Is time-travel possible? (Patreon)

[This is a transcript with links to references.]

We just talked about time travel next month, but it’s been a while, so let’s give this a closer look. What does physics say about time travel? Is MIT really building a time machine to find dark matter. Is time travel possible? That’s what we’ll talk about today.

This video comes with a quiz on quizwithit dot com. So listen closely, and at the end you can check how much you get right.

If time travel is possible, where are all the time travellers? Maybe the 21st century is just too boring. Or maybe they’re very secretive. The explanation that I personally prefer is that you need a receiver-station for time-travel, so you can’t travel back to any time before the first receiver was built. And we haven’t built one. At least I haven’t heard of it.

It's not that Einstein, yes, that guy again, said that time-travel is impossible. Indeed, his theories show that it’s possible. I don’t mean to say that we travel through time at one second per second. That may be right, but it was last funny around the time of baryogenesis so I can’t really make a joke about it can I. Can I?

Proper time travel means that our internal time doesn’t pass like that of the rest of the universe. It means we could go 100 years into the future or a thousand years into the past while only aging a second, preferably without being torn into pieces in that process.

Time-travel into the future is a rather uncontroversial consequence of Einstein’s theory about space and time. That’s because his theory implies that acceleration slows down the passage of time. This acceleration could come about by a strong rocket booster or by hovering near a black hole. Either way, it’d have the same effect: Time would slow down for you while you’re accelerated, but the rest of the universe would continue with business as usual. This isn’t a hypothetical effect, it’s actually been measured, though in practice the time-travel amounts to some nanoseconds at best.

Better than nothing you might say, but there are two problems with this time travel into the future. First, to get a noticeable slow-down you’d have to accelerate so much you’d end up flat as a pancake. It’d without doubt be interesting but not for very long. Also, you can’t go back. If you use acceleration, time travel is a one-way street. Once you’re in the future, you’ll have to stay there.

Aren’t there any better ways to travel in time? Yes, there are, at least theoretically. But to see how those work, we first have to talk a little more about Einstein’s theory of special relativity and then general relativity.

According to Einstein, space and time belong together to one common entity called “space-time”. In this space-time, time is a dimension, just like the three dimensions of space.

But time still remains different from space. As you have undoubtedly noticed, you can very well turn around in space, but you can’t turn around in time. We can see the reason for this by drawing a simplified sketch of space-time with only one dimension of space and one dimension of time. It’s called a space-time diagram.

If you just sit still, then in this diagram you’re at the same place at all times, so that’s just a vertical line. If you move at a constant velocity, that’s a straight line at some angle. By convention a 45-degree angle is the speed of light. The line that an observer makes in this diagram is called a “world line”.

If you want to turn around and go back in time, your world line needs to make a U-turn and that means that it needs to exceed the speed of light somewhere. As I explained in an earlier episode on faster than light-travel, this would take an infinite amount of energy. We can’t do that because it’d screw up the Green Deal and make many people very angry. But any argument involving something being infinite is somewhat fishy, because the infinity could mean it’s just a mathematical artefact.

And it’s not like Einstein’s relativity say it’s forbidden. It allow both faster than light travel and time-travel. We just don’t know how to do it. Though physicists have come up with a few ideas.

To see how these ideas work, we now have to talk a bit about general relativity, that’s Einstein’s theory for gravity. It says that space and time are not just combined to a four-dimensional space-time but that they’re also curved. So, special relativity is special because space-time is flat. In general relativity, space-time is in general curved.

And this curvature can be really wild, it can even change the connectivity of space-time. This can for example give rise to wormholes. Wormholes are the maybe most obvious way to travel faster than light, and also travel backward or forward in time.

Wormholes are possible space-time configurations in general relativity. They can connect any two places and any two times, and, yes, that is compatible with Einstein’s theories. If you pass through a wormhole, you can quickly go to a very distant place or forward in time or backward in time. Wormholes would be great, if they existed. They exist as mathematical possibilities, but whether they physically exist is an open question.

Wormholes are problematic for reasons that have nothing to with Einstein’s theory directly. It’s that they require negative energy to hold them open, and we’ve already used up all our negative energy on twitter. Wormholes have another issue which is that even if we had the necessary negative energy, we wouldn’t know how to make them so that they connect specific times and places, that we want to be connected.

But wormholes are not the only way you can travel in time in General Relativity. This is because sometimes space-time becomes so strongly curved that it drags objects back in time. It creates what’s called a closed time-like curve. This is a path in space-time which closes in on itself, but so that an object which moves on the path always moves slower than the speed of light.

Normally this isn’t possible. You can move on a closed curve in space. But once you’re back to the same place in space, you’ve moved forward in time. If there are time-like closed curves, it means that you return to the place *and time where you previously were. You’ve gone back in the time of the universe, while going forward in your own time. It’s exactly what we mean by time-travel.

Intriguingly enough, such closed time-like curves do exist in general relativity, and their existence isn’t even controversial. Physicists have known about them since the 1930s, but mostly they have dismissed them. They think that loops in time are just mathematical curiosities. And to be fair that’s for a good reason because, unfortunately, they come into being near matter configurations that are far from realistic.

The first such configurations that can create closed time-like curves was found by van Stockum in 1938. It requires an infinitely long rigid cylinder of rotating dust. Another solution from 1991 is known as Gott-space and requires a pair of infinitely long and infinitely thin strings that move past each other. A paper in 2017 showed that these strings don’t need to be infinitely long, you can use rings, but the energy density on the rings will still be infinite.

