The duality of space and time and the theory of relativity

International audienceSpace and time concepts cannot be defined independently of each other; thus, there is a mathematical link between the corresponding parameters describing our physical world. An expression of this link is met in that, to-day, assessments of space and time standards are both derived from one single phenomenon, light movement, whose velocity is decided at an arbitrary mathematical value. A way to describe the space-time-associated reality is done by means of a phase-space frame where the position of the entities are represented with respect to eachother without the need of a special time parameter. The “extraction” of a single time parameter from this frame is done by favoring, among all the physical entities, one that is assumed to be moving by itself (e.g. the photon), the position of which defines the time. Because time is related to position, one may give a pre-temporal significance to a three-dimensional spatial parameter. Three-dimensional pre-time, to which is associated three-dimensional space parameter through a tensorial duality, allows a straightforward expression of the consequences of space-time duality, particularly for frame transformations, with space and time parameters on an equal footing. If one wants to have a suitable connection between the physical descriptions of phenomena both in a mobile frame and in a rest one, the same ratio of space to time standards must be taken in both frames. As a result, effects similar to Lorentz transformation are obtained; they may be understood as picturing a non-Euclidean metrics for the mobile frame as represented in the rest frame. They may also be conceived as uncertainty relations connecting the values of time and space standards to that of light velocity