Technically, the moment science would show an interaction between physical entities and something else, that something else would immediately be classified as a physical entity. In a very real sense, the discovery of radioactivity involved physical entities being found to interact with an as-yet unknown, invisible, intangible force.

If ghosts existed, the same would happen as with radioactivity. They would be researched, hypotheses on their nature would be tested, and a scientific theory would arise, and then they would be a part of the “physical world” too. And then all the mystics would be bored with ghosts because they are just incorporeal noospheric echoes of old people, as boring as neurology or biochemistry or stellar fusion.