Don’t worry if you didn’t understand all this in detail, it doesn’t matter all that much, the point is that these aren’t configurations that we know how to create in reality.

But there is one case that we actually know exists, like, we know it exists for real. That’s a rotating black hole. We know that black holes exist, and we know that they almost all rotate. Firstly, because it’s highly unlikely that matter would undergo gravitational collapse without having any angular momentum. And secondly, we can tell from the stuff that they spit out.

But rotating black holes are mathematically extremely weird. They have not one horizon, but two. And between these horizons, you can travel into the past on one of those time-like loops. You could even get out of this region again, at least theoretically, but this is where things get complicated because it’s not clear where you would go if you could get out. Could be another universe. Or it could be our own universe, but the time-travel into the past doesn’t work outside the horizon, so you just come out in the future. Or maybe you can indeed travel into the past with those things.

Just exactly what happens in those rotating black holes is a big mystery and I don’t just say because I like the word, though I do. It really is a mystery.

The question what’s going on with rotating black holes has stumped physicists for almost a century. This is just my personal experience but I think at the moment most physicists just assume that if this kind of thing can happen in rotating black holes, it means something’s wrong with the maths, and it doesn’t actually happen in reality. The usual argument has it that if a space-time in general relativity would allow time-travel, then quantum effects would make it unstable, cause a reconfiguration, and end with a stable situation where time-travel is no longer possible.

The reason they believe this is that it’s difficult to make sense of time travel already by way of narrative, and if you try to work out the maths it becomes even more difficult. Think “Interstellar” but with differential equations.

The most famous problem is the grandfather paradox, were you go back in time, kill your own grandfather, and are never born to go back in time. Another not quite so well-known problem is the “bootstrap problem”. Suppose you have a time machine. One day you open it, and you find in it proof of the Riemann hypothesis. You publish it and become world famous. Then you send the proof back in time to your younger self.

Where did the proof come from? Worse still, the story’d work with any other proof. The twin prime conjecture? P equals NP? It could all be in your time machine. It seems that the content of your time machine doesn’t follow from what happened in the past. Of course it doesn’t, it came from the future.

This example shows that closed time-like curves generally ruin determinism. This might not be entirely a bad thing. Indeed, as you may remember, quantum mechanics seems not to be deterministic. So maybe quantum mechanics has something to do with time-travel. Indeed, this is the idea behind retrocausal approaches to quantum mechanics which I talked about in an earlier episode.

Causality paradoxes can be removed in two ways. Either you allow for multiple timelines and get parallel worlds. The problem with this is that we don’t have any parallel worlds in Einstein’s theories, so we have no idea how that should that work.

Or you just postulate that you can’t change the past. Leaving aside that this is kind of depressing for people who believe in free will, it doesn’t entirely solve the problem. Because it still seems that you can then violate the second law of thermodynamics. Just imagine that in your time machine you don’t send a proof of the Riemann hypothesis back in time, but just cold air because, I dunno, it’s winter and you feel like it. If your younger self opens the door of the time machine, entropy in their room decreases. But that shouldn’t happen.

And that finally brings me to the MIT paper about using time travel to detect dark matter. Because here's the thing about entropy.

The second law of thermodynamics is usually summarized by saying entropy can’t decrease. But this isn’t exactly true. The second law is a statistical statement, and it actually just says that it’s very unlikely for entropy to decrease. Entropy does in fact decrease slightly and coincidentally all the time around you. It’s just that this is for very short moments and very small amounts. Sometimes there’s a patch in which the air is a little bit colder to your right. Sometimes on the left. These are small fluctuations in the local entropy, and they don’t violate the laws of physics at all. So, yes, entropy can decrease. It’s just that large decreases are unlikely.

Moreover, you can decrease entropy in one place by increasing it elsewhere. And if you are careful enough, you can even use that to reverse the flow of time, at least in a small area of space. Think about it, all that the passage of time means is that, well, some particles interact in some way. If you can reverse the motion of those particles exactly, that will turn around time in the system. This is possible in principle. It’s just that usually it’s so complicated, that it’s for all practical purpose impossible.

You can do it for very small systems however, and that’s what these guys from MIT have done. Because reversing time and effectively decreasing entropy is a way of reducing noise in a detector, and that can enhance sensitivity.

So let us look at the paper and figure out what it says about time travel and dark matter. Here is the paper. “Time-reversal-based quantum metrology with many-body entangled states”. Would you be surprised to hear that it doesn’t say anything about time-travel. And the word dark matter appears exactly once, at the very end of the paper which I read to you in full: “the protocol can be used directly to search for transient changes in the fundamental constants induced by dark matter”. Of course most types of dark matter don’t lead to changes in the fundamental constants. So, no time-travel, no dark matter. That was a bit of a disappointment, MIT.

Okay, but here’s the thing. It is true that all those problems about causality paradoxes can be avoided if you look at systems that are small enough. This is because in small systems you can plausibly prevent entropy increase, and causality is not meaningful anyway. Single particles just perform interactions in some order. They don’t know anything about cause and effect.

This makes me personally think that while time-travel might be impossible for macroscopic objects, we shouldn’t entirely exclude the possibility that it’s possible on a microscopic scale. Maybe you and I will never be able to step into a time-machine, but maybe we can one day send a few bits of information into the past. That’d be huge already.

That said, while I don’t think time travel is strictly speaking impossible, I will admit that for all we currently know, it appears to be very implausible. As much as I’d like it to work, physics makes it really hard. Did you come from the future? Let us know what you think in the comments.