Definition
Coherence is χ-mode phase correlation—when oscillations maintain stable phase relationships:
If $\phi_1 - \phi_2$ is constant, the χ-modes are coherent.
Types of Coherence
Temporal coherence: Phase correlation over time
How long does a χ-mode "remember" its phase?
Spatial coherence: Phase correlation across space
How far does phase correlation extend?
Quantum coherence: Superposition maintained
Coherence and Interference
Coherent χ-modes interfere:
The interference term requires phase correlation. Without coherence, no interference pattern.
Decoherence
Decoherence is loss of phase correlation through environmental coupling:
When χ-modes couple to environment, phase information spreads into environmental degrees of freedom. Coherence is lost but not destroyed—it's diluted.
Coherence Times
How long does coherence last?
| System | Coherence Time |
|---|---|
| Free atom | > 1 second |
| Ion trap qubit | ~ 10 seconds |
| Superconducting qubit | ~ 100 μs |
| Room temperature spin | ~ μs |
| Photon in fiber | ~ km (length, not time) |
Longer coherence = more quantum behavior observable.
The Measurement Connection
Measurement induces decoherence:
"Collapse" is decoherence—the loss of phase correlation when quantum χ-modes couple to classical apparatus.
Applications
Lasers: Highly coherent photon χ-modes
Quantum computing: Maintaining qubit coherence
Interferometry: Using coherence for precision measurement
Coherence in SCU
Coherence defines the resonant regime:
| Regime | Coherence |
|---|---|
| Resonant | High (quantum) |
| Turbulent | Low (classical) |
| Laminar | Minimal (deterministic) |
The resonant→turbulent transition IS decoherence.
The Key Insight
Coherence is not just "waves in sync."
Coherence IS χ-mode phase correlation:
- Phase relationships maintained over time/space
- Enables interference and quantum effects
- Lost through environmental coupling (decoherence)
- Defines the boundary between quantum and classical
When χ-modes are coherent, they act as waves (interfere, superpose). When coherence is lost, they act as particles (distinct, probabilistic outcomes).
Coherence is the quantum property. Decoherence is the classical transition.