Altering the Principle of Relativity

Russell Clark Eskew

doi:10.5539/apr.v10n3p23

Abstract

A unique hyperbolic geometry paradigm requires altering the Relativistic principle that absolute velocity is unmeasurable. There is no absolute velocity, but in the case where a constant velocity is made from a half-angle velocity, a variable velocity is the same as (absolute) acceleration. Relativity is based on local Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory is given that time and our velocity are inversely related. The physical laws of motion by Galileo, Newton and Einstein are forged using the half-angle velocity to electromagnetic velocity. The field of kinetic, potential and gravitational force accelerations is established. An experiment exemplifies the math from the Earth’s frame of reference. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.

Highlights

Conventional trigonometry defines coordinates on a circle as: sin θ = y cos θ = x tan θ = y (1)r r x csc θ = r sec θ = r cot θ = x y x y where r = (x2 +y2)1/2, of which we will call angle θc tan−1 yc x H.S.M
(1907–2003), explains (Coxeter, 1998, pp. 238, 277, 295, 306) how in a right triangle ABC parallel lines BA = c = ∞ and CA meet in infinity (Coxeter, 1978)
With the calculus notation u the accelerations are the derivatives resulting in trigonometry and algebra: dv dθ dv dt dt dθ

Summary

Introduction

Sech α y k y = csc θ= cosh sinh−1 x = k(sinh−1 csc Π(x))= k(sinh−1 cosh x ) = coth α k sin θ =. By sinh−1 sinh x = ln(sinh x + (sinh x)2 + 1) = x, we have s√inh sinh−1 x = sinh a = (esinh−1 x − e− sinh−1 x)/2 = x = cot θ. Creates the distance scale x a for any concentric horocircles of distance x in the Bolyai-Lobachevskii plane A point (x, y) on the vertical hyperbola y2 − x2 = 1 is understood as an inertial frame of reference, or observer. Time can have an analytic quantity t = esinh−1 x = x +(x2 +1)1/2 = x +y seconds, which we are saying is about an event point P(t).

Vectors

Applying velocity in complex numbers

Discussion

Half-angle velocity and absolute acceleration

An experiment

Conclusion