Problem of Time: Wheeler-DeWitt Frozen Formalism Dissolved
The Wheeler-DeWitt "problem of time" (vanishing Hamiltonian → timeless theory) is dissolved in τ: time is not a background parameter to recover from a timeless state but IS the α-orbit (V.R23). V.T10 establishes bounded temporal extent; VII.P06 reconstructs time as persistence of NF-addresses.
Overview
Canonical quantum gravity produces the Wheeler-DeWitt equation, in which the Hamiltonian constraint annihilates the wavefunction — yielding a “timeless” or “frozen” formalism with no evolution parameter. V.R23 (No Background Time, Book V ch04) dissolves this problem by reversing the dependency: time is not a parameter to recover from a timeless theory but is constitutive — time IS the α-orbit. V.T10 (Bounded Time Theorem) establishes that the temporal extent is finite. Book VII ch24 (VII.P06, Temporal Ordering from Persistence) reconstructs time as persistence of NF-addresses through morphism sequences.
Detail
The problem of time is one of the central conceptual obstructions in quantum gravity: in the Wheeler-DeWitt formulation, the Hamiltonian vanishes on physical states, so nothing evolves and there is no natural notion of “now”, change, or measurement. Approaches such as the Page-Wootters mechanism (conditional probabilities on an internal clock subsystem), relational time, and emergent time each recover a proxy for evolution but none resolve the formal vanishing. Category τ’s treatment is constitutive rather than emergent. The α-orbit on τ¹, indexed by α_m (m ∈ ℤ), is the primitive temporal structure; V.R23 (books/V-CategoricalMacrocosm/latex/sections/part01/ch04-proto-chronos.tex) records that time is not a background parameter but the α-orbit itself. Proper time is derived from the arc length of the α-orbit on τ¹; there is no external time variable to eliminate. V.T10 (Bounded Time Theorem) proves the temporal extent is finite, ruling out pathological infinite-past or infinite-future configurations at the kernel level. Book VII ch24 (VII.P06, books/VII-CategoricalMetaphysics/latex/sections/part02/ch24.tex) reconstructs temporal ordering from persistence of NF-addresses through morphism sequences, completing the philosophical circuit. The Wheeler-DeWitt frozen formalism is not a problem to solve but a symptom of trying to quantize gravity with time already attempted as a derived concept; τ gives time constitutive status from the outset.
Result Statement
V.R23 + V.T10 + VII.P06: Time IS the α-orbit, not a parameter to recover. Temporal extent is bounded; temporal ordering reconstructed from NF-address persistence. The Wheeler-DeWitt problem of time is dissolved.