MATHEMATICAL EXPANSION OF SPECIAL THEORY OF RELATIVITY ONTO ACCELERATIONS

Jakub Czajko

doi:10.14710/jfma.v4i1.10197

Abstract

The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal and binormal that complement the instantaneous tangential speed and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential can be expanded onto within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.

Highlights

Some remarks are so impressive that one may feel compelled to reevaluate afresh everything we learned heretofore
The resulting mathematical lies spilled into physics where they led to creation of various tacitly veiled nonsenses, which were propagated with impunity and against the common scientific sense and sometimes even with open disrespect for reason
The main goal of the present paper is to present mathematically inspired enhancement of the classical special theory of relativity

Summary

INTRODUCTION

Some remarks are so impressive that one may feel compelled to reevaluate afresh everything we learned heretofore One of such profound remarks to me is that if physical laws evolve in time, time must play a preferred role in the world; it cannot be just another dimension and it cannot just disappear in a timeless block universe or “wavefunction of the universe” [1]. Hyperboloidal with respect to the [elapsing] time axis [4] Such statements (and many others, ) prompted me to reexamine several operational formulas of mathematics and reassess the scope of validity of some physical laws and principles which utilized the traditional mathematics that seems controversial to me. Paul Duhem already asked the question if the principle of universal gravitation is merely a generalization of Kepler’s laws and their extension onto the motion of satellites. Impacts of the expanded onto accelerations STR on the general theory of relativity (GTR) shall be discussed elsewhere

SUMMARY OF THE GOAL AND OBJECTIVES OF THIS PAPER

DIFFERENTIAL GEOMETRY IN A NUTSHELL

SOME GEOMETRICAL PERCEPTIONS RELEVANT TO PHYSICS

OPERATIONAL EXPANSION OF CLASSIC STR ONTO ACCELERATIONS

Findings

VIII. CONCLUSIONS