Wednesday, November 11, 2020

Covariant with respect to Lorentz transformations

Philosopher Harvey R. Brown has a nice new paper on Noether and symmetry. He comments:
Einstein's 1905 derivation of the Lorentz transformations rested on two fundamental symmetry principles: the relativity principle (dynamical equivalence of inertial frames) and the isotropy of space, alongside the postulate governing the constancy of the speed of light with respect to the "resting" frame.74 The justification of all these principles did not rest, for Einstein, on any a priori notions about the structure of space and time, but was based on "plenty of experiential knowledge" related to mechanics and electrodynamics.75 Later, he would stress that the theory of special relativity could be summarised in one principle: "all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations".76 This allowed Einstein to say that the theory transcended Maxwell's equations, and what he saw as the awkward emphasis on the role of light in his 1905 formulation.77 Special relativity is essentially a constraint in the sense that a symmetry is being imposed on the fundamental equations of all the non-gravitational interactions.
These EInstein opinions are from 1940 and later, long after that 1905 paper.

The principle that all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations was written by Poincare in 1905 and Minkowski in 1907, but not endorsed by Einstein until about 1915. If that is really the essence of special relativity, then all the credit should go to Poincare and Minkowski, as Einstein contributed nothing to this line of thought.

This is the biggest reason I believe Einstein should not be credited with the discovery of special relativity. It is not just that others had the formula earlier. It is that the essence of the theory is Lorentz covariance, and Einstein did not even understand the concept until many years after others had published it and gained widespread acceptance.

The Brown paper does have a good discussion of the history of Noether's theorem. Nowadays, conservation of momentum and energy are considered synonomous with symmetries of spacetime. This was one of the most important insights of XX century Physics.


  1. Lorentz and Poincare derived LT from the relativity postulate postulate applied to Maxwell equations. Lorentz work was motivated by Michelson experiment. LT imply c=const. Poincare formulated the reality postulate iirc in 1900.

    Einstein derived LT using (1) Relativity postulate and (2) c=const postulate. However it is not obvious which law of physics that is invariant was invoked to apply the (1) relativity postulate but the (2) c=const usage was apparent and critical.

    Then once having LT he demonstrated that Maxwell equations are invariant with respect to LT. He got to the point of departure of Lorentz and Poincare.

    A hypothesis: Einstein knew of LT and Lorentz and Poincare work and decided to derive LT by adding the postulate (2) c=0 which was necessary to avoid replication of Lorentz work and necessity of avoiding mentioning Michelson which he pretty consistently claimed that he knew nothing about him for the rest of his life except when he let it slip few times. This way he could claim that he knew nothing of LT and have zero references in his paper. IN First English translation of his paper. footnote was added about Lorentz and his LT. But till his death he claim he did not kn wo of Poincare. The finally somber gave him cope of Poincare paper he generously sta=siat that it was a major contribution. It was just before his death

    When Einstein derived (did not show details ) the superposition of velocities he stated that the operation constitute a mathematic group. Interestingly pretty much the same phrase was in Poincare 1905 paper. Somehow I have difficulty believing that Einstein would use such a cool and fairly modern at that time mathematical concept which obviously was natural for Poincare.

    It is interesting that in many textbooks Michelson precedes STR that is present as explanation of Michelson but it never is stated that Einstein did not use or was aware of Michelson. What motivated Einstein work, which experiments? He mentioned Fizeau and the stellar aberration but it is very vague. And if was that interested in Fizeau why he did not make a step further and did not derive Fizeau formula with STR. It was done 2 years later by Max von Laue.

  2. A related issue. Do you know about Klein paper "incident"?

    It is possible that Einstein had some character flaw because totally unnecessarily already after his Nobel prize and when he was more famous than any other physicist before him in 1927 he plagiarized 1926 paper of Oscar Klein that lead to the Kaluza-Klein theory. But he was caught and the editor of the journal forced Einstein to write a statement that everything he showed was done year earlier by Klein. That’s why we have the Kaluza-Klein theory and not Kaluza-Klein-Einstein or Einstein only theory. Furthermore there is a proof that Einstein had a copy of Klein paper because he praised it in a letter to Ehrenfest. What does it tell you about him? Why? Was he some kind of psychopath? Kleptomaniac? Sense of impunity? Entitlement? One journal dared to review his paper and had it rejected. Einstein was furious. Wrote a furious letter that “you do not review my papers” and he never tried to publish in the same journal again.

    (1) Find a copy of “Zu Kaluzas Theorie des Zusammenhanges von Gravitation und Elektrizit√§t. Erste Mitteilung” (1927). And you will find the disclaimer that the editor Hr. H. Mandel forced Eisntein to write:

    Hr. H. Mandel macht mich darauf aufmerksam, dass die von mir hier mitgetcilten Ergbnisse nich neu sind. Der ganze Inhalt findet sich in der Arbeit vo O. Klein (Zeitschr. f. Physik 37, 12, 1926, S. 895). Man vergleiche ferner Fochs Arveit (Zeitschr. f. Physisk 39, 226, 1926).

    (2) Then get yourself

    Introduction to Volume 15 of The Collected Papers of Albert Einstein. The Berlin Years: Writings and Correspondence June 1925 – May 1927

    where you will find the following:

    “Both Ehrenfest and Lorentz urged Einstein to come to Leyden and join their meetings with Klein. Einstein wrote that he had to finish some things before vacationing with his sons (Doc. 319), but asked to see Klein’s paper two and a half months after he had been first informed of it (Doc. 356). Most likely at Ehrenfest’s suggestion, Klein wrote to Einstein directly in late August 1926 (Doc. 363). He sent Einstein not only the manuscript of his paper (Klein, O. 1926), but also proposed how he wanted to develop the theory further. In particular, he explained his idea of assuming a periodicity of the fifth coordinate, averaging over it, and reconceptualizing Schr√∂dinger’s wave function as a component of the five-dimensional metric by effectively dropping the sharpened cylinder condition and using the same version of the condition that Kaluza had used seven years earlier.”