Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas - 124 | Solo: How Time Travel Could and Should Work

Episode Date: November 23, 2020

Time! It doesn't stop, psychological effects of being under lockdown notwithstanding. How we experience time depends on our situation, but time itself just marches forward. Unless, of course, it's possible to travel to the past, as countless science-fiction scenarios have depicted. But does that really make sense? Couldn't we then change the past, even so dramatically that our own existence would never have happened? In this solo podcast I talk about both the physics and fiction of time travel. I point out that it might be allowed by the laws of physics, and explain how that would work, but that we really don't know. And I try to make sense of some of the less-sensible depictions of cinematic time travel. Coming up with a logical theory that could account for Back to the Future isn't easy, but podcasting isn't for the squeamish. Support Mindscape on Patreon. But wait, there's more! I was contacted by Janna Levin, who we fondly remember from Episode 27. Janna moonlights as Chair and Director of Sciences at Pioneer Works, an institution dedicated to bringing together creative people in art and science. Like the rest of us, they've been looking for ways to offer more online content in these pandemic times, so we thought about ways to collaborate. Here's what they came up with: artist Azikiwe Mohammed has created an animated video backdrop to this podcast episode. The visuals are trippy, colorful, and inspired by (without trying to directly illustrate) what I talk about in the episode. You can check out a brief write-up at the Pioneer Works site, or view the video directly below. https://www.youtube.com/watch?v=kHy1j4LiyGQ

Hey, I just Venmoed you for rent. Nice. Now I can instantly spend it whether I'm checking out online with Venmo or using a Venmo debit card. Say more. More exactly. Because the more you do with Venmo, the more you get. Like earning up to 5% cashback with Venmo stash on a bundle of brands. So, order more pizza. The math demands it. Get the Venmo debit card.

Venmo Stash bundle terms and exclusions apply. See terms of Venmo.com.com. Venmo checkout not available at all merchants. Venmo Mastercard is issued by the Bank Bank N. Hello, everyone. Welcome to the Mindscape podcast. I'm your host, Sean Carroll. And I wanted to tell you, those of you have not already heard it, a little anecdote about one of the ways in which, in a very tiny manner, I have influenced popular culture myself. You may have heard of the movie Avengers Endgame. You probably have heard of it. It's the highest grossing movie of all time. And in that movie, a prominent role is played by the idea of time travel. So I'm not going to give away any spoilers for the movie, but there was a previous movie. Infinity War in which bad things happened, and the heroes in end game want to fix those bad things by going to the past. So when you want to have time travel in your movie, you have to make some choices about how it works. You know, we haven't seen time travel in the real world, so there's

different theories of how it could possibly happen. And at one point, Paul Rudd, who's the actor playing Scott Lang, aka Ant Man, he and everyone else are talking about the ideas of time travel, and Paul Rudd says, So you're telling me that Back to the Future is just bullshit? And I was actually serving as a science advisor for Endgame. Many people did. I was not the only one, but I remember I was in the room with the writers, the directors, the producers,

and we were talking about the idea of time travel, time being one of my areas of expertise purportedly as a physicist, and I explained why I had bad feelings about Back to the Future, why I thought it was illogical and so forth. and so one of the people in the room said, you're telling me back to the future is just bullshit, and I agreed. And so that line appeared in the movie.

I think I helped that line come into existence in a very tiny way. And I think for the most part, Endgame did a good job at time travel. It was a little bit hazy on this idea of whether or not you can affect the past by going into it, but it was much more respectable and logical than something like Back to the Future would be. But, you know, I always, it always bothered me a little bit. that line, because I have an attitude, a philosophy of how you should approach being a science advisor on movies. You know, it's easy to get a bad reputation in Hollywood as a scientist if all you do is hear what they want to do in the movie and say, no, you can't do that, right?

There are plenty of scientists who are very happy to join the writers and directors and tell them that they can't do that. They don't really need extra people doing that. So my attitude is when you get a screenplay or a detailed outline that already exists and you're the science advisor, your job is not to scold them or tell them why they're wrong or give them a bad grade, okay? Your job is to help them. Your job is to serve the movie, tell the best most interesting story it possibly can. And the way that I find is helpful to sort of mentally align yourself to that job, that responsibility, is to think of the screenplay as data. rather than as a theory. In other words, you're not looking at the screenplay and going, no, I don't think that's the way it would work.

I don't think that's an accurate description of reality. That's a bad attitude to have to a screenplay. The screenplay is, in this world, what actually did happen. And so a scientist who gets data, gets, you know, an experimental result and whose response is, no, that can't happen, is not going to get that far, right? Once you shift your mental orientation from explaining what can and cannot happen,

to, oh, this is what happened. It's now my job to come up with an explanation for it. It frees your mind quite a bit. And it's almost always possible to come up with explanations of how things can happen. So in my mind, a movie that would be the greatest challenge to turn into something logical would be something like Back to the Future. And it's sort of time travel, let's just say it was a little freewheeling when it came to the logic of time travel, which is actually admitted by the writers of the movie. know it, but it's a much beloved movie, right? Like, it served its purposes

narratively, so something good must be going on. And of course, time travel stories are still very, very popular. Recently, Ed Solomon tweeted the following tweet. Over the next few weeks, people will have a chance to watch an exquisitely crafted physics bending, very important filmic meditation on the quandaries of time and space, and also the much-anticipated Tenet. The joke, of course, here is that Tenet is a much-anticipated movie by Christopher Nolan that was just released. I haven't seen it since it's only in theaters and we're in the middle of a pandemic,

but I understand that time and space bendingness is a big part of it. Ed Solomon is one of the screenwriters on another such movie, namely Bill and Ted Face the Music. Ed was also a screenwriter for the original Bill and Ted movies, and Bill and Ted, in a very different way, have time travel as crucial

plot points. So we're not tired yet of time travel movies and time travel logic. It's important to see how far we can go in figuring it out. Thus, this podcast, which will be a solo job, I'm not going to talk to anyone else. I have my own things to say about time travel. I want to talk about what time travel would be like, like how it could possibly work. What is the science behind it? What do general relativity and quantum mechanics have to say about it? But then also philosophically, what would it mean? What would it mean for

issues of causality and predetermination and free will? And finally, what does it mean narratively? Why do time travel stories work? How can they work? How should they work? What is the guide to either understanding time travel stories that already exist or maybe going out there and writing your own time travel story? So bringing all of these different issues together and all these considerations is just the most fun thing in the world and it's intellectually a gas and that's what Mindscape is all about. And as if that were not too much fun already, we're doing something special with this solo episode of Mindscape. You might remember Jana Levin, who was the guest on the very successful episode 27 of Mindscape. That was two years ago almost. So Jana, in addition to being a working

physicist at Columbia, she's also the chair and curator of Pioneer Works in Brooklyn. Pioneer Works is an event space and a cooperative space that brings together artists and scientists to do fun, interdisciplinary, interconnected things. Of course, spaces in the physical realm are hard to operate these days. We're more and more virtual. So Pioneer Works has been doing more and more online things. And Janice suggested a collaboration where we take a podcast episode of Mindscape and make it visual. Make a YouTube video or some other kind of video where we have visual art in the background while you're listening to the Mindscape episode. So they recruited artist Azequi Muhammad, who is a New York City artist, who made these wonderful computer-generated

backgrounds that sort of relate to what I'm talking about here in the podcast about time travel. So they're a little spacey, a little technological, little imaginative. Sometimes they're literally about what I'm talking about. Sometimes they're a little bit more figurative. But it's a fun way to experience the podcast in a slightly different vein. So I urge you to check that out. You can go to the Pioneerworks website, pioneerworks.org slash broadcast. You can find the video there.

Or I'll put a specific link to it on the Mindscape podcast website. If you don't know, we have a website, preposterousuniverse.com slash podcast. If you look for the link for this particular episode, we'll link to the video there. It's a different way. It's optional. You don't have to do it, but I think it's a fun little departure from our norm. And fun departures from the norm. That's also what we're all about here.

So with that, let's go. These days we think of time travel as basically a genre, right? I mean, there's a whole millions of time travel stories and movies and TV shows and whatever. And there are tropes, right? We have certain things that we expect already. someone says, oh, it's a time travel story. So it's interesting that time travel stories aren't that ancient, right? They haven't been around that long.

Whenever I say that, you know, I'm going to stand by that statement, but whenever I say that, people bring up exceptions, there certainly were stories a long time ago that in one vague way or another could be classified as time travel stories. But let's just say it this way. They weren't that popular. If you can think of 12 time travel stories before the year 1850 or so, I'd be very, very impressed. Whereas in the middle of the 19th century, time travel stories started becoming really, really popular, right? Of course, H.G. Wells wrote the time machine in, I think, 1895, I think it was.

And after that, it truly took off. But it was somewhere, you know, around those years or maybe a little bit before that people started really coming up with this idea that time is a place to which we could go, right? And I think that this idea just hadn't been there before. Like, there was the past, there was the future, but these weren't places that we could go. And clearly, by the fact that the time machine was in 1895, this idea that time could be a place we could go isn't due to Einstein or general relativity or space time or anything like that. Those came along in 1905 or later. But something gave people the idea that we should think of space and time as kind of similar, as long as long as long as long. locations in some sense.

Some people have suggested it's because we began to build mechanical clocks and watches. And that might be true. I really don't know. Someone could look into it. I do know one of the earliest sources that says that you should think of time and space as similar is actually in a long poem by Edgar Allen Poe. Near the end of his life, he wrote a very long poem called Eureka, where he explained all of his theories about cosmology and physics. and fans of the poem, there aren't that many fans. It's kind of a weird, difficult poem.

So fans of the poem like to say that he prefigured things like the Big Bang cosmology and black holes and things like that. I don't know. I mean, I think that he was serious. Po really believed these ideas he was putting forward, but they weren't based on data or even scientific theories. You know, you can always say things that vaguely resemble a later scientific discovery. But one thing he does say very clear.

is space and duration are one. He states very, very clearly that we should think of intervals in space and durations in time as the same kind of thing. And once you have that idea in mind, then time travel stories become a natural thing. Once that you have the idea that space, which is clearly full of places you can go, is kind of like time, well, then maybe time is a place that you can go also, either the past or. the future. And again, it's not quite space time, right? Einstein comes along with special relativity around 1905, even when Einstein invented special relativity. He didn't use the word spacetime. That was his old math professor, Herman Minkowski, in 1908, who pointed out that you

could really formulate special relativity in an especially elegant and compelling way by thinking of it in terms of space time. Einstein's original reaction to that was that it was just unnecessary mathematical formalism, which does sometimes happen in physics. But in this case, he was eventually quickly converted to the idea that space time is a good way of thinking about it. He invented general relativity where space time is curved, and that's going to be important for our story here. But my point right now is that you don't need relativity to have this move where you start thinking about time as a location. Even if you were just Newtonian, right, even if you just had old school classical mechanics, where space and time are both

individually absolute, it still remains the case that in order to meet someone for coffee, you have to tell them both where you're going to meet them in space and when you're going to meet them in time. So there's obviously similarity there that has nothing to do with relativity. In fact, there's this very old debate, which I'm not going to go into great details here about now, but of presentism versus eternalism. These are two different ways of thinking about the nature of time. In presentism, what you say is that reality, what really exists, is the world at the present moment.

Okay. So that's why it's called presentism. Nothing tricky about the nomenclature there. You think that there's a three-dimensional reality with everything going on. That's what actually exists. The past used to exist, but it doesn't exist anymore. And the future will exist, but it doesn't exist as such as at this moment. okay.

Eternalism, by contrast, and by the way, as a footnote, it is very difficult to talk about these things using the English language. Natural languages are just not designed to talk about these deep ideas about space and time in a compelling way, so you have to fumble around a little bit. But an eternalist will say that all moments are equally real, okay? To an eternalist, there's the past, the present, and the future from the point of view of someone at any moment. in the four-dimensional world, but all of the moments and all of the locations in that four-dimensional world are equally real. To an eternalist, different moments in time

are really like different points in space. Like, if you're located here, if I'm located in Los Angeles, Chicago is very far away from me, but that doesn't mean I don't think it's real, okay? So someone who thinks that time and space are on an equal footing very naturally treats different moments of time as equally real. not real at the same time.

The past and future do not exist now, but they exist, if that makes sense, okay? This is where the language fails us a little bit. Sometimes in the philosophy literature, these are associated with ideas called the A theory of time for presentism and the B theory for eternalism. This is a very bad philosophical tendency to make perfectly good words that actually convey meaning and replace them with labels that are completely meaningless. decades after being introduced to these ideas, I can never remember which is the A theory and which is the B theory. But the A theory is a theory where time is tensed. There is now what is happening, what will happen, what did happen. The B theory is thought of as tenseless.

So there just are things. They're not happening or it's not that they will happen. So everything exists, okay? So I'm not going to go through which of these theories is correct, although it's obviously eternalism. If you want more about these theories, you can check out the video I did for my biggest ideas in the universe series where I talk about time and the nature of time, and so I go into presentism versus eternalism. Now, once relativity comes along, when it does come along in the early 1900s, it dealt a blow to presentism, okay? Relativity, one of the, let's go a little bit into

explaining what relativity says. You know, there's a way of teaching relative where this is special relativity, 1905, Einstein's first idea. General relativity was 10 years later. Special relativity is the theory that says, you know, the speed of light is the same to everyone. The amount of time that will elapse on a clock depends on the way in which you travel through space time, things like that. And there's a way of teaching special relativity that emphasizes length contraction and time dilation and a whole bunch of things that I don't think is the right way.

to think about it. To me, special relativity is all about not only does space time exist, not only should we think of space and time as being melded together in this single four-dimensional space time, but the structure of space time is something different.

In Newtonian classical mechanics, okay, in Newtonian classical mechanics, space and time both exist and are separately absolute. And that's, you know, fancy language, what it means when you get down and dirty about it. What is that mean? Space is absolute. Time is absolute. What it means is here

I am in my office and I can say, well, okay, it is 132 p.m. now. And I could ask what is going on on a planet orbiting Alpha Centauri right now at this moment at 132 p.m. That's a perfectly sensible

question in Newtonian mechanics because the four-dimensional universe is uniquely sliced into moments of time. Everyone agrees. Everyone agrees. If it's 132 here, what's happening at 132 everywhere else? Special relativity comes along and says,

space time exists, okay? There's a four-dimensional space time, but you shouldn't imagine some absolute slicing of space time into three-dimensional moments of time, okay, that we call space at any one moment of time. What special relativity, what it really says is, think locally rather than globally. Just don't even ask the question.

about what is happening at Alpha Centauri at the same time. That's not a sensible question to ask. What you can ask is, what do clocks read, what do meter sticks read, or whatever, and they need not be the same to different people, okay? What special relativity does is it replaces the idea of slicing space time into moments of time with a rule that says you cannot move faster than the speed of light. Now, look, this is difficult. this is a weird thing because those two ideas, one idea is that you can slice space time into moments of time.

