Appendix I — Derivation 9: Strong and Weak Interactions from Modal Anchoring

Overview

The Standard Model describes two non-electromagnetic forces:

• The strong interaction, responsible for confinement of quarks and gluons via SU(3) gauge symmetry
• The weak interaction, responsible for beta decay and flavour change via SU(2)

In modal dynamics, there are no forces, no mediating particles, and no gauge fields.
Instead, these behaviours emerge from anchoring structure, coherence saturation, and chirality-dependent modal dynamics.

1. Strong Interaction: Confinement from Anchoring Instability

Quark-like modes are incoherent in isolation: they cannot anchor stably alone because their internal phase structures are incomplete or imbalance the coherence field.

Let ${\psi }_1$, ${\psi }_2$, and ${\psi }_3$ be three modes with complementary internal phase orientations. Individually:

due to asymmetry and unbalanced anchoring.

Together, their combined structure:

can anchor in a balanced way:

This stabilising combination represents confinement:

Isolated colour modes cannot persist. Only combinations that neutralise anchoring imbalance can survive.

This reproduces:

• Colour neutrality
• Baryon and meson formation
• Inaccessibility of free quarks

2. Saturation and Gluon Analogue

There is no gluon particle.
Instead, modal overlap between confined components induces mutual anchoring distortions.

These distortions:

• Oscillate within the coherence envelope
• Preserve the integrity of the full bound mode
• Are responsible for binding energy and internal field-like effects

Energy is stored as coherence curvature, not in field excitations.

3. Weak Interaction: Chirality and Anchoring Drift

In the Standard Model, the weak interaction is chiral—it acts only on left-handed fermions and violates parity symmetry.

In modal dynamics, chirality arises from internal phase rotation handedness. Modes with phase windings of opposite sense exhibit different anchoring behaviour:

• Left-handed modes anchor with lower cost in biased coherence fields
• Right-handed modes fail to anchor or drift

This asymmetry produces:

• Structural parity violation
• Directional decay preferences
• Helicity-dependent interactions

It is not imposed—it emerges from how handed modes distort their coherence field.

4. Modal Decay Channels

A bound mode that enters a high-cost region may decohere into fragments. The available products must:

• Preserve anchoring continuity (e.g. charge, spin, winding)
• Be able to re-anchor in the surrounding $B(x)$
• Respect structural exclusion

This reproduces:

• Beta decay: a modal reconfiguration due to chirality instability
• Flavour transitions: coherent re-anchoring in a new winding state
• Neutrino emission: shedding minimally anchored phase packets

5. No Force, No Carrier, No Field

The strong and weak interactions are not mediated.
They are structural outcomes of modal cohesion and instability.

• Confinement is anchoring interdependence
• Decay is coherence failure and reorganisation
• Chirality is handedness in phase alignment
• Transition probabilities are structural—not stochastic

Conclusion

Strong and weak forces are not interactions.
They are the modal geometry of coherence clusters reshaping themselves under anchoring tension.

Appendix H | [Index](./Appendix Master) | Appendix J