Published October 7, 2026
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Neutrino Mixing and Projective Particle Identity
Description
Neutrino oscillations establish that the weak flavour basis and the mass propagation basis of the lepton
sector are not aligned.
This note examines what this misalignment means for the ontology of particle identity within the Cosmochrony
framework, where particles are invariants of a non-injective projection rather than primitive objects.
Three structural observations are developed.
First, basis misalignment is generic: neutral meson systems exhibit the same distinction between interaction
labels and propagating eigenmodes, and the neutrino is distinguished only by being elementary within the
Standard Model inventory.
Second, within the projective reading, alignment — not misalignment — is the feature requiring a
mechanism: an identity-stabilising projection channel.
Charged fermions possess such channels; neutrinos, singlets under ${\mathrm{SU}}(3)_C \times {\mathrm{U}}(1)_{\mathrm{em}}$,
do not.
The large PMNS mixing is then the unfixed default, consistent with the anarchy hypothesis, while the
near-diagonality of the CKM matrix becomes the non-trivial explanandum, requiring the charged channels to pin
the up-type and down-type mass bases to a common projective frame.
Third, the Dirac-or-Majorana alternative is reread as the degree to which the projection resolves relational
conjugation, with neutrinoless double beta decay as its standard discriminator.
The note is structural throughout: it derives no mixing angles and no masses.
It fixes the reading under which the neutrino sector is the sharpest available test case for projective
particle identity, and states one falsifiable structural expectation: sectors with fewer identity-stabilising
projection channels generically exhibit larger mixing between interaction and propagation bases.
Interpretive status: the reinterpretation of particle identity as a projection invariant is a structural
reading of standard neutrino phenomenology, not a competing prediction for it; all quantitative content of
the standard oscillation formalism is retained as the operational effective description.
Files
NeutrinoProjectiveIdentity.pdf
Additional details
Related works
- Is supplemented by
- Other: https://cosmochrony.org/science/neutrinos/ (URL)