Einstein proposed the equivalence of mass and energy in his final Annus Mirabilis paper. Over the next several decades, the understanding of energy and its relationship with momentum were further developed by Einstein and other physicists including Max Planck, Gilbert N. Lewis, Richard C. Tolman, Max von Laue (who in 1911 gave a comprehensive proof of from the stress–energy tensor , as opposed to Einstein's original presentation which has been criticized as incomplete ), and Paul Dirac (whose investigations of negative solutions in his 1928 formulation of the energy–momentum relation led to the 1930 prediction of the existence of antimatterEisberg, R., Resnick, R. (1985) Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. 2nd Edition, John Wiley & Sons. New York. p.132.). Einstein demonstrated that Poincaré's artifice was superfluous. Rather, he argued that mass-energy equivalence was a necessary and sufficient condition to resolve the paradox. In his demonstration, Einstein provided a derivation of mass-energy equivalence that was distinct from his 1905 derivation. Einstein began by recasting Poincaré's abstract mathematical argument into the form of a thought experiment: The reactionless drive described here violates the laws of mechanics, according to which the center of mass of a body at rest cannot be displaced in the absence of external forces. Einstein argued that the shuttle is not massless while transferring energy from the right to the left. If energy possesses inertia the paradox disappears  .
Einstein proposed the equivalence of mass and energy in his final Annus Mirabilis paper. Over the next several decades, the understanding of energy and its relationship with momentum were further developed by Einstein and other physicists including Max Planck, Gilbert N. Lewis, Richard C. Tolman, Max von Laue (who in 1911 gave a comprehensive proof of from the stress–energy tensor ), and Paul Dirac (whose investigations of negative solutions in his 1928 formulation of the energy–momentum relation led to the 1930 prediction of the existence of antimatterEisberg, R., Resnick, R. (1985) Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. 2nd Edition, John Wiley & Sons. New York. p.132.). Einstein demonstrated that Poincaré's artifice was superfluous. Rather, he argued that mass-energy equivalence was a necessary and sufficient condition to resolve the paradox. In his demonstration, Einstein provided a derivation of mass-energy equivalence that was distinct from his original derivation. Einstein began by recasting Poincaré's abstract mathematical argument into the form of a thought experiment: The reactionless drive described here violates the laws of mechanics, according to which the center of mass of a body at rest cannot be displaced in the absence of external forces. Einstein argued that the shuttle cannot be massless while transferring energy from the right to the left. If energy possesses the inertia the contradiction disappears. Modern analysis suggests that neither Einstein's original 1905 derivation of mass-energy equivalence nor the alternate derivation implied by his 1906 center-of-mass theorem are definitively correct. For instance, the center-of-mass thought experiment regards the cylinder as a rigid body. In reality, the impulse provided to the cylinder by the burst of light in step (b) cannot travel faster than light, so that when the burst of photons reaches the right wall in step (c), the wall has not yet begun to move. Ohanian has credited von Laue (1911) as having provided the first truly definitive derivation of .
D
, as opposed to Einstein's original presentation which has been criticized as incomplete
R
1905
original
R
is not
cannot be
R
inertia the paradox disappears
the inertia the contradiction disappears.
A
Modern analysis suggests that neither Einstein's original 1905 derivation of mass-energy equivalence nor the alternate derivation implied by his 1906 center-of-mass theorem are definitively correct. For instance, the center-of-mass thought experiment regards the cylinder as a rigid body. In reality, the impulse provided to the cylinder by the burst of light in step (b) cannot travel faster than light, so that when the burst of photons reaches the right wall in step (c), the wall has not yet begun to move. Ohanian has credited von Laue (1911) as having provided the first truly definitive derivation of