TL;DR – Time loops don’t really work. Either they degenerate into sources of infinite mass or they violate thermodynamics.

My last thought experiment on time travel struck a chord. “Surely, you must know about wormholes!” someone assailed me. “You could go through a black hole and come out in a totally different era!” “There could be time loops where everything keeps happening over and over!” And I thought to myself, “Didn’t I already have this conversation?”

There is something about time travel that makes people write really bad science fiction. People go back, change the past, new timelines are created at the risk of tearing apart the fabric of the space-time continuum! Personally, I hope one day we’ll be able to make underwear with such fabric: it must have an amazing texture.

One purported mechanism for time travel is the idea of having wormholes that connect distant space-time points allowing you to go back where you started. In the same way gravity makes the earth go round its orbit, making it come back where it started, gravity may also make you go round in time, making you come back when you started. And then you do it all over again… and again… and again… I don’t quite understand the excitement: seems very dull to me. But maybe it is possible, right?

Personally I don’t think this case makes sense either. At least, not in any way one would understand time travel. And why not explore the idea with another magnificent and ignominious thought experiment?

A loop in space-time

Suppose you are a space-time explorer. You travel the galaxy trying to find space-time anomalies onboard your spaceship. It’s actually a piece of junk: life is tough for space-time explorers… Funding is tight, the oxygen supply is limited, finding habitable planets is very unlikely… But let’s not dwell on the precariousness of your existence!

What you are hoping for is to find a space-time loop: a region of space-time that, if you keep going in the right direction, you go back to when and where you started. This seemed very exciting when you embarked on your adventure. After months of complete isolation… you are not so sure anymore.

You are also not sure what you’ll find. Suppose you do come back to when you started: how will that work? Will there be another copy of you, and you’ll see your old self? Or will there be one of you, that keeps going back and forth in time?

Well, suppose that there is going to be only one of you. That is: not only is there a loop in space-time but your life is a loop as well. That means that you’ll go back to being whatever age you were at that moment. That’s nice. But you’ll go back to the memories you had at that point… which means you’d forget you already had the trip. Maybe you have already looped multiple times?

But if you go back to being what you were before, it means at some point you started to get younger. All the food you ate in the spaceship should recompose itself from… your waste. That’s not very appealing. The oxygen level should resupply… so you’ll breathe in carbon dioxide and breathe out oxygen? Also, your spaceship is not perfectly insulated, so some heat has been dissipated. It would have to come back, probably violating the second law of thermodynamics. You are no expert, you are just a space-time explorer, but the second law of thermodynamics is pretty important. Imagine the fine!

So, ok, you convinced yourself: you won’t be the same copy. That means you’ll be a different copy. But how many? I mean: it’s a loop. You could do it over and over… Yes, you may run out of oxygen, but your spaceship will continue to drift. In fact: the more copies there are, the more mass there will be. Isn’t that like creating mass out of nothing? The more mass there will be, the more gravity will pull each copy preventing their escape. At some point there will be so many copies that a black hole would be created.

You start second-guessing the wisdom of embarking on such an adventure.

The problem with space-time loops

While the equations of general relativity may allow space-time geometries that present space-time loops, it does not mean that they are physically possible. Classical mechanics, in fact, allows the possibility that random bits scattered all over suddenly travel back on top of your plate to form a roast chicken. It is thermodynamics that says you shouldn’t count on it. So, when drawing conclusions, we have to be careful not to step out of the realm of validity of the theory we are considering.

General relativity hinges upon the idea that a space-time event only needs four values to be determined by all observers. Suppose you are able to come back to the same point in space-time and say, “I have been here before!” Then you have a way to distinguish the current copy from the previous copy of the space-time event. That is: space and time are not enough to distinguish those two moments. This contradicts the very foundation of relativity: the trip number is needed as well to determine an event in your life.

You may ask: what if I can’t distinguish between my trips? Then nothing must be able to. That means all those irreversible processes must be reversed. All those particles that decayed must “undecay”. All the radiation that was emitted must return. That’s a lot of work: I am definitely not going to do that! What you’ll end up requiring is either breaking the second law of thermodynamics or that this part of the universe is causally disconnected from everything else. I don’t know about you, but I kind of like the second law of thermodynamics and my scientific interest for things I will never be able to interact with/measure is negligible.

So we have gone full circle: time travel still does not make sense. So be careful because, whatever you do, the cosmos keeps having you push the big ethereal and mystical button with the words: “Are you sure you want to continue? This action cannot be undone.”