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There is a considerable literature discussing Poincaré's role in the development of relativity theory (see Darrigol (1995) and the references cited therein). Given that, during the years up to 1905, Poincare reduced gradually the significance of the ether in electrodynamical theory, it is surprising, perhaps, that he did not follow Einstein and eliminate it completely. Darrigol suggests that 'The most plausible answer is that he wished to maintain the notions of true space and time. These notions were so adequate in describing the course of current mechanical phenomena that it was foolish to give them up for the sake of the fourth or fifth decimal.' A thorough analysis of the philosophical positions with regard to relativity taken by Poincare, Lorentz, and Einstein can be found in Hirosige (1976). Hirosige emphasizes the fundamental contribution to the emergence of Einstein's theory made by Ernst Mach with his criticism of the dogmatic mechanistic worldview that characterized nineteenth-century physics. Zur Elektrodynamik bewegter Körper, published in Ann. Phys. 17. English translations can be found in, for example, Lorentz, et al. (1923), Stachel (1998), Miller (1998). In the latter, from which quotes reproduced here have been taken, Einstein's paper is analysed in great detail. Like the Galilean transformation, a general Lorentz transformation involves ten parameters: four for the arbitrary choice of origin in space and time, three for an arbitrary rotation of the space axes, and the remaining three as the components of the velocity of one frame with respect to the other. In the limit as c ^ <x>, a Lorentz transformation reduces to a Galilean transformation.

Before Einstein, people tried to remove the apparent contradiction between electromagnetic theory and invariance under Galilean transformations. Einstein, on the other hand, abandoned absolute time and created a theory in which invariance under the Lorentz transformation was fundamental, and applied to all dynamical phenomena. The consequences are profound, and for many people the physics of special relativity was extremely difficult to come to terms with, even when the mathematics was understood. The idea that the temporal order of two events is observer-dependent is certainly counter-intuitive. Length contraction and time dilation are also disturbing, but perhaps the most famous consequence is the association between energy and inertial mass in the form E = mc2, which Einstein derived later in 1905.

The relation between the mass and velocity of charged particles had been the subject of investigation since the 1880s, when Joseph John Thomson demonstrated that an electric charge had the effect of increasing the inertia of a particle. This was due to the moving charge creating a magnetic field which, in turn, acted back on the particle. Thomson is best known for his discovery of the electron in 1897 and his hypothesis that these tiny electrically charged particles were the building blocks of atoms. Around the turn of the century there were two main candidates for a theory of the electron: those of Max Abraham and Lorentz. Both predicted a variation in mass with velocity, mass being the constant of proportionality in the equation F = ma. Abraham introduced the concepts of longitudinal mass mL and transverse mass mT, these being the value of m when the force was in the direction of motion and perpendicular to that direction, respectively. In his original 1905 paper, Einstein obtained the expressions

mL = m0y , mT = m0y , where m0 is the 'mass of the electron, as long as its motion is slow'. He then proposed that these results must apply to all material bodies, since the electron was the building block of matter.

The problem with Einstein's approach is that F = ma is a poor choice for the definition of force when m is a varying quantity, a much better one being Newton's F = d(m v)/dt. It was Max Planck45 who, in 1906, demonstrated that with this definition one could simply write m = m0y and define the

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