  For hydrogen bonded crystals exhibiting proton transfer along hydrogen bonds,
namely $\mathrm{O1-H}... \mathrm{O2} \longleftrightarrow \mathrm{O1}...
\mathrm{H-O2}$, there is a dichotomy of interpretation consisting in that while
the crystal lattice is a quantum object with discrete vibrational states,
protons are represented by a statistical distribution of classical particles
with definite positions and momenta at any time. We propose an alternative
theoretical framework for decoherence-free macroscopic proton states. The
translational invariance of the crystal, the adiabatic separation of proton
dynamics from that of heavy atoms, the nonlocal nature of proton states, and
quantum interferences, are opposed to statistical distributions and
semiclassical dynamics. We review neutron scattering studies of the crystal of
potassium hydrogen carbonate (KHCO$_3$) supporting the existence of macroscopic
quantum correlations, from cryogenic to room temperatures. In addition, quantum
fluctuations calculated for superposition states in thermal equilibrium are
consistent with measurements of the correlation time. There is no temperature
induced transition from the quantum to the classical regime. The crystal can be
therefore represented by a state vector and the dichotomy of interpretation
must be abandoned.
