Inertial System and Special Relativity Finite Geometrical Field Theory of Matter Motion Part One

TL;DR

This paper presents a geometrical field theory of matter motion that derives Newtonian mechanics and special relativity from spacetime deformation, emphasizing the role of inertial systems and isotropy without relying on light speed.

Contribution

It introduces a finite geometrical field framework for matter motion, deriving fundamental physics equations from spacetime deformation and invariance principles.

Findings

Derives Newton's laws and special relativity from geometrical deformation of spacetime.

Shows Lorentz transformation arises from inertial system definition and time invariance.

Proposes a new perspective on inertial systems independent of light velocity.

Abstract

Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying concepts of relativity theory. In four-dimensional spacetime continuum, the displacement field of matter motion is measurable quantities. Based on these measurements, a finite geometrical field can be established. On this sense, the matter motion in physics is viewed as the deformation of spacetime continuum. Suppose the spacetime continuum is isotropic, based on the least action principle, the general motion equations can be established. In this part, Newton motion and special relativity are discussed. Based on the finite geometrical field theory of matter motion, the Newton motion equation and the special relativity can be derived simply based on the isotropy of spacetime continuum and the definition of inertial system. This research shows that the Lorentz transformation is required by both of the inertial system definition and the time gauge invariance for inertial systems. Hence, the special relativity is the logic conclusion of time invariance in inertial system. The source independent of light velocity supports the isotropy of inertial system rather than the concept of proper time, which not only causes many paradox, such as the twin-paradox, but also causes many misunderstanding and controversial arguments. The singularity of Lorentz transformation is removed in other parts of finite geometrical field theory, where the gravity field, electromagnetic field, and quantum field will be discussed with the time displacement field.