Mathematical Prediction of the Dysmetric Dimension: A2. Dysmetric Spaces

In the previous publication, entitled Dyadic Algebra of Magnitudes, we presented the specific algebraic structure developed for physical quantities. We continue with this presentation, this time to analyze the theory of dysmetric spaces. We define dysmetric density and examine the mathematics that arises from considering exclusively the dysmetry of length, without any other dysmetric effects, to discover how a dysmetric empty space would behave and its effects on physical laws. Concepts are developed to describe the dysmetry of length, such as dysmetric tensors, and the metric of a generic dysmetric space is formulated, achieving the goal of determining the dysmetric density at every point and time. Within this framework, we find that empty space acquires effective physical properties: spatial variations of dysmetric density lead to curved light trajectories and position-dependent light propagation speeds. This lays the foundation for analyzing the dysmetric component of any physical law, a component that, in any case, will disappear when the dysmetry is canceled.