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Suppose it is possible to travel back in time. If Bob traveled back in time, wouldn't he lose the memory of what happened since his neurons are also traveling back in time? In other words, traveling back in time would feel like the present moment. Consider this thought experiment:
Bob eats pizza at 12 PM.
Bob plays tennis at 2 PM.
Bob travels back in time to 12 PM.
Would Bob lose the memory of him playing tennis at 2 PM and essentially treat 12 PM as an ordinary experience?
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.
References
An analogy would be, if the person ate lunch at
Bob eats pizza at 12 PM.
Bob shaves off moustache at 12.30 PM.
Bob plays tennis at 2 PM.
Bob travels back in time to 12 PM.
Would Bob have his moustache back? If not, then he would retain his memory. As the changes are comparable. Both physical.
As memory requires LTP of the brain, which means there are physical changes to the brain, one would assume that the act of time travel, would not alter the person's brain chemistry (their rationality perhaps). As the person's physical body would be transported in space and time, not transmuted.
As a Doctor Who fan, during the doctor's travels, he has full memory of his previous experiences (unless there is another reason, not pertaining to the time travel itself, that has caused him to not recall who is is).
My questions would be the following:
Bob eats pizza at 12 PM.
Bob plays tennis at 2 PM.
Bob travels back in time to 12 PM.
Which psychotic illness is Bob most likely to have?
The answer presumably depends on how you conceptualise the experience of the time traveller relative to the time travel. In most movies the world and most other people in the world are just restored to the original time, but the time traveller is somehow immune to such effects.
For this version of time travel to be true and consistent with neuroscientific theories of the mind-body relationship, then presumably the brain of the time traveller is not altered by time travel, or at least is not altered in such a way to restore the brain to the state it was in at the time of return. Thus, memories of the future would be retained when going back in time.
In fact, if the mind of the time traveller was restored to the returned time, then this could result in non-existence if you travelled back further than when you were born. It would also seem inconsistent with the possibility of going back in time but being in the same location that you initiated the time travel.
You might also wish to see what answers you get on https://scifi.stackexchange.com/
