Special Relativity-Type Space-Times Naturally Lead to Quasi-Pseudometrics

The standard 4-dimensional Minkowski space-time of special relativity is based on the 3-dimensional Euclidean metric. In 1967, H. Busemann showed that similar space-time models can be based on an arbitrary metric space. In this paper, we search for the broadest possible generalization of a metric under which a construction similar to Minkowski space-time leads to a physically reasonable space-time model. It turns out that this broadest possible generalization is related to the known notion of a quasipseudometric. 1 Computational Motivations Status of this section. In this introductory section, we present the main motivation for this paper—to enhance computational modelling of space-time. The area of computational modelling of space-time is, by definition, very interdisciplinary, it includes mathematicians and computer scientists interested in physical applications and physicists interested in computational aspects of their research. To help readers with different backgrounds better understand our motivations, we decided to describe these motivations in a special section. To some readers, these motivations are well known; other readers may be interested only in our mathematical results and are thus not interested in reading 0