The Constancy of the Speed of Light as an Invariant Constraint and a Dissipative Spacetime-Life Dynamics Model via Virtual Dimensional Reduction

This paper points out the geometric contradictions of the two-dimensional Minkowski diagrams that have been conventionally used for decades, and proposes a rigorous three-dimensional and higher-dimensional spacetime analysis framework that strictly separates independent variables from dependent variables. The constancy of the speed of light, which is the fundamental premise of special relativity, can be reinterpreted as a powerful intrinsic constraint acting on the system of the universe. In this study, to fully accommodate this invariance, we introduce an extended five-dimensional spacetime by incorporating a new virtual dimension w and construct its corresponding Lagrangian density. By executing a dimensional reduction process that integrates out the higher-dimensional components into an integration constant based on the geometric symmetry along the virtual dimension, we prove that the effects of the hidden dimension are reduced to local density variations and dynamic movements (flows) of matter within the realistic four-dimensional spacetime. Furthermore, by injecting the metabolic rate (energy consumption rate) and the local entropy production rate—key characteristics of living systems—into the effective potential term, we mathematically derive how relativistic constraints enforce the dynamic rhythms and morphogenetic structures of life as a non-equilibrium dissipative structure, and discuss its profound physical implications.