Upper time limit, its gradient curvature and matter

摘要

Einstein equation of Gravity has on one side the momentum energy density tensor and on the other, Einstein tensor which is derived from Ricci curvature tensor. A better theory of gravity will have both sides geometric. One way to achieve this goal is to develop a new measure of time not as a coordinate but as a scalar field that will be independent of the choice of coordinates. One natural nominee for such time is the upper limit of measurable proper time measured along the longest geodesic curve from near the "big bang", either as a set of events or as a singularity, to any event. By this, the author constructs a scalar field of an upper limit of measurable time. Time, however, is measured by material clocks. What is the maximal time, that can be measured by a small microscopic clock, when our curve starts near the "big bang" - event or events - and ends at an event within the nucleus of an atom ? Will our tiny clock move along geodesic curves or will it move along a non geodesic curve within matter ? It is almost paradoxical that a test particle in General Relativity will always move along geodesic curves but the motion of matter within the particle, may not be geodesic at all. For example, the ground of the Earth does not move at geodesic speed. Where there is no matter, we choose a curve from near "big bang" event or events, to an event such that the time measured is maximal. The gravitational field, causes that more than one such curves intersect at events, which could results in discontinuity of the gradient of the scalar field of time. The discontinuity can be avoided only if we give up on measurement along geodesic curves where there is matter. In other words, our tiny test particle clock will experience force when it travels within matter.