USSR Academy of Sciences), M. F. Shirokov (Moscow), I. Z. Fisher (Minsk), R. I. Khrapko (Moscow), and A. L. Zel'manov (GAISh). These contributions examined various aspects of the expansion of the universe and the problem of a singular point in time (the beginning of the expansion).
Ya.A. Smorodinskii (Dubna), B.M. Pontecorvo (Dubna), and V.M. Kharitonov (Yerevan) presented reports discussing the role played by neutrinos in the structure of the universe (see V. S. Brezhnev's article in this collec tion).
The discussion of the classical theory of gravitation was resumed at the morning session of 28 June. The energy of the gravitational field, or rather the energy-momentum tensor of the field, was discussed by N. V. Mitskevich (Samarkand), I. I. Gutman (Uzbek SSR), M. E. Gertsenshtein (Moscow), and others. Although some interesting findings were reported by these investigators, this difficult problem is unfortunately still far from being solved.
The participants of the conference expressed considerable interest in the possibility of the existence of antigravitation (this term denotes repulsion instead of attraction between bodies). D. I. Blokhintsev considered the paradoxes which would be associated with the nonconservation of gravitational energy if antigravitation did exist. The question was also discussed in the report by Prof. Ya. P. Terletskii (MGU).
Podgoretskii, Okonov, and Khrustalev, of the Joint Institute for Nuclear Research, proposed an experiment designed to detect antigravita tional properties in antiparticles. This experiment would use vertical beams of K mesons, whose decay is strongly affected by the magnitude and sign of the mass. At the same session, some reports on gravitational waves were also read. As a spokesman for himself and his colleagues, (A. M. Brodskii and D. D. Ivanenko), G. A. Sokolik discussed the new "com pensating-field" treatment of the gravitational field. According to this new approach, which is based on the ideas recently developed by Sakurai, the parameters of the Lorentz group of transformations are considered to be functions of the coordinates. This leads to the appearance of some
additional terms in the Lagrangian and in the equations of motion. If the Lagrangian is to remain invariant under Lorentz transformations, some new field must be introduced which would transform from point to point in such a way as to compensate for the extra terms. It was shown in the report that the compensating field must be the gravitational field. The authors are of the opinion that the new approach should enable a re-exami nation of certain problems in the general theory of relativity and should facilitate their solution.
The evening session of the second day of the conference was devoted to a discussion of non-Riemannian generalizations of geometry. Under the very general requirements imposed upon geometry, there are 27 possible types of differential geometries, of which the Riemannian geometry employed in the general theory of relativity is a particular trivial case. At this session the physical implications of the spaces related to these geometries were considered, particularly with reference to spaces possessing a twist. This problem was discussed in the reports of A. E. Levashov (Kiev), O. S. Ivanitskaya (Kiev), V. I. Rodichev (Moscow), and Yu. S. Vladimirov (MGU). The report read by Rodichev was quite interesting; he demonstrated that if Dirac's fundamental equation is considered in twisted space, a nonlinear term of the Ivanenko-Heisenberg type appears. Thus, in the equation describing the basic elementary particles and the "protomatter" which apparently forms a basis for the entire world, any particle is shown to interact with itself, the interaction being precisely of the type established by Ivanenko and Heisenberg on the basis of other considerations. Similar subjects were also considered in the reports of D. F. Kurdgelaidze (MGU), S. F. Shushurin (MGU), and V. B. Lysikov (Kharkov), dealing with new exact solutions of nonlinear equations of this kind. Also at this session, A. Z. Petrov presented a brief survey and analysis of some unified field theories, and V.S. Brezhnev presented a study of Finslerian geometry.