In his fourth paper of 1905, Einstein put forward the idea of the equivalence of mass to any kind of energy (e. g. light or mechanical energy – as Miller notes on page 353). So increasing the overall energy of any system should increase its inertia. Weirdly enough, he goes on to demonstrate this equivalence for extended systems without any use of General Relativity. Instead, in a series of papers in 1906 and 1907, he uses the release of radiation, the conservation of momentum, electromagnetic forces, “envelopes,” and the center of mass to show that, no matter how you move or redispose the components (eg. some radiative events inside the system), or add up the forces, the relation of inertia to overall energy stays the same.
There wasn’t a lot of precise information about radiative energy in 1906 and 1907, but there were the newly-worked-out theories of black-body radiation, so some physicists looked at what would happen theoretically if you moved black-body radiation around. Planck summarized these formulations in his 1907 paper “The Dynamics of Moving Systems” which confirmed the coherence and usefulness of Einstein’s relativity. Working parallel to Planck (but avoiding an explicit quantization conditions) in 1907, Einstein rederived the mass of energy within an “Envelope” (Miller’s word for the construction, page 363), and again noted that the inertial mass of a system (in an envelope) was equivalent to its energy. In that context, Planck brought up the mass loss and the resulting radiant energy involved in radioactive decay. Einstein noted (as quoted by Miller on page 362), “In radioactive decay the quantity of free energy becomes enormous.” And from there he moved on into what that implied about how gravity worked. We will depart from his efforts in that direction and instead pursue the wanderings of his next revolutionary idea: the quantum energy of light, which will bring us to the Compton Effect and eventually the mysteries of the mesons.
Meanwhile – how was Special Relativity resolved so that it could be a standard part of phenomenological approaches in physics?
After Minkowski and Sommerfeld worked out the basic mathematics of the different kinds of intervals involved, the final completion of the theoretical picture (as Janssen and Mecklenberg point out in their “Electromagnetic Models of the Electron and the Transition from Classical to Relativistic Mechanics”) was due to Max von Laue in 1911. Von Laue showed that Minkowski’s “world tensor” could include the properties of physical systems under any kind of forces, not just the electromagnetic forces as Minkowski had originally intended. Thus, in 1911, using the world tensor formalism, von Laue could simplify the work of Planck and Einstein from 1907 when they had used “envelopes” and long series of direct Lorentz transformations to show the relativistic coherence of forces in physical systems. Von Laue also showed that because, in relativistic terms, the volume of an energic element was not the same from all points of view, questions of how the electron deformed and describing it as a point particle were all equally misleading. The world tensor also provides a way of picturing Poincaré Pressure as a stress or force included in the world tensor of the electron rather than as an interaction with the aether.
Max, not interacting with the aether:
