  We propose PET scanners using low atomic number media that undergo a
persistent local change of state along the paths of the Compton recoil
electrons. Measurement of the individual scattering locations and angles,
deposited energies, and recoil electron directions allows using the kinematical
constraints of the 2-body Compton scattering process to perform a statistical
time-ordering of the scatterings, with a high probability of precisely
identifying where the gamma first interacted in the detector. In these cases
the Line-of-Response is measured with high resolution, determined by the
underlying physics processes and not the detector segmentation. There are
multiple such media that act through different mechanisms. As an example in
which the change of state is quantum-mechanical through a change in molecular
configuration, rather than thermodynamic, as in a bubble chamber, we present
simulations of a two-state photoswitchable organic dye, a `Switchillator', that
is activated to a fluorescent-capable state by the ionization of the recoil
electrons. The activated state is persistent, and can be optically excited
multiple times to image individual activated molecules. Energy resolution is
provided by counting the activated molecules. Location along the LOR is
implemented by large-area time-of-flight MCP-PMT photodetectors with single
photon time resolution in the tens of ps and sub-mm spatial resolution.
Simulations indicate a large reduction of dose.
