3.6 The End of My Latin

The first published reference to Einstein's special theory of relativity appeared in a short note by Walter Kaufmann reporting on his experimental results involving the deflection of electrons in an electromagnetic field. Kaufmann's work was intended as an experimentum crucis for distinguishing between the three leading theories of the electron, those of Abraham, Bucherer, and Lorentz. In his note of 30 November 1905, Kaufmann wrote

Kaufmann's results were originally accepted by most physicists as favoring the Abraham theory, but gradually people began to have doubts. Although the results disagreed with the Lorentz-Einstein model, the agreement with Abraham's theory was not particularly good either. This troubled Planck, so he conducted a careful analysis of Kaufmann's experiment and his analysis of the two competing theories. It was an interesting example of scientific "detective work" by Planck.

Kaufmann in 1905 had measured nine characteristic deflections d₁,d₂,..,d₉ for electrons passing though nine different field strengths. Then he had computed the nine values that would be predicted by Abraham's theory, and the nine values that would be predicted by Lorentz-Einstein. However, in order to derive the "predictions" from the theories for his particular experimental setup he needed to include an attenuation factor "k" on the electric field strength. This factor is actually quite a complicated function of the geometry of the plates and coils used to establish the electric field. Kaufamnn selected a particular value of "k" that he thought would be reasonable.

Now, both the Abraham and the Lorentz-Einstein theory predicted the electron's velocity could never exceed c, but Planck noticed that Kaufmann's choice of k implied a velocity greater than c for at least one of the data points, and therefore was actually inconsistent with both theories. This caused Planck to suspect that perhaps Kaufmann's assumed value of k was wrong. Unfortunately the complexity of the experimental setup made it impossible to give a firm determination of the attenuation factor from first principles, but Planck was nevertheless able to extract some useful information from Kaufmann's data.

Planck took the nine data points and "backed out" the values of k that would be necessary to make them agree with Abraham's theory. Then he did the same for the Lorentz-Einstein theory. All these values of k were well within the range of plausibility (given the uncertainty in the experimental setup), so nothing definite could be concluded, but Planck noted that the nine k-values necessary to match the Lorentz-Einstein theory to the measurements were all nearly equal, whereas the nine k-values necessary to match Abraham showed more variation. From this, one might actually infer a slight tilt in favor of the Lorentz-Einstein theory, simply by virtue of the greater consistency of k values.

Naturally this inconclusive state of affairs led people to try to think of an experiment that would be more definitive. In 1908 Bucherer performed a variation of Kaufmann's experiment, but with an experimental setup taking Planck's analysis into account, so that uncertainty in the value of k basically "cancels out". Bucherer's results showed clear agreement with the Lorentz-Einstein theory and disagreed with the Abraham theory. Additional and more refined experiments were subsequently performed, and by 1916 it was clear that the experimental evidence did in fact support what Kaufmann had called "the Lorentz-Einstein fundamental assumptions".

Incidentally, it's fascinating to compare the reactions of Lorentz, Poincare, and Einstein to Kaufmann's results. Lorentz was ready to abandon his entire model (and life's work) since it evidently conflicted with this one experiment. As he wrote to Poincare in 1906, the length contraction hypothesis was crucial for the coherence of his entire theoretical framework, and yet

Poincare agreed that, in view of Kaufmann's results "the entire theory may well be threatened". It wasn't until the announcement of Bucherer's results that Lorentz regained confidence in his own theoretical model. Interestingly, he later cited those results as one of the main reasons for his eventual acquiescence with the relativity principle, noting that if Lorentz-covariance is actually as comprehensive as these experimental results show it to be, then the ether concept is entirely devoid of heuristic content. (On the other hand, he did continue to maintain that there were some benefits in viewing things from the standpoint of absolute space and time, even if we are not at present able to discern such things.)

Einstein's reaction to Kaufmann's apparently devastating results was quite different. In a review article on relativity theory in 1907, Einstein acknowledged that his theory was in conflict with Kaufmann's experimental results, and he could find nothing wrong with either Kaufmann's experiment or his analysis, which seemed to indicate in favor of Abraham's theory over relativity. Nevertheless, the young patent examiner continued

This is a remarkable defense of a scientific theory against apparent experimental falsification. While not directly challenging the conflict between experiment and theory, Einstein nevertheless maintained that we should regard relativity as most likely correct, essentially on the basis of it's scope and conceptual simplicity. Oddly enough, when later confronted with similar attempts to justify other people's theories, Einstein was fond of saying that "a theory should be as simple as the facts allow - but no simpler". Yet here we find him serenely confident that the "facts" rather than his theory will ultimately be overturned. This turned out to be the case.

This sublime confidence in the manifest correctness of certain fundamental ideas was a characteristic of Einstein throughout his career. Recall that when asked what he would have done if the eclipse observations had disagreed with his prediction for the bending of light, Einstein replied "Then I would have felt sorry for the dear lord, because the theory is correct."