Linking quantum mechanics and general relativity together ? Reflections and Propositions

We examine the possible relations between general relativity and quantum mechanics, from the point of view of their representations of space and time, which are different. We refer to our own understanding of space and time, built in opposition to each other from the physical phenomena, and not constituting an a priori external frame. Within a relation-based thinking, we can only compare the phenomena to the other phenomena, and, from this confrontation, space-time frames arise, as drawn by the trajectories of certain phenomena arbitrarily considered in a privileged way. It is within this framework that one must think the possible association of general relativity (which has not the monopoly of space and time) and quantum mechanics (which has not the monopoly of quantization, to be understood from the comparison of two classes of phenomena within a probabilistic approach). The general question to ask is that of possible exchanges between the different points of views, supported by the various possible phenomena, that is to say those on which space and time are defined, and the others. Space and time do not disappear, the points of views are exchanged. These exchanges are made possible by representing space and time, like the other phenomena, by a pair of fields (r, t); r and t are vectors in a three-dimensional space (time is marked by the position of a moving point in the same space as that defining the positions of the ordinary points), as opposed to field pairs (f, g) associated with the other phenomena (such as the pair of the electric and magnetic fields). One may ultimately envisage quantization of space and time; one may also envisage the definition of time and space solely by quantum mechanics. A preliminary and qualitative framework is presented as a basis for future quantitative research.