Kaufmann–Bucherer–Neumann experiments

The Kaufmann-Bucherer-Neumann experiments measured the dependence of the inertial mass of an object on its velocity. The historical importance of a series of this experiment performed by various physicists between 1901 and 1915 is due to the results being used to test the predictions of special relativity. Its developing precision and data analysis, 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, but later versions of this experiment confirmed it. See also Tests of special relativity.

Contents

Historical context

In 1896 Henri Becquerel had discovered the 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 the body. Thomson in 1893, and George Frederick Charles Searle (1897) also calculated, that this mass depends on velocity and becomes infinitely great, when the charge 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 denoted by these authors as "apparent mass", while the invariable Newtonian mass was denoted as "real mass".[A 1][A 2] [1] [2] [3]

Kaufmann's experiments

First Experiments

Walter Kaufmann began to experiment with cathode 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 a vacuated tube. He applied electric and magnetic fields to measure the ratio of the charge and mass of the particles, and since the charge of the electrons did not change with the speed of the particle, any change of the ratio must be the result of a change of its mass. Kaufmann published a first analysis of his data in 1901 – he actually was able to measure a change in the charge/mass ratio, thus he demonstrated the velocity dependence of mass. Based on Searle's formula, he separated the measured total mass into a mechanical (true) mass and an electromagnetic (apparent) mass, where the mechanical mass was considerably greater than the electromagnetic one. Additionally, he performed a series of experiments with updated and improved experimental techniques in 1902.[A 3][A 4][4] [5] [6] [7]

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. He also showed the earlier calculations of Searle are incomplete, since they only give the correct expression for the electron's energy and mass in the direction of motion – the "longitudinale electromagnetic mass". Abraham showed, that the expression for mass is different at right angles to the direction of motion (which was actually measured by Kaufmann), so he introduced the so-called "transverse electromagnetic mass". Consequently he demonstrated that Kaufmann's results are in full agreement with this predictions. Both Kaufmann and Abraham concluded that only electromagnetic mass exists, while the assumption of a constant Newtonian mass isn't necessary any more.[A 5][A 6][8] [9] [10]

Also Lorentz (1899, 1904) extended his theory of electrons, and assumed that electrons were spreading their charge throughout their volume and in Kaufmann's experiment their shape would be compressed in the direction of motion and stay unchanged in the transverse directions. To Kaufmann's surprise, Lorentz could show that his model agrees 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.[A 7][A 8][11] [12]

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.[A 9] [13]

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.[A 10][14]

Experiments of 1905

To bring a decision between those theories, Kaufmann again performed his experiments with higher precision. With respect to the increase of mass, the predictions of the various theories were:

\begin{array}{ll} \mathrm{Abraham} & \phi(\beta)=\frac{3}{4}\frac{1}{\beta^{2}}\cdot\left(\frac{1%2B\beta^{2}}{2\beta}\cdot\lg\frac{1%2B\beta}{1-\beta}-1\right)\\ \\\mathrm{Lorentz-Einstein} & \phi(\beta)=(1-\beta^{2})^{-\frac{1}{2}}\\ \\\mathrm{Bucherer-Langevin} & \phi(\beta)=(1-\beta^{2})^{-\frac{1}{3}}\end{array}

Kaufmann assumed, that he had conclusively disproved the formula of Lorentz-Einstein, and therefore also disproved the principle of relativity. In his view, the only remaining options were the theories of Abraham and Bucherer. Lorentz was perplexed and wrote that he was "at the end of his Latin".[A 11][A 12][15] [16]

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 predicted the measurements using the two competing theories. He showed, that Kaufmann's results are not fully decisive and would lead to superluminal velocities. Also Adolf Bestelmeyer (1906) criticized some technical aspects of Kaufmann's measurements. And Einstein remarked in 1907, that although Kaufmann's results are better in agreement with Abraham's and Bucherer's theories than with his own, the foundations of the other theories are not plausible and therefore have only little probability of being correct.[A 13][A 14][17][18][19]

Evolution of experiments

Bucherer's experiments

In 1908, Alfred Bucherer performed new measurements by using a velocity filter. Contrary to Kaufmann, he argued that those experiments confirmed the relativity principle and consequently the "relativity theory of Lorentz and Einstein". Bucherer was immediately applauded by Lorentz, Einstein, and Hermann Minkowski. On the other hand, Adolf Bestelmeyer published a paper, in which he cast doubt on the validity of Bucherer's result. What followed, was a polemic dispute between those two scholars in a series of publications. Thus, although many physicists accepted Bucherer's result, there still remained some doubts.[A 15][A 16][20] [21] [22] [23] [24] [25]

Further development

Using similar techniques, but improving their setup and analysis steps, others – Hupka (1910),[26] [27] [28] [29] Neumann (1914),[30] Guye and Lavanchy (1915)[31] – again repeated the experiments. Especially the experiments by Neumann were considered as conclusively in favor of special relativity.[A 17][A 18][A 19]

Lorentz summarized these efforts in 1915:[A 20]

Later experiments [..] have confirmed the formula [..] for the transverse electromagnetic mass, so that, in all probability, the only objection that could be raised against the hypothesis of the deformable electron and the principle of relativity has now been removed.

