Spin as a Transformation Class of Rotating Wave Modes

J. Beau, Independent Researcher, France

Status

Preprint, v1.3. Companion conceptual/structural audit of the fermionic-matter sub-programme. DOI: 10.5281/zenodo.21380026 v1.1 adds the soldering-audit section: the Veronese obstruction lemma and the spinorial-soldering indeterminacy proposition. v1.2 is a rigour consolidation after review: surjectivity argument completed in the real-form classification proof; the indeterminacy proposition's falsifiability clause restated exactly; the three missing data qualified as independently missing, with the joint-sufficiency question left open. v1.3 adds the mandatory labelled interpretive outlook in both abstract and conclusion: the audit neither confirms nor refutes the rotating-wave hypothesis; it turns its realisation within Cosmochrony into an explicit derivation problem with testable success and failure criteria.

Abstract

This note examines the hypothesis that the wave function is a combination of rotating and non-rotating wave modes, spin expressing the rotation of these components rather than the rotation of a particle-like object. For the photon the hypothesis is nearly literal: the transverse components of a circularly polarized wave rotate, and the associated angular momentum is mechanically measurable. A scalar counterexample shows that the rotation of components is not sufficient: spin is fixed by the way the components transform under rotations of physical space. The resulting hierarchy is: the relative phase is a measurable coordinate within a sector, the weight m is an axial winding degree, the spin j labels the irreducible representation of SU(2), and univalence (-1)^{2j} separates superselection sectors as a rule on the algebra of observables. The formulation avoids the historical superluminal-velocity objection, which constrains rigid bodies rather than internal rotations of wave components. Any rotational ontology of spin must involve a relational, extended, or topologically attached wave configuration, never a point particle endowed with a mere internal axis.

Epistemic status of the Cosmochrony-facing claims

1. Exact (proved): the central grading on tensor powers of the admissible module, with the central element acting on V_rho^(tensor n) as (-1)^n.
2. Diagnostic: Lorentzian spin and the weak doublet must act on distinct tensor factors.
3. Correction: in Q7, e_0 is the spin-weight m = 0 within the j = 1 module, not a j = 0 state (matching surgical fix applied to Q7.tex).
4. Conditional: the physical univalence interpretation of the tensor grading, conditional on the Lorentz-spin identification of V_rho.
5. Open: the representational problem (constructing the full Spin(3) action rho_rot with rho_rot(-I) = (-1)^n) and the stronger dynamical problem (whether the cascade canonically traces an axial one-parameter orbit, with axis and angle relation both derived).
6. Proved (v1.1, unconditional): the Veronese-null versus compact-real-form lemma — nonzero pure tensors w w^T lie on the null cone of the invariant form, so they meet no compact real form W_phi; the first internal real-form selector candidate (O28 outer products) is excluded.
7. Conditional on the listed corpus inventory (v1.1): the spinorial-soldering indeterminacy proposition — the derived data fix the complex carrier and its univalence but determine neither the spatial realisation, nor a physical rotation action, nor its scale; the missing soldering is typed as three data (phase-sensitive real-form selector, independent rotation action rho_sp, Casimir-independent normalisation), with rho_sp structurally blocking.

Position in the programme

Upstream input: O29 / Q7 (admissibility construction selects V_rho isomorphic to C^2). Downstream: Q14 and the fermionic-matter sub-programme (univalence, spinorial carrier, Lorentz / weak SU(2) separation).

Build

./compile.sh

Output: out/SpinRotationNote.pdf.