  This note has no new results and is therefore not intended to be submitted to
a "research" journal in the foreseeable future, but to be available to the
numerous individuals who are interested in this issue. The Debye-Waller factor
is the ratio of the coherent scattering or absorption cross section of a photon
or electron by particles bound in a complex system to the value for the same
process on an analgous free particle. It is often interpreted also as the
probability of the coherent process, normalized to unity, with the difference
between unity and the Debye Waller factor interpreted as the probability of
incoherent processes. The Debye-Waller factor is then interpreted as a measure
of decoherence. The breakdown of this description for a test particle which
cannot give or lose energy is not generally appreciated. Prime examples are:
Bragg scattering, the M\"ossbauer effect and related phenomena at zero
temperature. The physics of the change in the interpretation of the
Debye-Waller factor is summarized here in a hopefully pedagogical manner.
