Universal Description of Decoherence in Scale-Invariant Environments

When a quantum system couples to a scale-invariant environment, what form must its decoherence take? We prove that the answer is unique: under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an \emph{unparticle bath} – a scale-invariant continuum of states – characterized entirely by the scaling dimension $d_{\mathcal{U}}$ of the coupled operator. This is not a modelling choice but a consequence of conformal symmetry. All decoherence and dissipation exponents are fixed by $d_{\mathcal{U}}$ through exact consistency relations, providing falsifiable predictions independent of microscopic details. We validate the framework using multi-channel transport data from the unitary Fermi gas, where two genuinely independent observables yield a consistent $d_{\mathcal{U}}=7\mathrm{/}4$. We further show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos – spanning more than 25 orders of magnitude in energy – are unified as specific realizations of the same structure. A decoherence phase transition at $d_{\mathcal{U}}=5\mathrm{/}2$, where quantum coherence is \emph{protected} rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.