The Kaufmann–Bucherer–Neumann experiments measured the dependence of the inertial mass (or momentum) of an object on its velocity. The historical importance of this series of experiments performed by various physicists between 1901 and 1915 is due to the results being used to test the predictions of special relativity. The developing precision and data analysis of these experiments and the resulting influence on theoretical physics during those years is still a topic of active historical discussion, since the early experimental results at first contradicted Einstein's then newly published theory (1905), but later versions of this experiment confirmed it. For modern experiments of that kind, see Tests of relativistic energy and momentum, for general information see Tests of special relativity.
Historical context In 1896, Henri Becquerel discovered radioactive decay in a variety of chemical elements. Subsequently, the beta radiation from these decays was discovered to be the emission of a negatively charged particle. Later these particles were identified with the electron, discovered in cathode ray experiments by J. J. Thomson in 1897.
This was connected with the theoretical prediction of the electromagnetic mass by J. J. Thomson in 1881, who showed that the electromagnetic energy contributes to the mass of a moving charged body. Thomson (1893) and George Frederick Charles Searle (1897) also calculated that this mass depends on velocity, and that it becomes infinitely great when the body moves at the speed of light with respect to the luminiferous aether. Also Hendrik Antoon Lorentz (1899, 1900) assumed such a velocity dependence as a consequence of his theory of electrons. At this time, the electromagnetic mass was separated into "transverse" and "longitudinal" mass, and was sometimes denoted as "apparent mass", while the invariant Newtonian mass was denoted as "real mass".Miller (1981), pp. 45–47Pais (1982), pp. 155–159 On the other hand, it was the belief of the German theoretician Max Abraham that all mass would ultimately prove to be of electromagnetic origin, and that Newtonian mechanics would become subsumed into the laws of electrodynamics.Miller (1981), pp. 55–67
In 1904, Lorentz proposed that the mass along the trajectory of motion (longitudinal mass) and the mass in the directions perpendicular to the motion (transverse) are different. In his theory, the longitudinal mass and the transverse mass , where is the Lorentz factor and is the rest mass of the electron. The concept of (transverse) electromagnetic mass , which was based on specific models of the electron, was later transmuted into the purely kinematical concept of relativistic mass which concerns all forms of energy, not only electromagnetic energy. Currently, however, the concept of relativistic mass, although still frequently referred to in popular works on relativity, is now seldom used among professional working physicists, and has been superseded by the expressions for relativistic energy and momentum, which also predict that the speed of light cannot be reached by massive bodies. This is because all of those relations involve the Lorentz factor:
Therefore, the Bucherer–Kaufmann–Neumann experiments can be seen as early tests of relativistic energy and momentum. (For the following historical description of the experiments, the concepts of "transverse" or "relativistic mass" are still used).
Kaufmann's experiments
First experiments
Walter Kaufmann began to experiment with beta rays using a device similar to a cathode ray tube, where the source of the electrons was the decay of radium that was placed in an evacuated container. (See Fig. 1) Such rays emitted from radium were called "Becquerel rays" at that time. Contrary to the then known cathode rays which reached speeds only up to 0.3c, c being the speed of light, Becquerel rays reached velocities up to 0.9c. However, since beta particles have different velocities, the radiation was inhomogeneous. Therefore, Kaufmann applied electric and magnetic fields aligned parallel to each other, so that the deflections caused by them were perpendicular to each other. Their impacts on a photographic plate produced a deflection curve, whose individual points corresponded to a certain velocity and a certain mass of the electrons. By reversing the charge on the condenser, thus inverting the electric field, two symmetric curves could be obtained, whose center line determined the direction of the magnetic deflection.Miller (1981), pp. 47-54Staley (2009), pp. 223–233
Kaufmann published a first analysis of his data in 1901 – he actually was able to measure a decrease of the charge-to-mass ratio, thus demonstrating that mass or momentum increases with velocity. Using Searle's formula (1897) for the electromagnetic energy increase of charged bodies with velocity, he calculated the increase of the electron's electromagnetic mass as a function of velocity:
Kaufmann noticed that the observed increase cannot be explained by this formula, so he separated the measured total mass into a mechanical (true) mass and an electromagnetic (apparent) mass, the mechanical mass being considerably greater than the electromagnetic one. However, he made two mistakes: As shown by Max Abraham, Kaufmann overlooked that Searle's formula only applies in the longitudinal direction, but for deflection measurements the formula for the transverse direction was important. Therefore, Abraham introduced the "transverse electromagnetic mass" with the following velocity dependence:
Kaufmann also made a calculation mistake in deriving the deflection curves. Those errors were corrected by him in 1902.
In 1902 and 1903 Kaufmann performed another series of tests with updated and improved experimental techniques. The results were interpreted by him as a confirmation of Abraham's theory and of the assumption that the electron's mass is completely of electromagnetic origin.
Hermann Starke conducted similar measurements in 1903, although he used cathode rays limited to 0.3c. The results that he obtained were interpreted by him as being in agreement with those of Kaufmann.
