  We point out that the celebrated GRW master-equation is invariant under
translations, reflecting the homogeneity of space, thus providing a particular
realization of a general class of translation-covariant Markovian
master-equations. Such master-equations are typically used for the description
of decoherence due to momentum transfers between system and environment.
Building on this analogy we show the exact relationship between the GRW
master-equation and decoherence master-equations, further providing a
collisional decoherence model formally equivalent to the GRW master-equation.
This allows for a direct comparison of order of magnitudes of relevant
parameters. This formal analogy should not lead to confusion on the utterly
different spirit of the two research fields, in particular it has to be
stressed that the decoherence approach does not lead to a solution of the
measurement problem. Building on this analogy however the feasibility of the
extension of spontaneous localization models in order to avoid the infinite
energy growth is discussed. Apart from a particular case considered in the
paper, it appears that the amplification mechanism is generally spoiled by such
modifications.