The other is you can't go faster in the speed of light. They don't even sound comparable, right? I mean, they sound like a different kind of idea. So how can one replace the other? The answer is if you think visually, and this is where having an audio-only podcast is a handicap. Sorry about that. But think about the idea of light cones. Many of you have seen light cones portrayed in little diagrams before, but even if you have.

haven't, let's call an event a point in both space and time. Okay, so an event lasts for zero time. It's like right here at this location at one particular moment in time. And the rule in special relativity is from that event, nothing can travel faster than the speed of light away from it. So if you imagine at that event, a flash bulb goes off, okay? A light starts getting emitted in all directions. and you say, could I run fast enough or hop in a rocket and go fast enough to catch up to the light?

No, you cannot do it. So I can imagine the beams of light going in all directions in space, and they will also move toward the future. And that defines the light cone. If you imagine visually in your head sort of drawing two axes, a horizontal axis for space, a vertical axis for time, the beams of light would move out at some angle away from that point. That would be the light cone. So in special relativity, your future is not every moment in front of this moment of time that is simultaneous throughout the universe.

Your future is what's inside that light cone, okay? Things that are outside the light cone, like what's going on at Alpha Centauri at the moment that I would call now, okay, that's not in my past, present or future. I shouldn't think about it that way. It's just a place I can't reach. I would have to go faster than the speed of light to get to that moment. I don't need to go faster in speed of light to get to Alpha Centauri, but to get to Alpha Centauri at a certain moment that I call now, I would have to go faster than the speed of light,

because it would take me four years to get to Alpha Centauri moving slower than the speed of light or at the speed of light, okay? So the way that special relativity works is it says there's no such thing as simultaneity for events that are separated in space, For events that are literally at the same part of the universe, there you could be simultaneous. You are allowed to synchronize your watches if you're very, very close by. But once you get far away from each other,

there's just no such thing as the idea of two things happening at the same time. What you can ask is are two events in each other's light cones or not? If they're in each other's light cones, then one is in the past and one is in the future. But if they're not, we say that they are space-like separated from each other. No signal moving at allowed speeds slower than light can get from one event to another if those two events are space-like separated. Things that can travel on real trajectories slower than the speed of light are said to move on time-like paths throughout the universe. Things that are imaginary and hypothetical move faster than the speed of light are on space-like paths, okay? So rather than dividing space-time up into these slices of constant time, special relativity,

says, at every event, there is a future light cone where things that that event can influence in, and there's a past light cone where all the events that can possibly influence this other event are located. And then there's this outside region, the space-like separated region. There's no such thing as uniquely slicing the universe into moments of time. So you'll be unsurprised to learn that relativity delta blow to presentism, right? There's no way of saying what the present moment is in any unique way once special relativity comes along. Again, this is sometimes said

as observers moving at different velocities will choose to divide up space and time differently. And there's some truth to that, but that's not the point. That's sort of a down-the-road kind of implication of it. I can choose to divide space and time however I want in relativity. There's sort of a natural way to do it

if I'm moving at a constant velocity and that natural way is different for observers moving at different constant velocities, okay? But all the point I want to get across here is just that special relativity really removes the idea that there's something special about the present moment. The present moment where you are listening to this podcast

cannot be uniquely extended across the universe. And therefore, once relativity comes along, it's much more natural to speak of the four-dimensional block universe, as we sometimes call it. The eternalist presentation of both space and time together glued into this one thing called space time. Now notice that if time travel were possible,

we haven't gotten the time travel yet, but if time travel were possible, if you could travel to the past, then that would be an even bigger blow to presentism, right? I mean, how can you go somewhere that doesn't even exist? Time travel sort of is predicated on the idea of eternalism, that the past, present, and future are all places you can go in some sense. So therefore, from now on for the rest of this podcast,

I'm going to be assuming an eternalist view of space and time. We can treat all the moments in the history of the universe as equally real. There's one that I happen to be experiencing at this moment as I am talking. There's a different moment in my future that you are experiencing as you're listening, but all those moments are equally real. Okay. So a consequence of this, of this special relativity point of view, if you can only move slower than the speed of light, then if you move, if you again, imagine hypothetically moving faster than the speed of light, you know, we're allowed to let our imaginations roam a little bit. What would that mean? What would it imply if I could travel faster than the speed of light? Well, if I travel faster in the speed of light, so I go, you know, one minute into the speed. the future and also four light years. Okay, so I'm moving faster in the speed of light.

I'm traveling four light years in a minute. But to say that I am moving a minute into the future is a statement that implies that I've chosen some reference frame that is stretched across four light years of space. And the whole point of special relativity is that I can choose different reference frames. So the upshot of this is that if I can move faster than the speed of life, I might call it, I'm moving into the future, but I'm moving very fast in space. But in someone else's reference frame, they see me moving backward in time. To someone else's frame of reference, they would say that I arrived at a moment in time before I left.

Okay. This is just, again, if special relativity were correct, Einstein's going to update it to general relativity, but the lesson still remains pretty valid here. if special relativity is correct, then if you can move faster than the speed of light, that's equivalent to moving backwards in time. It is moving backwards in time from someone's point of view, okay? So if special relativity were correct, a warp drive would be a time machine, right? If you believe in special relativity and you believe that nevertheless someday we will build a spaceship that can go faster than the speed of light, that is equivalent to being able to travel into the past.

And I want you to remember that because this is going to happen. This is going to become an important point down later in the podcast. Once you realize that you can go fast in the speed of light, then you can build a time machine if special relativity is correct. Now, that doesn't mean, as another footnote here, that something like in Star Trek or Star Wars where we can travel faster in the speed of light, why don't they have time machines all over the place? I mean, Star Trek kind of does have time machines.

Star Trek helps itself to time travel whenever it wants to and then forgets that it has the ability to do that. But, you know, one answer, given our philosophy of the screenplay is the data, right, not the theory, rather than just saying, well, they're wrong, that's not how it would be, is it possible that there is a theory where you could have warp drive without the possibility of going backward in time? And the answer is yes. Namely, special relativity is not correct, okay? it would have to be not correct in a pretty dramatic way.

You know, one of the pillars of special relativity is the idea that nobody moving at any particular inertial trajectory through space. In other words, no one who's moving at a constant velocity is superior to anybody else. There is no absolute reference frame with respect to which you can measure your velocity. Remember, the ether was an idea that they had, circa 1900, where they could. They thought that they could measure their velocity. velocity with respect to it. We no longer think that exists. But maybe we're wrong, right?

So if you want to believe that there could be something like warp drive, there can be warp factor nine, which lets you go much faster in the speed of light, but somehow doesn't let you go backward in time, what you have to imagine is that somehow there is an absolute reference frame in the universe with respect to which you can measure your velocity. So when Jean-Luc says, you know, go warp factor nine, that's with respect to some. some ether, some sort of modern souped up version of the ether that you and I don't know about, but they've discovered sometime before the 24th century. I'm not going to go into any details about that, but you can always try your best to make it make sense after the fact.

Now, remember here when we talk about special relativity, that is in contrast with general relativity, special relativity came first. It's the theory that speed of light is the maximum, every inertial trajectory is equivalent, space time exists, but space time is rigid. Space time is a background. It has a geometry, but the geometry is flat. And in particular, there's no gravity. When general relativity comes along, and we'll get there in a bit,

but general relativity, 1915, 1916, says space time not only exists, and it's not only a mathematical convenience, but it's not rigid. It's dynamical. It can move. It can bend, it can bend, it can warp. And those bendings and warppings are what you and I perceive as gravity, whether it's the gravity here on Earth or the Earth moving around the Sun or a black hole or the Big Bang or whatever. All of that are different manifestations of the curvature of space time.

Okay, so we're not getting there yet, but that's what I mean by special relativity. There's no gravity. There's no curvature. Even though special relativity says there's no unique absolute way to divide up space time into space and time, it still takes space time as given, as flat, rigid background on which it is. everything happens. One way of thinking about, you know, the conceptual change when you go from Newtonian absolute space and absolute time to special relativity is that special relativity

distinguishes two things that were the same thing in Newtonian physics, namely universal time and personal time. Okay. So in a Newtonian world, had Newton been right? If you and I synchronized our watches, so they said the same time, so they were saying exactly what we thought they did, and they were good watches, right? You know, they did not ticket the wrong rate or whatever. Then you and I could go our separate ways.

We could walk off, and there would be a sensible answer to the question, what time is it? And I could measure it either on my watch or on your watch, and they would say the same thing. There is this universal time coordinate throughout the world in Newtonian physics, and it is what your personal clock measures, okay? In special relativity, these two ideas of a coordinate that stretches throughout the universe that helps you find yourself in space time, and the duration that is measured by a clock or a watch you carry with you become completely separate. It's like in space, again, everything in special relativity is just the motto, time is kind of like space or space time is kind of like space, suitably interpreted. So if you have two locations in space, two cities, right, you can say what is the distance between them? At most people will understand what you mean. There is a shortest distance path between those two cities, and you can say how long that shortest distance path is, okay?

But everyone also knows that when you actually travel between two cities, let's say by driving on roads, the distance you will traverse is not that shortest distance, right? because you're not going to go exactly in a straight line. That's as the crow flies or whatever you want to call it, okay? You will have to make twists and turns, and so the actual reading on your edometer will be longer than the shortest distance path. When it comes to space, that just makes perfect sense. Everyone agrees, right? So special relativity says time is also like that.

Time is something that we can personally measure, or we can talk about this abstract notion of a coordinate. it's not a universal given thing, but we can choose a coordinate on the universe that helps us find things, right? So, for example, when we do cosmology, we know that there's all this stuff in the universe, there are galaxies, and there's dark matter,

and there are photons in the cosmic microwave background, and all this stuff has sort of a rest frame. If you forget, just for convenience about the matter and the dark matter, just look at the cosmic microwave background. You can move to a frame, or you could, you know, in your mind, imagine a reference frame or a velocity, with respect to which the cosmic microwave background looks the same in all directions. And then if you change to moving at a different velocity with respect to where you started,

then the microwave background will be blue-shifted if you're moving toward it and red-shifted when you're moving away. There's only one reference frame cosmologically where there is no overall net blue-shift or red-shift for the cosmic microwave background. So you can think of that as the right-sift. rest frame of the universe. So when we talk about the universe being 13.8 billion years old or whatever, we mean as measured in that rest frame for the universe.

But you personally don't have to travel in that rest frame, right? You and I can move around. And this is what gives rise to the famous twin paradox in special relativity. A twin born here on Earth and another twin born at the same time. But one of them just stays here on Earth doesn't do anything, whereas the other twin goes out in a rocket ship near the second. speed of light and then comes back. And even though the two twins were born at the same time and they age at the same rate

and they have clocks, et cetera, the twin that went out in the rocket ship and comes back will experience less time. This is how you can remember the difference between space and time in general relativity, in special relativity, sorry. Space is kind of like time, but the difference is that in space, the straight line path is the shortest distance path. any other path will be longer distance. Time is the other way around.

In time, the straight line path is the longest time path. Any other path where you zip around in your rocket ship close to the speed of light, you will experience less time. So there is a difference between time and space in relativity. Okay? So that's the distinction between universal time that I might use to find things in the universe. You know, oh, these two black holes merged at such and such a time and place in the universe versus the personal time, every one of us carries around a clock, either literally or figuratively,

and those clocks will read slightly different amounts depending on how we travel through the universe. I mean, this is, of course, the most trivial and certainly true notion of what we mean when we say time travel, right? There's the old joke. You know, you can time travel into the future. The old joke is, yesterday I traveled a day into the future. It took me 24 hours, but here I am. Right? So whenever everyone asks you, whenever anyone asks you, can I travel in time? Well, you know, if you want to be a wise ass, you can say yes, you can travel into the future.

One second per second. In fact, it's kind of necessary that you do. The new wrinkle is that in special relativity, in some well-defined sense, you can get to the future faster. What we mean by that is if you think of the future as defined by some universal timekeeping parameter, like the rest frame of the microwave background, you can experience less time, but getting into the future. So if you zip off at the speed of light or very close to it in a rocket ship and zip back,

the universe can age by a thousand years and you've only aged by a week. And there's no limit, right? You can go as far into the future in as little time as you want if you have a sufficiently powerful rocket ship. Okay. 2020 has reshaped how we work.

Businesses across the globe are challenged to be their most efficient, which means every hire is critical. Indeed is here to help. Indeed is the number one job site in the world with more total visits than any other site. Indeed helps you find quality candidates quickly so you can focus on hiring the person you need to keep your business going. Unlike other sites, Indeed gives you full control and payment flexibility over your hiring. And now, Indeed's new way of matching you with candidates instantly delivers a short list of quality candidates whose resumes on Indeed match your job criteria

that you can contact the moment you sponsor a job. 73% of online job seekers in the U.S. visit Indeed each month. And right now, Indeed is offering Mindscape listeners a free $75 credit to boost your job post, which means more quality candidates will see it fast. Try Indeed out with a free $75 credit at Indeed.com slash mindscape. This is their best offer available anywhere. Go right now to Indeed.com.

slash mindscape, all for valid through December 31, terms and conditions applying. So that's the respectable physics. That is everything that we really do understand in special relativity about traveling in time, namely, you can travel to the future, just like you could have done in Newtonian mechanics. If anything, special relativity is a little bit more restrictive because you can't travel fast from the speed of light, whereas a Newtonian mechanics, you could. But at this point, this is when we have to sort of take a breath and say, like, wait a minute, what do we mean by all this traveling through time in the first place? Like, it was a joke and not an especially funny joke when I said, I traveled it yesterday, a day into the future, and it took me 24 hours, right? I mean, there's something that's not exactly in line with what I mean by traveling. And again, this is where our language fails us.

This is where we just don't have the vocabulary to talk about this stuff in a sensible way. When we travel through space, we can talk about the rate, right, the velocity, the speed with which we are traveling through space. I'm moving in the car at 80 kilometers per hour, okay? That's a sensible thing to say. We all know what it means. It's with respect to the rest frame defined by the road, et cetera, et cetera. But so what we mean by traveling through space is that as time passes, our location in space changes. That's what it means.

travel through space. So there's no exactly analogous notion of traveling through time. I mean, of course, as time passes our location and time changes, that's just trivial and obvious. And our personal rate of traveling through time can never be anything but one second per second. What could it possibly be? It could be different relative to other people, but there's never, like, as much they want to be nice to movies or whatever. Like, if you ever see a movie where someone is traveling near the speed of light or near a black hole and they look at their watch and it's stopped or it's moving really quickly or something like that, either way, that's nonsense.

Because whatever's happening to their internal perceptions of the world is also happening to the watch. As far as physics is concerned, if they've just been given time-wintering drugs, that's a completely different thing. Nevertheless, having put all those caveats down, there is a lot of. is a sense. There's a feeling that we have that we travel through time, right? There's actually two different ways of talking about it, which are pretty equivalent. In fact, most people just give and take equally between them, namely the idea that you move through time or the time

passes you by, right? Either that time flows around you or that you have this motion through time. Make up your mind, right, about which is actually happening. I did another podcast, I'm sure that you listen to with Lara Boroditsky about the language we use to deal with time and how we borrow all these spatial metaphors. Time is in front of us or behind us and different people, depending on circumstances, think of the future as being in front or behind you, etc.

Okay? If you are presentist, if you really did believe that only the present moment existed, then there's some reality to the idea of flowing through time, Right? What you mean by you is you now. And of course, you now changes and evolves. This is how the presentists think. There is some innate oomph to the flow of time with respect to which time is moving and pushing you and changing you.

And that's a very natural intuitive way to think. Like I said that presentism isn't the way that I would eventually think, but you can't blame presentists for thinking that way. This is how we grow up, right? I exist now and I am changing as time. passes. The way that the eternalist would say it is that there is a you at each moment. So the thing that is you is the collection of all these ewes at different moments. There's not some essence of you that is not only located in space but also at a particular time. There is the you that exists at January 1st, 2021 at noon.

there is the U that exists January 1st, 2021 at 1201, and the U at 1202, and all the other times, an infinite number of times in the approximation where time itself is continuous, okay? These are separate things, separate beings, but they're not independent. They're separate, but they're connected, right? They're related by causal and psychological continuity, right? The U at 1201 is not that different, I hope, unless something dramatic happens. the U at 1201 is not that different from the U at noon or the U at 1202. They're a little bit different. If you let a lot of time pass,

then the atoms that are in your body change, many of them, not all of them, but a lot of them do. Certainly you accumulate memories, not to mention aches and pains as you grow to a certain age over your life. So the U at age 50 is not the U at age 20, right? They're related to each other, the eternalist would say, in a very clear way. but they're two different things, okay?

And that's a shift in perspective that eternalism asks of us that can be hard to catch on to, but once you do, it does help understand a lot of worrisome features of personal identity, right? Derek Parfit, the philosopher, wrote about transporter machines,

right? The Star Trek transporter, right? You get beamed down to the location of the planet. As far as I know, you know, the Star Trek writers were ambiguous about whether or not when you get beamed down, do you send your actual atoms? Do you disassociate a person, atom by atom, send them down to the surface of the planet and then reassemble them? Or whether somehow they disassemble all the atoms keep in mind or store the information about how they were related to each other and then use matter on the planet where they were beaming them down to to reassemble the person somehow out of those new atoms.

I think it's the information that is sent down. I think that is the implication sometimes, but it's never made perfectly clear. And so you can ask, you know, did you kill the person to put them in the transporter machine? Is that death? Is that just a whole new person down there on the planet? I think that from a certain sort of intuitive, naive way of thinking,

that's absolutely true. It's a very natural thing to think. In fact, those of you who listened to my podcast on Mindscape with Seth McFarlane, who has his TV show The Orville, which is in many ways an homage to Star Trek. He very specifically did not have transporter machines, does not have transporter machines on the world of the Orville. And that's in part why.

He said he didn't want to keep killing his characters over and over again. So I think that Parfit would say, Derek Parfit, when he wrote about this, he tried to make the point that that's not killing the person. I mean, there's a person that is reconstructed from the transporter machine, but that person shares the continuity of memories and desires and personality of the person who was disassembled in the transporter machine. Therefore, at least if you're an eternalist and you think that any of this makes sense at all,

it makes perfect sense to think of them as the same person. There was a discontinuity of where that person happened to be located in space when they got transported, but the continuity of psychology and memory makes them two different, manifestations at different times and in different locations of space of the same entity, of the same person. There's no sort of metaphysical soul that has to travel. It's just the pattern of their atoms that makes them who they are, and it's the same pattern if you have a functioning transporter machine. Now, this all sounds very science fictiony because it is, but it's very relevant to things like the many worlds interpretation of quantum mechanics, right?

This is not, we're going to talk about quantum mechanics a little bit, but anyone who's been listening to the podcast for a while has heard me talk about many worlds. And the idea of many worlds is anytime you measure a quantum mechanical system that is in a superposition, like an electron could be spinning clockwise or counterclockwise. Before you measure it, it's a superposition of both. They're both really there. Afterward, there are now two worlds, two copies of reality, one in which you measured the spin clockwise, and the the other one counterclockwise. So there's the question people often have, like, which one is you? Which one are you going to end up being?

And if you follow this logic of personal identity from Parfit and elsewhere, you would say, well, there's no one that is the you. These are two people. They both were you, but they are now two different people. They're in two different worlds. They're non-interacting. So there's no answer to the question, which one do you become? And the reason why I go on this little tangent is that the question, is that the question,

is because these questions of personal identity, these questions of how we think about who we are, need to be updated when you go from manifest image, folk physics, the way that we grow up thinking about the world, to the slightly harder and more abstract notions that are given to us by modern physics. And that's very relevant for travel through time. So I say that, you know, relativity,

and certainly if you can have time travel, deals a blow to presentism. It suggests that eternalism is a better way of thinking about time and space, but you can't deny that we feel, we have the impression

that we are moving through time, right? That we are aging, that we are experiencing things. There's definitely some momentum or some feeling there. So where does that come from? And this is, you know,

as Dan Dennett, who I had on the podcast, likes to say, this is the job of philosophy. The job of philosophy is to reconcile the scientific image of the world

with the manifest image of the world. The scientific image says there's just different moments of time. They all exist, different copies of you at every moment. The manifest image says, I'm one person right here and right now, and I change through time. So you can ask, why do I feel like time is flowing around me or why do I feel like I am moving through time? It's very, very closely related to the question of free will. Why do I feel like I make choices and have an influence over the way? the future? Why do causes precede effects in time, right? Even though at the end of the day,

I might want to say, well, it's all just the laws of physics. It's not that I personally have the ability to do anything. I'm just a bunch of particles and forces obeying the laws of physics. Why do I feel like I can make choices? Is very closely related to why do I feel like I'm flowing through time? And if you want a more sophisticated answer to this question from the philosophical and neuroscience perspective, give another listen to the podcast that did with Janine Ismail, who wrote the book, How Physics Makes Us Free. But let me give you a little bit of an insight here because it does, it's an important thing to consider when we talk about why time travel bothers us. Why do we think that there are paradoxes in time travel and are they necessary or not?

The issue is that on the one hand, we have these impersonal laws of physics, right? It doesn't really matter whether the laws of physics are deterministic or not. That's a red herring. People often get stuck in. What matters is not the laws of physics are deterministic or non-deterministic. What matters is, are there laws of physics? And are we, human beings, purely physical creatures, obeying those laws, okay? That's kind of what matters.

And the question is, if we are, if we are just made of physical stuff, obeying the laws of physics and the laws of physics are impersonal and governed by equations, whether or not they're deterministic, how in the world can we reconcile that with our humanity and our feelings that we move through time and make choices and affect the future. This wouldn't really have been a question in a presentist universe, right? Like if you were Aristotle, you think of things, even if they're physical, they're teleological. They have goals. There's a future orientation toward how we talk about how things take place as the universe unfolds in time from the present moment to the future.

But then classical mechanics comes along, even before relativity. You all know this story, again, if you've been listening to the podcast, but Pierre Simone Laplace points out that you can imagine a vast intelligence, which we now call Laplace's demon, which if it knew everything about the universe at one moment of time and had infinite calculational power and knowledge of the laws of physics, to that vast intelligence, the past and the future are as equally evident as the present is, because there's a pattern. It's not directed toward the future or toward the past, but at every moment of time, the entire future and the entire past are determined by what's going on right then. That was, again, this might not be true because quantum mechanics came along, et cetera,

but that was the classical mechanics view of the world, the clockwork universe, Laplace's demon. And in that picture, where are we going to locate the flow of time in any sense? You know, the past, present, and future aren't different if you're Laplace's demon. So here's the bad news. You are not Laplace's demon. Or maybe that's the good news.

I don't know. But it's very, very true. You are not Laplace's demon. And the reason why I have to sort of hammer this home a little bit is because I think that people don't quite appreciate the extent to which you are not Laplace's demon. I mean, Laplace has this thought experiment. And, you know, you have in mind, I don't know, a box of gas or, you know, some billiard balls on a billiard table and they're banging into each other and you're like, well, I don't have perfect information about what those billiard balls are doing, where they're

located, or how they're moving. And I don't even have the calculational ability to figure out what would happen. But I can imagine extrapolating to being a little bit smarter and having a little bit more information and then I could do it and then I'd be Laplace's demon, right? So I really need to hammer home the idea that it is not that easy in extrapolation. Okay. La Placis' demon is a thought experiment. It was never meant to represent a goal that we should try to be Laplace's demon. The number of things going on in a single human being or even in a single insect or something very, very tiny is so enormously mind-bogglingly large. And the precision that you would need to understand what was going on in them is so absurdly high that it's just silly to even imagine you could be Laplace's demon. The analogy I sometimes use is, you know, imagine that you can bench press 150 pounds. And you think to yourself, you know, maybe if I practice and I get really good, I'll bench press 200 or 250.

And you think to yourself, you know, I can thought experiment myself into imagining I could bench press 500 pounds or 1,000 pounds. True, you could do that. But going from I can see the billiard balls on the table to I can imagine being Laplace's demon isn't like that. It's like saying I can bench press 150 pounds, so let me imagine that I could bench press the sun. Like the sun in the sky, right? It's just out of the realm of sensibility. It's not physically impossible,

but the sun is a different kind of thing. You can't even push it, right? It's not just that it's too massive. It's just a whole different world out there. And so you should not think that, well, you know, I'm not really the plossus demon, but maybe that's a good approximation. That's not a good approximation to anything.

What you are is a machine or a collection of physical stuff that possesses incomplete information about the world and tries to impose order on that world to try to make a kind of sense of it, right? If you go back to the podcast interview we did with Carl Friston, where he has a particular free energy principle, he thinks of the brain as being some kind of Bayesian reasoner, tries to understand what's going on in the world and minimize surprise, okay? And that's kind of what we try to do, and we're pretty good at it. But when you dig into the actual things going on in our brains, it's kind of amazing. It's very, very different than Laplace's demon. Let's put it that way. We both, in some very, very true sense, live in the past while constantly anticipating the future. Okay.

What I mean by living in the past is, you know, you think that you are right now, you're looking around you. You can see things, you can hear things, you can sense them with your fingers and your taste and smell and whatever. And you say, like, I have an understanding or an image of what the world is right now. But if you think about it, it takes time for your brain to put that image together, right? I mean, of course, it takes time for the light to get to you from what you're looking at to your eyeballs. And then the neurological signals to get from your eyeball to your visual cortex, likewise for sense. sounds and so forth, it takes some time for your brain to knit that all together into a coherent picture.

And depending on what aspect you're talking about, neuroscientists can actually pinpoint how much of a gap there is between what is literally happening now in the present moment and what you are perceiving as the moment of now. It's measured in milliseconds, right? Tens of milliseconds, depending on exactly what we're talking about. There are different timescales relevant to different phenomena. But you can see this, for example, my favorite demonstration is someone standing next to you and they're dribbling a basketball. Okay.

And so you see them dribbling, but you also hear the slap that the ball makes on the ground when it hits the ground. And your brain ties them together. You know that the visual image of the basketball hitting the ground gets to your eye a little bit faster than the sound waves from the basketball get to your ears, right? But you say, well, you know, it's nearby. it's not that big of a difference, okay? But now, let the person dribbling the basketball walk away from you while still dribbling, right? And what you see is your brain corrects

for the fact that it takes time for the sound waves to reach your ears so that even though they're moving away from you, even though that the difference in time between when the light gets to you and the sound gets to you gets bigger and bigger as they walk away, your brain knows that and your brain corrects for it and you still perceive the basketball hitting the ground

and making the sound at the same time until they get a certain distance away. When the person gets a certain distance away, your brain will give up. Your brain will stop trying to synchronize the visual and auditory inputs that it gets and you will see the basketball hit the ground at a different time than you hear it, okay?

Because the now is not the now you perceive. The moment you live in as a conscious creature is not quite now. It's a few milliseconds in the past. And at the same time, you are constantly anticipating the future. I don't mean like, what am I going to have for dinner tonight? Or, you know, should I go to graduate school or something like that? I mean, again, milliseconds into the future, your brain anticipates where your body's going to be, what it's going to be doing. There's a theory of motor control that says that if you have your hand,

on the table and you want to lift it up, the way that you do it is your brain tricks itself into thinking that it's already up, and then it tries to bring its tricked perception into alignment with its actual sensory inputs and therefore it lifts it up, okay? So what you're doing is you have an image in your brain of what your body's doing that anticipates the future and constantly tries to adjust to bring your vision of the future into alignment with its inputs. There is a constant give and take between you, the vision of what is happening now that you are constructing in your brain, and the changing environment that you're in. So even though there's a much longer, more complicated, incompletely understood story to be told here,

this is why we have the impression of flowing through time. Because even though to an eternalist, what exists are these different versions of yourself at different discrete moments of time, Every one of them carries an image of the immediate past and the immediate future, and they're sort of rolling through that succession of moments. A person at one moment of time has with them a little bit of the past and a little bit of the future in the form of images in their brain. And those are constantly changing, and it's that kind of surfing that set of impressions that gives us the feeling that time flows around us. And there's a very similar story to be told about making choices and having free will. You know, we know things about the past to an eternalist, not because the past is different from the future. We know things about the past we don't know about the future because, you know, we have records.

We have fossils and we have books and we have photographs and whatever, okay? We have memories. To an eternalist, there's no deep metaphysical difference between the past and future. We just have more access to the past. And that's because of the arrow of time and entropy. And again, I encourage you to check out the biggest ideas videos, both the video about time and also the video about entropy. We talk about why we seem to think there is such a big difference between the past and future, even if there isn't to an eternalist. And likewise, very glancingly, we talk about why we think we have the ability to make choices or the ability to affect the future, right?

Because we have incomplete information. We're not Laplace's demon. but we have more information about the past than about the future. So all of this sort of flowing through time gives us the impression that we can influence the future. I can make a choice right now that has an impact downstream in the future, but nobody thinks they can make a choice. No one in the right mind thinks they can make a choice now that affects the past. And again, that's completely compatible with eternalism and impersonal laws of physics,

but its work showing how that compatibility arises. So that's why, according to the laws of physics, we're not surprised or even sort of, you know, we roll our eyes when people talk about traveling to the future. Like, that's not what we mean, okay? When we talk about time travel, what we care about is traveling to the past. So can we do that, right?

