The question whether the canonical form of the energy-momentum tensor should be abandoned in favor of one recently proposed by Callan, Coleman, and Jackiw is considered by adopting the criterion that any such modification must not be motivated entirely by the specific framework and properties of special relativity. Thus the possibility of divorcing the issue of the finiteness of the matrix elements of these operators from a specific relativity group is examined in the Galilean or nonrelativistic limit. It is found that for the case of a scale-invariant spin-zero Galilean theory in four spatial dimensions, the matrix elements of neither the canonical nor the "improved" energy-momentum tensor are finite. This circumstance may be seen to be a consequence of an increase in the number of independent form factors required in the nonrelativistic domain. Inasmuch as there is no possibility of making finite the matrix elements of the energy-momentum tensor in the Galilean limit by a redefinition, it is suggested that the quite different situation which one encounters in special relativity is largely accidental and that there is consequently no compelling argument for a modification of the gravitational interaction.

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