Consider facts like:
- Soon you will be in pain.
- Eventually, you'll forget.
- That sad experience is already behind you.
The simplest account is just that "ahead" means in the future and "behind" means in the past. But if time travel is possible, this will not do. "Soon you will be in pain" can be true even though the pain is millions of years in the past, as long as what you're about to do is to go into a time machine, quickly go back millions of years, and then experience the pain. Likewise, the sad experience that is already behind you may be one that you experienced a hundred years in the future, traveling to the future and back.
We can, of course, say that "ahead" means in the subjective future and "behind" means in the subjective past. But that is just to give a name to the problem—the problem of what constitutes subjective time for a given person, or, perhaps more generally, what constitutes inner time for a given substance.
The problem of subjective time is related to, but not the same as, the problem of personal identity. Suppose I accept a memory theory of personal identity. Then it is natural to say that some experience E is in the subjective future provided that E is conjoined with a set of quasi-memories that form a chain back to my present state. One might also say this even if one does not accept a memory theory of personal identity. Note that this account of the subjective future, even if accepted apart from the memory theory of personal identity, has some of the counterintuitive consequences of the memory theory. Suppose that in five minutes you will suffer total amnesia immediately followed by horrible pain. Then it seems quite right to say that soon you will be in pain—the pain is in your subjective future. But not if this memory theory of subjective time is correct.
David Lewis in his famous piece on time travel handles this by means of causal connections. What makes person-stage y a subjectively future person-stage with respect to person-stage x is that there is the right kind of chain of causal connections leading from x to y. (Put that way, the memory theory is a special case.) But what sorts of causal connections will do the job? We can imagine here fun time-travel scenarios involving swapping brains, or parts of brains, or memories, with your past self, and we're probably going to get some cases that are at least somewhat problematic for any particular causal connection account.
Note that dualist theories have a much easier time with the various puzzles about personal identity than non-dualist theories. Swinburne shows this: Dualist theories can always make indeterminacies be merely epistemic, and doing so fits very well with our intuitions. But it's much less clear that dualist theories have any easier time with the problem of subjective time.
On the other hand, non-realist or conventionalist accounts, while deeply implausible for personal identity, may be rather more plausible as answers to the problem of subjective time. While it really does matter much whether someone who does some horrible deed or experiences something wonderful is really me, maybe it does not matter much whether the deed or experience is ahead or behind, except insofar as I am causally connected to it. So one could accept a theory on which subjective time is constituted by causal connections, and not worry about the more outlandish counterexamples with mind-swapping, etc., because what matters are the causal connections, not the subjective time relations. One might hold that there can be vagueness in or degrees of aheadness/behindness that is more plausible (to me!) than vagueness in or degrees of identity .
There is a further option. It may be that it is a basic fact about substances in time that they are continuants and come with an internal clock.
A final question is what the relationship between objective and subjective time is. My present view is that external or objective time is constructed out of the inner or subjective times of things. In our universe this can be done because most inner times run in the same direction. There may, however, be universes without much coherence between inner times, and in such universes there will be no objective time, only inner or subjective time.