Quantum measurement and fuzzy dark matter
  It has been suggested that dark matter is a superfluid of particles whose
masses are on the rough order of $10^{-22}$ eV. Since the occupation numbers
are huge, the state is coherent, and the speeds typical of orbital velocities
in halos, it has generally been assumed that a classical effective
non-relativistic treatment is adequate. However, the Compton wavelength would
be $\sim 1\, {\rm pc}$, and around the Compton scale concerns about some
aspects of quantum measurement theory, known in principle but not
quantitatively significant in previous cases, become pronounced. I estimate
here the stress--energy operator, averaged over a few Compton wavelengths; a
rough but useful approximation has a remarkably simple form. Conventional
quantum measurement theory gives physically unacceptable results: a
thought-experiment to measure the stress--energy is described which would
involve only a modest apparatus but would excite particles in the observation
volume to relativistic energies; these particles would escape the Galaxy, and
there would be a substantial violation of energy conservation. Related
foundational questions come up: the meaning of measurements of observables with
continuous spectra, and the problem of predicting when measurements occur. The
effective classical theory of fuzzy dark matter is not affected; however, the
underlying quantum theory cannot be regarded as satisfactory without resolving
these issues. But we may interpret the results more broadly. The macroscopic
Compton scale amplifies inadequacies of measurement theory which have not
previously seemed pressing.
