  It has recently been claimed that the dynamics of long-wavelength phason
fluctuations has been observed in i-AlPdMn quasicrystals. We will show that the
data reported call for a more detailed development of the elasticity theory of
Jaric and Nelsson in order to determine the nature of small phonon-like atomic
displacements with a symmetry that follows the phason elastic constants. We
also show that a simple model with a single diffusing tile is sufficient to
produce a signal that (1) is situated at a "satellite position'' at a distance
q from each Bragg peak, that (2) has an intensity that scales with the
intensity of the corresponding Bragg peak, (3) falls off as 1/q-squared and (4)
has a time decay constant that is proportional to 1/(D q-squared). It is thus
superfluous to call for a picture of "phason waves'' in order to explain such
data, especially as such "waves'' violate many physical principles.