And so far, with the laws of physics I've talked about, either Newtonian classical mechanics, where space and time are both absolute, or with special relativity, where the speed of light is a limit, the answer is very simple. No, you cannot travel to the past in either Newtonian mechanics or special relativity. If either one of those theories had been correct, then travel to the past would just not be possible. Okay.

Now, nevertheless, they wrote stories about it in the 1800s before we knew any better, when we still thought that Newtonian mechanics was possible. And so you could go back and read those stories and ask, you know, how did it happen? And the answer is basically magic, right? Like none of those stories had any detailed theory of why you could travel to the past using a time machine of some sort. He just sort of, you know, got in your steampunk sled and lights flashed and smoke was emitted. And then you were there, either in the future or the past or whatever, okay? So it was in a work of imagination, but it was not something that actually.

really had a grounding in scientific understanding in any way whatsoever. Now, general relativity comes along, okay? It comes along in circa 1915, and Einstein now says, well, I think that space time is important. I was wrong, Professor Minkowski. Space time is a big deal. In fact, energy and mass and all those things affect space time. They bend it, they warp it. And we appreciate those bending and warppings as gravity.

as the reason why the Earth goes around the sun, et cetera, okay? And that's going to change things a lot when it comes to time travel. Let me note, parenthetically, here, that you see what's happening in our discussion of what we mean by time travel is that, number one, we've never seen time travel. We've never experienced it. We don't have any empirical evidence of what it's like. Number two, we don't know the once and for all final laws of physics. Okay.

So what we're forced to do is make all sorts of conditional statements. We say, well, if Newtonian mechanics had been right, it would be like this, if special relativity had been right, it would be like that, if general relativity, etc. And now soon we're going to bring in quantum mechanics to the game and it's going to change things again. But the fact is we don't know. Okay. So whenever you hear anyone pontificating about time travel and saying, well, it would have to work this way, you don't need to listen to them because we don't know how it would work.

As far as we know, it's never happened to time travel. In fact, if I were to bet, it's not going to happen. My simple bet is that time travel is just not possible in the real world. But we don't know for sure. So what we're doing is we're imagining different possible ways the laws of physics could turn out. Some of those ways might be very, very different from what we're used to. And so we don't know what time travel would be like.

But general relativity at least lets us talk. about what time travel could be like in the context of a well-formed physical theory. Okay? General relativity says that space time is not fixed and rigid, right? That it's not just given to us once and for all, that it changes over

time, if you want to put it that way. But more generally, this is just general, that general relativity says space time is dynamical and a little bit unpredictable. We can at least imagine different kinds of space times. It's not fixed by, you know, just saying that there is space time. You have to say,

more than that. So in fact, there's a very simple way to imagine building a time machine. So what do we mean in general relativity by a time machine? Well, the rule that we had from special relativity was that we would have to travel slower than the speed of light. Let's imagine that we are not ourselves photons or other massless particles. Okay. We were made of massive particles. So I want to think of a real human being. Real human beings always move more slowly than the speed of light. And the technical term we attached to that was we move on a time-like trajectory. Okay?

So we move slower in the speed of light. That means we move time-like, because in a very real sense, we're moving more through time than through space. In the image of that diagram, we imagine drawing where time was on the vertical axis and space was horizontal. If you're not moving at all,

you're still moving through time, right? You're aging toward the future, one second per second. If you're not moving through space at all. If you move through space as fast as you can, if the beam of light is at 45 degrees, if the beam of light is equally moving through space and time, then you're always at an angle with respect to the vertical less than 45 degrees. You are always, if you're moving slower in the speed of light,

moving more in the time direction than in the space direction. So we say you are moving on a time-like trajectory, okay? And if special relativity had been true, then time-like trajectories have a very simple feature, namely that they begin in the past and they end in the future. That's all they can ever do. They can't loop in on themselves. They cannot reconnect, okay?

In space, you can draw a circle. You can draw a closed curve in space. But in space-time, you cannot draw a time-like curve that is closed in on itself, that loops in on itself as a circle. You can draw a curve through space-time that is a little. loop, but it would be time-like in some places, space-like in others. Okay, that would be a necessary feature in special relativity. What general relativity lets you imagine doing is having closed time-like curves. Time-like curves that are everywhere time-like, you're always moving

locally slower than the speed of light, but yet the global structure of space-time is such that you go on this curve, this trajectory through the four-dimensional universe, and you're traveling slower than speed of light, slower, slower, slower, and yet you come back to exactly the point in both time and space where you left. Okay, that is a closed time-like curve, or just a CTC. Sometimes closed-time-like loop or closed-time-like lines, CTL, but closed-time-like curves is the most common label for these kinds of things. This is what cannot exist in special relativity.

General relativity lets you imagine. So I'm not going to say that general relativity, a lot of it. allows for it. And the reason why is because the phrase general relativity by itself does not quite fix a physical theory. For those of you who know a little bit of general relativity, it's saying that the curvature of space time is influenced by stuff, right, by matter and energy and so forth. So to have a complete theory of the world, you need to not only give me general relativity, but also a theory of the stuff. What is the stuff that makes up matter and energy and causes space and time to curve.

You need that. So the reason why I can't tell you once and for all whether general relativity allows time travel and close time-like curves is because it depends on the stuff that is in the universe pushing around space-time. But I can say the general relativity allows us to imagine closed-time-like curves.

Here's a very simple example. Imagine that we did not live in an expanding universe. Imagine that there was almost nothing in the universe except like maybe one galaxy with us in. it, okay? And outside our galaxy, there was nothing, literally nothing else, okay? So it's just flat, empty space time outside of our galaxy. And imagine that time itself was a cycle. Okay, so imagine there was some moment, call it T-equal zero, and a hundred billion years in the future, the stuff that is in the universe reaches exactly the same condition that it had at T-equal-zero.

then it's as if, and perhaps it literally is, as if you take the universe at 100 billion years, and you identify it with the universe at time zero. So it's like just taking a piece of paper, taking the top of it, the bottom of it, and looping them together, right, to make a cylinder. So space time could be a cylinder, just like you could draw a curve on that piece of paper that always moved toward the top and yet met itself at the bottom, because the whole thing became a cylinder. time could be like a cylinder in general relativity.

Even, in fact, that's even true without any stuff in the universe. Forget the galaxy, forget you. In fact, it's easier to imagine that there's nothing in the universe, okay? Empty space with nothing in it but space and time itself could be identified from one moment of time to another with some interval in between where things could be different, okay? And that would be a universe where every point in space time lived on a set of closed time like curves.

namely curves that just started where they were, went to the future, came back, and ended up back where they were. That's the simple example of a time machine in general relativity. You can just basically fold the universe in on itself to make a cylinder. And once you do that, well, you've opened a large can of worms, a can of both physical and metaphysical worms. Like, if you imagine a version of this kind of universe where you could, where you did exist, there was people in it,

And, you know, maybe it wasn't a hundred billion years between the start and end. Maybe it was just 10 years. So could you meet yourself from 10 years ago in that universe? Or I guess more worrisome to a physicist, you know, we usually think of the way that we do physics as saying, I can have some initial conditions, right, for my billiard balls or my oscillators or my quantum fields. I can have any initial conditions I want. And then I tell you how the system evolves toward the field. future using laws of physics, whether it's Newton's laws F equals M.A. or Schroederger's equation

or whatever. Again, in the usual way of doing things, it would not be the case that a complicated physical system would ever come back to exactly where it started. So what if it fails to match? Like, what if I say, well, okay, 100 billion years from now, the universe is going to wrap in on itself? That is a precondition on what is going to happen in the universe now. not just what will happen 100 billion years from now, because what's happening now must be compatible with the idea that everything will be back where it started in exactly 100 billion years.

Huh, that's a worry. Okay? What are you going to do about it? All right, put aside that worry for right now. So forget about these issues that arise if this can happen. Let's just think about space time. Let's just think about general relativity, right? I mean, that's a trivial example that we gave you

of the cylinder universe where time closes in on itself. And you might say, well, I can easily avoid that by saying the universe is not like that, right? The universe is not wrapped in on itself. But then there has been, ever since Einstein came up with general relativity, there was for a long time a little bit of a, you know, a sideline of people inventing solutions to Einstein's equation in general relativity that predicted the existence of closed time-like curves. You know, the cylinder universe example that I gave you is a little bit artificial, right? Just a global identification of two different moments of time.

And who's to say that happens, right? That's not something you predict by pushing things around. It's like God has to had to do it or something like that. It was built into the universe from the start, but it wouldn't naturally arise. So there's a question, you know, can you sort of make a time machine in some way? Can you dynamically push stuff around in the universe so as to bring closed time-like curves into existence if they weren't there already? And this has a long history. There's a famous example from Kurt Gödel, who was a buddy of Einstein's and famous for his incompleteness theorems about the impossibility of having a sufficiently powerful number theory or other formal system that could prove all true statements, right?

There were statements which either were provable and false, which would be bad for your theory, or unprovable and true, which means your theory is incomplete in its ability to prove things. But Gertl also, you know, again, he was friends with Einstein. He knew about general relativity. He was an expert in it, actually, and he proposed a solution to Einstein's equation, which is sort of a cosmological solution. It was, you know, a universe filled with matter everywhere. But with the property, I have no idea how he came up with this.

But with the property that the matter had angular momentum. So unlike our universe that has matter scattered everywhere, but on average, you know, galaxies are rotating in one direction, one place, another direction somewhere else. There's no overall orientation. Gertl imagined that there was matter in the universe with a net angular momentum everywhere. And he solved Einstein's equation with this kind of condition put in by hand. And he found a solution that had closed time-like curves in it, cosmologically. And interestingly, he cared about. this. He wasn't just, you know, taking the piss. He wasn't just having a laugh with it. You know, Kip Thorne, who will, his name will appear again very, very soon. But Kip Thorne is my colleague at Caltech, one of the, probably the world's experts on time travel and general relativity. Also, and he was also a podcast guest. You can listen to our discussion about time travel and interstellar and things like that in the discussion with Kip Thorne. But he also, many years ago, wrote a textbook. in general relativity. And when he was writing it, along with John Wheeler and Charles Mizner, they actually talked to Kurt Gertl. Gertl was alive back when they started coming up with this idea for the book.

And they went, they visited him in his office at the Institute for Vance study, and they talked to him. And they had, I don't know exactly what they were interested in, but what Girdle cared about, what Gertl had as a question for them was, have observations in cosmology progressed to the point where we can say whether or not the. universe has a net angular momentum or not, is the universe spinning overall? Because he kind of, you know, he held out some hope that his weird cosmological solution will be relevant to the real world. But in some sense, the girl universe bears a family resemblance to the artificial

universe where we just identify one moment of time or another. In some sense, the close time like curves are infinitely big, or, you know, they wrap around the universe the whole way. That's the thing to say. They're not infinitely big, but they're everywhere and they wrap all throughout the universe. So you could say, again, well, maybe the universe just isn't that way, as a matter of fact, even though I can imagine the solution and write down the equations. There was another solution that was proposed by Frank Tipler, which was a cylinder, and this is not a cylinder in time. Okay, so this is not a cylinder where I take one moment of time and identify with another one. He's thinking of literally a cylinder of matter. And this is a cylinder, a cylindrical source of matter and energy that is infinitely long. Okay, because this is what physicists can do. We can imagine unrealistic things. And furthermore, Tippler's cylinder is spinning, spinning.

It's spinning very fast. So he has a small, thin, thin, dense cylinder of matter that is infinitely long and rapidly spinning. So he saw, again, I don't know what inspired people to think of these things. But he solved Einstein's equation for that kind of source. Remember, Einstein's equation relies on having some source of matter and energy. So Tippler solved it. And what he found was that there are closed times. like curves as you get close to the cylinder, okay?

If you go in, I forget whether it was along with, I think against the sense of rotation of the cylinder, you travel in such a way that the space time is just so curved there that you can travel in your rocket ship and you can end up arriving before you left, meeting yourself as you started your journey. Okay. But again, you could say, well, I don't know, an infinitely long cylinder. I don't think I'm going to find any of those lying around. round. The lesson that I want to get here is that in all of these examples, what would it be

like to travel backward in time? And the answer is, you would hop in a spaceship and travel through space. Okay. In general relativity, in the presence of closed time-like curves, time machines are not like, you know, a flying phone booth that you hop into and you pop into existence. You disappear and then teleport somewhere other in time. That's not how it would work. Time travel and the presence of closed time-like curves is like space travel. You hop in a rocket ship and you point it along the right trajectory through space and through space time, and you arrive before you left, okay? This is the idea that just wasn't there back in the 1800s. It's there now, but, you know, still people who write TV shows or movies or books.

They like the magic version. They like the disappearing version. You know, sometimes what I use as another analogy is, like, imagine that there are a bunch of, sentient trees who were trees. They were not ants. They could not walk around. They've never traveled through space, right? They're rooted to the ground, but they're smart and they can talk to each other.

And they like to imagine what it would be like to travel through space. And the only thing they can imagine is you would just sort of disappear at one location and reappear somewhere else. The idea of actually traveling through all the points in between never occurs to them. The respectable way to travel through time and general relativity does not involve appearing and disappear. It involves traveling through all the points in between, but wrapping space in on itself in such a dramatic way

that the trajectory you go on closes in on itself. Okay. However, all these examples I've still given you, the girdle universe, the cylinder universe, these are still sort of require the whole universe to conspire in some way to make a time machine. So we still can ask, can we build a time machine in our garage? Okay.

According to the rules of general, Are there things we can do? And our garage might be very big and very advanced, but it's still finite in size. Okay? In other words, let's put it this way. Could we imagine a universe which, to the past of some moment, had no closed time-like curves, and in a local region of space, we manipulate matter and energy and space-time in such a way as to bring closed time-like curves into existence through our actions and therefore build

time machine. That's the real question that is sort of, you know, what could an arbitrarily advanced civilization do is the way that it's sometimes put. And the reason why this became a hot topic in physics briefly in the late 80s, early 90s, actually, the way I heard the story goes back to Carl Sagan because he was working on his novel contact and he had his hero, Ellie, Arrowway, fall into a black hole and get spit out somewhere else in the universe. And Sagan was smart enough to know that's probably not really how black holes worked, but he was a planetary scientist. He was not a theoretical physicist, so he didn't really know for sure how black holes worked. So he talked to his friend, Kip Thorne, about how black holes worked, because Thorne is an

expert on black holes. And Kip explained, you know, no, that's not what you want. You don't want a black hole, which would destroy someone. You want a wormhole. You want, because wormholes were invented, not invented, but they were invented by Einstein, Einstein, Piedolsky and Rosen, sorry. Einstein and Rosen invented wormholes, and then the name wormhole was invented by John Wheeler,

who was Kip Thorne's PhD thesis advisor. So Kip Thorne knew what a wormhole was. It's not a black hole where you're sucked in and can't leave. It is a tube, if you want. It's a connection between two regions of space where you can travel in, if you like, they call it the throat of the wormhole

is in between, and the two mouths of the wormhole or the two ends, okay? So it's like a shrubes. shortcut through space time. And usually when you draw a wormhole, it kind of is drawn like a worm's hole in the ground, right? Like there's a hole that gets dug into the ground

and then it comes up somewhere else. There's a better way to think of it more realistically, because we have this image of if we were inside a wormhole, it would look like we're in some subway tunnel or something like that, which is not quite right. The way that a wormhole should be thought of is just imagine taking two spheres in space. Okay?

