That’s an interesting question, but I think the answer would be this: as long as it would seem simpler and just as analytically fruitful, we might as well take the definitional position that time doesn’t pass in such situations [basically, take whatever perspective allows the math to come out cleanest]. This isn’t necessarily a metaphysical claim, as such, but just a position on how we’d like to use our words. (But, then, that’s generally all I would take metaphysical claims to be anyway…). Certainly, Occam’s Razor, at least in its original form, would lead us to such avoiding of unnecessary multiplication of entities, for whatever normative force that’s worth.
Oh, ok. Apologies for taking such impressions, then.
After thinking about it some more, I think the question is another rephrasing of the original (essentially, is time quantized). If so, then I would think we would have to say that time doesn’t pass during the interval because we are defining it to only occur at the interval boundaries.
Well, I wouldn’t say “Time doesn’t pass during the interval”; the interval is, by definition, a collection of points situated further along in time, no? Rather, I would say, in that situation, “Why bother having an interval, then? Let’s just quotient it all out into discrete points of time, at nonzero distances from each other but without further points of time between them.” So time would pass in discrete steps, but it’s not as though it’s “holding back” over some intervals in order to do so, as there isn’t anything else for those to be intervals of.
That is, if you’re committed to time being quantized, then, by god, have it be quantized; there’s no need to carve that quantized structure out from some other continuously varying structure of ‘underTime’ (as though, plotting time as a function of underTime, one would get a staircase graph).