Kaufmann–Bucherer–Neumann experiments

The Kaufmann- Bucherer - Neumann experiments (1901-1915) examined the dependence of the inertial mass (or momentum ) of electrons from their speed. In the early days of the development of the special theory of relativity, these experiments were very important for the recognition of this then new theory. The results of these experiments have long been controversial, and could be fully verified decades after its first implementation in the sense of special relativity (see Tests of relativistic energy - momentum relation and general tests of special relativity ) only.

• 3.1 Bucherer
• 3.2 Hupka
• 3.3 Neumann and Guye / Lavanchy

• 8.1 Secondary Source
• 8.2 Primary Sources

Prehistory

Henri Becquerel discovered in 1896 the radioactive decay of various chemical elements. Thereafter, the resulting beta radiation was discovered, which was interpreted as emission of negatively charged particles. Later these particles were identified with the electron, which was proved by Joseph John Thomson's 1897 experiments on cathode rays.

This was associated with the theoretical derivation of the so-called electromagnetic mass by JJ Thomson ( 1881). Thus, increased electromagnetic energy, the mass of a body apparently. Thomson ( 1893) and George Frederick Charles Searle (1897 ) also calculated that this electromagnetic mass is dependent on the speed and infinitely large when an electric charge is moving at the speed of light relative to the ether. Also Hendrik Lorentz (1899, 1900) could derive such a velocity dependence as a consequence of his theory of electrons. At this point, the electromagnetic mass as " apparent mass ", and refers to the immutable Newtonian mass as "true mass ". [A 1] [A 2]

The (transverse ) electromagnetic mass corresponded to the later-developed concept of " relativistic mass ", the latter is also valid for all other forms of energy besides the electromagnetic energy. This mass concepts are, however, hardly used. Instead, the relativistic energy or pulse is applied, which also include the inaccessibility of the speed of light (symbol c ) for massive particles, because it is:

Therefore, the Kaufmann- Bucherer - Neumann experiments can also be interpreted as an early test of the relativistic energy - momentum relation. ( Hereinafter, for historical reasons, the notions of " transverse " or " relativistic mass " is used. )

The experiments of Kaufmann

Initial experiments

With the then usual cathode rays would have a maximum of 0.3 c can be achieved, so Walter Kaufmann used beta radiation ( formerly known as " Becquerel rays ") having speeds of about 0.9c for his experiments. Here, the decay of radium used in an evacuated tube as a source of electrons (FIG. 1). The charge to mass ratio of the particles was measured by the use of electric and magnetic fields. These fields were aligned parallel to each other, whereby the deflections caused by them were made perpendicular to each other. The impact of the particles on the photographic plate produced a deflection curve fit to a certain speed and mass. By reversing the electric field, two symmetrical curves were generated, the center line defined the direction of the magnetic deflection. Since the electron charge was independent of changes in speed, had a possible change of the charge - to-mass ratio e / m the result of a change in the mass or the momentum to be. [ A3 ] [ A4 ]

Kaufmann published his first results in 1901, and could actually notice a decrease of the charge - to-mass ratio. This can only be explained if the mass or momentum increases accordingly with greater speed. Based on Searle (1897 ) established the formula for the dependence of the electromagnetic energy from the velocity of charged bodies, businessman defined the increase in electromagnetic mass as a function of speed:

Kaufmann noted that this formula results could not explain why he assumed that the total mass of the electrons mainly to "true mechanical mass " belong, but only a smaller part belong to the "apparent electromagnetic mass ". However, he committed two errors in the evaluation: On the one hand Max Abraham was able to show that the above formula is correct only in the longitudinal direction, but for these experiments the transverse direction is crucial. This applies upon acceptance of the electron as a rigid sphere:

On the other hand, committed Kaufmann a calculation error in the calculation of the deflection curves. In a reanalysis of 1902 he corrected this error, and found agreement with Abraham formula fixed.

1902 and 1903 led Kaufmann further experiments under improved conditions. The results were interpreted by him as further confirmation of Abraham's theory, and as evidence of the complete electromagnetic origin of mass.

The increase in the electron mass with velocity was also confirmed by Hermann Starke, who conducted experiments with cathode rays in 1903 of about 0.3 c.

