Claim: Time’s arrow is not fundamental. It emerges when transport non-closure accumulates irreversibly across scales.
The Classical Puzzle
- Microscopic laws are time-reversible
- Macroscopic processes are not
- Entropy increases
This asymmetry is usually taken as axiomatic.
Standard Explanations (Symptoms)
- Special initial conditions
- Probabilistic irreversibility
- Information loss
None explain mechanism.
Transport Reinterpretation
All dynamics are transport.
Transport closure can fail in one direction and not the other.
When closure failure accumulates, reversibility breaks.
Path A — Geometric Irreversibility
Primitive: Composition of transport maps
Forward transport through evolving frames:
$$ T_+(t_2,t_1) = \prod_{k} \mathcal{T}_k $$
Reverse transport is not the inverse:
$$ T_-(t_1,t_2) \neq T_+^{-1} $$
Because frames themselves have evolved.
↓
Path B — Phase Irreversibility
Primitive: Phase accumulation under transport
Forward evolution:
$$ \Phi_+ = \sum_i \delta \phi_i $$
Backward evolution requires phase re-alignment:
$$ \Phi_- \neq -\Phi_+ $$
Phase correlations are lost.
↓
Agreement Condition
$$ \text{Transport non-invertibility} \iff \text{Phase decoherence} $$
Why Entropy Always Increases
Entropy counts unrecoverable transport histories:
$$ S \sim \log(\text{irreversible transport paths}) $$
Entropy growth is geometric, not probabilistic.
Connection to Earlier Problems
- N-body → saturation of non-closure
- Turbulence → scale cascade
- Quantum chaos → phase non-recoverability
Transport-First Summary
- Time has no intrinsic arrow
- Irreversibility emerges from frame evolution
- Closure failure accumulates directionally
- The arrow of time is bookkeeping asymmetry