Problems with Time Travel
Aside from the obvious technological problems, let's look at some different possible theoretical outcomes involved with time travel. I'm only going to focus on traveling to the past because that's the only one I can see any problems with at the moment.
To start, let's say there's something I want to change. I think it's impossible to go back and change that particular problem without causing yourself to be sent off in some sort of infinite loop. Think about it. You have this problem, you go back and you fix the problem. Simple right? wrong. You go back and fix the problem, which means that the problem, as you knew it and had instigated you to go back, no longer exists. Thus, you didn't go back to change it, causing it to never be fixed (and subsequently remain), causing you to go back again. This loop will continue on forever, since you'll constantly be altering the time-line and you will have no memory of any of the activities.
Now, some of you might say, what if time isn't linear, what if when you travel back in time, it's another dimension that you actually stepped into that happens to be parallel to ours and exactly the same, only a specified amount of time behind us. If this happens, then if you were to fix the problem, you would return to one of two dimensions: your original dimension, or another (Mind blowing!). Within those two return possibilities, if you jump to your original, the problem will most likely still be there because you only changed the reality in that alternate dimension and not your own. If you happened to go to another, it could have any random repercussions along with it, which would lead to a post hoc, ergo propter hoc fallacy (after this, therefore because of this (we would wrongly conclude that our actions caused this outcome)). Of course, there's always the one in an infinite number of chances that you end up in the future that your actions caused. Again, it's not the most likely of outcomes. This problem also relates to the initial trip to go back.
How about if time is linear and we're capable of leaving time clones of ourselves (a previously acted alternate version of ourselves in the past who is our previous or future time traveling self). Well, as I see this one, we're allotted a certain amount of time to be alive, we'll just be spending it in another time that we've already lived through. So, me at age 27 visits me at age 26, I'd either have to skip ahead the amount of time I was in the past for, or cut that bit off the end of my life, causing my death to be earlier than it would have otherwise been. You could look at this as being when my death is permanently set because all my time traveling actions could have been incorporated in my original lifespan, but who knows about that side of things. This "solution" would also apply to a Dr.Who-style view of time travel, as portrayed in the picture to the side of this paragraph (click to see enlarged version), where time actually bends around and has periods that are linked via a perpendicular pathway between the two parallel time lines.
Another potential explanation that was brought to my attention is called the theory of compossibility. It puts the theory in the context of a man named Tim. Tim hates his grandfather. He hates his grandfather so much that he wants to kill him. The only problem is that his grandfather died a year ago. So, Tim builds a time machine and goes back to attempt to kill his grandfather. Essentially, since his grandfather is supposed to die in a specific year already, something will logically stop Tim from killing him. Say he's trying to shoot him: a bird might block the shot, his gun might jam or backfire, something could fall on him as he's about to shoot. This theory is along the same lines as a quantum theory proposal for time travel that was proposed by Daniel Greenburger and Karl Svozil. Their theory states that viewing the past from the present makes it deterministic; viewing the future gives it multiple paths it can take. So, in the same case as Tim, either something would stop the event from happening, or it would already have been incorporated into the outcome. Like that one Twilight Zone episode where a woman is sent back in time and comes across Adolf Hitler as a baby. She decides that it would be best to kill infant Hitler, and she does. As soon as the woman leaves, another woman happens by who doesn't want her baby and places it in the now vacant crib. The woman's actions caused Adolf, as we know him, to be given the opportunities he otherwise wouldn't have had.
Future-Self Edit: An interesting problem: suppose you travel to the future with a friend. In that future, a catastrophic even has happened, and you get split up. Then, you travel back to the past, solo, and stop that catastrophic event from ever happening. What happens to your friend?
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