  We study the conservation of energy, or lack thereof, when measurements are
performed in quantum mechanics. The expectation value of the Hamiltonian of a
system can clearly change when wave functions collapse in accordance with the
standard textbook (Copenhagen) treatment of quantum measurement, but one might
imagine that the change in energy is compensated by the measuring apparatus or
environment. We show that this is not true; the change in the energy of a state
after measurement can be arbitrarily large, independent of the physical
measurement process. In Everettian quantum theory, while the expectation value
of the Hamiltonian is conserved for the wave function of the universe
(including all the branches), it is not constant within individual worlds. It
should therefore be possible to experimentally measure violations of
conservation of energy, and we suggest an experimental protocol for doing so.