Competing theories
In 1902, Max Abraham published a theory based on the assumption that the electron was a rigid, perfect sphere, with its charge being distributed evenly on its surface. As explained above, he introduced the so-called "transverse electromagnetic mass" besides the "longitudinal electromagnetic mass", and argued that the entire electron mass is of electromagnetic origin.Miller (1981), pp. 55–67Staley (2008), pp. 229–233
Meanwhile, Lorentz (1899, 1904) extended his theory of electrons, assuming that an electron's charge was spread throughout its volume, and that in Kaufmann's experiment, its shape would be compressed in the direction of motion and would stay unchanged in the transverse directions. To Kaufmann's surprise, Lorentz could show that his model agreed with his experimental data as well. This model was further elaborated and perfected by Henri Poincaré (1905), so that Lorentz's theory was now in agreement with the principle of relativity.Miller (1981), pp. 55–67Janssen (2007), section 4
A similar theory was developed by Alfred Bucherer and Paul Langevin in 1904, with the difference that the total volume occupied by the deformed electron was assumed unchanged. It turned out that this theory's prediction was closer to Abraham's theory than to Lorentz's.Janssen (2007), section 4A.H. Bucherer, Mathematische Einführung in die Elektronentheorie, Teubner, Leipzig 1904, p. 57
Finally, Albert Einstein's theory of special relativity (1905) predicted the change of the point-like electron's mass due to the properties of the transformation between the rest-frame of the particle and the laboratory frame in which the measurements were performed. Mathematically, this calculation predicts the same dependence between velocity and mass as Lorentz's theory, although it assumes very different physical concepts.Staley (2008), pp. 241–242. See also: English translation.
As regards the increase of transverse electromagnetic mass, the predictions of the various theories were (Fig. 3):
Experiments of 1905 In order to make a decision between those theories, Kaufmann again performed his experiments with higher precision. Kaufmann believed that he had conclusively disproven the formula of Lorentz–Einstein, and had therefore also disproven the principle of relativity. In his view, the only remaining options were between the theories of Abraham and Bucherer. Lorentz was perplexed and wrote that he was "at the end of his Latin".Miller (1981), pp. 228–232Staley (2008), pp. 242–244
However, criticism of Kaufmann's experiment arose.Miller (1981), pp. 232–235Staley (2008), pp. 244–250 Shortly after Kaufmann published his results and the conclusions of his analysis, Max Planck decided to re-analyze the data obtained by the experiment. In 1906 and 1907, Planck published his own conclusion on the behavior of the inertial mass of electrons with high speeds. Using just nine data points from Kaufmann's publication in 1905, he recalculated the exact setup of the fields for each point, and compared the measurements against the predictions of the two competing theories. He showed that Kaufmann's results are not fully decisive and would lead to superluminal velocities. Einstein remarked in 1907 that although Kaufmann's results were better in agreement with Abraham's and Bucherer's theories than with his own, the foundations of the other theories were not plausible and therefore had only little probability of being correct.
Subsequent experiments
Bucherer
The main problem of Kaufmann's experiments was his use of parallel magnetic and electric fields, as pointed out by Adolf Bestelmeyer (1907). Using a method based on perpendicular magnetic and electric fields (introduced by J. J. Thomson and further developed to a velocity filter by Wilhelm Wien), Bestelmeyer obtained considerably different values for the charge-to-mass ratio for cathode rays up to 0.3c. However, Bestelmeyer added that his experiment was not precise enough to provide a definite decision between the theories.
Therefore, Alfred Bucherer (1908) conducted a precise measurement using a velocity filter similar to Bestelmeyer's. See Figs. 4 & 5. A radium beta source was placed at the center of a circular condenser consisting of two silvered glass plates spaced 0.25 mm apart and charged to about 500 volts, set in a homogeneous 140 gauss magnetic field. The radium emitted beta rays in all directions, but in any particular direction α, only those beta rays exited the velocity filter whose speed was such that the electric and magnetic fields exactly compensated each other. After leaving the condenser, the rays were deflected by the magnetic field, and exposed a photographic plate set parallel to the condenser rim and perpendicular to the non-deflected rays.
For his final analysis, Bucherer recalculated the measured values of five runs with Lorentz's and Abraham's formulas respectively, in order to obtain the charge-to-mass ratio as if the electrons were at rest. Since the ratio doesn't vary for resting electrons, the data points should be on a single horizontal line (see Fig. 6). However, this was approximately only in the case when the data were calculated with Lorentz's formula, while the results of Abraham's formula sharply deviated (the red and blue lines represent the average value according to both formulas). The agreement with the Lorentz–Einstein formula was interpreted by Bucherer as the confirmation of the relativity principle and the Lorentz–Einstein theory – a result immediately applauded by Lorentz, Einstein, and Hermann Minkowski.Miller (1981), pp. 345–350Staley (2008), pp. 250–254