WHEELER

## Ambiguity in a Gravitational Stress Energy Pseudotensor Interpreted in Terms of Arbitrariness in a `Base Line Coordinate System' *W. R. Davis*

In order to avoid the non-localizability to*difference* between the gravitational pseudotensor defined by the
and
itself transforms like a tensor under coordinate changes. This result might seem to give a certain uniqueness to the definition of a gravitational stress energy tensor if one could imagine that the quantities,
, were unique. However, a simple investigation shows that
the
's are highly arbitrary. In fact, for every coordinate system,
, that is asymptotically straight at infinity one can introduce a set of
's which have the
normal Lorentz values everywhere. By this procedure the
's are of course defined in any other coordinate system. The ambiguity in the choice of the
's in some specific coordinate system is therefore as great as the ambiguity in the choice of the original coordinate system which becomes asymptotically flat - an ambiguity can be regarded as a base line. Motions with respect to this base line can be thought of as due to “gravitational” forces. These gravitational forces define a gravitational stress energy tensor. This point of view has the following usefulness: One is in this way easily able to extend the discussions of the equivalence principle *the choice of the base coordinate system is arbitrary.* Once one has selected this base coordinate system all else is uniquely determined.