But there is no super-clock. Our hero can only be in the Pleistocence with a watch reading 11 AM, a million years before he exists with a watch reading 10 AM, and he has no more "come from" a million years hence than I have "come from" tomorrow morning . The illusion of travel arises only because of the unusual state of our hero in the Pleistocene, namely that he "remembers" events from a million years in the future and his watch, along with other parts of his local environment, maintains the same sequence of internal states which it will have again in that future time.
All this can be represented within mathematical holism as follows:
Suppose a comes into existence in world state t0, with a subcomponent m which contains its 'memories'. a remains in existence until t1, at which point it goes out of existence until a later world state t2 ; in the case of a human time-traveler, t2 might be the time of the traveler's birth. At some later world state t3, a goes out of existence again and the state of m at that point (let's call it m(t3)) is identical with the intial state m(t0) -- it is exactly this identity which allows us to characterize the relationship between a on the epoch from t0 to t1, and a on the epoch from t2 to t3, as one of "time travel".
The theory of time implicit in mathematical holism rules out some forms of time travel as logically impossible. The story of the Time Traveller who changes the past to prevent her own birth is not paradoxical; it is simply false. At the point where the Traveller acts so as to eliminate her future existence, she may believe that she will nonetheless exist at a future point, but she won't. There is only an illusion of time travel here, caused by the fact that the Traveller comes into existence with "memories" of future states -- that is, she arrives in a state which happens to contain information which coincides with what she would "remember" were such information to be transmitted to her at a future time. But that is just coincidence; we know from what we are told about her actions that she will not exist at that future time; so the "memories" are actually not true.
On the other hand, one kind of time travel, "jumping forward in time", occurs trivially -- it happens all the time, if you'll pardon the expression. For suppose X is a state of the World component a. If the World enters a state in X, a remains unchanged for as long as the World state is in X, so a is in "stasis", with its local time "suspended" until the World state leaves X.
This form of time travel has been ably explored in the Peace War novels of Vernor Vinge, but it is not a fiction; mathematical holism asserts that it is a real and necessary and constantly occuring phenomenon! For if the World has more than two states, then in any state s, there is at least one World component A(s) which enters stasis in that state -- namely, the component A(s) = { {s} union T(s), - ({s} union T(s)) }. (I am assuming here that {s} union T(s) <> S, so that A(s) <> O.)
In Real Time (p. 172), D. H. Mellor writes
"All in all, real forward time travel is neither a problematic or especially remarkable phenomenon. It is really only an overly grandiose description of processes slowing down or stopping. Describing a stopped watch as having turned literally into a time machine does rather doll up the situation, and a repairer advertising cures for cases of forward time travel in watches and clocks would be more derided than enriched -- as I shall be if I waste more ink on so trifling a topic."
But perhaps it is only Mellor's examples of forward time travel which are trifling; a clue as to what he is missing is found in his dismissive comment (p. 171) that
"in most science fiction it is also de riguer for future bound time travellers to disappear during the intervening decades, and I know of no way of doing that. But disappearing for the duration is only a melodramatic embellishment, by no means essential to the end result."
Now the concept of "disappearance" can be interpreted as "going out of existence" which is equivalent to going into, and remaining in, stasis (see "Existence: Coming Into & Going Out Of "). Forward ("future bound") time travel thus requires disappearance in the epoch through which the travel occurs. Backward time travel likewise requires disappearance or stasis at the moment at which the traveller appears to "depart for the past". So Mellor's comment should be reversed -- disappearance is not an embellishment; it is an an essential ingredient of time travel.