  For theories of relativistic matter fields there exist two possible
definitions of the stress-energy tensor, one defined by a variation of the
action with the coframes at fixed connection, and the other at fixed torsion.
These two stress-energy tensors do not necessarily coincide and it is the
latter that corresponds to the Cauchy stress measured in the lab. In this note
we discuss the corresponding issue for non-relativistic matter theories. We
point out that while the physical non-relativistic stress, momentum, and mass
currents are defined by a variation of the action at fixed torsion, the energy
current does not admit such a description and is naturally defined at fixed
connection. Any attempt to define an energy current at fixed torsion results in
an ambiguity which cannot be resolved from the background spacetime data or
conservation laws. We also provide computations of these quantities for some
simple non-relativistic actions.
