Notes on Minkowski's Geometric Relativity

Einstein scholar Tilman Sauer writes a new paper:

Minkowski's Geometric Explanation of Lorentz Contraction

Hermann Minkowski's original explanation of relativistic length contraction using a space-time diagram and conic section geometry of a standard hyperbola is reconstructed on the basis of unpublished manuscript notes dated to the spring of 1908. The manuscript notes likely reflect Minkowski's preparation of a lecture to physics and mathematics teachers. They reveal Minkowski as an educator as well as a promoter of a mathematization of the physical sciences. I also comment on his interpretation of Einstein's work and on the use of language in his popularization of mathematics.

He did not find anything particularly interesting in the notes.

It is not clear that Einstein's work had much influence on Minkowski, if any.

He mentions Einstein’s work on the relativity principle as a continuation of Lorentz’s work. ...

He did not identify the principle of relativity and the principle of the constancy of the speed of light as the two defining principles for the special theory of relativity. Instead, he singled out Lorentz’s contraction hypothesis as a fundamental postulate, and the existence of a limiting velocity as an axiom. ...

He then stated his impression that Einstein had not yet achieved “full understanding of the facts” (“volle Einsicht der gegebenen Tatsachen”).

Minkowski mentions crediting Einstein for this:

Lorentz himself told me in a conversation in Rome that Einstein’s merit is to have recognized that the time of one electron is just as good as that of the other, i.e. to have recognized the equivalence of t and t′.

That may be Einstein's merit, but Lorentz surely understood that in 1895, because he used it to explain the Michelson-Morley experiment. And Poincare believed that Lorentz understood it, because it was part of the recommendation for Lorentz to get the 1902 Nobel Prize.

The whole point of the Lorentz 1895 theory was that Maxwell's equations held in the moving frame, for the transformed coordinates. For that to work, the transformed time has to be genuine time in the moving frame. Perhaps Lorentz was missing some conceptual details, but he had to believe that what he called "local time" was the locally observed time.

Discussion of Poincare is strangely absent. Minkowski wrote two papers on relativity, citing Poincare prominently in the first but not the second. Some of Minkowski work, such as the 4d spacetime, indefinite metric, and Lorentz covariance, appear to be straight out of Poincare. Minkowski died shortly afterwards, so we got no more explanation.

Sauer is loyal to Einstein, as evidenced by:

Minkowski knew about and cited Einstein’s famous paper from 1905 on the Electrodynamics of Moving Bodies (3), which introduced the special theory of relativity.

It is pretty clear that Minkowski would not have said that Einstein introduced the theory. If anyone, it was Lorentz, Poincare, and Minkowski.

Update: I happened to see a 2013 Sauer paper:

As is well-known,12 Einstein’s attempts to obtain an assistantship any- where failed flatly despite various letters of application. To make matters more difficult, Einstein and his fellow student Mileva Mari´c had fallen in love and, unfortunately, Mari´c had become pregnant in the spring of 1901, an unplanned circumstance that surely contributed to her failing the final examinations again at her second attempt in summer 1901. ...

Since Einstein now had a tenured job, he was able to marry Mileva Mari´c in January 1903.

This is such a strange way of describing the situation. The daughter Lieserl is believed to have been abandoned. He could have married and taken responsibility for the child, even without a tenured job.