Time, gravity and the exterior angle of parallelism
Author: Eskew, R.C.
Source: Speculations in Science and Technology, Volume 21, Number 4, 1998 , pp. 213-225(13)
Abstract:Applying calculus to the horizontal and vertical unit hyperbolas we derive the obtuse exterior and the acute angle of parallelism formulas for the arc length of a unit circle. When the analogous arc length of a hyperbola is figured, we further define metric distance with radian measure. Employing a non-conventional velocity of light formula, we explain several aspects of physics with a logical geometry. The hyperbolic geometry Lobacevskii angle of parallelism is mathematically measured to agree with the physical measure, without using the gravitational constant, but rather the electromagnetic spectrum and geodesics. Space is hereby measured with units of radians and time. Half-angle formulas for slopes and boosts pertain to spinor algebra. The new light velocity is justified when its derivative results in Einstein's mass–energy formula. Relativity is reformulated with these half-angle formulas.
Keywords: Bolyai; Einstein; Galileo; Gudermann; Lobacevskii; Lobachevskii; Lobachevsky; Lorentz; Lorentz transformation; Time; acceleration; angle of parallelism; arc length; arclength; c, light; curvature; dimension; geodesics; geometry; gravity; hyperbola; hyperbolic geometry; measure; meter; metric; number; parallel lines; radian; relativity; spacetime; velocity
Document Type: Regular Paper
Affiliations: P.O. Box 8117, Austin, Texas 78713-8117, USA email@example.com
Publication date: 1998-01-01