Identifies Dirac freezing as a mechanism allowing systems to lose degrees of freedom, suggesting implications for theory of gravity and quantum physics.
I identify a universal mechanism---Dirac freezing---through which a constrained dynamical system loses all physical degrees of freedom without producing gauge symmetry.The loss comes about through a singular collapse of the constraint algebra into a maximally second‑class configuration.A finite rank gap separates the frozen phase from any dynamical phase, so the two cannot be connected continuously; a universal barrier theorem follows from rank semi‑continuity.Embedding the frozen sector into a dilaton reveals that, although freezing is fine‑tuned under conservative evolution, dissipation or quantum tunneling makes it generic. More fundamentally, the frozen phase can be realized as the true vacuum of a finite‑field quantum field theory; quantum tunneling out of a metastable dynamical phase then eliminates the need for any fine‑tuning of initial conditions.Higher‑derivative terms evade the mechanism entirely.Extensions to field theory and gravity show that matter can freeze while gravitational waves remain untouched; a complete spacetime freeze requires breaking diffeomorphism invariance, which cleanly separates the phenomenon from Carroll and strong‑coupling limits.In an expanding universe, Hubble friction restricts freezing to the dark‑energy‑dominated era, where it produces a characteristic kink in the growth of structure, a non‑phantom equation of state, and a non‑thermal small‑scale cutoff in the matter power spectrum.In the dissipative quantum regime, the adiabatic invariants of the field modes decay exponentially, and any initial entanglement is destroyed irreversibly. This yields a quantitative, falsifiable signature that cleanly separates Dirac freezing from ordinary decoherence.
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Youming Huang (2026) studied this question.
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