The temporal parameter t ∈ ℝ carries three surplus properties (negative extension, loop-admitting topology, and reversal symmetry) that no experiment has confirmed. This paper traces this conclusion from the mass-shell relation E² = p²c² + m²c⁴, which functions as a conserved-total resource constraint. The Pikovski Hamiltonian formalizes this as Ĥ₀/γ, and the Page-Wootters framework derives time emergence from entanglement correlations in a globally static state. Smith and Ahmadi (2020) showed that PaW conditioning recovers Pikovski time dilation; Höhn, Smith and Lock (2021) proved the full three-way equivalence. Combined with the SI definition of a second (grounding time in internal state transitions), these results establish that the physical content of the temporal parameter is a constraint on internal state-transition rates. Following Gisin and Weatherall, three ℝ-domain properties of t are identified as surplus structure per Weatherall's framework: closed timelike curves, parameter reversal in T-symmetry, and the block universe. The arrow-of-time problem decomposes into a process-accumulation arrow (a spectral property of the clock operator) and a thermodynamic arrow determined by boundary conditions. The argument extends Einstein's 1905 relativization of simultaneity to the temporal parameter itself.
Badriram Rajagopalan (Wed,) studied this question.