Like just, you know, imagine something something feasible, like a sphere, a meter across in one region of space, and another sphere, a meter across, another region of space. And I don't mean like a sphere made of steel or dirt or anything. I just imagine a region of space, spherical in shape. And imagine, again, this is all in your imagination, removing the region of space interior to that sphere, to both of these spheres, and instead identifying the sphere in one region with the sphere in the other ones.

So what I mean by that is if I put my hand into one sphere, it comes out the other one. Okay? That's a wormhole. That's a wormhole whose throat is of zero size. A wormhole is just a region of space time, which connects two regions of space time, the outside of which seem to be far away. So it's a shortcut, if you like, through space time. So I take these two spheres, identify them, something that travels into one sphere, pops out the other one instantly.

There's no subway ride, there's no glowing lights or anything like that. It's just curved space time in a very particular way. Okay? That's the way to think about a wormhole. And so what Kip Thorne said was, that's what you want. A wormhole is a shortcut through space time. And that's what you want. And that's what Sagan did.

And he wrote it into his novel, made into a movie, Jody Foster, the whole bit. Okay. But, you know, look, Kip Thorne is no dummy. He knows physics. He knows the bit of physics that we've already talked. about, namely that, according to relativity, moving faster than the speed of light is just as good as moving into the past, right? If you can travel faster than the speed of light, then from someone's point of view, you're traveling into the past. So what Forne realized is that if you really could, you know, it got him thinking, Sagan's question got him thinking about how wormholes would work.

Like, people had talked about them, his advisor had talked about them, but, you know, he, you know, he, you know, he, you know, he, you know, he's it is like the 1980s and he starts thinking about them personally in a careful way for the first time. And he realizes, you know, from the point of view of someone outside the wormhole, someone who uses the wormhole for space travel is moving fast in the speed of light. So from someone's point of view, someone could use that wormhole to go into the past. And he and his students figure out elaborate systems of multiple wormholes where you could sort of go into one. and then go into the other one, and you could make a close time like her. You could go back, you could go around through space time by traveling through the wormholes,

and you could get back before you left. Okay. Now, in fact, they later worked it down to just a single wormhole, and this is a little bit elaborate, but it's worth explaining because it's just so cool. Okay, so imagine one wormhole. Imagine we make a wormhole. Don't ask me how we make it, but we have these two spherical regions of space, the mouths of the wormhole, and you go in one, you instantly come out,

other one, okay? And imagine that somehow we can manipulate the mouths of the wormhole. We can basically put a tractor beam on and move one end of the wormhole around independently from the other one. So this is the point that there remains zero distance if you travel through the wormhole. You don't actually traverse any distance going from one sphere to the other one, but from the point of view of someone outside, the two mouths of the wormhole could be very close or they could be very far away. And so what Thorne and his friends say is imagine that we move them, that we start them right next to each other, so they're very close, and we move one of them far away, and then we move it back. Okay. And they know the other one just stays constant. The other one stays put.

This little thing that we just did, one mouth of the wormhole stays put. The other one moves out, let's say close to the speed of light, and then comes back. That should remind you of the twin paradox, right? If you put a clock on one wormhole and on the other one, the clock on the wormhole that stayed the same might, you know, it reads an hour has passed. Well, let's say this. Yeah, let's say two hours have passed on the wormhole that stayed the same, on the mouth of the wormhole that stayed put, whereas the other one that went out and came back, its clock only reads one hour. Okay. So initially, the two clocks, again, from the point of view of someone outside who's watching all of the shenanigans.

There's two clocks. They both say noon, and then two hours pass from the point of view of the wormhole that stays stationary. So its clock now says 2 p.m. But the wormhole that went out and came back, its clock just says 1 p.m. So they're now out of sync by an hour. Okay. And you say, all right, that's fine, good, special relativity, twin paradox. I get it.

But here's the twist. When you look through the wormhole, you see what's on the other side, right? You don't see flashing lights. It's not a subway. You see whatever's on the other side. It's like a window. It's like, you know, a telescope or something, okay? You're seeing through a view portal in space time.

And let's imagine that our clocks are so arranged that you can see the clock on the other side. You can see the other wormhole's clock, right? The other mouth of the wormhole's clock by looking through either sphere, right? So when you're moving, when the one wormhole is moving, it's going out and coming back, What would I see if all along I was looking through that wormhole at the stationary clock? Well, from the point of view of looking through the wormhole, nothing's moving. Okay? There's still zero distance between the two mouths of the wormhole from the point of view of through the wormhole, as opposed to outside.

Outside, the wormhole mouths are moving apart and then back together. but from looking through the wormhole, there's always no change in distance whatsoever. And so you don't see the other clock moving. You see it stationary. And therefore, what you see is that clock ticking at one second per second just like your clock. And that sounds paradoxical, okay,

because you say that, well, if I'm outside and I look at both clocks, one does a little twin paradox motion and goes forward one hour in time, one just stays stationary and goes forward two hours So now they're out of sync. But if I, instead of looking them from the outside, look through the wormhole, to borrow a phrase, they're in sync, right? They both read the same time.

So once the wormhole that went out on a journey comes back, it says 1 p.m. Its friend that stayed behind says 2 p.m. But when we look through the wormhole from the one that went out and came back to the other direction, we still see it saying 1 p.m. because it still has to say the same thing as the clock that was moving out and came back. And what that means is, I hope you followed this, I hope you bought everything I just said, what it means is if you go through the wormhole yourself, from starting in the mouth that went out on its journey and came back, and its clock says 1 p.m., you come out the other wormhole,

not just in a different location in space, but also at a different moment in time, compared to the point of view of the external. observer. Since you are looking at the clock on the other side of the wormhole and it says 1 p.m., you come out at 1 p.m. from the point of view of that wormhole mouth. So you have moved into the past from the point of view of the external observer. What the external observer sees is at 2 p.m., you entered the wormhole, and at 1 p.m., you exited. You exited before you left. And then you could hang around, and there could be another copy of you that said hi to the copy of itself that went through the wormhole, okay? And honest to goodness, closed time-like curve, that you made in a local region of space. You didn't just put it into the universe from the start. Wow, that was a big realization that they had. Like, oh, my goodness, we can do this in a way that seems pretty straightforward. Now, having said that, let's back up and take some reality pills here.

I haven't seen any wormholes lying around recently. Like, we are very unclear about whether or not wormholes actually exist in the real world. In fact, we're pretty confident that no macroscopic wormholes do exist in the real world. There's no reason to think that they're out there waiting to be found. In fact, it's worse than that. If you didn't try, like, if you didn't have a vested interest, if you didn't really want wormholes to exist, and someone said, well, could you find configurations of curved space

time out there in the universe that had the form of a wormhole, you would think about it for a you would say, no, I don't think so. And the reason why is because if you just somehow make a wormhole. Now, by the way, you can't. In classical general relativity, there's a theorem that is much like the theorems that say if you have a black hole, there will always be a singularity at the center, right? Singularity theorems. So in general relativity, classical general relativity, there's a theorem that says if you try

to change the topology of spacetime, you will also make a singularity. Now, it doesn't say you can't do it. singularities in the universe, but the thought is if you tried to bend and rip space time so badly that you made a wormhole, you would almost always end up just making a black hole instead, and the whole thing would just collapse inside a black hole. So when Thorne and his friends wrote these papers, they said, well, maybe there are quantum fluctuations of space time at really tiny plank scale sizes, and we could somehow seize a quantum wormhole and, you know, nurse it to be bigger and grow it up to macroscopic sizes.

But here's the problem. Imagine that wormhole model that we invented, where there's just two spheres that are identified. And I said that if you put your hand in on one wormhole, it comes out the other side of the other one. But now imagine you send in two particles, right? So you send them like they're both oriented perpendicularly to the sphere, right? So they're going to hit the sphere at, you know, 90-degree angles. So what that means is the trajectory. of the two particles have to be slightly pointed toward each other, right?

Like two trajectories pointing toward the center of the earth or perpendicular to the surface of the earth will be at an angle where they're coming toward each other very gently, right? But when they pop out the other side, when they come out on the other side of the wormhole, now they're coming perpendicularly to the sphere, so now they're moving away from each other, right? They were initially moving toward each other, they go through the wormhole, and they're now moving away. So the kind of curvature of space time that is involved with a wormhole takes particles that were moving toward each other and deflects them away from each other. So it's kind of the opposite of what gravity usually does, right? Gravity usually bends things toward each other. If you have two particles moving on a straight line,

you put some gravitational mass below them that will attract them and cause them to move together. So the way we think about this conceptually is, ordinarily, gravity only ever works to bring particles together. Now, there's a footnote there with the cosmological constant and vacuum energy, but let's not go there. That's a different story. It's all completely consistent with what I'm saying here. Gravity usually is attractive, okay?

But the wormhole is repulsive. It takes particles that were coming together and pushes them apart. So what it's equivalent to, and this is not just figurative equivalents, you can go through the equations, you require negative energies to make wormholes happen and to make them stay open. So again, if you didn't care about wormholes, if someone just said, well, all right, I start with a wormhole, what happens? What usually happens is the wormhole just collapses before you can actually get from one end of it to the other, before you can actually go in one mouth of the wormhole and pop out the other one. So we say that with reasonable conditions on the energy of the universe, right?

like actual sources of energy are positive energy, not negative energy, you could not make a traversable wormhole. Again, this is not a theorem. This is not something that is 100% proven true, because there are places with quantum field theory where maybe you can get some negative energies, and there's other things you can do that are fancier and so forth. But the general impression is that making wormholes and keeping them open is hard,

maybe impossible. We don't know enough about the fundamental laws of physics to say for sure. And then even if you had one, even you could keep it open, you would still ask questions about, what do you mean manipulate it? What do you mean,

take one end of the wormhole and move it out at the speed of light and bring it back? How do I do that? You can try to answer these questions, but it's not at all obvious that your answers make sense. So it's a wonderful thought-provoking experiment,

thought experiment. It makes you think very hard about what general relativity is capable of, but it also makes you worry that you're really granting yourself an enormous amount of control over space time that maybe you don't actually have in the real world. So because of that, let me just take a little detour

into something that doesn't always get mentioned when people talk about time travel, but it's personally meaningful to me. It's one of the first physics papers I ever wrote or was a co-author on was about time travel and close time-like curves. But it was not about wormholes. It was about cosmic strings.

At approximately the same time when Kip Thorne and others were thinking about wormholes, Richard Gott at Princeton published a paper pointing out that you could find an exact solution to Einstein's theory of general relativity that was similar in spirit to Frank Tipler's spinning cylinder, but it seemed a little more physical. And what Gott had was a cosmic string. So a cosmic string is not just a cylinder, but is a very, very particular type of object that can appear in quantum field theories that has both a density and a press. and it's sort of an infinitely long, in this idealization, an infinitely long straight string of energy. Okay? And one of the nice things about cosmic strings is that you can solve Einstein's equations exactly for them.

If you have a single cosmic string just sitting there in the universe, there's a fascinating thing that happens. If you're standing next to it, you feel no gravitational attraction. Even though it has an enormous amount of energy, there's no force of gravity from the cosmic string toward you. What there is is a global effect on the geometry of the universe. What happens is it's actually, the point is that the actual energy and pressure inside the cosmic string has the property, that there is no rest frame for the cosmic string. If you travel in the direction of the string and the direction of the string is pointing, you cannot measure your velocity with respect to it. It's kind of like the cosmological constant.

You know, the cosmotrial constant, dark energy. It's an energy and empty space that exists everywhere, but it doesn't have a rest frame. You can't measure your speed with respect to it. So a cosmic string, likewise. You can travel toward the string or away from it, but if you travel along it in the same direction that it's stretching, you cannot measure your velocity with respect to it. All the velocities are the same. And what that means is all of the physics of an infinitely long,

straight cosmic string is happening in the plane perpendicular to the string. There is no information that you get by moving up and down the string. Everything is in that plane that is perpendicular to and includes the cosmic string. So it's a model of, or an inspiration for, three-dimensional space-time gravity, right? So ordinarily, when we think about the world, we say it's four-dimensional space-time, three dimensions of space, one dimension of time. Imagine what life was like in a three-dimensional space. in a three-dimensional space-time. So space is two-dimensional, flatland, right? Except it's not

perfectly flat. You have energy, little particles in this two-dimensional space, and they can cause a gravitational impact on the world around them. And the gravitational impact on the world around them is to cut out an angle, to turn a flat space-time to kind of like a cone. Okay? So if you imagine a piece of paper, and that's two-dimensional flatland space time, space, time is still time, So you put a dot representing a particle, and you say, what is the gravitational field of that particle? The answer is, take scissors, cut out an angle from the edge of the paper to the dot. So the dot is now the vertex of a cone. You identify the opposite sides of the little wedge that you just cut out.

So this is a weird thing about the geometry of space time. The cone looks curved, right? If you see a cone, there's sort of curvature there, but that's just an artifact of how you embedded it in three-dimensional space. if you unfold the cone so that it's just a flat piece of paper with a deficit angle removed, you can see that it's completely flat. There is no gravitational force, because gravitational forces come from the curvature of space time. Okay. So that's not a time machine.

That's just the gravitational field of a cosmic string, which, again, back in the 80s and 90s, people actually thought a lot about cosmic strings as potential sources of structure in the universe. Cosmic strings are easy to make in the universe. early universe, and they could cause gravitational ripples that could give rise to galaxies and things like that. Those real-world cosmic strings would not be infinitely straight, and therefore they're not the same as point particles in two plus one dimensions, but it's a similar physical

motivation for it. So what Richard Gott did is say, well, okay, instead of just one cosmic string, I could get the exact solution for two cosmic strings moving with respect to each other, which is exactly the same as saying two-point particles in a three-dimensional space time moving past each other. I just orient their deficit angles not intersect with each other or with their trajectories, and I can solve all the equations exactly. So what he's done by having, let's forget about the cosmic strings, let's imagine we're in two plus one-dimensional space time, flatland with little dots in it and deficit angles. What he's done is given the system some angular momentum.

