The relational theory of time says that a moment is just a bundle of co-occuring events. 4:20 PM on April 20th of the year 420 B.C.E. was nothing above and beyond the events that occurred then. The substantival theory says that times are something like independently existing abstract entities that happen to contain various events but could have contained entirely different events, or perhaps even no events at all.
(The suggestion that there could be "empty times," where nothing changed and nothing happened is incoherent on the relational view.)
The standard Benaceraff-style objections to abstract objects would all seem to apply to substantival moments. (If they all disappeared tomorrow, how would we ever know the difference? Given that a human being having an intuition is surely ultimately a certain sort of neurological event, explainable in terms of some mixture of biological hard-wiring, socialization, and so on, and that an abstract object could play no role in the causal chains leading up to such events, why on earth should we think that our intuitions track its true properties?, and so on.) Given that, what possible argument could there be for the substantival view?
Quentin Smith has argued in many places for the substantival view on the grounds that some counterfactual statements about time seem to be true. If I arrived on time to the meeting at 4:20 PM, it still seems to be true that, for example, if I had gotten pulled over by a traffic cop on my way to the meeting, I would have been late. Put differently, if I had been pulled over by a traffic cop on my way to the meeting, the moment 4:20 PM would not have included the event of my showing up at the meeting. It would have, indeed, included entirely different events, like people asking each other why I wasn't there. Intuitively, all of this would have happened at 4:20. But wait! If 4:20 just *is* a set of co-occurring events, then it wouldn't have existed in the possible world where I didn't show up on time to the meeting. For some such counterfactuals to be true, it seems, moments need to have a separate existence above and beyond the things that happened at them.
However unattractive the idea of substantival moments might be to me, this has always seemed to me like a pretty tricky problem for the relational theory. Now I'm not so sure.
Notice, though, that if one sees time-terms ("4:20," "yesterday afternoon" and so on) as shorthand definite descriptions, like "that bundle of events which includes Event E" or even "that bundle of events that's related in such-and-such order to the bundle of events that includes Event E," the problem goes away. Smith, of course, who's written extensively on phil of language, realizes that this is a way out. I don't have the link handy--his website seems to be down at the moment--but in a short article on this a while back, he presents the objection as a dilemma between rejecting the relational theory of time and rejecting the "New Theory of Reference" (i.e. the Kripkean* theory of proper names as rigid designators). To become a full-fledged argument for a substantival view, one needs compelling arguments for the Kripkean view and against the old Russellian descriptivist view. Smith, of course, like a great many people, takes it that we have such comeplling arguments.
Fair enough, but, the more I think about this, the less convinced I am that the dilemma really exists. There's only a dilemma if one thinks that *all* proper names and proper-name-like terms rigidly designate, and one can certainly be a Kripkean about reference without making that sweeping universal claim. For example, Kripke himself never claimed it and has always explicitly disowned it, being careful to emphasize all along that he was making a general claim about most normal uses of most normal proper names and nothing more.
Of course, Kripke could be mistaken in holding back from the universal claim, but there are good reasons, quite independent of the Phil of Time issues under discussion, to think that he isn't. For one thing, taking names that don't pick out any existing object--e.g. "Santa Clause"--as rigid designators (of what?) raises all kinds of sticky problems. Of course, that itself raises all kinds of deeply controversial philosophical issues, but more banal and uncontroversial examples are plentiful. To pick an obvious one (not original to me), "Jack the Ripper" is a lot more like an archetypal ordinary proper name than "4:20 PM" is, but "Jack the Ripper" pretty clearly really is a shorthand definite description, along the lines of "whoever murdered and mutilated the bodies of those prostitutes in London." Given (a) the incompatibility of the package of the relational view and the assumption that time words rigidly designate on the one hand and the apparent truth of some temporal counterfactuals on the other hand, and (b) the obvious epistemic and ontological parsimony-based objects to the substantival view, it seems to me that (c) even if one adopts a rigid designator view of most ordinary proper names--"Quentin Smith", "Saul Kripke", etc.--it's a mistake to extend that analysis to time terms.
*Smith himself probably wouldn't call it that. He has heterodox views on history of the philosophy of language that would lead him to think of it as the Marcusian theory--he and Scott Soames have killed a lot of trees with their essays arguing back and forth on this issue--but we can put that historical dispute to one side for the moment.