E=mc² Is Not a Relativistic Formula

The mass-energy formula \(E = mc^{2}\) is thought to be derived by Einstein from special relativity. The present study shows that Maxwell’s electromagnetic momentum \(P = E/c\) and the Newtonian momentum \(P = mv\) imply this formula. It can be derived from classical physics with _c_ as the constant velocity of light in its medium, ether. The present study demonstrates that this classical physics-based formula is also correct in other inertial frames that move relative to the ether frame. In contrast, Einstein’s derivation in 1905 is logically flawed as a relativistic proof because 1) it ignored that the difference rather than the sum of the emitted energy between the opposite directions affects the kinetic energy of the emitting object and made incorrect assumptions; 2) its mass and energy are measured in different reference frames whereas the mass-energy equivalence should be for mass and energy measured in the same reference frame; 3) its result is an approximation and valid only at low velocity whereas the term relativistic usually means “also correct at high velocity.” Einstein’s nonrelativistic derivation in 1946 is incorrect from a relativistic point of view because it ignores the relativistic effects in the moving (observed) frame. It is unnecessary from a classical point of view because it uses the two classical equations \(P = mv\) and \(P = E/c\), from which \(E = mc^{2}\) can be obtained directly. Therefore, \(E = mc^{2}\) is a classical rather than a relativistic formula. The relativistic formula that Einstein should have derived from his thought experiments is \(E = E_{0}/\sqrt{1 - v^{2}/c^{2}} = m_{0}c^{2}/\sqrt{1 - v^{2}/c^{2}}\) derived by Laue and Klein, which corresponds to the relativistic mass-velocity equation derived by Lorentz.