Minkowski‐Einstein spacetime: Insight from the Pythagorean theorem

The Pythagorean theorem, combined with the analytic geometry of a right circular cone, has been used by Minkowski and subsequent investigators to establish the four-dimensional spacetime continuum associated with Einstein’s special theory of relativity. Although the mathematics appears sound, the incorporation of a hypercone into the analytic geometry of a right triangle in Euclidean three-space is in conflict with the rules of pure mathematics. A metric space of n dimensions is necessarily defined in terms of n independent coordinates, one for each dimension. Any coordinate that is a combination of the others for a given space is not independent so cannot be an independent dimension. Minkowski‐Einstein spacetime contains a dimensional coordinate, via the speed of light, that is not independent. Consequently, Minkowski‐Einstein spacetime does not exist.