Consequences of Relational Time
Andre K. T. Assis
There are two competing formulations of time in physics. Newton defended in the Principia the utilization of absolute time which, according to him "flows equably without relation to anything external." Leibniz, on the other hand, was against this concept and proposed relative time to replace it: "As for my opinion, I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistences, as time is an order of successions." Leibniz's ideas were accepted and developed by Ernst Mach in his book The Science of Mechanics. Mach proposed to replace Newton's absolute time by the angle of rotation of the planets relative to the frame of fixed stars.
In this work we consider the implementation of relational time and its consequences for physics. We concentrate our analysis in a single phenomenon, namely, the flattening of the Earth due to its diurnal rotation. We consider the figure of the Earth in Newtonian mechanics. We point out some philosophical problems with this classical formulation. We then present the flattening of the Earth from the point of view of Relational Mechanics, which is a mathematical implementation of Mach's principle utilizing Weber's law for gravitation.
