Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The ...Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.展开更多
Dramatic simplification of mathematical apparatus,special relativity’s hyper-bolic versus circular versions,some equivalence of SR and Newton’s theories,algebra of relativistic and the corresponding Galilean velocit...Dramatic simplification of mathematical apparatus,special relativity’s hyper-bolic versus circular versions,some equivalence of SR and Newton’s theories,algebra of relativistic and the corresponding Galilean velocities.Complex model,say 3C,of para-space as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced.As it turned out,the model and its theory have the power to bridge two and very likely also three physical theories in one common framework.The model,originally thought of as the model for special relativity only,exhibited the pos-sibility also to model the classical Newtonian mechanics and,moreover,the two mechanics turned out to be equivalent in their algebraic and topological structures.As it follows from some additional analysis,placed in section 10,also the quantum mechanics(QM)may[hypothetically]be described as the-ory of the same 3Ccomplex domain.If so,the bridging power of the intro-duced complex model is striking even if QM does not seem to be just equiva-lent to the remaining two theories.As for the SR,in the new complex Euclid-ean framework,it is not only totally preserved but at many important issues extended.Thus,in the new model,several hardly understood facts from the real SR such as the universality of speed of light,the Lorentz contraction or twins’paradox(especially the phenomena associated with the rocket’s chang-ing direction)find clear explanation unknown in the real M4 version of this beautiful theory.The transition from the real to complex description(the only necessary prize)yields dramatic simplification of all the three theories which is specially striking in the case of quantum mechanics(provided that my hy-pothesis on QM will turn out to be the true one).Moreover,in this work,the algebraic structure of isomorphic vector spaces was imposed and analyzed on both:the set of all relativistic velocities and on the set of the corresponding to them“Galilean”velocities.In some association with that,the relativistic the-ory was closer analyzed.Namely,the two approaches:the hyperbolic(“classi-cal”SR)with its four-vector formalism and Euclidean,where SR is modeled by the complex para-space 3C,were analyzed and compared.展开更多
文摘Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.
文摘Dramatic simplification of mathematical apparatus,special relativity’s hyper-bolic versus circular versions,some equivalence of SR and Newton’s theories,algebra of relativistic and the corresponding Galilean velocities.Complex model,say 3C,of para-space as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced.As it turned out,the model and its theory have the power to bridge two and very likely also three physical theories in one common framework.The model,originally thought of as the model for special relativity only,exhibited the pos-sibility also to model the classical Newtonian mechanics and,moreover,the two mechanics turned out to be equivalent in their algebraic and topological structures.As it follows from some additional analysis,placed in section 10,also the quantum mechanics(QM)may[hypothetically]be described as the-ory of the same 3Ccomplex domain.If so,the bridging power of the intro-duced complex model is striking even if QM does not seem to be just equiva-lent to the remaining two theories.As for the SR,in the new complex Euclid-ean framework,it is not only totally preserved but at many important issues extended.Thus,in the new model,several hardly understood facts from the real SR such as the universality of speed of light,the Lorentz contraction or twins’paradox(especially the phenomena associated with the rocket’s chang-ing direction)find clear explanation unknown in the real M4 version of this beautiful theory.The transition from the real to complex description(the only necessary prize)yields dramatic simplification of all the three theories which is specially striking in the case of quantum mechanics(provided that my hy-pothesis on QM will turn out to be the true one).Moreover,in this work,the algebraic structure of isomorphic vector spaces was imposed and analyzed on both:the set of all relativistic velocities and on the set of the corresponding to them“Galilean”velocities.In some association with that,the relativistic the-ory was closer analyzed.Namely,the two approaches:the hyperbolic(“classi-cal”SR)with its four-vector formalism and Euclidean,where SR is modeled by the complex para-space 3C,were analyzed and compared.
