I thought of this problem with time travel years ago, and I thought I was pretty clever at the time for noticing it. But the internet has shown me that many authors and sci-fi fans came up with this before I did: It’s impossible to make any slight change to history. The only possible changes are massive ones.
The timeline is a lot more fragile than is usually portrayed in sci-fi. Marty McFly didn’t need to worry about getting his parents back together. He irrevocably erased himself and all of his siblings from the timeline the moment he skateboarded into town and interacted with someone.
Imagine a man gets a great big armful of individual twenty-sided dice, and gives them a toss. They scatter in a particular pattern of numbers. Now, time-travel back to just before he rolls those dice and stop him for a five-second conversation. Will he roll all the same dice in the exact same pattern? Of course not. The ever-so-slight different movement and timing will have him roll a completely new arrangement.
Now apply that same thinking to an even more chaotic event: Conception. Anyone that you interact with in the past will be nudged off of their original rails and onto an imperceptibly new path. This change will be slight only until the moment when they are involved with the conception of a child. Even if the kid is conceived on the same day at roughly the same time (which isn’t a guarantee) it’s going to be a different kid than was rolled in the timeline before you began mucking about. That different kid will live their entire life, nudging everyone else off of their behavior rails, resulting in different children for everyone they meet, and so on.
Poor farmer Bob originally had a son Alan, but thanks to your meddling ends up having a daughter Alice instead. Later, the woman who originally married Alan will marry someone else, and have a completely different slate of kids. Moreover, Alice will likely end up “stealing” a husband from elsewhere in the gene pool, and she will also produce a completely new mix of kids who never appeared in the history you’re familiar with. When the wave of change hits the ruling class you’ll end up with different rulers and wars and different discoveries being made. Every single historical figure born more than a generation away from your arrival will be obliterated, and new ones will appear in their place.
Every time traveler now has unthinkable power. Their slightest action will remove billions of people from the present, and replace them different billions of people. Their every action is re-rolling their future, every moment.
If you time-travel back to (say) 1909, you don’t need to worry about erasing yourself from history by accidentally killing your (N-great) grandfather as he (say) got off the boat on Ellis Island. You’ll obliterate yourself even if you travel to San Fransisco instead of New York, and all you do is bump into someone on the street.
It’s hard to say how small a change you can make, and fiddling around with parts of the timeline becomes a study in chaos theory. What if I warp to an empty pasture in Wales in the mid-1650’s and swipe a single stone off the ground? Will that initiate a ripple effect and overwrite the timeline? What if I swipe a large stone from a wall around someone’s property? What if I bury an out-of-place stone from another part of the world? What if I swat someone’s livestock on the head when they aren’t looking and then poof back to my own time? It seems like you’ll end up with a binary outcome: Your change will either be be noticed and thus alter the behavior of a single human being (and eventually everyone) or it will go unnoticed and have no effect.
You could play around with this and make “sleeper” changes to the past. Locate some ruin that was disconnected from the rest of the world, and leave some change to confound archaeologists. Pompeii is an excellent candidate for this sort of time-traveling prank. Go there just before the eruption of Mount Vesuvius and hand out a few iPods or revolvers or something. Since the city was buried, your historical shenanigans will be concealed for 1,700 years, and the timeline will proceed unchanged in the outside world. From AD 79 to AD 1748 the outside world will proceed along the familiar path, but the moment a digger sticks his shovel into some fragment of plastic or precision-machined metal your changes will suddenly manifest and propagate.
This means pretty much any time travel ends up in a paradox. I dislike this paradox that emerges from any meaningful leap through time from a purely science-fiction point of view. It’s much more interesting to write (or, I suppose, read) about situations where you can travel through time. (The technology required to do so is usually hand-waved by authors and readers alike, but the repercussions of the technology are not. People are funny.)
One way around this would be to eliminate the possibility of a paradox. You could come up with a set of rules where changes to the future don’t have any causality link to the past. So, you can erase your own grandfather (and thus yourself) from the time line, but you won’t instantly vanish the moment you shoot the old boy dead on Ellis Island. You’ll still be standing there, but if you go forward in time you’ll find a different arrangement of people in place, one where your family doesn’t exist and nobody has ever heard of you. This seems to be a common approach to writing about time travel. (Although most stories allow the protagonist to “fix” the changes they made and set things “right” again, which isn’t possible if we take conception into account.)
If we really want to start playing around with scientific buzzwords and write some rules for time travel, we could devise a system where your “changes” propagate at the speed of “time”. (How much this makes sense depends on how much we want to lean towards magic or science for our time-travel ability.) So, if you go back and kill (say) Hitler in 1939 and then jump back to the present, everything will look the same. Your change will be creeping forward through time at the same rate you are, and if you want to see 2009 with your changes in place, you’ll need to wait 70 years. You can stay in 1939 and watch the new history unfold, or you can bugger off to 1 million BC and do your waiting there.
Imagine your time machine is simply a device that will teleport you from A to B instantly. If you fire a laser beam at Alpha Centauri and then teleport over there, you’ll still have to wait for your beam to arrive. The time machine works the same way, except with time instead of distance.
This system suggests time is “layered”, and that one dimension of time is contained within another. String theory suggests that there are 11 dimensions, and so you could borrow from that to explain your time layers. If you go back and kill Hitler, you’ll need to travel in the 4th dimension. To see the result in 2009, you don’t just need to go into the future, you need to go into the future of the future. So you’ll need to travel in the 5th dimension. Or wait.
I’m sure a physicist would scoff at this for various reasons, but this explanation is probably good enough to sell the reader on time travel without them putting the book down.
Anyway, use caution if you’re going to be time-traveling. I’m having a pretty good run here and I’d really rather not be erased. Thanks.
EDIT: To be clear, I’m not arguing that time travel IS possible, I’m just musing about effects and rules that would be involved if it was.