Neutrino Mixing and Projective Particle Identity

Basis misalignment is the generic situation; basis alignment requires an identity-stabilising projection channel. Neutrinos, lacking such channels, are the sharpest elementary test case.

Read the preprint DOI: 10.5281/zenodo.21207750

Overview

Neutrino oscillations establish a standard but philosophically loaded fact: the states produced and detected by the weak interaction ($\nu_e$, $\nu_\mu$, $\nu_\tau$) are not the states that propagate. The two descriptions are related by the PMNS matrix, and the observed identity of a neutrino depends on which basis the observation accesses. This structural note examines what that means for the ontology of particle identity within the Cosmochrony framework, where particles are invariants of a non-injective projection rather than primitive objects.

The note is deliberately non-quantitative: it derives no mixing angles and no masses, and it retains the standard oscillation formalism as the operational effective description. What it fixes is a reading — which features of the neutrino sector are generic, which require a mechanism, and which structural expectation is falsifiable.

Scope statement. This page provides a structured summary. The authoritative technical reference is the preprint linked above.

The reversal: alignment, not misalignment, needs a mechanism

Dirac versus Majorana as conjugation resolution

The Dirac-or-Majorana alternative is reread as a question about the resolution of the projection: a Dirac neutrino corresponds to a configuration whose conjugate projected realisations are distinguished, a Majorana neutrino to one whose partial projectability collapses the conjugate classes. Neutrinoless double beta decay then acquires a structural interpretation — it probes whether the projection resolves relational conjugation in the neutral chiral sector. No rate prediction is made.

What is and is not claimed

Standard (imported). Flavour–mass misalignment, oscillations, neutral meson mixing, near-diagonal CKM, large-angle PMNS, anarchy consistency of the oscillation data.

Structural (this note). The stabiliser reading of alignment, the neutrino as a neutral chiral matching mode, the PMNS-default/CKM-explanandum reversal, the conjugation reading of Dirac–Majorana, and the mixing-versus-channels expectation.

Conditional. The common projective frame assumption behind CKM near-alignment (load-bearing, underived).

Open. The quantitative pinning mechanism, the derivation of mixing magnitudes (blocked at the trivial chiral polar class of the present stratum), the Dirac–Majorana resolution criterion, and any oscillation correction.

Relation to the Cosmochrony programme

This is a companion note of the fermionic matter sub-programme, developing the identity-theoretic core of the white paper's description of neutrinos as partially projectable modes. Its quantitative counterparts — the explicit Lorentzian projective residue and the Yukawa sector — remain the primary open deliverables of the sub-programme; the chiral polar factor carrying generation mixing is invisible at the present stratum (PYO). The note also resonates with a pressure point independently identified in the philosophy of particle physics: neutrino mixing challenges a naive one-to-one correspondence between particle type, flavour label, and mass eigenstate.

References

Jérôme Beau. Neutrino Mixing and Projective Particle Identity: A Structural Note. Working paper, 2026. 10.5281/zenodo.21207750