However, Zahn and Spees showed in 1938, that many assumptions employed in those early experiments as to the nature and the properties of electrons and the experimental setup, were wrong. The Kaufmann–Bucherer–Neumann experiments would only show a qualitative increase of mass, and were incapable of deciding between the competing theories.[A 21][A 22][32] So, Rogers et. al. (1940) repeated the experiments with improved setup and eventually found a clear agreement with the Lorentz-Einstein-formula. [33]

While those experiments were disputed for a long time, the investigations of the fine structure of the hydrogen lines already in 1917 provided a clear confirmation of the Lorentz-Einstein formula, and the refutation of Abraham's theory.[A 23] Today, in modern particle-accelerators, the predictions of special relativity are routinely confirmed beyond any doubt.

See also

References

Secondary sources

  1. ^ Miller (1981), pp. 45-47
  2. ^ Pais (1982), pp. 155-159
  3. ^ Miller (1981), pp. 47-54
  4. ^ Staley (2009), pp. 223-233
  5. ^ Miller (1981), pp. 55-67
  6. ^ Staley (1982), pp. 229-233
  7. ^ Miller (1981), pp. 55-67
  8. ^ Janssen (2005), pp. 16-25
  9. ^ Janssen (2005), pp. 16-25
  10. ^ Staley (2009), pp. 241-242
  11. ^ Miller (1981), pp. 228-232
  12. ^ Staley (2009), pp. 242-244
  13. ^ Miller (1981), pp. 232-235
  14. ^ Staley (2009), pp. 244-250
  15. ^ Miller (1981), pp. 345-350
  16. ^ Staley (2009), pp. 250-254
  17. ^ Pauli (1921), p. 636
  18. ^ Miller (1981), pp. 350-351
  19. ^ Staley (2009), pp. 254-257
  20. ^ Lorentz (1915), p. 339
  21. ^ Miller (1981), pp. 351-352
  22. ^ Janssen (2005), pp. 41-43, 57
  23. ^ Pauli (1921), pp. 636-637