Competing theories

1902, Max Abraham a theory in which the electron was a rigid sphere whose charge is uniformly distributed on its surface. As described above, he led the " transverse electromagnetic mass " in addition to " longitudinal electromagnetic mass " field. According to this theory would be the total electron mass of electromagnetic origin, while a mechanical mass no longer exists. [ A5 ] [ A6 ]

Also Lorentz (1899, 1904) extended his theory of electrons by introducing the Lorentz transformation, which revealed that the electrons are subjected in the direction of shortening, the so-called length contraction. This led to terms for the electromagnetic mass, which differed from those of Abraham. Nevertheless, Lorentz showed that they were consistent with the businessman between results as good as those of Abraham. 1905 Henri Poincaré was able to develop the theory of Lorentz further, so that they with the principle of relativity, that is, from now on, fully consistent with the possibility of defining an absolute inertial motion. [ 5 A ] [A 7]

Another theory was developed in 1904 by Alfred Bucherer and Paul Langevin. It differs from the Lorentz in that, together with the contraction in the direction perpendicular to an elongation occurs, whereby the volume remains constant. [ A7 ]

Finally, Albert Einstein developed in 1905 is still valid today special theory of relativity, which included a change of mass due to the Lorentz transformation between relatively moving inertial frames. Despite completely different conditions, the predictions of this theory correspond to those of Lorentz. [A 8]

With regard to the transverse mass increase in the following predictions of each theory were:

Experiments of 1905

To bring about a decision between these theories, businessman leading his experiments again through with greater precision. By comparing the above formulas with its results concluded merchant, that he would have the Lorentz -Einstein formula, and thus the principle of relativity, clearly refuted. Therefore, were the only remaining theories those of Abraham and Bucherer, which equally well coincided approximately with the results. Lorentz was clueless and wrote in a letter: " I am at the end of my tether " [A 9] [A 10].

Shortly after Kaufmann published his findings and conclusions, this [A 11] [A 12], however, were subdued by Max Planck to a new analysis. In two papers in 1906 and 1907 published he was able to find any experimental error or miscalculation, but he showed that Kaufmann's results were not completely conclusive. Thus, the curves would arise the possibility of superluminal speeds with further extrapolation. Thus, these measurements would not constitute a final decision. And Einstein gave in 1907 to be true that the merchant results would better fit the theories of Abraham and Bucherer than to his own, but the basics of these theories are not plausible and broadly enough so that they would have a low probability to proven correct.

Further experiments

Bucherer

Adolf Bestelmeyer (1906-1907) criticized some technical aspects of Kaufmann's experiments, particularly the use of parallel electric and magnetic fields. That's why he led himself through experiments with cathode rays of about 0.3 c. He developed a velocity filter using mutually perpendicular electric and magnetic fields. Similar methods were previously used by JJ Thomson and Wilhelm Wien. He received results for the charge - to-mass ratio, which significantly differed from those merchant. However Bestelmeyer adding that his data did not allow deciding between the theories.

Therefore, led Alfred Bucherer 1908 new experiments with beta-rays of up to 0.7 c using a velocity filter, similar to that of Bestelmeyer, by (Fig. 4 & 5 ) A radium source was located here in the middle of a circular, charged capacitor, which in turn, was in a magnetic field. Only those rays that spread out in the direction α and had a certain speed, magnetic and electric fields exactly compensated, so that they spread in a straight line. After the jets had left the capacitor, they were deflected by the magnetic field and met on the photographic plate.

For the final analysis Bucherer used the formulas of Abrahm and Lorentz -Einstein to calculate from the measured values, the charge - to-mass ratio for electrons at rest. Because this ratio is in the idle state is constant, the values ​​must all lie on a line (Figure 6). That was nearly only Lorentz -Einstein case, while Abraham's data significantly differed from each other. Therefore, concluded Bucherer that the results would have the principle of relativity and thus the theory of relativity or the " Lorentz -Einstein theory " confirmed. Bucherer's results were received with relief and satisfaction of Lorentz, Einstein and Hermann Minkowski. [ A13 ] [ A14 ]

Kurt Wolz, a student Bucherer, led by further experiments in which he also consistent with the Lorentz -Einstein formula noted (Fig. 7).