It's sort of similar in spirit to Tipler's rotating cylinder, but nothing's actually rotating. Two little particles are moving past each other. And what Gott showed is that very similar to Tipler, if the particles move past each other fast enough and close enough, when they're right near each other, you can zip around a circle and form a closed time-like curve. You can travel backward in time. Okay. So, who cares? This seems almost more unrealistic than wormholes. It's not more unrealistic than wormholes because unlike wormholes, we know physically that cosmic strings are constructable in theory, if not in practice, but they wouldn't be infinitely long and perfectly straight.

So it's still an idealization. But what it is, it's an idealization that lets you solve the equations exactly. This is the great thing. All of these talk about wormholes passing by each other and blah, blah, blah, blah, we're doing a lot of hand-waving in all these papers. And it's, you know, there are also equations that are very carefully solved, but there's no exact solution to Einstein's equation for a wormhole that starts not making a time machine and then making one. You just sort of assert that it's conceivable. But in this toy flatland example, where you have particles moving by each other fast enough to create a closed time-like curve, maybe you have a hope of solving the equations exactly and asking yourself, could you start? with particles that are stationary,

or not moving at all, or even just slowly moving, and accelerate them, right? Could you build a time machine, albeit in a 2 plus one dimensional universe, could you build a time machine that is an exact solution to Einstein's general theory of relativity

where the time machine did not start in the beginning of the universe, but was created by the motions of the particles, right? That's a sensible question you can ask. And this is the question that my collaborators and I asked. This is with Edward Fari, Alan Gooth, and Ken Olam.

We said, well, you know, how do you accelerate a particle? Well, we invented a complicated way that a single particle could blow up. That basically one particle could decay into two particles moving fast back to back. And just energy conservation is enough to tell you how fast they could possibly move. And then you can do the work, you know, you're highly paid theoretical physicists. So you solve the equations for the metric on space time. this particular configuration. So you start, in your thought experiment, with two particles in two plus one

dimensional space that are not moving. Then you let both of them explode. So they both have two little offspring particles, two little children that go back to back, and you have two of the children zoom right close to each other. And that's exactly what Richard Gott said would make you a time machine. Okay. So as long as the particles are heavy enough and moving fast that. enough, that kind of setup sounds like you should be able to build a time machine starting

from a universe where everything was stationary, where there was no time machine, where there were no close time like curves. But what we did was when we actually sat down and worked through the math, you know, this is one of the times when it's useful to work through the math because your intuition is not quite up to the task. Remember, the way that we think about the gravitational field of a single point particle in two plus one dimensions is start with a piece of paper, and we can. cut out an angle and then we identify the sides to make a cone.

Okay? So we asked ourselves, we checked, how much deficit angle would you need? How much energy would the particles need to have in order to have their little offspring particles move fast enough to make a time machine? All we found was, when you added up the deficit angles of all the particles, you always got a number greater than 2 pi, 2 pi radians, i.e. 360 degrees. So if you think about it, starting from a point on a piece of paper and you cut out an angle, you can't cut out an angle more than 360 degrees from a piece of paper, right?

There's only so much angle in a piece of paper starting from the middle. There's only 360 degrees there. What we're saying is what we found is kind of like, you know, in cosmological solutions to general relativity, there are open universes and closed universes. Open universes are one that go out spatially forever in all directions. Closed universes are ones that close in on themselves to make a compact-sized space. So what we proved is that in an open universe, you will never have enough energy to make a time machine. And, you know, we didn't put it in, right?

We didn't cheat. It's just general relativity forced you into that conclusion, which I thought was just enormously neat. and we even came with a very, very clever way of proving that using anti-dissitter space and some complicated geometry. But it was a lot of fun to think about, although not much practical application. And we also goofed. We didn't goof in any of our detailed calculations,

but we goofed in our guess, because we guessed that even though there was not enough energy in an open universe to make a time machine, in a closed universe, the total deficit angle in a closed universe, again, a little geometry fact here for you, the deficit angle of a closed universe adds up to 4 pi. Okay?

So you can think about that if you think about a cube, for example, and you think there's eight vertices on a cube. Each one of them has a deficit angle of 90 degrees. You can go through the math. It adds up to 4 pi. 90 degrees is pi over 2. So we said in our first draft of our paper, you know, we showed that you can't do this in an open unit.

but it seems like you can probably do it in a closed universe that's worth thinking about. In a closed universe, you do have enough energy. And it was actually Gerard Attoft, who is a very famous physicist Nobel Prize winner, showed that the Electra Week quantum field theory is renormalizable, did a whole bunch of other good things. He became interested in this problem, and he showed through, he argues, it's not quite a proof, I would say, but he put forward a very convincing argument that it's true. that in an open universe, you don't have enough energy

to make a time machine, in a closed universe, you do. But what a tough showed is that in a closed universe, you don't have enough time to make a time machine. And you're like, well, what in the world? What does that even mean?

You don't have enough time to make a time machine. In an open universe, you know, the thing about open universes in 2 plus one dimensions is, you know, there's an infinite amount of space, right? This just goes on forever. But a closed universe has an area. you would say a volume in three dimensions, but now we just have two-dimensional space,

so it has an area. And guess what? As soon as you do our trick, have a couple of particles, let them explode into sub-particles, offspring particles, the volume of space, the area of your two-dimensional surface

begins to shrink. It's like the universe is collapsing. And what a tuft showed is that it always shrinks to zero size before you make a time machine. So to me, that was just another amazing, unpredictable fact. Like, somehow, you know, the thing about the time machine or the thing about the cosmic strings or point particles in 2 plus 1 dimensions, it's very non-general, right? It's obviously extremely specific, extremely delicate and unrealistic in some sense.

But it's a toy model. It's a spherical cow. You can solve all the equations exactly. And we got counterintuitive results from solving the equations, namely, you know, you. You cannot build a time machine in either an open universe or a closed universe. And an open universe, there's not enough energy. In a closed universe, there's not enough time. So that's good to know.

It's indicative. It's suggestive that somehow general relativity doesn't want you to make time machines. And around that time, Stephen Hawking also wrote a paper called the chronology protection conjecture, where, you know, he used high-powered differential geometry from, you know, his old days as a, as proving singularity theorems in black holes. And he proved a theorem that basically said, and this is back in the real world, three plus one dimensions, that if you started without closed time-like curves

and you put ordinary reasonable restrictions on what matter you have, no negative energies or things like that, if you did things dynamically in a compact region of space in an attempt to make closed-time-like curves, you would always make a singularity. And the implication is that rather than building a time machine, everything just collapses to a black hole. That's not a theorem. There's something called the cosmic censorship conjecture, which says that when you have singularities, they're always inside black holes.

But it's not quite a theorem, and maybe you could get around it. But again, the suggestion is there, that when you try to make close time-like curves, even with wormholes or whatever, you will instead collapse everything to a black hole. And this was also backed up by some of the more explicit calculations people did with wormholes. When they actually tried to look at the behavior of quantum field theory in the background of these wormholes moving around, what you find is that as you try to make a close-time-like curve, as you try to manipulate the one wormhole mouth to the point where there is a path that takes you to the past, even though you're going forward in time, the energy density on that path just from quantum fluctuation, tends to diverge,

tends to become infinitely big. And I say tends to because they tried to get around it and, you know, there were arguments and I'm not even sure that they ever decided, whether there was a theorem one way or the other. But over and over again,

from very different angles, we got the impression that the real world wanted to prevent you from making time machines. So this is why, when I say, you know, general relativity allows you to imagine making time machines. I also say, but at the end of the day,

I suspect that in the real world, time travel is just not possible. And, you know, even if all of this discussion about building time machines and general relativity is a little bit deflationary, is a little bit like it's harder than you think, even though it's conceivable, it's not ruling out once and for all, the idea that you can do it. So we still have the ability to ask, you know, if you did do it, if you did have a time machine, if there were close time-like curves generated by the curvature of space time, what would it be like, right? what would the consequences be? How would time travel work in that kind of context? We have a much better framework for thinking about the physics and the philosophy of time travel

than we would in the magic world of HG Wells or whatever. So for example, there's two things that we instantly get, two conclusions from this. One is that if you do have a world where you make a time machine by building closed time like curves by pushing things around and having their gravitational fields. Sorry, by the way, I should say, like, if you wanted to have a time machine that you could actually travel through, even if you forgot about the fact that probably you just make a black hole, wormholes require negative energies, all of that, you're thinking here about manipulating amounts of energy that are truly astrophysical in size, right?

you're thinking about solar-sized mass concentrations packed into a very small region of space. So there's yet another engineering reason why it's hard. But okay, forgetting about that. One lesson is you can't travel into the past, into the time before you made the closed time-like curves. So let's say that somehow you could conjure a wormhole, let's say out of the quantum foam, and then manipulate it so that it created close time-like curves. You couldn't use that to travel to moments before you did that. You could keep the wormhole around, maybe, arguably,

and then toward the future, you would always be able to come back to that moment when you made it. Even if there was only a one-hour shift when you went through the wormhole, you could just keep going into it, right? If you were a year in the future, you could just go through that wormhole many, many, many, many times and come all the way back a year into the past, but you couldn't go into the past before you actually built the time machine, as it were, in the first place.

So sometimes people, including Stephen Hawking, like to make a joke that we have evidence against the possibility of building time machines because we've not been invaded by tourists from the future. But that's not actually a valid argument. It's a good joke. But it's not a valid argument because maybe we haven't yet built the time machine.

And then once we do, we can go back to that moment, but not to any moments before it. The other thing, of course, which is perfectly obvious, is that what a time machine would look like is it would look like a rocket ship, right? It would not look like a sled or a telephone box. It would look like a spaceship that could move across the right trajectory through space time. So time machines are kind of down to earth in that sense. It's the existence of the closed time-like curve that is exotic,

not the transportation method we use to get around there. Okay. Having all that in our bag of tricks, what can we say about the traditional issues that are raised by the possibility of time travel? You know what they are, right? You could travel into the past and kill your grandfather before he met your grandmother, and then you wouldn't be born, right? In fact, this is called the grandfather paradox. Not quite sure why it's always your grandfather, who's the target of this? Someone has issues there, but this is a paradox, right?

What if you went back and killed baby Hitler? That's another popular target. For one thing, is it morally right to kill baby Hitler? I mean, we know grown-up Hitler did terrible things, but baby Hitler hadn't done anything yet. It's sort of a precognition, pre-crime kind of thing. I mean, maybe baby Hitler could have just been treated better and things would have turned out very, very differently.

But putting aside those moral dilemmas, what does it mean to go into the past and kill Hitler, whether as a baby or not? we have memories of Hitler existing. We have photographs, right? Changing the past in that way seems to be, if not, completely paradoxical,

then at least apparently paradoxical in the following sense. There's a tension between the fact that we know and have records of certain things having happened in the past, but as we discussed, we have a feeling personally, since we're not Laplace's demon, of an ability to make choices. So if you can go into the past and make the choice to kill Hitler and therefore change the course of history,

how is that compatible with the fact that we know that Hitler really existed? That's the essence of all the different grandfather time loop paradoxes that we face. After Kip Thorne and his friends wrote about wormholes, Joe Polchinski, who's another physicist, sort of formalized these worries into a more tractable toy model paradox, the billiard ball paradox. He pointed out that if you had a wormhole that had a close time like curb generated by it, that you could throw a billiard ball, you could imagine anyway, throwing a billiard ball into the wormhole so that it came out the other way,

and if you aimed it exactly right, the wormhole would shoot the billiard ball out into the past in such a way, way that it would deflect the original billiard ball from ever entering the wormhole. So basically, the billiard ball is killing its own grandfather. You throw a billiard ball into the closed time-like curve, and it goes to the past and prevents itself from entering the closed-time-like curve. So what happens? Okay, that's the billiard ball. That's Polchinsky's billiard ball paradox. And Thorne and his friends, you know, took this very seriously. And again, we're not, let's just stick to the laws of physics as we currently know them. In fact, less than

as we currently know then. Let's think of classical physics, okay? By classical, I don't mean obeying Newton's laws. Relativity counts as classical. But what I mean is not quantum mechanical. Okay, there's only one world here. We're not doing many worlds quantum mechanics or anything like that. But also, you know, we're trying our best to generalize the laws of physics a little bit.

I mean, after all, part of classical mechanics is Maxwell. I said Maxwell's demon. Laplace's demon. The idea that you could in principle know the exact state of the universe at one moment in time, and from that predict the past and the future. The thing about the grandfather paradox or the billiard ball paradox is this is calling into question the idea, the motivating principle behind Laplace's demon, the idea that you can think of the history of the world, starting from some initial values, and integrating forward in time and,

backward in time, right? Because that makes perfect sense when time is only one dimensional and never loops back on itself, right? It makes sense to say in ordinary Newtonian space time or special relativity, if I know the state of the universe at one time, I can use the laws of physics to extend that state into the past and the future. But when time can in principle loop back on itself, what does it mean to have an initial value problem? This goes back to the work. This goes back to the that we had about the cylindrical and time universe, right, where we just identify one moment of time with another moment of time by hand. Doesn't that seem to impose some global, weird, invisible constraint on what the initial values for matter inside such a universe can be? Because they need to be such that the matter returns to exactly its same condition 100 billion years later,

or whatever that time period was later. So in some sense, I mean, maybe you shouldn't be surprised. We've opened Pandora's box and scared away Laplace's demon. We've said that we are changing the rules of the game to allow for these closed time-like curves. And so maybe we shouldn't be surprised that some of the old rules and ways we had of doing physics, of setting up initial value problems, aren't going to work anymore. Now, it doesn't mean that we throw away the laws of physics entirely, or that we throw away the idea that there should be laws of physics.

What we should do is ask, are there different kinds of laws of physics that work in the presence of closed time-like curves and also reduce through the laws of physics that we know and love when there are not closed time-like curves? And I think, you know, I actually haven't kept up on this as much as I did some number of years ago when I first started thinking about time machines,

but my impression is that we're not completely sure, about what the answer to that question is. So if you ask the question in the most ambitious form, are there rigidly expressable, perfectly clear, an unambiguous laws of physics that both completely avoid any possible paradoxes but give unique answers in the presence of closed time-like curves and reduced to ordinary laws of physics

when there are not closed-time-like curves? I'm not... I don't think that there are, or I don't think that we know, whether there are such generalizations or not. What there are, what Thorne and others proposed, including Igor Novakov, who is one of their collaborators, something called the Novakov Consistency Condition, which is even though you can imagine that in, let's say, Polchinsky's billiard ball paradox, that the billiard ball prevents itself from entering the wormhole, there is a different trajectory, which is self-consistent. So even though this one trajectory you started imagining prevented itself from happening is therefore, not consistent, you could argue that there are other trajectories that are consistent.

So there is a trajectory where the billiard ball goes in and knocks itself into exactly the right position to enter the wormhole at the right time. And you can't necessarily know what these trajectories are by starting with initial conditions and just letting the laws of physics chug forward in time. But there's some global way of stating them, right? Again, my impression is, as far as the existence of these consistent solutions is concerned, that there is good evidence that they exist. There's a very real worry that there's more than one of them, that they're not unique, right? Like, that given it's unclear what information you have to give me to pin down exactly what the behavior has to be.

