Relative and Absolute Time

Abstract

Abstract In this paper, we derive a new identity that relates the proper time and the observer time as a contact transformation on configuration space. This leads to a consistent relativistic extension of the special theory to include Newtonian mechanics. The basic conclusions of this paper are: (i) There always exist two unique inertial frames for any given system of particles: one with a unique speed of light and time relative and one with unique simultaneity and the speed of light relative. (ii) If the ratio of the total energy of the universe to the total mass energy of the universe is constant, then a unique definition of Newtonian time exists for the universe with zero set at the big bang. (iii) There are two mathematically consistent representations for the same physical system. (iv) Data collected from distant objects in the universe does not have a unique physical interpretation. We also use the isotopic dual of ℝ to provide a basic improvement in the big bang model. This leads to a model with conservation of energy, momentum, angular momentum, charge, a natural arrow for time and a natural explanation for the lack of antimatter in our universe. We predict that protons and antiprotons (respectively electrons and positrons) are gravitationally repulsive.