It seems physical means it can be measured.
If that were true, things like depression, anxiety, political orientation, etc., are all physical, while the state of any quantum system is not.
It interacts with something else and that interaction can be measured.
The problem with this is that given some set of interactions that produce a given phenomenon, we can easily claim to be measuring what is merely and only a construct. Consider psychiatric disorders: there is no way to test for even the existence of any disorder in the DSM/ICD except through the use of their definitions (which is also the method we use to state they exist). Imagine that I develop a reliable instrument for Annoying Personality Disorder (APD), which we'll call the APD-scale. I can define the symptoms as follows:
1) Writing posts that are often longer than one page
2) Using twitter
3) Enjoying reading, using, and discussing advanced data/statistical analysis.
4) Repeatedly posting on RF due to insominia
5) Thinking Alien vs. Predator was a fun movie while Freddy vs. Jason was god-awful.
I now have an instrument with greater test-retest and inter-rater reliability than most for diagnoses in the DSM or ICD. I can "measure" who does or doesn't have APD, and what I am measuring is the result of many interactions. But as I made APD up for this post, am I measuring anything? I would say no. Unfortunately, it isn't just psychology, psychiatry, sociology, and more that present difficulties here. We know, for example, that space-like separated measurements of two physical systems can be causally linked regardless of distance and instantaneously (violating classical causality). We have no idea what we are "measuring" when we measure such links. Heck, we don't know what relation is between quantum systems or particles and physical reality. Hence the multitude of "interpretations" of quantum mechanics (nobody had to "interpret" Newtonian mechanics or classical physics).
If it is measurable, it's physical.
Measurement is fundamentally concerned with the application of statistical theories of measurement error, or quantifying the error of instruments. In other words, we only ever measure errors. This makes it a little hard to associate that which is physical with that which we measure.