58 SUPERLUMINAL VELOCITIES clusions concerning the impossibility of such motion. In his letter Wien apparently used the "standard" expression for the group velocity u=v-x!- (1) where V is the phase velocity and X the wavelength, to support his case.[12] In two letters, written only a day apart (Docs. 49 and 50), Einstein presents an alternative expression for the group velocity, which he claims to be valid for absorptive media, as well as a more general argument, designed to show that superluminal influences are incompatible with Maxwell theory. He cites a paper by Wiechert, in which the field of a moving point charge is obtained not by solving the inhomogeneous Maxwell equations directly, but by assuming that influences between electromagnet- ic masses propagate at the velocity of light to obtain "retarded" potentials.[13] If su- perluminal causal influences lead to contradictions with Wiechert's result, they lead to contradictions with Maxwell theory as well. In Einstein's third letter (Doc. 51), however, almost everything stated in the first two letters is retracted. Only the gen- eral argument, based on Wiechert's results, remains. Wien's reply to Einstein's letter of 29 July (Doc. 51) presumably pointed out that rigid electrons could attain light-velocity. Einstein responds in his next letter (Doc. 52) that the rigidity of such electrons sets up physical influences (between volume elements connected by rigid bonds) that are of a nonelectromagnetic nature. Since Einstein confines himself to cases where only electromagnetic influences occur,[14] his argument against superluminal signals does not apply to the rigid electron. Einstein's fifth letter (Doc. 53) makes clear that Wien has discarded superluminal rigid electrons as an example of superluminal velocities and has returned to contem- porary dispersion theory,[15] apparently again putting forward the standard expres- sion for the group velocity (eq. 1). In the face of Wien's example, Einstein's concern in his fifth, as well as in his sixth and final letter (Docs. 53 and 55) is twofold. First, he wants to explain why group velocity does not qualify as a signal velocity in ab- sorptive media. Second, he wants to formulate an acceptable definition of signal ve- locity in media. In Doc. 53, Einstein concedes that in absorptive media eq. (1) gives the velocity with which the maxima and minima of the wave packet propagate, but argues that in absorptive media this velocity does not have the character of a signal velocity. Ein- stein defines signal velocity essentially as the speed with which the crest of a wave- train moves from a previously closed diaphragm to an observer and he tries to con- vince Wien that eq. (1) does not give the velocity with which a signal, thus defined, propagates through absorptive media. In the remainder of the letter Einstein introduces a signal velocity as the velocity of propagation of a plane in which the amplitude of the electric field is always zero and he succeeds in deriving an expression for this velocity in terms of the (complex) dielectric constant and the frequency. But in the final letter of 26 August (Doc. 55) Einstein retracts this derivation, because the waveform he used violates boundary
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