  At first glance the definition of mass and momentum appears to be uniquely
defined. We show here, however, that this certainty can be misleading for many
coarse grained systems. We show that particularly the fluctuating properties of
common definitions of momentum in coarse grained methods like lattice gas and
lattice Boltzmann do not agree with a fundamental definition of momentum. In
the case of lattice gases, the definition of momentum will even disagree in the
limit of large wavelength. For short times we can give analytical
representations for the distribution of different momentum measures and thereby
give a full account of these differences.
