graz 2006, printed in the Proceedings of the History of Physics Group, European Physical Soc.
Poincaré , Kaufmann , Abraham , und Hasenöhrl  have shown already before 1905 that the mass of electrons increases during acceleration. The mass increase can easily be derived for the case the energy is transferred through an electromagnetic wave by the help of the Poynting-vector  as shown below:
is the mass equivalent of free radiation . According to equ. (1), the Poynting-vector , i.e., the flux of radiation, is related to the velocity of light, , via the expression
The expressions and have been introduced by Poincaré  already in 1900 and by Abraham  in 1904 as the energy density and the momentum of radiation (units: kg/m²s), respectively. The energy-mass relation, , can be derived for the case that the radiation is fully absorbed by a metal plate of cross section and Mass . Using equ. (1) the energy of the plate increases by the amount , and this leads to an increase of both, velocity and mass of the plate according to the following equation
For the case of total absorption, the mass increase of the plate, , must be equal to . Using and for one obtains by solving equ. (3) the well-known expression for the velocity dependent mass:
Substituting equ.(4) into equ. (3) yields for the energy transfer the expression:
And, integrating equ. (5) yields the law of equivalence of energy and mass:
In this derivation thermodynamic aspects had been excluded. However, Hasenöhrl  had pointed out that the internal energy of a body must consist in part of radiation and, hence, the mass of a body will depend in general on its temperature. By studying the problem of a hollow enclosure filled with radiation he calculated similar expressions
The expressions (6) and (7) indicate that both energy and mass can be transferred via electromagnetic waves and that electromagnetic waves exhibit inertia.
Another equally important conclusion drawn from Hasenöhrl’s derivation  is that the velocity v appearing in the equations (3) through (6) is an absolute rather than a relative velocity and that one has to calculate mass increases by starting off from an absolute frame of reference (“ether”).
Einstein’s 1905 derivation  of the energy-mass relation which also neglected thermodynamical effects had been criticized by Planck  in 1907 for an un-permissible approximation and for using the principle of relativity, and by Ives  in 1952 because of circularity in the derivation. In 1987 Fadner  repeated this critique (Fadner’s article suffers from not referring to the important work of Abraham ). Anyway, Einstein  based his derivation on the principle of relativity by using the Lorentz transforms where the square root of 1-v²/c² also appears. This procedure yielded another paradox of special relativity in addition to the clock paradox. Einstein’s derivation suffers from the fact that mass increase depends on the observer platform and does not consider energy transfer. At this point it is important to emphasize that the Lorentz – transforms have been derived by postulating that the one-way speed of light is isotropic in all inertial frames of reference, i.e., by :
However, Penzias and Wilson , Smoot et al.  and Marinov , have falsified one of the equations (8) experimentally. Finally, it was Max Planck  who presented the first valid and authentic derivation of the mass energy relation , by using the argument that the entropy of a body cannot depend on the choice of the platform and by using the principle of the smallest action instead of the principle of relativity. By doing this he found that the inertial mass also depends on temperature.
The experiments carried out by Penzias und Wilson  and Smoot et al. ,  indicate that for properly calculating the masses of the universe a fundamental frame of reference (the former ether, now the cosmic microwave background) should be used. Very recently, T. A. Jacobson and R. Parentani  wrote an article (in the December 2005 issue of the Scientific American) showing that by assuming „the ether of pre-Einsteinian physics“ many puzzles of black holes can be solved much more satisfactorily than without making this assumption.
The correct explanation of the Michelson/Morley null result  is obtained by using phase velocities rather than group velocities for calculating the phase shifts in the two interferometer arms as shown in ,  and in the Appendix. This leads to the conclusion that the Michel-son/Morley-interferometer is, in principle, not suited to detect an ether. The authors  had obviously been aware of this fact as they suggested in their famous paper in 1887 to measure the velocity of light without returning the ray to the light source, i. e., to perform a one-way light velocity measurement with mechanical synchronisation of the clocks. Marinov  actually did that in his “coupled mirrors experiment” thereby detecting the anisotropy of the light velocity on earth, or, in other words, thereby detecting the cosmic microwave background previously measured by Smoot et al.  by another method. Marinov  thus carried out the first experimental falsification of special relativity in 1975.
Since all of the derivations of W=mc² known up to date are more or less incomplete the discovery of the mass-energy-relation should not be ascribed to a single person but rather to a group of scientists including Poincaré, Abraham, Hasenöhrl, Kaufmann, Einstein und Planck. This new view should be adopted by all Physical Societies.
-  H. Poincaré, Arch.néerland sci., vol.2, No.5, p. 232, 1900
-  W. Kaufmann, Phys. Z., vol. 4, pp. 55, 1902
-  M. Abraham, Ann. d. Phys., vol. 10, pp.105, 1903 (p 125: )
-  M. Abraham, Ann. d. Phys., vol. 14, pp.236, 1904 (pp. 243 and 244)
-  F. Hasenöhrl, Ann. d. Phys., vol. 15, pp.344, 1904
-  A. Einstein, „Zur Elektrodynamik bewegter Körper”, Ann. d. Phys., vol.17, pp. 891, Juni 1905 und Supplement, September 1905
-  M. Planck, “Zur Dynamik bewegter Systeme”, Sitzungen der preuss. Akad. Wiss.,vol. 13, 1907
-  H. E. Ives, “Derivation of the Mass-Energy Relation”, J. Opt. Soc. Am., vol. 42, No. 8, pp. 540-543, 1952
-  W. L. Fadner, “Did Einstein really discover E = mc²?”, Am. J. Phys., vol. 56, No. 2, pp. 114, 1988
-  A. A. Penzias and R. W. Wilson, Astrophys. J., vol. 142, p. 419, 1965
-  G. F. Smoot, M. V. Gorenstein and R. A. Muller, “Detection of anisotropy in the cosmic blackbody radiation”, Phys. Rev. Letters, vol. 39, no. 14, pp. 898-901, 1977
-  S. Marinov, „Measurement of the Laboratory’s Absolute Velocity“, Found. Phys., vol. 9, pp.445, 1979, siehe auch http://www.mahag.com/marin.htm
-  G. F. Smoot, Lawrence Berkeley Laboratory and NASA: U2 Anisotropy Experiment
-  T. A. Jacobson and R. Parentani, “An Echo of Black Holes”, Scientific American, vol. 293, No. 6, pp. 48-55, December 2005
-  A. Michelson and E. Morley, 1887, „On the Relative Motion of the Earth and the Luminiferous Ether”, Am. Journal of Science, vol. 14, No. 203, Nov. 1887
-  W. Voigt, “Theorie des Lichtes in bewegten Medien”, Königliche Gesellschaft der Wissenschaften, Sitzung am 10. Juli 1886 zu Göttingen, Seiten 233-238
-  J. P. Wesley, „The two velocities of classical waves“, Phys. Essays, vol.17, No.2, 2004
For the Appendix refer to the Abstract from the Proceedings of the First European History of Physics (EHoP) Conference, Graz/Austria, 2006
Hartwig W. Thim is professor emeritus of mechatronics at Johannes Kepler University, Altenbergerstrasse 69, 4040 Linz, Austria (e-mail: firstname.lastname@example.org).
- Abstract from the Proceedings of the First European History of Physics (EHoP) Conference, Graz/Austria, 2006
- German translation of the abstract from the Proceedings of the First European History of Physics (EHoP) Conference, Graz/Austria, 2006
- Talk with others to “The Long History of the Mass-Energy Relation” in our forum Alpha Centauri
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