In many ways, the theory of relativity could have been named the theory of constancy, since it relies upon things that are invariant like the speed of light and the Lorentz factor. This post aims to derive the mysterious Lorentz factor, Spacetime Invariant for flat space, and Spacetime Coordinate Transforms through an intuitive, geometrical approach … Continue reading The Lorentz Factor and the Invariance of Relativity

In the previous post https://mathintuitions.com/2024/08/14/orbiting-around-the-truth-approximations-involved-in-newtons-and-einsteins-orbital-equations-part-i/, we were able to derive the elliptical orbital path of a planet, where its radial length r is a function of its angle, phi: where L, the angular momentum, is equal to Before arriving at the above expression for r in terms of phi, we arrived at a simpler, more … Continue reading Orbiting Around the Truth Part II: Adjusting the Orbital Path Equation Using General Relativity

image from https://en.wikipedia.org/wiki/General_relativity#/media/File:Spacetime_lattice_analogy.svg

     In Paul J. Nahin's book "An Imaginary Tale," a very interesting mathematical puzzle is introduced regarding imaginary numbers that leads to connections to wormholes in the space-time continuum. (image of wormhole is from Wikipedia AllenMcC. Vector: KES47 - Own work based on: Lorentzian Wormhole.jpg by AllenMcC., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=30231987 ). He discusses the discovery of … Continue reading Imaginary Numbers and Wormholes