But it seems, from the work that has been done, that you can always find some consistent solutions. to the behavior of matter and the presence of closed time-like curves. So at least it opens up the possibility that even though there's not this sort of Laplacean way of doing physics, starting from the conditions right now and just chugging forward in time,

there might be a more global way of looking at the entire space time and saying here are the allowed conceivable trajectories and here are not. And after all, that wouldn't be the weirdest thing in the world, even in ordinary physics, even forget about closed time-like curves. We know that there's something called

the principle of least action, which for those of you who don't know, again, I recommend checking out my videos on the biggest ideas in the universe. There's one on force, energy, and action. And what we talk about there is the fact that there's a way of formulating the laws of physics that says, starting from some initial point and ending in some final point, consider all the possible trajectories that a system can take between them. And there's a quantity that we can write down, called the action. It's an integral of kinetic energy, It's potential energy, but who cares? It's a quantity.

And the real physical motions of actual systems in the universe are the minimum values of that action. And that's a global quantity. You know, it requires knowing the whole shebang from the beginning of the system to the end. It's not this, you tell me what's going on now when I chug forward in time. I calculate a quantity knowing the whole system over time. And maybe you could argue that that's a sensible way to think from my, this eternalist perspective, right? From the block universe perspective, where we don't think of time as something that literally propels the universe from moment to moment, time is just a coordinate

on what exists, which is a four-dimensional space time. Maybe the laws of physics should be intrinsically four-dimensional from the beginning. So I think that's a fascinating possibility. I don't know what the state of the art is about that. I'm just telling you what my most recent impressions are about it. The nice thing about that is that we, that idea of a consistency condition, the idea that when you have closed time like curves, you can't just start anywhere you want and chug forward in time, but there are still consistent stories to be told in this background might translate over to literal stories, right?

From toy model physics scenarios into movies and novels and, and, and, you know, and TV shows, okay? So the idea of this consistency condition in a more narrative context is, so what happens, what gets in the way if you try to go back and kill baby Hitler, right? I think the answer was succinctly summed up on Lost, the TV show of all places. They had time travel in season five or whatever it was, and they were worried about, it was kind of funny since Lost was not always worried about making sense, but when it came to time travel, they were sort of weirdly insistent on making sense.

And so they had a motto, which is whatever happened happened. And what that means is, if you know that World War II happened in this world, in their fake time travel world, you could imagine traveling back to World War II, but you cannot imagine killing baby Hitler. You can imagine trying, but you know you will fail because baby Hitler was not killed, okay? The same thing is true with, you know, preventing JFK from being shot or preventing yourself from doing that embarrassing thing at the senior prom. Whatever it is, whatever way you want to change the past. You can imagine, in other words, visiting the past.

But if you do, you always did, right? You were always there in the past. Your older self is always part of the preexisting past. And it's what you might call a single consistent world approach. to time travel. There's a block universe, but time does not simply flow forward. Sometimes time can loop in on itself.

But at every point in the block universe, at every set of events, at every location in space and time, something happened. And there was only one thing that happened. This is the single consistent world approach. Whatever happened, happened. There are other, you know,

movies and stories that try to get this right and, you know, are a little bit more detailed than lost. I can mention two of my favorites, which are 12 monkeys. It's a consistent time travel story in this single consistent world sense. There's an even more elaborate one called time crimes. I mean, 12 monkeys tries to trick you into thinking that they're changing the past, but then you find out that they're not really.

Sorry, spoiler alert. Time crimes is this elaborate time loop kind of thing where a person interacts with themselves. The master of this, of course, was Robert Heinlein, who wrote several stories involving time travel, and where he tried to sort of make time loops. He wasn't worried about wormholes or consistent general relativity. He had the magic disappearing and reappearing in time idea, but it was completely consistent. Okay, so a person could interact with themselves

at different points along their personal timeline, but in ways which always at the end of the story, you realized only one consistent thing, a set of things happened. The most intricate and impressive version of this was his story, All You Zombies, which I only recently realized, like this week, because I was looking up time travel movies, was made into a movie with Ethan Hawk. They changed the title, so it's called Predestination,

is an Ethan Hawk movie based on Heinlein's All You Zombies story. It's not a super great movie. I mean, Hawk is good, but the story does not lend itself to becoming cinematical very easily. and to my enormous frustration at the end of the movie, I'm not giving anything away here, but at the end of the movie, they hint that maybe you can change the past, which is like destroying the entire point of the story.

The whole point of the story was, everything was perfectly consistent in a single consistent world, and they hint maybe that's not true. It's, you know, kind of defeating the purpose. But it's interesting because storytellers, just when they are given the toy to play with of time travel, they really, really want to change the past. Like, this is something deeply rooted in human psychology,

that if you tell people you can visit the past, there's this enormous desire to fix it, right, to change it somehow. So if you try to tell them, well, no, there's laws of physics. You're not allowed to do that. They don't want to hear it. And in fact, they will tell you that, you know, all the interesting stories are where you change the past. Which is weird because there are many, many interesting stories

called mystery novels or detective stories where you're not changing the past because you can't visit it because there is no time travel but you're nevertheless telling an interesting story because you are discovering the past. I think there are many, many interesting time travel stories to be told where you visit the past

and don't change it but you learn something about it. So for any budding screenwriters out there or novelists or short story writers, still plenty of room to write interesting time travel stories that do not necessarily violate the single consistent world approach. But you understand why it is tempting, because remember, we had this idea that you are not Laplace's demon personally. You do not have all that information. You are a tiny, very, very incomplete, imperfect set of atoms and molecules with incomplete knowledge about the world.

and that in your view, as an emergent, effective, higher-level macroscopic thing in the manifest image of the world, you think that the past is fixed, right? You think that the past is there, I can't change it, but you also think that you can change the future, that you have volition, that you have free will, that you can make a choice,

and that the causal ramifications of your choices propagate forward into the future. And this is, I think this is fascinating. This is why, time travel stories puzzle us or, you know, intrigue us at the same time, it's because in a time travel story, the past of the universe gets mixed in with the future of you, with the future of the people who travel into the past. And if you have this conviction that, you know, because you are, this finite person, you're not really embedded in this eternalist ideology, you think that

the past is fixed, unchangeable, but the future is effective. then when your personal future, like, what are you going to do next, becomes part of the past, it's just really hard to resist the conclusion that I can change the past. Like, what stops me from going and killing baby Hitler? And the answer in a single consistent universe picture is, I don't know. I don't know what stops you, but something will stop you. That's what I know. I know you will be stopped.

So in fact, this is what gives a little bit of dramatic tension to these stories, as rare as they are. But the dramatic tension comes from the fact that you know not to try to change the past because you know you will fail, but you don't know why. You know that what happened happened. You need to work in the constraints of what knowledge you have about the past. It might be that you fail because you get killed or you get sick and die or you fall off a cliff. It's very, very dangerous to try to change the past, and you know you won't succeed. So I think that actually kind of has dramatic possibilities for it. I'll give you another example of a good example of time travel, which actually was Bill and Ted's excellent adventure.

We mentioned Ed Solomon and Bill and Ted at the beginning. In the original movie, there's this famous scene where Bill and Ted need the keys to, I don't know, a car or a door or something like that. they don't have the keys, and they don't have enough time to go get them. But they also know that they know about the existence of a time machine. So they figure out, aha, in the future, we can go into the past, steal the keys, and leave them for ourselves behind this sign. So they go, they look behind sign it, there they are. There's the keys, okay? So this is a slightly different twist on it because they're not constrained by no.

knowing the past, what they're doing is by getting a favor from their future selves, they are obligating their future selves to do the thing, to go into the past, get the keys, and put them there. And they say this, they mentioned this, right? Like, you know, Keanu Reeves, Ted says like, but what if we don't actually do it? And then he says, but I guess we did do it because the keys were there. Or sorry, I guess he says, I guess we will do it because the keys are there. That's the point.

You can say, well, what if they just get the keys and then their future selves? decide not to go back and steal them, well, that's not allowed by the laws of physics. Their future selves, or an equivalent thereof, did and will and always have been stealing the keys. It's hard. It's hard to sort of wrap your mind around that, but it is consistent.

This is why time travel breaks our brains a little bit. These single consistent world scenarios make it hard to believe in human choices in exactly the same way. And by the way, again, footnote here, that is important, if it bothers you to think that there's some non-local global consistency rule that makes certain choices impossible and not something that you have the free will to carry out, don't worry about that because time travel is probably not possible, right? What we're doing here is saying, if time travel were possible, what would the rules be of the game and speculating about that? Okay. Now, all of you know that in the world of time travel stories, very, very few of them hew to this logic of the single consistent world. Some of them do. Good for them. But most of them want to let us change the past. And you might say, well, doesn't logic prevent this? Didn't we just give an argument that you can't change the past because whatever happened happened? It's already there. Well, you know, that would be true.

except, of course, as you also all know, there is the conceit that there are multiple timelines or multiple universes. So there's the idea that since we're inventing things anyway, we're not sure how to make them happen. Let's invent the idea that when we go to the past, we go to a different past than what we actually remember happening. So maybe there is a universe where we remember World War II as we remember it and we have documentary evidence for it. But let's imagine that if we could travel to the past, we also bring into existence a whole new world, right? A world where we can kill baby Hitler or whatever, prevent A of K from being shot, okay? And typically, this is just invented by magic. You know, again, there's no physical explanation given for where these new timelines come from,

hands are waved, you know, pictures are drawn, whatever, but it's not the laws of physics. But you also know that there is a version of the laws of physics where something is, kind of like this sounds like it happens, right? Namely in quantum mechanics, especially in the many worlds interpretation of quantum mechanics. Now, quantum mechanics, as you know, as most of you know, have heard me say, we have rules of quantum mechanics, but we don't know the final once and for all formulation of it. They're competing what we call interpretations.

They're not really interpretations. They're competing physical theories. But there are different theories, all of which look like quantum mechanics to us as we see it, experimentally. Most of these different theories do not have multiple worlds parallel timelines or anything like that, but one of them, the Everett's interpretation, or the many worlds interpretation, does. Now, for those of you who for some reason or another have not heard me talk about this,

the idea behind the many worlds interpretation is not that Hugh Everett, who invented it, sat around and said, like, what if there were like a billion worlds, man, that'd be awesome. It's actually much, much simpler than that. There's an equation, the Schrodinger equation, which is the equivalent of Newton's laws of physics, but for quantum mechanics. It's the equation that says what the quantum state does, how it evolves. It's a perfectly deterministic equation. It's perfectly definite in what it predicts.

It is not, by any stretch of the imagination, anything goes. Many worlds interpretation of quantum mechanics does not say that whatever you want to imagine happening is going to happen somewhere in the multiverse. Instead, what it says is go back to what we said before about measuring a quantum mechanical system, right? You can measure an electron to be spin up or spin down. You only ever see one response. You either see the electrons spinning clockwise or counterclockwise, never both.

And the many worlds interpretation says that's because the wave function in the universe splits. And there was only one world before, a world where the electron was in a superposition clockwise and counterclockwise, and there are two worlds after. So Everett's idea is just that that's the whole story. That's it. Everett's idea is just that the Schrodinger equation, which every version of quantum mechanics uses sometimes, is the entire story.

The Schrodinger equation, like it or not, predicts that there are multiple branches of the wave function of the universe, which we can interpret as multiple worlds. Other versions of quantum mechanics try to get rid of, the other worlds one way or the other, by hook or by crook. So the many-world's interpretation of quantum mechanics is a physical theory. It's not just hand-waving. There are very definite equations to tell you what happens.

And it predicts that there are, if you like, multiple worlds, okay? Many, many different copies of reality, all of which are slightly different from each other, all of which have slightly different things happening. In some, the electron was spinning clockwise and some it was spinning counterclockwise. So it is just irresistibly delicious to think about combining the idea of the many world's interpretation with the idea of time travel, the idea of closed time-like curves. In other words, we can ask ourselves the question. Before we were talking about general relativity in the classical world, okay? Now, let's say, what if we have closed-time-like curves in general relativity, but the fundamental laws of nature are quantum.

So what if we can have multiple worlds and closed time like curves in the same package, does that mean that if I hop in my closed timeline curve, I can travel to the past and either enter or create a new world, a new branch of the wave function, a new universe, a new timeline, whatever you want to call it, where things are not exactly what I remember them being in my good old passion timeline, okay? I think that the answer is we don't know. I don't think this has ever really been worked out to anyone's complete satisfaction. There's a famous work by David Deutsch, who is a famous physicist, a pioneer of quantum computing,

and also a famous proponent of the many worlds interpretation, where Deutsch looked at quantum mechanics in the presence of closed time-like curves, okay? And I think that people know that fact. They know that David Deutsch wrote a paper about quantum mechanics in the presence of close time like curves, and David Deutsch is a proponent of the many worlds interpretation, and therefore they leap to the conclusion that David Deutsch says that I can hop in a time machine and enter a different world and change the past, okay? But he didn't quite say that. There's a certain apparatus and formalism that goes along with the many worlds, okay?

And I'm not going to go into all the details, but branching of the wave function into multiple copies happens in certain specific ways under certain conditions when a tiny quantum system becomes entangled with the rest of the outside world. And so there's a very well-understood procedure for branching and creating different worlds. Deutsch wrote a paper where he imagines evolving a quantum system in the presence of closed time-like curves,

of a particular, not very realistic, but easy to analyze variety. That's okay. But he doesn't, and he shows that there can be a consistency C condition. Okay. He shows that it is possible to imagine quantum states in the presence of these closed time-like curves that are completely consistent.

That's what he shows, roughly speaking. He does not show that you can travel into the past and branch off a new world. There's no discussion about decoherence, branching, entanglement with the environment, any of those things. You could talk about those things as far as I know no one has. I think this is an interesting research project that I'm sort of. have tempted to do myself. Could you actually not only do what Deutsch did or take what he did and build on it by saying

not only is there a consistency condition, but here is how you could bring into existence extra branches of the wave function where different things happened, okay? Maybe not. Like, it's not at all clear that the answer is yes. You know, there are very basic questions when you open this kind of can of worms. Like if your future self travels to the past and your past self is still there, what about things like conservation of energy? Did the universe suddenly get more massive because there's now two copies of you?

Or does a copy of you shift over one universe in every single branch, right? Like there's n branches and you move from branch number n to branch number n plus one or whatever it is. But regardless, all of this discussion, it's important to distinguish the actual. physics paper discussion by Deutsch and others from movie discussion, okay? What Deutsche and others have been discussing is quantum mechanics in the presence of closed time-like curves. None of it is about changing the past. So here is another, you know, in the spirit of thinking about closed-time-like curves in

general relativity and drawing some conclusions from them, even if you could sort of fulfill the fantasy of having a closed-time-like curve, traveling into the past, and creating a new branch of the wave function, one of the implications of the many world's interpretation is the old branch is still there. You didn't get rid of it, right?

