Appendix C Redshift from Coherence Drift

Appendix C — Derivation 3: Redshift from Coherence Drift

Overview

In standard cosmology, redshift is interpreted as the stretching of spacetime itself—wavelengths elongate as the universe expands. In modal dynamics, there is no spacetime substrate to stretch.

Instead, redshift arises from coherence drift: as a latent mode (like a photon) propagates through a varying coherence field $B (x)$ , its internal phase structure deforms. The result is a shift in frequency and energy.

This is a structural, not geometric, explanation—grounded in coherence preservation and anchoring tension.

A photon is a latent mode: it propagates without anchoring into the surrounding coherence field. Its structure is internally stable, defined by a coherence function:

ψ_{γ} (x, t) = ρ (x, t) e^{i ϕ (x, t)}

Its motion is determined by the principle of coherence preservation: it follows a path that minimises decoherence cost while avoiding anchoring saturation.

2. Drift Through a Gradient

As the photon travels through a varying field $B (x)$ , its phase structure must adapt to avoid increasing anchoring cost.

Assume the photon moves along a radial coordinate $r$ , and $B (r)$ decreases with distance from a source (e.g. galaxy or coherence centre). Then the coherence medium becomes less dense as the photon moves outward.

To maintain phase preservation:

The photon must lengthen its phase interval
The result is a decrease in frequency (i.e., redshift)

This is not due to energy loss, but due to structural adaptation to the coherence landscape.

3. Redshift Definition

Let the photon have a coherence frequency $ω$ at emission and $ω^{'}$ at detection.

The redshift $z$ is defined by:

1 + z = \frac{ω_{emit}}{ω_{obs}}

In modal terms, this ratio reflects the difference in coherence field strength between emission and observation points.

4. Frequency Scaling from Anchoring Drift

Let $B (r)$ be the coherence field at position $r$ . The effective frequency of a latent mode in a region of coherence field $B$ scales with the gradient cost avoided during propagation.

Assuming $ω \propto B (r)$ (up to calibration), we obtain:

1 + z = \frac{B (r_{emit})}{B (r_{obs})}

If $B (r)$ is known—e.g., from Appendix B:

B (r) = \frac{A}{r} e^{- k r}

then the redshift becomes:

1 + z = \frac{r_{obs}}{r_{emit}} e^{k (r_{obs} - r_{emit})}

This is a coherence-based redshift–distance relation. It resembles the exponential behaviour seen in high- $z$ supernova data without invoking accelerating expansion.

5. Consequences

Redshift reflects coherence history, not geometric scale
Late-time acceleration is explained by steepening field decay, not dark energy
Time dilation and spectral line broadening arise naturally from internal phase stretching

There is no need for expanding spacetime, no cosmological constant, and no inflation. Just coherence gradient, anchoring cost, and phase drift.

Conclusion

Redshift is not caused by space stretching.
It is the structural memory of a mode drifting through a weakening coherence field.

Appendix B | [Index](./Appendix Master) | Appendix D