Albert Einstein (1879-1955).

Autograph letter signed ('A. Einstein') to Wilhelm Wien, Aeschi (Switzerland), 11 August 1907.

In German. 5½ pages, 180 x 112mm, on two bifolia, including four diagrams, 11 free-standing mathematical formulae and several other formulae in the text. Provenance: by descent from Wilhelm Wien.

Signal velocities may not exceed the speed of light according to the theory of relativity. Einstein expresses agreement with a calculation that Wien has sent him, but adds a note: 'The velocity you have calculated is in fact equal to the velocity with which the temporal maxima and minima of the amplitude of the wave-train under consideration propagate, so a kind of group velocity which, as you have noted, in certain cases is a superluminal velocity. On the other hand, this velocity loses the character of signal velocity as soon as absorption becomes noticeable'. Einstein sets out an equation for his understanding of signal velocity (distance A-B / t₁ - t₀) and goes on 'according to the theory of relativity (and more generally according to Maxwell's theory) [this quantity] may not be a superluminal velocity'. Einstein demonstrates with four diagrams showing the amplitudes of the group velocity how it can be interpreted as a signal velocity in one case but not in another. Evidently intrigued by the problem, he goes on to consider some further ramifications: 'It also works in the case of an absorbent medium to construct a process from which one can infer a signal velocity. One need only construct a wave-train which exhibits a plane moving in the direction of the propagation of light in which the amplitude of the light vector is permanently zero': he works through the resulting equations, before concluding: 'The value of Φ so obtained is a signal velocity in the sense defined above; for one will also have here, on both sides of the plane of vanishing amplitude, mutually independent optical processes, of which only one fulfills the differential equations, i.e. is capable of existing'.

Martin J. Klein, A.J. Kox and Robert Schulmann (eds), Collected Papers, vol. 5, no.53

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