A Physical Causality—Information Manifold With a Pythagorean Metric in Special Relativity

The spacetime vectors with the Minkowski metric are cornerstones of special relativity, with the Minkowski metric and physical causality invariant under the Lorentz transformation. It is here demonstrated that the Minkowski metric can be reformulated into a metric of (mechanistic) causality through a division of the spacetime vector by the speed of light c, yielding the proper time as the Lorentz-invariant line element. The proper time is, as such, the metric of physical causality. Consequently, the four-dimensional manifold is reformulated by exchanging time with the proper time along with the use of the Pythagoras metric, generating a physical causality-driven special relativity theory with a physical causality—information manifold.