Proceedings Series

Vol. 1 (2008), No. 1, pp. 1 – 225

International Conference Devoted to Myron Mathisson: His Life, Work and Influence on Current Research

Warsaw, Poland; October 18-20, 2007

Myron Mathisson: What Little We Know of His Life


Myron Mathisson (1897–1940) was a Polish Jew known for his work on the equations of motion of bodies in general relativity and for developing a new method to analyze the properties of fundamental solutions of linear hyperbolic differential equations. In particular, he derived the equations for a spinning body moving in a gravitational field and proved, in a special case, the Hadamard conjecture on the class of equations that satisfy the Huygens principle. His work still exerts influence on current research. Drawing on various archival and secondary sources, in particular his correspondence with Einstein, we outline Mathisson’s biography and scientific career.

Mathisson’s New Mechanics: Its Aims and Realisation


In 1937, Myron Mathisson published in this journal a paper entitled A New Mechanics of Material Systems. This showed for the first time how an extended body in general relativity could be described by an infinite set of multipole moments and how approximate equations of motion could be obtained by retaining only a finite number of these moments. He obtained such equations of motion when only the monopole and dipole moments are retained and also partial results when the quadrupole moment is also retained. This was the start of a programme of work that he continued until his death in 1940. This paper identifies the aims of this work and the obstacles that still needed to be overcome. It outlines subsequent developments by the present author and others that have continued this programme and brought it to fulfillment.

Hadamard’s Problem of Diffusion of Waves


The status of Hadamard’s problem of diffusion of waves for second order hyperbolic equations of normal hyperbolic type in four independent variables is reviewed wherein the contributions of Myron Mathisson are highlighted. A new family of non-trivial, non-self-adjoint wave equations which satisfy Huygens’ principle in the strict sense is given.

Huygens’ Principle and Anomalously Small Radiation Tails


This is a short account of recent joint work with Chmaj and Rostworowski on late-time asymptotic behavior of linear and nonlinear waves propagating on even-dimensional Minkowski spacetime.

Classical and Quantum Spins in Curved Spacetimes


A comparative analysis of the Mathisson–Papapetrou and Pomeransky–Khriplovich equations is presented. Motion of spinning particles and their spins in gravitational fields and noninertial frames is considered. The angular velocity of spin precession defined by the Pomeransky–Khriplovich equations depends on the choice of the tetrad. The connection of such a dependence with the Thomas precession is established. General properties of spin interactions with gravitational fields are discussed. It is shown that dynamics of classical and quantum spins in curved spacetimes is identical. A manifestation of the equivalence principle in an evolution of the helicity is analyzed.

Fundamental Relativistic Rotator


Professor Jan Weyssenhoff was Myron Mathisson’s sponsor and collaborator. He introduced a class of objects known in Cracow as “kręciołki Weyssenhoffa”, “Weyssenhoff’s rotating little beasts”. The Author describes a particularly simple object from this class. The relativistic rotator described in the paper is such that its both Casimir invariants are parameters rather than constants of motion.

Spin-Gravity Coupling


Mathisson’s spin-gravity coupling and its Larmor-equivalent interaction, namely, the spin-rotation coupling are discussed. The study of the latter leads to a critical examination of the basic role of locality in relativistic physics. The nonlocal theory of accelerated systems is outlined and some of its implications are described.

On the Relations Between Field Equations and Equations of Motion in Newtonian and Einsteinian Gravity


A pseudo-field theoretic reformulation of the Newton–Euler dynamics of isolated, gravitating fluids is given. The basic equations of that theory are shown to be regular limits of Einstein’s gravitational field equation. It is reviewed how the equations of motion for mass points can be obtained as approximations from those for extended bodies without use of a regularisation to remove infinities. Finally Einstein’s (1916–1918) approximation method is revived; its similarity to Newtonian theory suggests the possibility of avoiding infinities also in General Relativity.

Current Status of the Frame Dragging Experiments


We present a brief history of the proposed satellite experiments to detect effects of frame dragging in the general theory of relativity and discuss recent data.

Hamiltonian Description of Motion of Charged Particles with Spin


Equations of motion of a classical charged particle carrying a non-vanishing internal angular momentum (spin) are derived from first principles in the special relativistic context. The equations are implied by the conservation law of both the energy-momentum four-vector and the angular-momentum tensor carried by the total physical system, composed of the particle and the field. Our method leads directly to the variational and the hamiltonian formulations of the dynamics. It is based on the programme formulated in Kijowski, Gen. Relativ. Gravitation J. 26, 167 (1994) and Acta Phys. Pol. A 85, 771 (1994) and may be treated as an implementation of the idea of “deriving equations of motion from field equations”, formulated by Einstein.

Equations of Motion in the Gauge Gravity Models


In the gauge gravitational models, the geometry of a spacetime manifold becomes non-Riemannian. The curvature, torsion and nonmetricity are all nontrivial in these models, in general. The study of the dynamics of the physical matter (particles, bodies, continuous media, etc.) in such manifolds is crucial for determining the actual geometrical structure of the spacetime. Here we briefly describe a model of a test particle with hypermomentum which can be used as a tool for detecting the non-Riemannian geometry, and recall that the conservation laws in the gauge gravity theories underlie the general analysis of the equations of motion in such models.

The Motion of Test Bodies with Microstructure in Gauge Gravity Models


We report on the explicit form of the equations of motion of pole–dipole particles for a very large class of gravitational theories. The non-Riemannian framework in which the equations are derived allows for a unified description of nearly all known gravitational theories. The propagation equations are obtained with the help of a multipole expansion method from the conservation laws that follow from Noether’s theorem. The well-known propagation equations of general relativity, e.g. , as given by Mathisson and Papapetrou, represent a special case in our general framework. Our formalism allows for a direct identification of the couplings between the matter currents and the gravitational field strengths in gauge gravity models. In particular, it illustrates the need for matter with microstructure for the detection of non-Riemannian spacetime geometries.

Highly Relativistic Motions of Spinning Particles According to Mathisson Equations


The physical effects following from the Mathisson equations at the highly relativistic motions of a spinning test particle relative to a Schwarzschild mass are discussed. The corresponding numerical estimates are presented.

A New (Very) Unorthodox Approach to Equations of Motion in General Relativity


From the study of the asymptotic behavior of the Einstein or Einstein–Maxwell fields, a rather unusual new structure was found. This structure which is associated with asymptotically shearfree null congruences, appears to have significant physical interest or consequences. More specifically it allows us to define, at future null infinity, the center-of-mass and center-of-charge with detailed equations of motion, for an interior gravitating-electromagnetic system. In addition it allows for a definition of total angular momentum with its evolution equations. Though at the present time the details remain obscure to us, nevertheless we feel that our version of equations of motion are closely related to the point of view of Myron Mathisson.

Spinning Relativistic Particles in External Fields


The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin corrections to the equations of motion is built with the noncovariant description of spin and with the usual, “naïve” definition of the coordinate of a relativistic particle.

On the Quest for Information about Myron Mathisson


The purpose of the article is to indicate details connected with the search for any information on the life and work of Myron Mathisson (1897–1940), a not so widely known Polish theoretical physicist who made outstanding contributions to the problem of motion in general relativity and to the theory of the wave equation. The search started in about 1978. Since Tilman Sauer and Andrzej Trautman in their article published in the current issue of Acta Physica Polonica B have acknowledged some of the results of the search, one may regard the present article as a sort of an appendix to that by these authors.

A Few Words in Conclusion


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