TLS in German, signed “A. Einstein,” one page both sides, 8.75 x 11, personal letterhead, August 8, 1931. Letter to physics student M. Frenkel in Vienna, offering a proof that Relativity does not hold if the speed of light is not constant. In part (translated): "My situation with regards to your work is such that I can't see the forest for all the trees, that is, I don't know what you are actually trying to prove...The theory usually called Special Theory of Relativity contains two assumptions: 1.) The principle of Special Relativity (R) 2.) The independence of one speed c from the relative system. (L[...]) (That this is the speed of light does not enter into the derivations of the results (e.g. the Lorenz-Transformation). You seem to believe now that Ritz's law of the dispersion of light, that is, the hypothesis that the dispersion velocity of light is equal to c+v (c being a constant, v the velocity of the emitting body) can be consolidated with the Lorenz-Transformation. This, however, is a misconception.
Proof: Let a light be sent from a body resting opposite to K, from the point of origin in the direction of a positive x-axis. By applying Ritz's hypothesis twice, we get the propagation-equation opposite to K': x'=ct' opposite to K: x= (c+v)t
Both these equations are supposed to present the same occurrence, that is xt and x't' are supposed to be connected by the Lorenz-Transformation. That is not the case, because x2-c2t2 =x'2-c2t'2 is not valid. Thus, if I have understood you correctly, you are mistaken. Should you, however, mean to express something else, then you need to state that briefly and clearly." In very good condition, with heavy intersecting folds, and small areas of paper loss, repaired and reinforced by complete silking to the front.
Einstein's theories created controversies for many years and in all levels of scholarship. The speed of a ball thrown at a velocity of 40 miles per hour, thrown forward from a train going 30 miles per hour, actually travels at 70 miles per hour with respect to someone standing on the station platform. Einstein's basic assumption is that the speed of light emitted from a flashlight on that train does not add on the 30 miles per hour of the train. Not all scientists agreed with him. Ritz's theory, developed by Swiss physicist Walther Ritz, insists among other things that the light does travel 30 miles faster from that train.
Here, a student insists that Relativity still holds true, even under Ritz's theory. Einstein attempts to show his correspondent that he is in error. In offering his proof, Einstein hand-writes portions of the formulas "x'=ct'," expressing the distance traveled by light in t' seconds, and "x=(c+v)t" expressing the distance traveled by light in t seconds from a train going v miles per hour, as proposed and seen by Ritz standing on the platform. He also pens "x2-c2t2 =x'2-c2t'2" in his closing lines. A superb and thoughtful piece of instructive correspondence from Albert Einstein, who revolutionized modern physics through the theories of special and general relativity.
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