The classical Maxwell equations are constructed under the hypothesis of rigid static time background, which denies electromagnetic fields dynamic degrees of freedom to evolve and oscillate along the time dimension. Based on the spacetime fluid hypothesis, this paper proposes the axiom of four-dimensional total speed of light conservation, and defines a spacetime scalar field (x^) as the time distribution ratio of light speed. We introduce the intrinsic pure-time coordinate, defined as a scalar function of the Ricci scalar R, Kretschmann scalar K and distribution ratio, establishing a direct connection between spacetime curvature and elastic time effects. The classical rigid time derivative is replaced by the elastic time derivative operator to reconstruct the extended Maxwell equations. In the flat Minkowski spacetime limit where 0 and 0, the extended equations strictly reduce to the standard vacuum Maxwell system. Under extreme conditions including strong gravitational fields, ultra-intense laser fields and high-refractive-index media, the wave equation generates spacetime cross-coupling terms and pure-time oscillation terms that produce observable physical effects. This paper clearly limits the current theory to the local approximation of flat spacetime, and the full generalized covariant extension for curved spacetime is reserved for follow-up research. Three classical unsolved puzzles—the reduction of light speed in media, phase shift under ultra-strong electromagnetic fields, and residual gravitational redshift of compact celestial bodies—can be uniformly interpreted under the four-dimensional geometric framework of this work. Meanwhile, three quantifiable and falsifiable experimental schemes are proposed to provide feasible paths for theoretical verification.
Q Chen (Tue,) studied this question.