A Unified Framework for Relativity and Curvilinear-Time Newtonian Mechanics

Classical mechanics is presented so as to render the new formulation valid for an arbitrary temporal variable, as opposed to Newton’s Absolute Time only. Newton’s theory then becomes formally identical (in a precise sense) to relativity, albeit in a three-dimensional manifold. (The ultimate difference between the two dynamics is traced to the existence of the relativistic ‘mass-shell’ condition.) A classical Lagrangian is provided for our formulation of the equations of motion and it is related to one of the known forms of the corresponding relativistic Lagrangian, which is the analogue of the Polyakov Lagrangian of string theory. Dedicated to Emeritus Professor D. Speiser (Université Catholique de Louvain, Belgium) who provided the inspiration for this article.