  It is proposed to give up the description of physical states in terms of
ensembles of state vectors with various probabilities, relying instead solely
on the density matrix as the description of reality. With this definition of a
physical state, even in entangled states nothing that is done in one isolated
system can instantaneously effect the physical state of a distant isolated
system. This change in the description of physical states opens up a large
variety of new ways that the density matrix may transform under various
symmetries, different from the unitary transformations of ordinary quantum
mechanics. Such new transformation properties have been explored before, but so
far only for the symmetry of time translations into the future, treated as a
semi-group. Here new transformation properties are studied for general symmetry
transformations forming groups, rather than semi-groups. Arguments are given
that such symmetries should act on the density matrix as in ordinary quantum
mechanics, but loopholes are found for all of these arguments.

Quantum Physics