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 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}} = 7/4. 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}} = 5/2, where quantum coherence is protected rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.