User:Dc.samizdat/Dimensional relativity

"There is a newer version of this article, which is original research hosted at Wikiversity."The theory of spherical relativity is an equivalent formulation of the standard theory of relativity based on a spherical Euclidean metric in four spatial dimensions. It is one of several Euclidean relativity theories with the same simple geometry, which differ in their precise formulation and interpretation.

This theory holds that the universe has four orthogonal spatial dimensions (in addition to time), one of which is hidden from each observer as a consequence of the fact that everything in nature is constantly in motion at the speed of light. Nothing is at rest, or in motion at any speed other than lightspeed, in any frame of reference, even and especially each observer in his own frame. The theory implies that the large scale structure of the universe (cosmology) and its fine structure (quantum mechanics) can only be visualized as the motions of objects of four dimensional extent (4-polytopes), all at the same constant speed, in a space with four orthogonal axes (rather than as the motions of three dimensional objects, at various speeds, in a space with three orthogonal axes, which is an accurate visualization only at everyday scales).

Origin
"“The universe is a sphere whose center is wherever there is intelligence.”"This statement by the 19th century American essayist and natural philosopher Henry David Thoreau is the original precise articulation of the principle of spherical relativity. Thoreau did not provide a theory of how it could be raised to the status of geometric physical law alongside Copernicus’ heliocentric principle and Newton’s laws of motion, but he wrote it more than half a century before Einstein’s theory of relativity.

Einstein himself was the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere (the first mathematical articulation of the principle). He did this as a gedankenexperiment in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe. But when in his 1921 Princeton lecture he invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", he was careful to note parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice."

Informally, the theory of spherical relativity may be given as the dual inverse of this formulation of Einstein's: the Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding the observed universe as a quasi-spherical manifold of three dimensions, embedded in the physical Euclidean continuum of four dimensions.

Like Einstein’s theories of special relativity and general relativity, the precise form of the theory of spherical relativity arises in two developmental phases: a special form restricted to conditions of negligible gravity, and its generalization applicable to all kinds of acceleration. Also by analogy to Einstein’s theory, it is predicated on a complementary pair of postulates: a relativity principle, and an observation of constant velocity.

Formulation
The special theory of spherical relativity:


 * The laws of physics are the same in all inertial reference frames of a Euclidean space of four dimensions.
 * All objects with proper mass, including the observer, move with constant velocity c through four dimensional Euclidean space, in the inertial reference frames of all observers. Light signals propagate through four dimensional vacuum at the constant velocity 2c for all observers, regardless of the motion of the signal source.

The general theory of spherical relativity:


 * The laws of physics are the same in all reference frames of a Euclidean space of any number of dimensions.
 * All tangible objects, regardless of mass, including light signals and the observer, move with constant velocity c through their proper Euclidean space, in the reference frames of all observers, regardless of the motion of their source.