The commonly held understanding of time travel is something that is inherently inconsistent: if you were to “travel to the past”, from your subjective perspective, there would still be a “before” time travel, and an “after” time travel. If a continuity of subjectivity is implied where you would be in the present and then suddenly you would pop up in the past, clearly, in some sense, you are still traveling forward. That is to say, time travel cannot “cause” a change in the past, nor can it cause any kind of subjective experience in the past, because “going somewhere” is an action that necessarily entails a before and an after, therefore a move forward in time. A cause produces an effect, and the effect always happens in the future with respect to the cause, this is true on a basic semantic level.
So if you are preparing yourself for a travel to year 1000, keep in mind that you are most probably moving into a sort of place where the past is reenacted, not the “true past”. Conversely, if you are reading this with memories of the year 3000 you came from, either of two things can be the case: the events you remember either truly happened, in which case they necessarily happened in the past, or they didn’t, in which case your memories are probably completely fictional and you should probably investigate from where exactly you come from.
A corollary of all this is that if you want to go in the past in order to “kill Hitler”, you wouldn’t “cancel” what he did. At best, you would create a new timeline where the Holocaust never happened and copies of the victims can live their lives, at worst you’d destroy the whole universe in order to replace it by whatever it was at the time, which is a dangerous and utterly pointless endeavor.
Here are a few novel and reimagined ways you might “travel through time”, even though ultimately they still make you move forward in time in some sense (they have to, or they would be absurd!)
Reversal of the laws of physics
We could imagine that a “switch” exists that allows one to reverse velocities and the laws of physics everywhere except for where they stand. This would have the added bonus of tracking location, but maybe also the complication of having to minimize interactions at the boundary of the time machine. Indeed, these interactions could cause a rippling effect through space (keep in mind that the laws of physics, in reverse, are not very different from the forward rules, look up T-symmetry for more information) and corrupt the reversal process. I am not sure what the exact consequences would be, it could range from total annihilation to only having a mild effect.
If it is possible to reverse these properties in select locations, then we could presumably do some cool things, though I am not completely sure what. The thing is that inverse rules of the universe still fall prey to the second law of thermodynamics, in the sense that you could reverse glass shattering or gas seeping into a vacuum, but once the reversal is accomplished, the glass can still shatter and the gas will immediately seep back in, and in both cases the forward rules would reverse the process. The idea is that both the laws of physics and its inverse will cause gas to fill a vacuum, but they will fill it in such a way that the inverse law will conveniently undo the process, up to the point where it will redo it.
One drastic way to accomplish time travel would be to outright erase the universe and replace it by a “backup” of what it was at a past time. This of course implies that such a backup exists. This method could also be used to restore select parts of the universe. It is also rather contrived.
A second dimension of time
A relatively neat way to frame time travel is by imagining that there is a second dimension of time, and that time travel simply shifts the whole timeline into the future in that dimension, with the only difference being that the time traveler disappears from her present and appears in her destination. So far this is equivalent to the oft-mentioned idea that traveling through time creates a new timeline, but it could be argued that all instances of time travel occur simultaneously and appear in the same “next timeline” (and so forth). This would mean that if I travel to the year 1000 and you travel to the year 1001, you will see me around, as opposed to us being sent to two distinct timelines. If we travel again, we will end up in a third timeline, and so on.
The chaotic spacetime
Yet another idea, which I find interesting (but perhaps quite complex, so I’d appreciate feedback on whether whoever is reading this understands), is to imagine the universe a bit like a pipeline. A large set of universes are aligned one after the other, and each passing second, each universe tells the next one what it should be next. That is, imagine that three moments in time exist: the moment where you read the first sentence of this paragraph, the moment where you read this sentence, and the moment where you read the next one. Now, imagine that “you” exist simultaneously in these three states, and when time passes, what happens is that the first you reads the second sentence, the second you reads this sentence and the third you reads the next. It is like a pipeline, with all “moments” existing simultaneously, and as time passes they move on to their next state. This does not seem absurd – I can conceive the universe working like that.
Now imagine that time travel simply means that instead of moving to the next universe in the pipeline, you move to a previous one, so that the third you, instead of reading the third sentence, decides to go visit the second you. There is no paradox here. However, something really, really strange would happen. I will try to explain to the best of my ability.
(Note: if this paragraph is too awkward to read, just skip it) Let’s say that R means reading. The state of you reading was RRR. Now imagine that T means thinking about time travel, V means deciding to visit the past, X means not existing, and S means being surprised. Reading evolves into Thinking, unless an unexpected event puts you into the Surprised state for a while. Thinking evolves into deciding to Visit, and deciding to Visit causes you to not exist in the next universe and exist in your past destination instead, which obviously creates a Surprise there. So at first you have R????, where ? means the future universes are still fresh and we don’t know what’s in them yet. R???? becomes RT??? – the first you is always reading, and the second you is thinking, because the first was reading. RT??? becomes RTV??, because thinking leads to deciding to visit the past. RTV?? becomes RSVX?, because the deciding to visit (V) means you are absent from the next universe (X), and cause a surprise by popping in the previous universe instead (S). But now, the surprise means that you will not decide to visit anymore, because you are still shocked. So RSVX? becomes RSSXX. But now there are no visits anymore, so you get RTSSX, and then RTVSS, and then RSVXS, and so on! So overall in the long term this will cause a “ripple” in the future where universes alternate between having two copies of you and having zero.
In other words, this is a version of time travel which would cause quasi chaotic ripples through space time. If you travel back in time thirty years, there would be a thirty year long “ripple” through time where you are a time traveler, like a mini-timeline that moves along spacetime. What happens is that the time frame where you time travel continuously exists as a consequence of the previous universes, therefore there is, continuously, a “you” that travels to the time frame thirty years back. After thirty years, however, the ripple would catch up to the time frame where you travel, and would prevent it for thirty years. After these thirty years, the original past will yet again produce a “you” that will time travel, hence leading to another ripple, and so forth. The fun starts when more than one instance of time travel occurs, and when they occur from ripples. The end result would presumably be complete chaos, a bit like throwing a handful of pebbles into a pond rather than just one. This being said, the awareness of time travel might range from extremely aware to not aware at all, depending on how many ripples-within-ripples are created. The world would also look relatively stable, besides frequent occurrence of time travelers.