Primary sources

  1. ^ Thomson, J. J. (1881), "On the Effects produced by the Motion of Electrified Bodies", Philosophical Magazine, 5 11 (68): 229–249 
  2. ^ Searle, G.F.C (1897), "On the Steady Motion of an Electrified Ellipsoid", Philosophical Magazine, 5 44 (269): 329–341 
  3. ^ Lorentz, H.A. (1900), "On the Apparent Mass of the Ions", Physikalische Zeitschrift 2 (5): 78–80 
  4. ^ Kaufmann, W. (1901), "Die magnetische und elektrische Ablenkbarkeit der Bequerelstrahlen und die scheinbare Masse der Elektronen", Göttinger Nachrichten (2): 143–168 
  5. ^ Kaufmann, W. (1902), "Über die elektromagnetische Masse des Elektrons", Göttinger Nachrichten (5): 291–296, http://resolver.sub.uni-goettingen.de/purl?GDZPPN002499444 
  6. ^ Kaufmann, W. (1902), "The Electromagnetic Mass of the Electron", Physikalische Zeitschrift 4 (1b): 54–56 
  7. ^ Kaufmann, W. (1903), "Über die "Elektromagnetische Masse" der Elektronen at the Internet Archive", Göttinger Nachrichten (3): 90–103 
  8. ^ Abraham, M. (1902). "Dynamik des Electrons". Göttinger Nachrichten: 20–41. 
  9. ^ Abraham, M. (1902). "Principles of the Dynamics of the Electron (1902)‎". Physikalische Zeitschrift 4 (1b): 57–62. 
  10. ^ Abraham, M. (1903). "Prinzipien der Dynamik des Elektrons". Annalen der Physik 10: 105–179. 
  11. ^ Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity smaller than that of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences 6: 809–831 
  12. ^ Poincaré, Henri (1906), "On the Dynamics of the Electron", Rendiconti del Circolo matematico di Palermo 21: 129–176 
  13. ^ A.H. Bucherer, Mathematische Einführung in die Elektronentheorie, Teubner, Leipzig 1904, p. 57
  14. ^ Einstein, Albert (1905), "Zur Elektrodynamik bewegter Körper", Annalen der Physik 322 (10): 891–921, Bibcode 1905AnP...322..891E, doi:10.1002/andp.19053221004 . See also: English translation.
  15. ^ Kaufmann, W. (1905), "On the Constitution of the Electron", Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften (45): 949–956 
  16. ^ Kaufmann, W. (1906), "On the Constitution of the Electron", Annalen der Physik 19: 487–553 
  17. ^ Planck, Max (1906), "The Measurements of Kaufmann on the Deflectability of β-Rays in their Importance for the Dynamics of the Electrons", Physikalische Zeitschrift 7: 753–761 
  18. ^ M. Planck, Nachtrag zu der Besprechung der Kaufmannschen Ablenkungsmessungen, Verhandlungen der Deutschen Physikalischen Gesellschaft, 9 (1907)
  19. ^ Einstein, Albert (1908), "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen", Jahrbuch der Radioaktivität und Elektronik 4: 411–462, Bibcode 1908JRE.....4..411E 
  20. ^ Bucherer, A. H. (1908), "Measurements of Becquerel rays. The Experimental Confirmation of the Lorentz-Einstein Theory", Physikalische Zeitschrift 9 (22): 755–762 
  21. ^ Bucherer, A. H. (1909). "Die experimentelle Bestätigung des Relativitätsprinzips". Annalen der Physik 333 (3): 513–536. Bibcode 1909AnP...333..513B. doi:10.1002/andp.19093330305. 
  22. ^ Bestelmeyer, A. H. (1909). "Bemerkungen zu der Abhandlung Hrn. A. H. Bucherers: Die experimentelle Bestätigung des Relativitätsprinzips". Annalen der Physik 335 (11): 166–174. Bibcode 1909AnP...335..166B. doi:10.1002/andp.19093351105. 
  23. ^ Bucherer, A. H. (1909). "Antwort auf die Kritik des Hrn. E. Bestelmeyer bezüglich meiner experimentellen Bestätigung des Relativitätsprinzips". Annalen der Physik 335 (11): 974–986. Bibcode 1909AnP...335..974B. doi:10.1002/andp.19093351506. 
  24. ^ Bestelmeyer, A. H. (1910). "Erwiderung auf die Antwort des Hrn. A. H. Bucherer". Annalen der Physik 337 (6): 231–235. Bibcode 1910AnP...337..231B. doi:10.1002/andp.19103370609. 
  25. ^ Bucherer, A. H. (1910). "Erwiderung auf die Bemerkungen des Hrn. A. Bestelmeyer". Annalen der Physik 338 (14): 853–856. Bibcode 1910AnP...338..853B. doi:10.1002/andp.19103381414. 
  26. ^ Hupka, E. (1910). "Beitrag zur Kenntnis der trägen Masse bewegter Elektronen". Annalen der Physik 336 (1): 169–204. Bibcode 1909AnP...336..169H. doi:10.1002/andp.19093360109. 
  27. ^ Heil, W. (1910). "Diskussion der Versuche über die träge Masse bewegter Elektronen". Annalen der Physik 336 (3): 519–546. Bibcode 1910AnP...336..519H. doi:10.1002/andp.19103360305. 
  28. ^ Hupka, E. (1910). "Zur Frage der trägen Masse bewegter Elektronen". Annalen der Physik 338 (12): 400–402. Bibcode 1910AnP...336..519H. doi:10.1002/andp.19103360305. 
  29. ^ Heil, W. (1910). "Zur Diskussion der Hupkaschen Versuche über die träge Masse bewegter Elektronen". Annalen der Physik 338 (12): 403–413. Bibcode 1910AnP...338..403H. doi:10.1002/andp.19103381210. 
  30. ^ Neumann, Günther (1914). "Die träge Masse schnell bewegter Elektronen". Annalen der Physik 350 (20): 529–579. Bibcode 1914AnP...350..529N. doi:10.1002/andp.19143502005. 
  31. ^ C.E. Guye, C. Lavanchy (1915). "Vérification expérimentale de la formule de Lorentz-Einstein par les rayons cathodiques de grande vitesse". Compt. Rend. Acad. Sci. 161: 52–55. http://gallica.bnf.fr/ark:/12148/bpt6k3114b/f52. 
  32. ^ Zahn, C. T. and Spees, A. A. (1938), "A Critical Analysis of the Classical Experiments on the Variation of Electron Mass", Physical Review 53: 511–521, Bibcode 1938PhRv...53..511Z, doi:10.1103/PhysRev.53.511 
  33. ^ Rogers, M. M. et al. (1940), "A Determination of the Masses and Velocities of Three Radium B Beta-Particles", Physical Review 57: 379–383, Bibcode 1940PhRv...57..379R, doi:10.1103/PhysRev.57.379 

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