About Space-Time and More

Abstract

Intuitively, one can think that the time may be assimilated with the space. One of the big differences between the time and the space is the fact that actually travels into the past and/or future are only possible on movies. In science, Newton had introduced the notion of an absolute and universal time but Einstein told us that time is relative, is strongly connected with the space and depends on the observing point. In the theory of relativity, the gravitational field is assimilated with the ‘space curvature’ and has as independent variable the ‘space-time’. To make a mathematical separation between the time and space, imaginary time had been considered. As living creatures must conceive mentally their future actions in space, may one consider this ‘imaginary time’ as a kind of ‘mirror of these future actions’? The paper presents mathematical models for 1D to more than 3D space based mainly on trigonometric, hyperbolic, elliptic and ultra-elliptic functions. All these functions have only the ‘complex time’ as independent variable. They may represent a transformation (of the space for example) during a given time interval and/or equivalently, the ‘dynamic of this transformation’. The time interval for a given transformation depends evidently on the used technology (then its ‘speed’) and as results, some locally parameters of the space (and/or objects) may be modified. The time may then be considered as equivalent to the ‘order’ in which a given transformation is realized. As application, extension of the bandwidth compression loop for 3D system may allow to a locally modification of some parameters of the objects and/or of the local gravitational field. Associated with a good and convenient technology, all these are of strategic importance. Applications may be found in strategic forecast, interplanetary telecommunications and treks. The presented tools may be used for modeling the fields and also insure their more comprehensive understanding.