A Theory of Global Mass Duality for Subluminal‒ Superluminal Motion Based on the Paradigm of Analytic Continuation

Abstract
The mass‒velocity relation in classical special relativity is defined only for subluminal motion. It
diverges at the speed of light and yields no real physical definition in the superluminal regime,
which artificially splits the physical system of velocity into a one-sided valid domain. By analogy
with the analytic continuation of the Riemann zeta function in complex analysis: an original
mathematical expression is convergent only on one side of the domain; cross-pole continuation
can construct a globally self-consistent functional structure and establish cross-singularity
duality relations. Following the same paradigm, this paper takes the speed of light as a firstorder pole and extends the relativistic mass function from the subluminal interval to the full
positive real velocity domain including superluminal velocities. Through induction of the
essential rules governing variable motion, we derive the core cross-light-cone singularity duality
relation . It is demonstrated that subluminal and superluminal objects paired by the
product equal to possess identical relativistic mass, establishing a unified global mass‒
velocity framework covering both subluminal and superluminal regimes. This work fills a
theoretical gap in conventional physics, which only investigates one-sided motion and lacks
summarization of cross-singularity multiplicative duality.
c
v1 v2 = c
2
c
2
Keywords: analytic continuation; mass‒velocity relation; superluminal motion; duality
symmetry; singularity; kinematic law