Trans-Coordinate Physics

TL;DR

This paper introduces a novel approach called trans-coordinate physics that eliminates the need for space-time coordinates, redefining fundamental principles and challenging existing gravitational detection methods.

Contribution

It proposes a coordinate-free framework for physics using differentials from a new limiting process, redefining conservation principles and the Einstein field equation.

Findings

Gravitational detectors like LIGO and Weber bar are predicted not to work.

Gravity is assumed to be solely due to gravitons.

Gravitational uncertainty is shown to be compatible with quantum certainty.

Abstract

Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken from a novel limiting process are defined for a particle's wave function, allowing the particle's dynamic principle to operate locally without the use of coordinates. These differentials replace the covariant differentials of Riemannian geometry. With coordinates out of the way regional conservation principles and the Einstein field equation are no longer fundamentally defined; although they are constructible along with coordinate systems so they continue to be analytically useful. Gravity waves as presently understood are not defined, so we conclude that the gravitational detectors LIGO and Weber bar will not work. We assume that gravitons alone are fundamentally responsible for gravity. It is shown how gravitational uncertainty can be reconciled with the certainty of quantum mechanical dynamics. Keywords: covariance, invariance, geometry, gravitons, metric spaces, state reduction; 03.65.a, 03.65.Ta, 04.20.Cv