Accession Number : AD0708491

Title :   THE SANDWICH CONJECTURE,

Corporate Author : SYRACUSE UNIV N Y DEPT OF PHYSICS

Personal Author(s) : Bergmann,Peter G.

Report Date : JUN 1970

Pagination or Media Count : 15

Abstract : The 'Sandwich Conjecture' (SC) was originally formulated by Wheeler and his coworkers. In the course of several years both the original author(s) and others have proposed the statement in several different forms, and with different qualifications. Roughly, the SC asserts that in a purely gravitational field the internal geometries of two distinct three-dimensional space-like hypersurfaces determines the geometry of a four-dimensional space-time (i.e. pseudo-Riemannian) manifold that is required to obey Einstein's field equations (i.e. to be Ricciflat). In a careful formulation one will have to specify further whether the two three-surfaces are to be 'close together', whether the distance between them is to be given as additional data, and what sort of conditions are to be imposed at space-like infinity. The SC is suggested by similar theorems that hold in classical mechanics, where knowledge of the configuration of a system at two distinct times may determine its trajectory throughout the period of time bounded by the two instants. If the SC were to hold, one would hope that the metric field can be quantized by Feynman integral methods. Quite apart from its bearing on quantization, the SC, and its possible limitations and qualifications, possesses considerable interest for the structure of Einstein manifolds per se. (Author)

Descriptors :   (*RELATIVITY THEORY, DIFFERENTIAL GEOMETRY), PARTIAL DIFFERENTIAL EQUATIONS, INTEGRALS, GRAVITY, FIELD THEORY

Subject Categories : Quantum Theory and Relativity

Distribution Statement : APPROVED FOR PUBLIC RELEASE