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
The work analyzes the basic assumption in Mach’s principle, namely that the inertia of material bodies is determined by their gravitational interaction with distant masses in the universe. However, while Mach’s prin...The work analyzes the basic assumption in Mach’s principle, namely that the inertia of material bodies is determined by their gravitational interaction with distant masses in the universe. However, while Mach’s principle is based on the so-called “long-range gravitational interaction” characterized by an infinitely large propagation velocity, our study is based on a “modified” long-range principle, assuming a very large but finite propagation velocity of the gravitational interaction between local material objects and distant matter. Thus, it is postulated that there are two types of gravitational interaction—short-range gravitational interaction between local objects and long-range gravitational interaction between local objects and distant matter in the universe, which are characterized by different propagation speeds, but with the same gravitational constant. On the basis of the modified long-range principle, a model of distant matter is built in the form of a hollow spherical layer with negligible thickness. The phenomenological assumption is made that the movement with acceleration of the local reference frame (RF) is related to a change in the spherically symmetric distribution of the lines of gravitational interaction of this RF with distant matter, which is expressed in a corresponding asymmetric distribution of the effective mass density on the hollow sphere. A simplified (idealized) model of the effective change of the hollow sphere of distant matter by cutting off separate segments of the sphere is proposed. On the basis of the model, the possibility of representing the inertial effects in three simplest types of reference frames through a corresponding gravitational interaction is considered: 1) inertial RF;2) RF moving in a straight line with constant acceleration;3) RF rotating with constant angular velocity. Expressions were obtained for the gravitational accelerations acting on the test body located inside the hollow sphere with a corresponding change (“cutting”). It is concluded that these accelerations can in a first approximation represent the inertial accelerations of the main types noted above. It is shown that in order to obtain reasonable values of the truncation parameters of the hollow sphere, it is necessary to assume that the gravitational interaction inside this sphere is not of the Newtonian type, i.e. the same depends on the distance not according to the law 1/r2, but according to modified law with a non-integer (fractional) exponent. This law corresponds to a fractal structure of the source of attraction inside the truncated sphere of distant matter. The issue of the possibility of the supposed modified long-range interaction is briefly discussed on the basis of a comparison of the finding a connection with the lines of force of the same with the “cosmic strings” assumed by a number of researchers, along which corresponding excitations (waves, particles) moving at super-light speed. The work advances the idea of the presence of unity and at the same time oppositeness of the inertia of material objects and the known gravitational interaction between them, which are generated by the properties of symmetry of the long-range gravitational interaction. Moreover, while the inertia of the bodies is due to the violation of this symmetry caused by their movement with acceleration, the gravitational interaction between the bodies is due to the aspiration to restore the symmetry of a far-reaching gravitational interaction, which is disturbed by the presence of local material bodies. In the conclusion of the work, the important physico-philosophical significance of Mach’s principle is emphasized, expressed in the understanding that not only the world of microscopic objects (“micro-world”), but also the world of huge cosmic objects (“mega-world”) can have a corresponding impact on our “macroscopic” world.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The work analyzes the basic assumption in Mach’s principle, namely that the inertia of material bodies is determined by their gravitational interaction with distant masses in the universe. However, while Mach’s principle is based on the so-called “long-range gravitational interaction” characterized by an infinitely large propagation velocity, our study is based on a “modified” long-range principle, assuming a very large but finite propagation velocity of the gravitational interaction between local material objects and distant matter. Thus, it is postulated that there are two types of gravitational interaction—short-range gravitational interaction between local objects and long-range gravitational interaction between local objects and distant matter in the universe, which are characterized by different propagation speeds, but with the same gravitational constant. On the basis of the modified long-range principle, a model of distant matter is built in the form of a hollow spherical layer with negligible thickness. The phenomenological assumption is made that the movement with acceleration of the local reference frame (RF) is related to a change in the spherically symmetric distribution of the lines of gravitational interaction of this RF with distant matter, which is expressed in a corresponding asymmetric distribution of the effective mass density on the hollow sphere. A simplified (idealized) model of the effective change of the hollow sphere of distant matter by cutting off separate segments of the sphere is proposed. On the basis of the model, the possibility of representing the inertial effects in three simplest types of reference frames through a corresponding gravitational interaction is considered: 1) inertial RF;2) RF moving in a straight line with constant acceleration;3) RF rotating with constant angular velocity. Expressions were obtained for the gravitational accelerations acting on the test body located inside the hollow sphere with a corresponding change (“cutting”). It is concluded that these accelerations can in a first approximation represent the inertial accelerations of the main types noted above. It is shown that in order to obtain reasonable values of the truncation parameters of the hollow sphere, it is necessary to assume that the gravitational interaction inside this sphere is not of the Newtonian type, i.e. the same depends on the distance not according to the law 1/r2, but according to modified law with a non-integer (fractional) exponent. This law corresponds to a fractal structure of the source of attraction inside the truncated sphere of distant matter. The issue of the possibility of the supposed modified long-range interaction is briefly discussed on the basis of a comparison of the finding a connection with the lines of force of the same with the “cosmic strings” assumed by a number of researchers, along which corresponding excitations (waves, particles) moving at super-light speed. The work advances the idea of the presence of unity and at the same time oppositeness of the inertia of material objects and the known gravitational interaction between them, which are generated by the properties of symmetry of the long-range gravitational interaction. Moreover, while the inertia of the bodies is due to the violation of this symmetry caused by their movement with acceleration, the gravitational interaction between the bodies is due to the aspiration to restore the symmetry of a far-reaching gravitational interaction, which is disturbed by the presence of local material bodies. In the conclusion of the work, the important physico-philosophical significance of Mach’s principle is emphasized, expressed in the understanding that not only the world of microscopic objects (“micro-world”), but also the world of huge cosmic objects (“mega-world”) can have a corresponding impact on our “macroscopic” world.
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.
