Minkowski never mentioned the Erlangen Program

Here is an example of an Einstein historian who looked at the original documents, finds that Poincare and Minkowski discovered spacetime, but still finds strange reasons for discrediting them.

Thibault Damour wrote in a 2008 paper:

This contribution tries to highlight the importance of Minkowski's ``Raum und Zeit'' lecture in a ``negative'' way, where negative is taken in the photographic sense of reversing lights and shades. Indeed, we focus on the ``shades'' of Minkowski's text, i.e. what is missing, or misunderstood. In particular, we focus on two issues: (i) why are Poincaré's pioneering contributions to four-dimensional geometry not quoted by Minkowski (while he abundantly quoted them a few months before the Cologne lecture)?, and (ii) did Minkowski fully grasp the physical (and existential) meaning of ``time'' within spacetime? We think that this ``negative'' approach (and the contrast between Poincaré's and Minkowski's attitudes towards physics) allows one to better grasp the boldness of the revolutionary step taken by Minkowski in his Cologne lecture.

He finds that Minkowski got crucial relativity and spacetime ideas from Poincare, and credited him in 1907 papers, but not in his famous 1908 paper.

This contribution tries to highlight the importance of Minkowski's ``Raum und Zeit'' lecture in a ``negative'' way, where negative is taken in the photographic sense of reversing lights and shades. Indeed, we focus on the ``shades'' of Minkowski's text, i.e. what is missing, or misunderstood. In particular, we focus on two issues: (i) why are Poincaré's pioneering contributions to four-dimensional geometry not quoted by Minkowski (while he abundantly quoted them a few months before the Cologne lecture)?, and (ii) did Minkowski fully grasp the physical (and existential) meaning of ``time'' within spacetime? We think that this ``negative'' approach (and the contrast between Poincaré's and Minkowski's attitudes towards physics) allows one to better grasp the boldness of the revolutionary step taken by Minkowski in his Cologne lecture.

Another odd omission:

I therefore find rather surprising that Minkowski never points out the link between his group-approach to a 4-dimensional geometry and Klein’s famous Erlangen programme (which consisted in defining a geometry by its symmetry group, rather than by the ‘objects’ on which it acts). This is all the more surprising since Klein was the organizer of the mathematics section in which Minkowski was invited to speak. Knowing also all what Minkowski owed to Felix Klein, I would have expected Minkowski to add at least a passing allusion to his Erlangen Programme. For instance, Pauli’s famous article (and book) on Relativity contains a section (§8) on how Relativity fits within Klein’s “Erlangen Programme” [17].

To this day, the flat non-Euclidean geometry of Minnkowski space is not appreciated. It is a wonder that Poincare does not mention it either.

Briefly, the Erlangen Program was an 1872 plan to unify study of non-euclidean geometries by symmetry groups or invariants.  Euclidean geometry has the symmetries of rotations, translations, and reflections, and ordinary distance is invariant. Similarly other geometries can be described by symmetries and invariants. Spacetime fits that program, with the Lorentz group being the symmetries, and the metric dx² + dy² + dz² - dt² being the invariant. While Euclidean geometry was defined by Euclid's Elements, non-euclidean geometry is based on the Erlangen program.

I don't know why Minkowski did not mention the Erlangen program. More curious is why most of the relativity textbooks of the next century do not mention it either. I think physicists have a hostility towards geometry, and towards the mathematicians who appreciate geometry.

Damour concludes by attacking Poincare:

To conclude these somewhat disconnected remarks, let me try to characterize the greatness of the conceptual leap achieved by Minkowski in his Raum und Zeit lecture by contrasting it with the attitude of Poincar´e. We recalled above that, at the purely technical level, several (though certainly not all) of the key mathematical structures of “Minkowski spacetime” were already, explicitly or implicitly, contained in Poincare’s Rendiconti paper. But, what made the difference was that Minkowski had the boldness of realizing and publicizing the revolutionary aspects of these structures.

Then he goes on to explain a section of Poincare's 1905 paper where he makes an analogy, saying his new relativity theory is replacing Lorentz's analogously to the way that Copernicus replaced Ptolemy.

The analogy is that in the Ptolemy theory, the Earth's year appears coincidentally in the orbits of the Sun and other planets. With Copernicus, the number has a common origin in the orbit of the Earth. Likewise, in Lorentz, gravity and electromagnetism coincidentally propagate with the speed of light. In Poincare's spacetime theory, the speeds have a common origin in the geometry of spacetime.

And Damour complains that this is not bold or revolutionary!

This citation clearly shows the deeply conservative bend of Poincare in physics. He is happy to contribute to the Lorentz-Ptolemy programme, and he steps back from any move that might shake its kinematical foundations. Minkowski, by contrast, had a lot of ambition and self-confidence (not to say chutzpah), and was keen on breaking new ground in mathematical physics. Without fully understanding what Einstein had done, nor (at least initially) what Poincare had already achieved, he was lucky to unearth elegant and deep mathematical structures that were implicitly contained in their (and others’) work, and had the boldness to embrace with enthusiasm their revolutionary character. One must certainly admire him for this achievement, though one might regret his unfairness towards Poincare.

This is crazy stuff. Minkowski obviously understood everything Einstein did, and much preferred Poincare's geometrical spacetime theory. Poincare said he had a theory as revolutionary as Copernicus. Einstein made no such claim, and only said he had an elaboration of Lorentz's theory. Einstein never goes against Lorentz the way Poincare does.

I would criticize Minkowski for not properly crediting Poincare and the Erlangen program, except that he died about a year later. Maybe he would have credited them better if he had lived.