Recent calculations in both flat and de Sitter spacetimes have highlighted a
tension between the decoupling of high-energy physics from low-energy degrees
of freedom and the expectation that quantum systems decohere due to
interactions with unknown environments. In effective field theory (EFT),
integrating out heavy fields should lead to Hamiltonian time evolution, which
preserves the purity of low-energy states. This is consistent with the fact
that we never observe isolated quantum states spontaneously decohering in the
vacuum due to unknown high-energy physics. However, when a heavy scalar of mass
$M$ is traced out, the resulting purity of a light scalar with mass $m$
typically appears to scale as a power of $1/M$ (when $m\ll M$), an effect that
cannot be captured by a local effective Hamiltonian. We resolve this apparent
paradox by showing that the purity depends on the resolution scale of the EFT
and how the environment is traced out. We provide a practical method for
diagnosing the purity of low-energy states consistent with EFT expectations,
and briefly discuss some of the implications these observations have for how
ultraviolet divergences can appear in decoherence calculations.