The Grandfather Paradox
Episode #1 of the course Brain-twisting paradoxes by John Robin
Welcome to a ten-day tour of the world’s most interesting brain-twisting paradoxes.
My name is John Robin. I’m an author and entrepreneur, and I’ve also written several Highbrow courses on writing and math. I enjoy using my skill as an author to teach others about interesting topics, and what’s more fun than paradoxes that show just how wonderfully complex our world is?
Let’s dive into our first one!
Step into the Time Machine …
Traveling back in time—if it’s possible—should be relatively safe, right?
Not according to today’s paradox. It goes like this:
Suppose you could travel back in time, like in Back to the Future. Now, while there, you encounter your mother’s father before your mother was born. Let’s say you don’t quite like each other and you get into an argument. Things escalate and a knife comes out. Suddenly, Grandpa is dead.
What happens to you?
Logic tells us that you would stop existing. Your grandfather will not go on to meet your grandmother and have one of your parents, which means your mother does not exist and you can’t have been born—not you, whose DNA half comes from that now-nonexistent parent.
Just like that, your grandfather’s younger self dies and you flicker out of existence.
Now, here’s the problem:
If you don’t exist, then you couldn’t have existed to have the time machine in the first place and travel back in time and kill your grandfather, which must happen in order for you to not exist.
So, there we have it, the heart of the paradox—which science fiction writers have aptly named the grandfather paradox: If you kill your grandfather back in this time, you stop existing, but if you don’t exist, then that means you couldn’t have gone back and killed your grandfather.
Does that twist your brain in a knot? Good, that means you’re seeing the validity of this problem.
I’ll give you a moment to think about how we might resolve it.
Go on, have a sip of coffee. Get a piece of paper if you want to draw a diagram. How is it possible you can go back in time and kill your grandfather but somehow still exist?
Philosophers have really dug into this problem, and in fact, there are several possibilities.
One of them is that you might travel to a parallel universe where there is a whole other timeline. There are many possibilities, all explored in different science fiction films and books, but the Many-Worlds Interpretation of spacetime would allow you to travel “back in time” to a different branching universe, where killing your grandfather would cause your parallel self in that universe to not exist, but not impact this universe at all.
Reasoning by Modal Logic
The most straightforward explanation, where we stick with literally traveling back to our universe at an earlier time, requires modal logic.
When we reason by modal logic, we think about how any one thing exists at any one time. There are what are called necessary conditions for it to have come about. This means if these conditions did not happen, then the current existing state would not exist. Therefore, the conditions must have happened.
The interesting thing about this logic is when we consider a state, we can reason that the necessary conditions for it to happen are not always unique. We merely want to know: Is this one state possible, and if so, what exact conditions are required (necessary)?
Let’s take you existing to go back in time and kill your grandfather in the past (of your universe and timeline) and still existing after that, so you can still exist in the future to go back in time and kill your grandfather. What’s necessary for this to be true?
We would consider just what it takes for this to be possible:
You exactly as you were, down to every particle and arrangement of particles (and the trajectories of their behaviors, which relies on their histories at the moment you entered the past) must exist exactly like that in the future. This means you can’t take any action that will prevent every particle, their trajectories, and histories from being any different in you or anything that came back in the time-traveling capsule with you. Modal logic will ensure that no matter what you do, events turn out differently to conserve this.
It’s therefore impossible to kill your grandfather. You might go so far as to say the universe will conserve itself by this modal logic by not even letting you meet your grandfather; even further, it might not even let you go anywhere near anyone or anything that will change any event that is any bit related to your life.
One thing is certain about this possibility: Traveling back in time will have more restrictions than any other form of travel we know.
Look out for tomorrow’s lesson, where we will see just how complicated going to prison can be.
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