This is a tricky topic and my answer will be clearly speculative. I will say that this is also largely a matter about metaphysical allowances and involves personal identity implications. Assuming that time travel is physically possible, we need to make assumptions around how time is interpreted within the time travel journey.
Scenario 1: Time travel based on external time and fatalism
Lewis (1976) distinguishes between two interpretations of time, i.e. personal and external time:
Instead I reply by distinguishing time itself, external time as I
shall also call it, from the personal time of a particular time
traveler: roughly, that which is measured by his wristwatch. His
journey takes an hour of his personal time, let us say; his wristwatch
reads an hour later at arrival than at departure. But the arrival is
more than an hour after the departure in external time, if he travels
toward the future; or the arrival is before the departure in external
time (or less than an hour after), if he travels toward the past.
Should Bob decide to travel back to 12 PM relative to external time, we can speculate implications on his continuity of personal identity. Le Poidevin (2005) elaborates on discontinuous movement through time:
... it seems that discontinuous movement is possible: one can move
from A to B without occupying places in between.
If so, it seems probable that Bob could lose his memory of playing tennis at 2 PM if discontinuous movement is allowed. Based on external time, he is in fact moving back 2 hours, however, implied is the suggestion that he won't be psychologically continuous and thus, won't remember that experience. Whether he will treat 12 PM as an ordinary experience or a completely new experience depends on how we interpret causal relations between past and present.
Fatalism suggests that we are unable to deliberate about the future or change it (Taylor, 1962). It is logically and physically impossible to change any events preceding the time travel point. From a fatalist viewpoint, Bob would experience all those events from A to B as they had occurred.
Scenario 2: Time travel based on personal time
The other scenario presupposes that time travel is continuous from the time traveller's personal time in which the person is psychologically continuous - there is no disconnect between the stages of the psychological and physical continuum when travelling time. If so, it may be possible for Bob to travel back to 12 PM, re-experience eating the pizza while his memory of playing tennis remain intact. Although time travel isn't physically possible, we can still project ourselves backwards in time and recall events (Suddendorf & Corballis, 2007).
Since this scenario doesn't sever the continuity of Bob's personal identity, it seems probable that he would still remember the experience of playing tennis at 2 PM while able to freely experience new events (given that fatalism is rejected) thereafter and the mere possibilities that follow.
- Lewis, D. (1976). The paradoxes of time travel. American
Philosophical Quarterly, 13(2), 145-152
- Le Poidevin, R. (2005). The Cheshire Cat problem and other spatial obstacles to backwards time travel. The Monist, 88(3), 336-352
- Suddendorf, T. & Corballis, M.C. (2007). The evolution of foresight: What is
mental time travel, and is it unique to
humans? Behavioral and Brain Sciences, 30, 229-351