Lorentz Invariance as a Regime Constraint

This section interprets Lorentz invariance not as a fundamental axiom,
but as a regime-level constraint that characterizes a specific class of closure-stable realizations within the Dimensional Emergence Framework (DEF).

DEF does not assume Lorentz invariance.
It explains under which structural conditions Lorentz-invariant descriptions become admissible.

Lorentz invariance in conventional physics

In relativistic physics, Lorentz invariance expresses the requirement that:

physical laws are invariant under changes of inertial reference frame,
spacetime admits a fixed invariant interval,
and no preferred frame exists.

These properties are usually postulated at the foundational level.

Structural reinterpretation in DEF

Within DEF, Lorentz invariance is reinterpreted as a constraint on regime realization, not on ontology.

Specifically, Lorentz-invariant regimes are those in which:

Existence-side relations (Structure · Space),
and Happening-side relations (Exchange · Dynamics),

remain symmetrically coupled under transformation.

This corresponds directly to the Core constraint:

(S · R) ≡ (X̂ · D)

Symmetry as constraint satisfaction

Lorentz invariance emerges when:

constraint tension between Existence and Happening is minimized,
no operative mode dominates under transformation,
and phase ordering admits reversible traversal without divergence.

In this view, Lorentz symmetry is not primary.
It is a stable equilibrium configuration of constraint satisfaction.

Metric emergence

In Lorentz-invariant regimes:

relational structure admits metric interpretation,
phase ordering can be coordinatized as time,
and exchange–dynamics coupling can be represented geometrically.

The Minkowski metric is thus understood as a representation of balanced kernel coupling,
not as a fundamental geometric substrate.

Breakdown of Lorentz invariance

DEF naturally allows for regimes in which Lorentz invariance fails.

Such breakdown may occur when:

constraint tension becomes asymmetric,
one dimension (Existence or Happening) dominates,
or phase resolution cannot restore symmetry.

Examples include:

extreme interaction regimes,
non-equilibrium transitions,
or structurally divergent configurations.

In DEF, Lorentz violation signals regime transition, not inconsistency.

Relation to observation

Observers embedded in Lorentz-invariant regimes will:

measure invariant light speed,
observe relativistic time dilation,
and infer spacetime symmetry.

Observers in non-Lorentz regimes may:

lack global time ordering,
observe anisotropic propagation,
or fail to coordinatize interactions spacetime-wise.

Lorentz invariance thus conditions what can be observed, not what can exist.

Scope

This interpretation does not modify relativistic physics.

It situates Lorentz invariance within a broader structural framework,
in which symmetry is a consequence of closure and constraint balance.

Lorentz invariance is therefore understood as a regime constraint
that identifies a particularly stable and symmetric realization of the DEF kernel.