Ludwik Silberstein

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Ludwik Silberstein (1872 – 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework. His textbook The Theory of Relativity was published by Macmillan & Co Ltd in 1914 with a second edition, expanded to include general relativity, in 1924.


Silberstein was born May 17, 1872 in Warsaw to Samuel Silberstein and Emily Steinkalk. He was educated in Cracow, Heidelberg, and Berlin. To teach he went to Bologna, Italy from 1899 to 1904. Then he took a position at Sapienza University of Rome.[1]

In 1907 Silberstein described a bivector approach to the fundamental electromagnetic equations.[2] When E and B represent electric and magnetic vector fields with values in R3, then Silberstein suggested E + i B would have values in C3, consolidating the field description with complexification. This contribution has been described as a crucial step in modernizing Maxwell’s equations,[3] while E + i B is known as the Riemann–Silberstein vector.

Silberstein taught in Rome until 1920, when he entered private research for the Eastman Kodak Company of Rochester, New York. For nine years he maintained this consultancy with Kodak labs while he gave his relativity course on occasion at the University of Chicago, the University of Toronto, and Cornell University. He lived until January 17, 1948.[4]

Textbook inaugurating relativity science[edit]

At the International Congress of Mathematicians in 1912 at Cambridge, Silberstein spoke on "Some applications of quaternions". Though the text was not published in the proceedings of the Congress, it did appear in the Philosophical Magazine of May, 1912, with the title "Quaternionic form of relativity".[5] The following year Macmillan & Co Ltd published The Theory of Relativity, which is now available on-line in the Internet Archive (see references). The quaternions used are actually biquaternions. The book is highly readable and well-referenced with contemporary sources in the footnotes.

Several reviews were published. Nature expressed some misgivings:[6]

A systematic exposition of the principle of relativity necessarily consists very largely in the demonstration of invariant properties of certain mathematical relations. Hence it is bound to appear a little uninteresting to the experimentalist...little is done to remove the unfortunate impression that relativity is a fad of the mathematician, and not a thing for the every-day physicist.

In his review[7] Morris R. Cohen wrote, "Dr. Silberstein is not inclined to emphasize the revolutionary character of the new ideas, but rather concerned to show their intimate connection with older ones." Another review[8] by Maurice Solovine states that Silberstein subjected the relativity principle to an exhaustive examination in the context of, and with respect to, the principle problems of mathematical physics taken up at the time.

On the basis of the book, Silberstein was invited to lecture at the University of Toronto.[9] The influence of these lectures on John Lighton Synge has been noted:

Synge had also been strongly influenced a few months previously [in January 1921] by a Toronto lecture series organized by J.C. McLennan on "Recent Advances in Physics", at which Silberstein gave eighteen lectures on "Special and Generalized Theories of Relativity and Gravitation, and on Spectroscopy", all from a mathematical standpoint.[10]

The Einstein–Silberstein debate[edit]

In 1935, following a controversial debate[11] with Einstein, Silberstein published a solution[12] of Einstein's field equations that appeared to describe a static, axisymmetric metric with only two point singularities representing two point masses. Such a solution clearly violates our understanding of gravity: with nothing to support them and no kinetic energy to hold them apart, the two masses should fall towards each other due to their mutual gravity, in contrast with the static nature of Silberstein's solution. This led Silberstein to claim that Einstein's theory was flawed, in need of a revision. In response, Einstein and Rosen published a Letter[13] to the Editor in which they pointed out a critical flaw in Silberstein's reasoning. Unconvinced, Silberstein took the debate to the popular press, with The Evening Telegram in Toronto publishing an article titled "Fatal blow to relativity issued here" on March 7, 1936.[14] Nonetheless, Einstein was correct and Silberstein was wrong: as we know today, all solutions to Weyl's family of axisymmetric metrics, of which Silberstein's is one example, necessarily contain singular structures ("struts", "ropes", or "membranes") that are responsible for holding masses against the attractive force of gravity in a static configuration.[15]

Other contributions[edit]

According to Martin Claussen,[16] Ludwik Silberstein initiated a line of thought involving eddy currents in the atmosphere, or fluids generally. He says that Silberstein anticipated foundational work by Vilhelm Bjerknes (1862 – 1951).

Books by Ludwik Silberstein[edit]

See also[edit]


  1. ^ Jordan D. Marche II (2007) "Ludwik Silberstein", Biographical Encyclopedia of Astronomers, Thomas Hockey editor, pp 1059,60.
  2. ^ L. Silberstein (1907) "Electromagnetische Grundgleichungen in bivectorielle Behandlung", Annalen der Physik 22:579–86 & 24:783–4
  3. ^ V.M. Red’kov, N.G. Tokarevskaya, & George J Spix (2012) "Majora-Oppenheimer approach to Maxwell Electrodynamics: Part I Minkowski Space", Advances in Applied Clifford Algebras 22:1129–49
  4. ^ Allen G. Debus, "Ludwik Silberstein", Who's Who in Science, 1968.
  5. ^ Ludwik Silberstein, "Quaternionic form of relativity", Philosophical Magazine 23:790–809.
  6. ^ Anon. (1914) Review: Theory of Relativity Nature 94:387 (#2354)
  7. ^ Morris R. Cohen (1916) Review of Theory of Relativity, Philosophical Review 25:207–9
  8. ^ Maurice Solovine (1916) Review:Theory of Relativity, Revue philosophique de la France et de l'étranger 81:394,5
  9. ^ Published in a slightly expanded form as The Theory of General Relativity and Gravitation (1922).
  10. ^ E. Riehm & F. Hoffman (2011) Turbulent times in Mathematics, p. 80, American Mathematical Society ISBN 978-0-8218-6914-7
  11. ^ P. Havas, The General-Relativistic Two-Body Problem and the Einstein–Silberstein Controversy, in J. Earman, et al. (eds) (2003). The Attraction of Gravitation. Birkhäuser. ISBN 978-0-8176-3624-1. 
  12. ^ Ludwik Silberstein (February 1, 1936). "Two-Centers Solution of the Gravitational Field Equations, and the Need for a Reformed Theory of Matter" (subscription required). Physical Review 49: 268–270. Bibcode:1936PhRv...49..268S. doi:10.1103/PhysRev.49.268. 
  13. ^ A. Einstein and N. Rosen (February 17, 1936). "Two-Body Problem in General Relativity" (subscription required). Physical Review 49: 404–405. Bibcode:1936PhRv...49..404E. doi:10.1103/PhysRev.49.404.2. 
  14. ^ "Einstein Archives Online Nr. [15-258.10]". 
  15. ^ Hans Stephani et al. (2003). Exact Solutions to Einstein's Field Equations Second Edition. Cambridge University Press. ISBN 0-521-46136-7. 
  16. ^ Martin Claussen, Bericht uber die 4. FAGEM Tagung, S. 16 .
  17. ^ Eisenhart, L. P. (1924). "Review: The Mathematical Theory of Relativity, by A. S. Eddington; The Meaning of Relativity, by A. Einstein; The Theory of General Relativity Theory and Gravitation, by L. Silberstein". Bull. Amer. Math. Soc. 30 (1): 71–78. doi:10.1090/s0002-9904-1924-03854-3.