I asked this question of a physicist and he told me to ask a philosopher. If one was to observe a closed, isolated region of space under vacuum conditions, i.e. there are no particles in this region and none may enter into it. Also there are no fields (i.e. gravitational, electromagnetic, etc.) acting or existing on or in this region. The only interaction with this system is as an outside observer. Can this observer notice the passing of time? If so, how? And does the act of observation make the observer part of the system, since the observer is technically interacting with it? Currently we measure time by the movement of quantum mechanical particles, such as the molecules in a ticking clock; the vibrations of atoms; and the decay of radioactive isotopes. But could we perhaps, in this hypothetical system, justify using properties of space itself, such as quantum foam or the expansion of space (expanding universe), and, if so, how would we observe these features?
Thank you for your question. Let me touch it up just a bit: There are no gravitational fields in general relativity over and above the curvature of space(time). In the spirit of the question, I will assume that the spacetime geometry is unchanging. An observer might be able to notice the passing of time in lots of ways (e.g., from his own heartbeats or passing thoughts or wristwatch). I presume that the question is asking whether the observer could notice it on the basis of some observed changes in the region of space in question. I am inclined to think not. Nothing is changing there. If spacetime geometry were changing, then the passage of light through the region to us would betray the change to us. But the question stipulates that nothing passes through the region.