Temporal Density as a Scalar Unifier of Time Dilation in Curved and Expanding Spacetimes

Time dilation in special and general relativity is traditionally attributed to relative velocity or gravitational potential. This paper proposes that both phenomena arise from a single geometric property of spacetime—its temporal density, denoted Θ(x^μ). Temporal density quantifies the local causal capacity of spacetime: how much change or information flow it can sustain per unit proper time. High curvature or energy density focuses causal structure and reduces Θ (dense, slow time), while large-scale expansion defocuses it and drives Θ → 0 (thin, vanishing time). Θ is defined geometrically from null-congruence expansion and informationally from causal-diamond channel capacity, both derived from Einstein’s equations via the Raychaudhuri–Sachs optical formalism. This framework unifies gravitational, kinematic, and cosmological time dilation, and predicts small, direction-dependent corrections to redshift and frame-dragging laws that may be observable with current precision timing experiments.