In 1918 the war between Poland and Russia broke out and Mathisson undertook military service for two years. At the end of the war he returned to continue his work at the University of Warsaw, also undertaking research at the Universities of Kazan and Cracow. However the death of his father forced him to take a break from his studies and researches. At the end of 1925 Professor Czeslan Bialobrzeski approved his paper Sur le movement d'un corps tournant dans un champ de gravitation Ⓣ as his PhD Thesis.
He spoke Hebrew, Polish, Russian, French, German and English and for many years his only profits were got by his translations from Hebrew and by making technical calculations for those working with reinforced concrete. Mathisson went to Cracow in 1937 where he collaborated with Professor Weyssenhoff, who held the chair of theoretical physics in the Jagellonian University, working on the theory of spin particles. He remained there for two years before he went to Cambridge in England in 1939. There he developed his more important studies but sadly he died in Cambridge at the early age of forty-three only a year later.
Mathisson studied general dynamical laws governing the motion of a particle, with possibly a spin or an angular momentum, in a gravitational or electromagnetic field, and developed a powerful method for passing from field equations to particle equations. The subject was of particular interest at that time, as it had become clear that quantum mechanics cannot solve the difficulties that had arisen in connection with the interaction of point particles with fields, and a deeper classical analysis of the problem was needed. Dirac wrote that the death of Mathisson:-
... has cut short an interesting line of research.In fact, he died at the early age of forty-three before the relations between his method and those of other researchers on the subject had been completely elucidated.
The synthesis of his method was published in 1940 [Mathisson, 1940]. Mathisson proved that the variational equation can be solved when it has been defined so that the equations to be imposed upon the characteristic tensor will be compatible with the variations allowed in the fields. The transition from the characteristic tensor to the dynamical variables is conveyed by an analysis of the physical meaning of the constituents. The ideas in this paper were developed further in a second part [Mathisson, 1942], which was edited by P A M Dirac after Mathisson's death, who wrote in a footnote to the introduction:-
This work was found in an unfinished state among the papers left by Dr Myron Mathisson, who died on 13 September 1940. I have edited and have added a summary. There was also some works to show that the condition of integrability of the magnitude of the angular momentum requires the electric momentum to vanish (and not merely to be parallel to the magnetic moment), but I was not able to follow the argument and have omitted this part.In this last paper Mathisson applied his general variational method to the case of a particle for which second moments are important but third and higher moments are negligible. He obtained the equations of motion for the angular momentum and for the centre of mass with arbitrary external forces. Then he calculated the angular forces for a charged particle with electric and magnetic moments moving in a general electromagnetic field. Finally, he calculated the linear forces for the case of no electric moment, leading to the equations for linear motion. He obtained the result that, in order that the mass may be integrable, the ratio of the magnetic moment to the angular momentum must be constant.
Here is a list of Mathisson's publications:
- M Mathisson, Die Beharrungsgesetze in der allgemeinen Relativitätstheorie Ⓣ, Z. f. Physik 67 (1931), 270-277.
- M Mathisson, Die Mechanik des Materieteilchens in der allgemeinen Relativitätstheorie Ⓣ, Z. f. Physik 67 (1931), 826-844.
- M Mathisson, Bewegungsproblem der Feldphysik und Elektronenkonstanten. Ⓣ, Z. f. Physik 69 (1931), 389-408.
- M Mathisson, Eine neue Lösungsmethode für Differentialgleichungen von normalem hyperbolischem Typus Ⓣ, Math. Ann. 107 (1932), 400-419.
- M Mathisson, Metoda parametrysy w zastosowaniu de hiperbolicznych ukladöw röwuafi Ⓣ, Prace matematyczno-fizyczne 41 (1934), 177-185.
- M Mathisson, Neue Mechanik materieller systemes Ⓣ, Acta Physica Polonica 6 (1937), 163-200.
- M Mathisson, Das Zitternde Elektron und seine Dynamik Ⓣ, Acta Physica Polonica 6 (1937), 218-227.
- M Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes Ⓣ, Acta Math. 71 (1939), 249-282.
- M Mathisson, The variational equation of relativistic dynamics, Proc. Cambridge Philos. Soc. 36 (1940), 331-350.
- M Mathisson, Relativistic dynamics of a spinning magnetic particle, Proc. Cambridge Philos. Soc. 38 (1942), 40-60.
Article by: Umberto Lucia, Sociaetà Italiana di Storia delle Matematiche