Mass from Anchoring

In the modal framework, mass is not a fundamental quantity. It is not an intrinsic property of a particle, nor does it arise from coupling to a scalar field. Instead, mass emerges from how a mode anchors—how much effort is required to preserve its phase structure in space and time.

Anchoring Resistance

A mode that persists in place, rather than drifting, must constantly resist phase disruption. This resistance is anchoring cost, and the greater the cost, the more persistent the mode appears.

This persistence is what we call inertial mass.

A mode that anchors deeply into the coherence field experiences a strong bias gradient if displaced. It tends to return to its original anchoring configuration. In this way, mass is not a substance—but a structural stiffness in phase space.

Derived Inertia

The action functional for a mode includes a term:

S [ψ] \supset - γ | \partial_{t} ψ |^{2}

This term penalises rapid phase evolution in time. A mode with high anchoring cost cannot change quickly—it has high temporal stiffness, which appears as high mass.

Thus:

Low anchoring cost → flexible → low mass
High anchoring cost → rigid → high mass

Mass Without Matter

There is no need for matter, no need for a Higgs field.
Mass is not added—it is resisted.
It is the cost of remaining coherent under time evolution.

(See Appendix L — Gravitational analogue and in Appendix AK.)

Next: Charge from Phase Winding