interstellar (the movie)

the astronauts in the movie “interstellar” use rotation of their space ship to generate artificial gravity by means of a centrifugal force. would there be a way to distinguish the two? if inertial and gravitational forces are indistinguishable, how would you explain that the artifical gravity onboard the space ship is in fact actual gravity, i.e. what generates this gravitational field? if space was completely devoid of matter, would that still work?