A New Mechanics That Is Symmetrical to the Present Classical Mechanics

Newton published his mechanics in the form of an axiomatic system just as the Euclidean geometry. The Newton’s three laws are three axioms, from which, together with the necessary definitions of physical concepts and propositions, all contents of classical mechanics can be derived. Non-Euclidean geometries tell us that one of the axioms in an axiomatic system may take different forms. Modified axioms can lead to new axiomatic systems that are logically rigorous and self-consistent. The fifth axiom in the Euclidian geometry was modified to be two other different form, and consequently, two non-Euclidean geometries were developed. We think that Newton’s second law can be modified. The second law can be simply stated as: force is the cause of acceleration. It can be modified as: force is the cause of deceleration. This results in a new axiomatic system called new classical mechanics. This paper presents the fundamental formulas of the new classical mechanics. The most distinctive feature of the new mechanics is that the direction of momentum is opposite to that of velocity, and the kinetic energy is negative, i.e., a negative sign is attached to usual positive kinetic energy (PKE). Therefore, the new classical mechanics can be called negative kinetic energy (NKE) one, while the existing classical mechanics can be called PKE one. These two parts can be collectively referred to as a whole classical mechanics, which includes both PKE and NKE parts. The formulas of these two parts have symmetry with respect to positive and negative kinetic energy. The PKE classical mechanics describes the motion of macroscopic matter that we can observe, while the NKE classical mechanics describes the motion of macroscopic matter that we cannot observe, i.e., the motion of dark matter. Our universe has symmetry with respect to PKE and NKE, which is also the symmetry with respect to matter and dark matter. The basic equations of quantum mechanics describing the motion of micro-particles also have symmetry with respect to PKW and NKE, which has been elaborated in the author’s previous work. The theory presented in this paper describe the motion of macroscopic NKE matter.