What happens when you go back in time and change an event? Do the memories of the people in the present suddenly change to reflect the new past? Or were their memories always of that 'new past' because in effect, the old version of the past never happened? Except it did, because you obviously went back to it and changed it.
If that wasn't enough to contort the brain, try this:
One slight change in the past could mean the deaths of thousands--if not millions--of people. Because maybe you got in the way of Mr. A and Miss B meeting each other, and so they never got married, never had children, and a whole string of people were never even born. So you could come back to the present and find out that your best friend just never existed, because she was a descendant of A and B who never met. (Or, you know, what if you ended up killing your own ancestors before their children were conceived? Have you erased your own self?! And if you don't exist, you couldn't have gone back in time to kill anyone. This is apparently called the "grandfather paradox.")
Then again, since Mr. A never met Miss B, maybe he meets Miss X instead, and they marry and have children . . . and so you come back to the present and discover a whole whackload of brand new people who were never there before.
Or what about all those time travel stories where characters want to prevent the disasters of the past? Stop the Holocaust or keep the Titanic from sinking? That's all well and good, very commendable, I say. Except what if, by diverting one disaster, you give rise to a new disaster that's just as bad? Or worse? What if one of the Titanic's passengers you rescued turns out to be a murderous psychopath who goes on to decimate a whole city?
(And then of course you have multiple cases of generations not existing anymore. And all of the Titanic's descendants living.)
Forget people living and dying, though. What if you go tell Thomas Edison how to make a lightbulb before he's even tried it five times? Then maybe he turns his attention to other inventions, and winds up giving the world something that wasn't supposed to exist for another couple of decades. What then? With one lightbulb, you just accelerated the world's technology. Of course, if you want to be malicious, you could also go do something like keep Galileo from discovering that the earth revolves around the sun. And then where would we be? Or maybe you decide to impart some other knowledge to the people of history, like the importance of hygiene? (I think the world would be a much fuller place now. A lot less people would have died.)
Okay, so what if you decide it's too messy to deal with the past, and instead you travel to the future? (ACK, MY POOR BRAIN.) Let's say you jump twenty years ahead to see where you'll be. You see yourself living in Metropolis (hello, Superman), working a Nice Job, married to a Great Person, etc. You also happen to notice that you're suffering the after-effects of an Old Hamburger the future-you ate a week ago.
So you return to the present and go on with life as usual. But when you meet Great Person, you already know you're going to marry them. What if that blinds you to that other Even Better Person in your life? And when it comes time to move, you pack up and head right to Metropolis, because that's where you're supposed to be. But is it really? And then you're offered a Nice Job, but what you don't know is that if you wait another week, someone's going to offer you a Stellar Job.
And thus what you saw in the future becomes a self-fulfilling prophecy. It could've been different. It could've been better. It could've been worse. (Or could it? Is that future you saw inevitable? Or just one of millions of possible outcomes?)
Of course, because you know your future, you're smart enough to avoid that Old Hamburger twenty years from now, so you don't get sick. But you also don't take that sick-day and read that life-changing blog post whilst sprawled on the couch.
And how about the bigger picture? When you go to the future, you see their technology, their government, the future of the world. You see how they solved world hunger, or how sexism warped the opposite way and now men are discriminated against instead of women, or how football evolved into a Roman coliseum type of thing!
Knowing all this, you could fix world hunger right now.
Knowing all this, you could try to eradicate sexism entirely and help the world respect and value both genders.
Knowing all this, you could ban football.
But then that future changes. Good things happens sooner, but new problems also arise.
All this to say: aren't you glad we can't actually mess with time? And, more importantly, this mind-bending topic makes me realize that we all make a difference. The smallest things go on to change the world.
What say you? Do you like time travel in fiction/movies? Does it hurt your brain? If you could witness--but not actually be in--a certain historical event, what would it be? (Because obviously inserting yourself into that situation could be very bad, so we'll just stick to watching it from a nebulous room outside of time. That's totally a thing.)
Wikipedia has an article on time travel that talks about things I didn't even think of, like tourism in time.