  Some hybrid systems models are unsafe for mathematically correct but
physically unrealistic reasons. For example, mathematical models can classify a
system as being unsafe on a set that is too small to have physical importance.
In particular, differences in measure zero sets in models of cyber-physical
systems (CPS) have significant mathematical impact on the mathematical safety
of these models even though differences on measure zero sets have no tangible
physical effect in a real system. We develop the concept of "physical hybrid
systems" (PHS) to help reunite mathematical models with physical reality. We
modify a hybrid systems logic (differential temporal dynamic logic) by adding a
first-class operator to elide distinctions on measure zero sets of time within
CPS models. This approach facilitates modeling since it admits the verification
of a wider class of models, including some physically realistic models that
would otherwise be classified as mathematically unsafe. We also develop a proof
calculus to help with the verification of PHS.