Thus, although the majority of the Physicist Bucherer accepted results, remained in doubt. So there was, especially by Bestelmeyer, objections relating to the technical implementation, which resulted in a polemical dispute between Bucherer and Bestelmeyer in several publications. Bestelmeyer argued for example, that a single experiment does not justify such far-reaching conclusions that accurate data logs are missing, and the influence of non-compensated beams could not be excluded. Also Wolzs experiments would not invalidate his objections.

Hupka

In contrast to Kaufmann and Bucherer, used Karl Erich Hupka (1909 ) cathode rays by up to 0.5 c for his experiments. Rays generated by a copper cathode were accelerated by a field between the anode and cathode of the discharge tube evacuated. The anode served as the diaphragm, which was passed by the rays at a constant speed, and which threw the silhouette of two Wollaston wires on a Phosphoreszenzschirm behind a second diaphragm. When a current was generated behind the diaphragm, the rays were deflected and the silhouette shifted. The data were consistent with the Lorentz -Einstein formula, but Hupka added that his experiment could bring no definitive decision. W. Heil subsequently published several works in which he analyzed and criticized the results. Hupka commented on them and defended his results and methods.

Neumann and Guye / Lavanchy

1914 led Günther Neumann new measurements using Bucherer of equipment through which he continued to improve. He focused particularly on Bestelmeyer objections, such as the question of the non-compensated radiation, and extensive data protocols. His experiment showed that even here the data for charge -to-mass ratio according to the Lorentz -Einstein formula as requires approximately on a horizontal line was while Abraham's data showed a clear curve ( Fig. 8). Neumann concluded that his experiments with those of Bucherer and Hupka matched, the Lorentz -Einstein formula would definitively confirmed in the range 0.4-0.7 c, and Abraham's formula would definitively refuted. Since instrumental error occurred in the range of 0.7-0.8 c, the deviation found in this area of the Lorentz -Einstein formula is not significant.

1915 observed Charles -Eugène Guye and Charles Lavanchy the deflection of cathode rays at speeds of 0.25-0.5 c. In a tube with a cathode and an anode, the beam has been accelerated. The diaphragm at the anode generated the beam was deflected out. The Rays beat on a screen on which the results were photographed with a camera. Then they calculated the ratio of the transverse electromagnetic mass mT and rest mass m0, and found agreement with the Lorentz -Einstein formula ( 9 ). This Neumann's result was also confirmed at lower speeds.

These experiments were interpreted as positive confirmation of the Lorentz -Einstein formula, so Lorentz was able to write in 1915: [A 15]

Further developments

Decades later, however, argued tooth and Spee (1938 ) and Faragó and L. Jánossy (1957 ) that many assumptions about the nature of the electrons and the properties of the experimental arrangement, which were made by the former experimenters were very inaccurate. The Bucherer - Neumann experiments would just like Kaufmann's measurements only showed a qualitative increase in the pulse or the mass that were not accurate enough to decide between the competing theories. [A 16] [A 17]

So while these experiments were to remain controversial, studies on the fine structure of the hydrogen lines by Karl Glitscher delivered in 1917, a clear confirmation of the Lorentz -Einstein formula, and a refutation of all competition theories. For the calculation of the fine structure of the exact values ​​for relativistic energy and momentum are in fact necessary, which is not possible with Abraham's formula. [A 18]

To bring about a final decision even at electron deflection experiments, led Rogers et al. (1940 ) by using improved equipment new experiments. The decay chain of radium produces a spectrum of beta rays with a broad energy range. The earlier measurements by Kaufmann, Bucherer or Neumann used flat parallel plate capacitors, which did not permit the focusing of beta particles. Rogers et al. (FIG. 10 ), however, use an electrostatic Spektrographn which enabled accurate focusing. The spectrograph was constructed from two segments of two cylinders, and was surrounded by an evacuated iron box. Beta -rays were generated by a fine platinum wire was coated with active radium. The radiation encountered a gap in front of a Geiger counter. The analysis showed that the measuring points was on the curve for the ratio of the transverse mass and rest mass according to the Lorentz -Einstein formula ( 11 ). It thereby an accuracy of 1 % was achieved, which Abraham 's theory was ruled out.

Modern tests

Today, the exact confirmation of special relativity theory in particle accelerators is already routine, see tests of the relativistic energy - momentum relation