Related papers: Projective geometry and special relativity

This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…

We describe a post-Minkowskii approximation of general relativity as a power series expansion in G, Newton's gravitational constant. Material sources are hidden behind boundaries, and only the vacuum Einstein equations are considered. An…

The question of whether it is possible or not to surpass the speed of light is already centennial. The special theory of relativity took the existence of a speed limit as a principle, the light postulate, which has proven to be enormously…

General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…

We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly…

There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects, i.e. via the finite quotients of the group. But how much understanding can…

In a generalized Heisenberg/Schroedinger picture, the unitary representations of the Lorentz group may, for a massive relativistic particle, be used to attribute to waves an extra wavelength that is longer than the de Broglie wavelength.…

This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…

Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article,…

We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the categorical approach. A structure is observed on…

A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…

This paper shows one way to construct phase spaces in special relativity by expanding Minkowski Space. These spaces appear to indicate that we can dispense with gravitational singularities. The key mathematical ideas in the present approach…

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…

In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…

It is proved that local Lorentz transformations for different systems cannot derive varying speed of light. Based on the special relativity principle, an invariant speed is necessarily obtained. Therefore, the exact basic principles of the…

The root of the divergence problem in the current quantum field theory seems to be in the special theory of relativity. Here we propose a modified special relativity theory by introducing the primed inertial coordinate system, in addition…

This article shows how to express relativistic concepts in a visual manner using the full power of hyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space are used in conjunction with hyperbolic triangles. Elegant…

I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in…

Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…

In General Relativity, the propagation of electromagnetic waves is usually described by the vacuum Maxwell's equations on a fixed curved background. In the limit of infinitely high frequencies, electromagnetic waves can be localized as…