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Mach's principle and mass in an expanding universe
ABSTRACTS
165
Modijied Determinantal Method. S. M. ROY AND 11. BLANKENBECLER, Palmer Physical Laboratory, Princebon University, Princeton, New Jersey. An improved version of the determinantal method for solving N/D equations is developed. Unlike the determinantal approximation, the accuracy of this method is not limited to small coupling constants. Further, this method guarantees a real residue at the position of a pole in the partial wave amplitude, whereas the determinantal approximat,ion yields a complex residue when the pole lies on the left-hand cut in the s-plane. Both nonrelativistic and relativistic cases are considered. Numerical accuracy of the new method is examined in some typical applications. Mach’s Principle uncl Mass in an Expanding Universe. NATH.\N ROSEN, Department of Physics, Israel Institute of Technology, Haifa, Israel. The equations of motion for a particle in a homogeneous closed universe are investigated in the cases of no force, a gravitational force, and an electrostatic force. From the form of these equations one is led to an inertial mass which increases as the universe expands. One also finds that the passive gravitational mass changes in the same way as the inert,ial mass, while the active gravitational mass remains constant. The change in mass can be regarded as a manifestation of Mach’s principle. The results can be interpreted in terms of the gravitational constant decreasing with t,he expansion of the universe.
165
Modijied Determinantal Method. S. M. ROY AND 11. BLANKENBECLER, Palmer Physical Laboratory, Princebon University, Princeton, New Jersey. An improved version of the determinantal method for solving N/D equations is developed. Unlike the determinantal approximation, the accuracy of this method is not limited to small coupling constants. Further, this method guarantees a real residue at the position of a pole in the partial wave amplitude, whereas the determinantal approximat,ion yields a complex residue when the pole lies on the left-hand cut in the s-plane. Both nonrelativistic and relativistic cases are considered. Numerical accuracy of the new method is examined in some typical applications. Mach’s Principle uncl Mass in an Expanding Universe. NATH.\N ROSEN, Department of Physics, Israel Institute of Technology, Haifa, Israel. The equations of motion for a particle in a homogeneous closed universe are investigated in the cases of no force, a gravitational force, and an electrostatic force. From the form of these equations one is led to an inertial mass which increases as the universe expands. One also finds that the passive gravitational mass changes in the same way as the inert,ial mass, while the active gravitational mass remains constant. The change in mass can be regarded as a manifestation of Mach’s principle. The results can be interpreted in terms of the gravitational constant decreasing with t,he expansion of the universe.