  The Quantum Cheshire Cat experiment showed that when weak measurements are
performed on pre- and post-selected system, the counterintuitive result has
been obtained that a neutron is measured to be in one place without its spin,
and its spin is measured to be in another place without the neutron. A
generalization of this effect is presented with a massive particle whose mass
is measured to be in one place with no momentum, while the momentum is measured
to be in another place without the mass. The new result applies to any massive
particle, independent of its spin or charge. A gedanken experiment which
illustrates this effect is presented using a nested pair of Mach-Zehnder
interferometers, but with some of the mirrors and beam splitters moving
relative to the laboratory frame. The analysis of this experiment using the
counterparticle ontology of Aharonov et al. is also given.
