In addition to the points that Richard makes above, we might consider the fact that the expression "time" functions oddly in lots of constructions. Having too much time on your hands is quite different from having too much lotion on your hands, having time on your side is different from having Jack your side, and time's running out is different from Jill's running out.
It might also be useful to remember that we should always be careful not to put too much weight on the surface grammar of our language. Lewis Carroll got a lot of mileage out of this, e.g., in Through the Looking Glass:
"I see nobody on the road," said Alice.
"I only wish I had such eyes," the King remarked in a fretful tone. "To be able to see Nobody! And at that distance too! Why, it's as much as I can do to see real people, by this light."
Let's distinguish between physics and common sense: an adequate physics might or might not include a temporal dimension along which events occur, and this dimension might or might not possess various of the features that common sense attributes to time. That much is familiar from Einstein: it's not automatic that the commonsense conception of "time" is an accurate one---that it correctly captures some real aspect of the physical world. So we have to be careful when answering questions like "Does time have a preferred forward direction?". If we're exploring common sense the answer has to be "of course!", but if we're doing physics then it's a question of whether there really are important asymmetries in a physically real temporal dimension (which is actually a controversial matter: a fascinating discussion is David Albert's Time and Chance). Similarly for questions like "Did time have a first (or last) moment?". As a commonsense matter, the answer is "surely not!", but here too physics might require revision of common sense.
Your questions ask if anything would count as the stoppage of time, or the beginning (or end) of time, or the reversal of time, or travel backwards in time? Distinguish:
- Physical: could the physics of a universe have a temporal character that includes these phenomena?
- Commonsense: does time as common sense conceives it allow these phenomena?
It's fairly plausible that the answers to the physical questions are all yes: there are possible universes that work in such a way that there is something that counts as "time", which in a good sense sometimes stops, or has a start and an end, or reverses, or admits of time-travel. What counts as "time" in these universes departs in various ways from our commonsense conception, but not so badly as to lose the right to be called "time" by their inhabitants. If our universe turned out to be these ways, we'd want to say it was time that had these surprising features, not that there is no time after all.
What about the commonsense questions? Does time as ordinarily conceived allow these things? Surely not a beginning or an end. But the issue is less clear as regards stoppage, reversal, and time-travel. There we run into interesting interactions between two important strands in the commonsense picture of time. On the one hand, time is an infinite, objective dimension along which events occur. This dimensional conception of time seems to rule out not only a beggining and end, but also stoppage, reversal, and time-travel (one's being at an earlier time after being at a later one). On the other hand, time is what orders the progression of a process, from its earlier stages to its later stages. This narrative conception of time seems to allow reversal and time-travel. While the standard way of reconciling the dimensional and narrative conceptions of time requires that narratively "later" maps to dimensionally "later", nothing obviously precludes a different mapping, on which some processes unfold or jump backwards in dimensional time.
You won't be suprised to hear that philosophers disagree a lot about the reality of times. Some say that time is a lot like space, and that all times are equally real at all times. On this view, the present is where we happen to be at the moment, but right now the past and the future are also equally real, much as here is the place we are, but other places are equally real even though we are not at those places. At the other extreme, there are those, appropriately called 'presentists', who think that only the present is real: the past has gone out of existence and the future has yet to come into existence. Your view is intermediate: the past and present are real but the future is not. This too can be seen as a kind of spacial view of time, but in an expanding universe. If it helps, think of the universe as an inflating balloon: on your view the temporal dimension is inflating too, so there are more and more real times.
I too find the expanding view of time attractive, in part because the past really does seem to have a kind of reality that the future so far lacks. But one thing we might worry about is whether this expanding view of time can make sense of the truth of future tense statements. It's true, alas, that I am going to die someday, and I think moreover that it's true now that I am going die. But if it's true now that I'm going die, then is looks like there has to be something real now that makes it true. Yet on the expanding view there doesn't seem to be any such thing, since what in fact makes it true that I am going to die is something that will only take place in the future.
These are interesting and difficult questions about time. First of all, it's helpful to distinguish our sensation of time from time itself. Time would exist even if there was no consciousness in the universe. It is less clear whether would be any interesting notion of past, present and future. Acording to a 'spacial' view of time, time is very much like space. In particular, just as 'over there' is just as real is 'over here', so on this view all times are equally real at all times. But on other views of time, the present is a priviledged moment, and would be even if there were no creatures to enjoy it. (I'm afraid I'm going to pass on the duration question.)
As for our sense of the passage of time, I don't think this can just be a result of fading impressions. For it would seem that an impression that we are having now, say while half-asleep, could be just as 'dim' as an impression we have of a past experience, yet we still would judge the former to be about the present and the latter to be a memory. Similarly, a memory may become more vivid to us as we think about it, but what we remember need not thereby seem to have happened more recently.
I suspect the point of this question was to see whether you could articulate the idea of a "category error," that is a statement that is syntactically correct but is nonsense because its predicate cannot meaningfully be attributed to its subject.
If this is what the interviewer had in mind, your answer was essentially correct but could have been stronger if you had explained that this was one example of a more general problem. If your interview was at an Oxford college, you probably would have earned bonus points if you had referred to Gilbert Ryle's classic discussion of category errors.
The thesis that time is more fundamental than space is not uncommon among philosophers -- although the significance attached to this, and the meaning of 'fundamental' varies widely. At least arguably, Aristotle, Leibniz, Kant and Heidegger, are committed to some variety of this claim.
Kant's argument has some similarities to yours. All propositions about things and events must, when fully analysed, include a subordinate proposition about time (if only the location in time of the act of thought itself). But not all propositions about things and events must include a subordinate proposition about space. Kant then uses this analysis to argue further that the basic categories of all thought must be understood to be rules for the determination of time relations.
You are right that Superman's feat of resurrecting Lois Lane makeslittle sense. The same is true of nearly all films (or stories)involving time travel. The trouble arises when characters 'change thepast'. That whole idea is of doubtful consistency. If Superman makes itthe case that Lois didn't die yesterday, then how come we saw a realityin which she got squashed by the earthquake? Maybe some sense can bemade of this by supposing that reality has a branching structure, andthat Lois dies on one branch but not the other. But even this doesn'tseem to do the trick. Isn't Superman supposed to be saving Lois, not just adding something to a structure in which she is also still squashed?
Analternative would be to suppose that Superman (and we viewers) inhabita Supertime, such that at Superdate 1 ordinary reality contains Loisdying yesterday, but by Superdate 2 Superman has changed ordinaryreality so that Lois survived yesterday. This is no doubt how weunderstand the movie, and why it seems plausible enough at first pass.But I'm not sure that even this really makes sense. (For a start, howexactly do Supertime and ordinary time relate to each other?)
All the above puzzles come from the idea of 'changingthe past'. By contrast, that is nothing immediately incoherent in theidea that the past is (and always has been) influenced by a travellerfrom the future. (Thus Mack Reynolds' classic story 'CompoundedInterest' (1956): a hugely rich man uses most of his fortune to build atime machine in which he then goes back 500 years to depoisit 1 ducatat compound interest so that in 500 years time . . .)
Still, once we admit time travel itself, won't the more paradoxical ability to changethe past inevitably be admitted too? If I can go back to the past,what's to stop me killing my own grandfather? It is a matter of currentcontroversy among philosophers whether the apparent freedom of a timetraveller to cause such paradoxial consequences shows that the idea oftime travel itself is incoherent. (What about the episode of Futuramawhere Fry does accidentally kill his own grandfather, and then consolesthe bereaved fiancee, and walks her home, and stays the night . . .?But of course that wasn't then his real grandfather that he killed.)