thesis

Hermann minkowski et la mathematisation de la theorie de la relativite restreinte, 1905-1915

Defense date:

Jan. 1, 1996

Edit

Institution:

Paris 7

Disciplines:

Authors:

Directors:

Abstract EN:

The role of mathematicians in the discovery, reception and development of the non-gravitational theory of relativity is studied from the angle of hermann minkowski's work. It is argued that minkowski effectively expanded the disciplinary frontier of mathematics to include the principle of relativity, thereby paving the way for mathematical engagement with the theory of relativity. This view finds support from a bibliometric analysis, in which europeanlanguage publications on non-gravitational relativity are correlated against author discipline and geographic location, as well as periodical type and site of publication. Minkowski's manuscripts shed light on his discovery of space-time mechanics, and show that prior to november, 1907, he was not in possession of the notion of a worldline in spacetime. Following minkowski's death, the extension of the concept of rigidity to space-time kinematics was attempted by his followers, including theodor kaluza, who in 1910 studied the riemannian geometry of a rigidly-rotating disk, incorporating an approach resembling that of the general theory of relativity discovered two years later by albert einstein. From the frequency with which non-euclidean geometry was encountered in the scientific literature of this period, einstein's choice of a riemannian space-time metric as the foundation of the theory of general relativity takes its place as a natural response to the elaboration of minkowskian kinematics. In this order of ideas, by the turn of the century, henri poincare's conventionalist doctrine appears to have obtained few disciples among leading continental mathematicians ; with the advent of minkowskian relativity, several scientists found a confirmation of their views on the necessity of an empirical determination of the geometry of space.

Abstract FR:

Le role des mathematiciens dans la decouverte, la reception scientifique, et le developpement de la theorie de la relativite restreinte est aborde sous l'angle des contributions de hermann minkowski. L'effet produit par l'intervention de minkowski s'interprete comme une expansion de la frontiere disciplinaire des mathematiques ; en effet, minkowski a ouvert la porte de la physique relativiste aux mathematiciens. L'interpretation s'appuie sur l'analyse bibliometrique des publications en langues europeennes, ou le fait de publier sur la theorie de la relativite restreinte est mis en rapport avec la discipline et la region geographique de l'auteur, ainsi que le type de periodique l'emplacement geographique de sa redaction. Certains manuscrits de minkowski portent sur sa decouverte de la mecanique de l'espace-temps, et montrent que jusqu'a novembre 1907 la notion d'une ligne d'univers lui etait inconnue. Apres la mort de minkowski, les deplacements des corps 'rigides' dans l'espace-temps ont ete etudies par ses disciples, y compris theodor kaluza, dont l'analyse en 1910 de la geometrie riemannienne du disque tournant etait proche de la theorie de la relativite generale, decouverte deux ans plus tard par albert einstein. Le travail de c dernier, est-il suggere, sortait d'un contexte scientifique dans lequel l'emploie de la geometrie non euclidienne se banalisait. Dans cet ordre d'idees, il est montre qu'au debut du siecle la doctrine conventionnaliste de henri poincare avait seduit peu de mathematiciens de haut niveau ; et meme que plusieurs savants trouvaient dans la theorie minkowskienne la confirmation du point de vue empiriste sur la geometrie de l'espace.