Maybe you can create a new branch, maybe not, but you didn't change in any way, the old branch. It branched or it didn't. And so there's still a world, the world in which we live, in which baby Hitler

grew up to be old Hitler and do a bunch of terrible things, right? So you can ask yourself whether it's sort of fulfilling the narrative purpose of traveling into the past, if all you're doing is creating a different world where things turned out differently, but not changing the old world where things turned out badly at all.

Maybe it is. Like, we can argue back and forth, but this is why I think it would be interesting to have a better handle on how you could have branching and new world creation in the presence of closed time-like curves. So you could really talk about the moral and human implications, even if it was far outside of our actual technological capabilities to actually do this. So I think maybe that's a little unsatisfying that discussion

because what I'm saying is there's a lot we don't know. But, you know, sometimes that's what is happening. So let me, you know, hit the finish line here by circling back to movies like Back to the Future. You know, what we were just talking about was sort of a hypothetical multiple world theory where you literally create a new branch of the wave function, but you didn't get rid of the old one. By the way, footnote to that, if you do the sort of science fictiony idea

that you create a new branch of the wave function or you create a new world by traveling backward in time, and then the old world does disappear. So let's imagine you're not doing many worlds interpretation of quantum mechanics. Let's imagine you're inventing some new fictional version of multiple world theory where you go back, change the, timeline to do something else, and then the old timeline disappears, then you are clearly history's greatest monster, right? Because you're erasing from existence billions of people who

have their memories. Like, even in a bad timeline where the Holocaust happened, there's still other happy things that happened, and you would be erasing them from history, right? Is that really something good that you want to do? Is that really something that is a moral good overall? of course, all time travel stories or many time travel stories have this lesson of hubris built in, like you try to change the past and you make things worse. I think that's just storytelling laziness. But as a real question, it's not at all clear what the moral value is of creating new timelines and destroying old ones. Happily, that's not what the many world's interpretation says you can do.

But also, most time travel stories are not in the context of the many worlds interpretation. They just make things up. and this is where we get back to back to the future. Why is back to the future bullshit as far as time travel is concerned? Again, it's a great movie. It works narratively, really, really well, but logically it does strain one's credulity. So one way, in many ways, but one way, just to make it a simple, straightforward example, Marty McFly, played by Michael J. Fox, goes back into the past.

You know, he starts in the 80s, goes back to the 50s, and he carries with him a photograph of he with his siblings, and he messes with his parents in the past in various ways. And what happens is as he changes their lives in the past, the photograph that he's carrying with him from the 1980s begins to change. It is clear that the things that he is doing in the 50s to the lives of his parents are changing their futures in such a way so that they did not have kids. And so therefore this photograph of Marty and his brother and his sister,

his siblings begin to gradually disappear from the photograph, okay? This makes no sense. Like, at least at face value, this just drives you crazy if you try to make any sense of it. Just let me of all the many, many objections one could raise. Let me just raise the most obvious one. Why is it happening now? Like, if Marty changes the past so that his parents, let's say, don't have any kids at all, then where did he come from?

Why did he have a photograph at all? Why did the photograph change and not him, right? And why is it happening now as he's doing this in real time as we're watching the movie? Okay, like none of this makes any sense whatsoever. There's another example, which is actually more to the point of a more recent movie,

Looper, if you've ever seen Looper, it's a great movie, again, terrible time travel logic in some sense, but a wonderful narrative movie, a wonderful story. Joseph Gordon Levitt and Bruce Willis play one time traveler at different moments in their lives. So the idea behind Looper is we're in the present day, not our present, the future to us, but the present day of the movie. And there are people whose job it is to assassinate people from the future.

So basically there's a future where there's a government or something that is trying to get some people out of the way. And the way they do it is they send them to the past and these people in our present day from the point of view the movie, kill them, okay? And that includes themselves. So what you buy into is a bargain, as if you're one of these assassins called loopers, is that you will eventually be sent back and you will be killed, okay? But along the way, you get a lot of money and rich and famous or whatever.

Okay. So, inevitably, there's going to be, I don't know, it's a bad system. I don't know whoever set up this system, but the people who are sent back, who were loopers, who are assassins, they know what the deal is. So, of course, they're going to try to escape. So a minor character named Seth in the beginning of the movie, he's a looper, and he shows up to kill someone being sent back. And it is, in fact, his older self, okay? His future self, old Seth.

So old Seth comes and it's supposed to be killed by young Seth. Young Seth just can't do it, right? Old Seth, sweet talks to him in a don't kill me, like, and then he escapes. But then, so old Seth is escaped. That's against the rules. And so the syndicate or whatever, the powers that be, capture young Seth and start torturing him. They start snipping off his fingers with garden shears, right?

So he's losing fingers. And what you see is it's exactly equivalent to the fact of the future thing. Old Seth, he's trying to escape, he's trying to run away. In real time, as we're watching the movie, he's looking at his hand, and every time he looks at it, it has fewer fingers on it, okay? Because at that time, as the movie goes, young Seth is being tortured and his fingers are being snipped off. Hmm.

How does that make sense? So you can see very, very clearly why that doesn't make sense. If young Seth was tortured and had his fingers snipped off, why did old Seth ever have those fingers? Why did he have a full set of fingers on his hand when he came back? His younger self had been tortured, right? This is not a single, consistent world in any sense. So the traditional response to this, and certainly the response that I've given is that's just bad time travel.

That is just not logical in any way. But here we are. We're giving ourselves the homework of being a responsible consultant on a movie like this. The movie already exists, so they don't need consultants. But the question is, as imaginative scientists, can we invent a set of laws of physics? Can we invent a way the world works that could make sense of movies like this? Where what the viewers see is changes that seem to propagate in weird ways between different versions of reality. Like none of these are even simply reconcilable just by saying, oh, there's a new timeline, right?

Because if there's a new timeline, if Marty McFly goes to the past and creates a new timeline, then he just either, brings the picture back with him or doesn't. And if the picture is with him, the picture shouldn't be changing as he does things in real time in that timeline. The picture is a picture of a different world from a different timeline. So we need to imagine

inventing a new version of the laws of physics where that thing that he is doing in the 1950s leads to changes that propagate into a different world and then is noticeable by him. Or in the looper example, what is being done to young Seth, his fingers are being cut off, only now is being noticeable by old Seth, even though he has no memory of not having fingers

for the last 30 years or whatever. Okay. Can we do it? I think we can. I would not be building up to this. I think that if we really try hard, we can make sense of this. But, you know, there's a rule in physics or whatever

that the more surprising and weird the phenomenon is, the more you're going to have to work to introduce some weird elements into your theory to explain it. That's not surprising, right? So we're going to need some leaps of faith here. But I think I can come up with a scheme that involves four ingredients on the basis of which we can actually make sense of Back to the Future, Looper, and other similar movies. So one ingredient is we clearly need multiple parallel worlds. So if you're going to make sense of this, you have Young Seth, and there was Young Seth, who, we see being tortured, his fingers are being snipped off, but there's also a world in which

young Seth does not have his fingers chopped off, because that young Seth needs to grow up into the old Seth that we see who has his fingers when the movie starts, okay? So at the very least, we need a world with Seth with fingers and a Seth where fingers gets, where Seth's fingers get chopped off, or we need a world where Marty McFly was born with his siblings and the photograph was taken of them. There's another world. in which his parents either do not meet or do not have those siblings or the photograph was not taken, etc. We need all those worlds. That's the least to ask. The second ingredient is these worlds are not completely separate. The worlds can interact in complicated, ongoing ways. So it's not just that

the wave function of the universe branches and now you have two separate worlds like you do in the usual many worlds interpretation of quantum mechanics. There needs to be ways that the different worlds can sort of continuously share things back and forth from each other at the right time. So when you literally see the photograph beginning to fade, or when you literally see Seth's fingers disappearing from his hand, what's happening is the reality of one world is being moved into another world. You might think that that's a lot to ask, but again, we're taking, we're trying to figure out the minimal set of ingredients to make sense of this craziness, and we're going to have to

have to be asking a lot. It's only going to get worse from here. So ingredient number one is multiple parallel worlds. Ingredient number two is they interact with each other in constantly ongoing, complicated ways. Ingredient number three, and here the buys become rather costly, you need to imagine that minds can move and evolve independently from, or at least in ways not directly tied to their physical bodies. Okay. So you have to be a mind-bodied. dualist to explain this. How do we know that or what makes us insist on that? Well, think of old Seth looking down at his hand, seeing his fingers disappearing.

When he sees them disappearing, he's surprised. He's upset. He's like, ah, I guess my young self is now having his fingers chopped off, right? But he remembers having his fingers. They're disappearing now, but Seth's mind is from a world where the fingers were. there the whole time. So what gets knitted together, this is ingredient number three in our list of four ingredients, there needs to be a knitting together of different things going on in different worlds that allows us to take the minds and memories of experience from one world and put them in the

bodies of people from other worlds. So by the end of the narrative in Looper, the body of Seth that had the fingers chopped off is together with the mind of the Seth to not have the fingers chopped off, at least not originally, right? So good. Mind-body dualism, Renee Descartes would be very happy with this. Plenty of other modern philosophers would also be happy, although a minority. Okay. The fourth ingredient, which is maybe the biggest and hardest to make sense of, is the following. Remember that with both the images in the pictures dissolving and in the fingers dissolving, one question was, why now? Right? Like, what is it? It's actually worse in Back to the Future than in Looper. Like in Looper, the fingers are disappearing on Old Seth

at the same time in that world when they're being chopped off of Young Seth. So that kind of makes some sense. But in Back to the Future, like Marty McFly's back in the 50s doing things, and gradually the photograph is changing. And, you know, in both cases, whether it's fingers or photograph, why did they wait until this moment to do that changing? How do they know, right? That it's supposed to be at this time when things are happening. So, especially when you have, as you always do in these movies, the focus of the movie jumps back and forth in time, right? There's scenes from the future and scenes from the past, et cetera.

But that's also a clue to how we solve it. So ingredient number four is there needs to be another time dimension of some sort. So what you need in addition to many, many worlds that have both physical reality, and mental reality in each of them. Each one of these worlds has a time coordinate, okay, in the sense of this universal time that just tells you how the universe is evolving from moment to moment.

But there's a separate idea of time, which we might call narrative time. It is the time as seen by the audience of the movie or as experienced by the person reading the book if it's a time travel story, okay? And this narrative time is what stitches reality. together. I know it's a big leap. It's very different than the usual laws of physics, but this is what we need. It's roughly reminiscent of hidden variable theories of quantum mechanics. If you know about hidden variable

theories of quantum mechanics, they also have the Schrodinger equation, and there's a wave function, and it branches, but there are variables, hidden variables, that sort of say this branch is the one that counts as real. Okay. So what I'm saying here is that there needs to be an extra ingredient, which takes all of these different worlds, all these different minds, all these different bodies, all these different experiences, and stitches them together

to make a single coherent reality that evolves according to this narrative time. And it's that reality that says that, oh yeah, young Seth, having his fingers chopped off is in some sense at the same time as old Seth realizing that he no longer has fingers

and stuff like that, okay? Now, you might say, well, where does that? narrative time come from? Who decides what it is? And there, I don't know. I can imagine two different ways of making it work. One way is the most direct way, like, there's an audience, right? Like, that's what actually makes it all make sense in the movies. You know, when you watch Back to the Future or Looper or whatever, you can get puzzled and confused and scratch your head, but overall, they're good, sensible stories. You know that when the image on Marty's photograph starts to

become altered, you understand his emotional reaction to it. He realizes that the world that he left behind, even though it's in the future, is becoming threatened, right? The emotional resonance is perfectly clear. So there must be some possible logic behind these stories if they make sense to us and affect us. So maybe it's something like the simulation argument, right? The simulation argument, if you heard my recent podcast with Nick Boss

says that all of what we think of as reality is actually just a computer simulation being run by a much more advanced civilization, potentially obeying very different laws of physics. So maybe you could imagine that this narrative time element that stitches reality together is literally smarter people, aliens, that play the role of editors or writers or whatever it is. They create a story by stitching together different things that happened in. different universes or God, if you want to call it God, or the devil, whoever, some supernatural force, okay? That's fine. It's kind of a cop-out. It's kind of like too cheap, right? It's sort of cheapening the experience that we live in. It's not the laws of physics. It's some external force that is constructing our reality. Okay, but it does hang together. The other possibility, which I'm not sure at all, whether it's one of these like half-baked ideas, which you

would have to ask, could you make it into a fully baked idea? Maybe there is some minimization procedure, right? Like, remember, the principle of least action. The principle of least action says you can derive the laws of physics for ordinary physical bodies, the laws of motion, by saying that there is some quantity that you get by integrating over all the motion that is minimized in real world happenings. Okay. maybe there is some quantity that is minimized or extremized or whatever by these particularly narrative coherent stories.

So stories like Back to the Future or Looper are not coherent by ordinary laws of physics, but they make sense as stories. So when old Seth sees his fingers disappearing, he is upset. And you get it. You get why he's upset. even though he's lived for the last several decades with those fingers, now he has lost them and he's upset. And you get that, okay? So if the fingers disappeared but he suddenly switched to having no memory of having those fingers, then there's no emotional resonance there at all. It's just, it's not a new timeline.

It's just a different timeline. And that's less interesting. So maybe there is some narrative version of the principle of least action. Maybe there is some quantity we could imagine calculating that makes the story make sense when you stitch together all the different multiple worlds, including close time like curves in this particular way. Or maybe not. I don't know. It's not something that I sat down and written anything about. I'm not even sure it could be done.

But my point is the following. That it's fun to think about time travel stories, even the ones that don't make sense. Like I stitched together, you know, I came up with this scheme involving, okay, multiple parallel worlds. They can interact with each other. Minds and bodies are independent from each other. And there's a narrative time that stitches them all together as my best attempt to make sense of what happens in movies like Back to the Future Looper and elsewhere. I think that's a useful exercise, if only philosophically or for storytelling purposes, maybe not for physics purposes. you know, how making sense of things is what we do as intellectually curious creatures that try to make sense of the world.

Time travel is a wonderfully interesting provocation to our urge to make sense of the world because it takes things that we take for granted and brings them into question. It raises questions of fate, our ability to change the past, the importance of the past, as well as just curiosity about what things would be like. if things had gone very, very different. It makes us think, and it makes us think in a novel way. That's why time travel is fun. That's why the stories are so irresistible. Time travel stories make us think about who we are and about how we live in the real world, not just the fake world.

And that kind of inspiration is always a good thing.