Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with different...Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.展开更多
Relativity theory formulation is proposed, based not on the axiomatic postulation of its main principles but on their inference out of a thought experiment. With this approach, the experimentally observed independence...Relativity theory formulation is proposed, based not on the axiomatic postulation of its main principles but on their inference out of a thought experiment. With this approach, the experimentally observed independence of the speed of light from the motion of source and observer is a necessary consequence of the finiteness of propagation speed of all kinds of information. The mechanism of relativistic effects origination is described;the formulas of Lorentz transformations, Doppler quadratic effect, electromagnetic interaction and centrifugal force of inertia are derived.展开更多
文摘Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.
文摘Relativity theory formulation is proposed, based not on the axiomatic postulation of its main principles but on their inference out of a thought experiment. With this approach, the experimentally observed independence of the speed of light from the motion of source and observer is a necessary consequence of the finiteness of propagation speed of all kinds of information. The mechanism of relativistic effects origination is described;the formulas of Lorentz transformations, Doppler quadratic effect, electromagnetic interaction and centrifugal force of inertia are derived.
