Speaker
Description
We’re in the phase of the old quantum theory that begins—after Sommerfeld’s refinements (1915) to Bohr’s atom—to involve sophisticated analytical mechanics; Schwarzschild (1916) has just turned atomic mechanics into a Hamiltonian ‘micro-celestial’ mechanics, with action-angle variables, resonances etc. The two names in my title represent the two research programmes I propose to compare. On the one hand there’s Einstein on his own, with three texts from his annus mechanicus 1917—but mainly “Zum Quantensatz von Sommerfeld and Epstein”; whereas “Epstein” stands for what I’m considering the ‘other research programme,’ which in addition to Paul Epstein himself involved his teacher Sommerfeld, Schwarzschild &al. Both programmes (Einp stein) involve ancestors of the invariant tori that emerge decades later—developing them in very different ways: Einstein through his Riemannisierung, Epstein through canonical action-angle variables. Whereas Epstein have a quantum condition for every (angle) coordinate, Einstein proposes a highly invariant theory with a condition for every homotopy class of the N-torus. Each of his quantum conditions is doubly invariant: with respect to loop deformations, and to coordinate transformations. Epstein use perturbations to obtain as much ‘ergodicity’ as possible—the more the better; whereas Einstein needs some but not too much—which would render his Riemannisierung inapplicable.
