  Diverse calculations have shown that a relativistic field confined to a
cavity by well defined boundary conditions can have a negative Casimir or
vacuum energy. Why then can one not make a finite system with negative mass by
confining the field in a some way? We recall, and justify in detail, the not so
familiar subdominant trace energy condition for ordinary (baryon-electron
nonrelativistic) matter. With its help we show, in two ways, that the
mass-energy of the cavity structure necessary to enforce the boundary
conditions must exceed the magnitude of the negative vacuum energy, so that all
systems of the type envisaged necessarily have positive mass-energy.
