- I'm delighted this evening, as well as by the crowd, to be introducing Professor Peter Vranas.

Peter is a deep and broad philosopher. He's a pioneer in the development of deontic and imperative logics, systems studying the formal features of what we ought to do, and of imperatives or commands. Is it the case, for instance, that it follows from the truth of, you ought to save the world, that you can save the world? If you want to know this, Peter's your man. He's taken a floundering area and resurrected it from the ashes, leading it to exciting new areas of research. Professor Mark Schroeder, University of Southern California, big deal philosopher, for those of you who don't know, reports, "To say that Vranas's work on imperative logic "is head-and-shoulders above that "of anyone else would be an understatement. "His work simply defines the topic at the present."

Peter's published on a truly impressive array of topics. Aside from his work in logic, which already borders on ethics, he's worked on moral character, formal epistemology, philosophy of science, philosophy of language, and as we'll learn more tonight, time travel.

Peter's well known throughout the profession as the most thorough researcher anyone knows. When he sets about writing on a topic, his knowledge, by the time he writes it, is completely comprehensive. And one can be sure that if he says a view is novel, it really is.

Peter first received a PhD from MIT in operations research, but was already well involved in philosophy, and went on to get his philosophy PhD from Michigan in 2001, where he also, while he was there, managed to pick up an MA in psychology. After a brief period at Iowa State, he's been here since 2006, collecting Vilas and Kellett awards along the way. Peter's an extremely effective and popular teacher of logic, as well as the other areas of his interest. He's spoken at many places throughout the world, including China, Poland, Denmark, and Germany, and is wanted everywhere.

So I'm happy to introduce him to you tonight to speak on time travel, processes and paradoxes, welcome please Professor Peter Vranas. 
(audience applauds)
- Thank you very much. I am very excited to give this talk on time travel. Which is one of my favorite topics.

I would like to start by explaining a distinction between two kinds of time travel.

Multiple universe time travel,

and single universe time travel.

In multiple universe time travel,

the assumption is that there are multiple universes.

For example, in our universe, universe #1,

I was born in 1965, and I got married in 2017.

In another universe, universe #2, I'm again born in 1965, but I never get married.

In yet another universe, universe #3, I'm born later, in 2017.

In universe #4, I'm never born, I don't exist.

So the idea is that there are countless universes, which exist just like our universe exists. I'm not saying that this idea is true, I'm saying instead that this idea underlies many time travel stories.

Strictly speaking, it is not accurate to say that, for example, in universe #3, I'm born in 2017. Strictly speaking, in that universe, someone else is born in 2017. Someone who maybe looks exactly like me, but is not me. He's a copy of me, or a counterpart of mine. I am only born in our universe. In other universes, my counterparts are born.

In multiple universe time travel,

one travels between universes, from one universe to another.

Suppose, for example, that in the year 2018 of our universe,

I enter a time machine, determined to go back in time and kill Hitler in 1930, before he does the awful things that he in fact did. In our universe, Hitler did not die in 1930. We are told that he died instead in 1945, committing suicide.

But those who believe in multiple universes will say that there is some other universe in which Hitler does die in 1930, killed by a time traveler.

So, I travel with my time machine to such a universe in 1930, and I kill Hitler.

But notice that there's something unsatisfactory with this kind of time travel. Strictly speaking, in the other universe, I don't kill Hitler. I kill instead a counterpart of Hitler.

In our universe, the actual Hitler lives beyond 1930, and does a lot of awful things. I plan to say more about multiple universe time travel later on in the talk. For the moment, I just want to contrast it with another kind of time travel, single universe time travel.

In single universe time travel, one travels from one moment to another within the same universe. Suppose again that in the year 2018 of our universe, I enter a time machine, again determined to go back in time and kill Hitler in 1930.

If there is only one universe, or if there are multiple universes, but for some reason I can only travel within our universe,

then when I arrive in 1930, my plan to kill Hitler will fail.

Since Hitler was not killed in 1930 in our universe, there's no way I will manage to kill him. If there is only one universe with a single timeline, then it is a contradiction to say that there is the first 1930, in which Hitler does not die, and a second 1930, in which Hitler does die. Some time travel stories do say things like that, but the fact that they are self-contradictory time travel stories does not mean that they correspond to a possible kind of time travel.

Most of my talk will be about single universe time travel.

Because this is the kind of time travel in which most of the philosophical literature has focused.

When you are reading a time travel story, or you are watching a time travel movie, how can you tell whether it is about multiple universe time travel or single universe time travel?

In some cases, it is easy to tell.

Suppose a time traveler starts now and goes back to 1930. But things look there very different than from the actual 1930. There are smart phones and laptops everywhere. Then you know that the traveler has reached 1930 in a different universe, and the story is about multiple universe time travel.

In other cases, however, it is very hard to tell, at least initially.

If a time traveler exits a time machine in 1930, and things look there just as in the actual 1930, then you don't know whether he has reached 1930 in our universe or in a different universe.

However, you may get some hints as the story unfolds. For example, if the traveler repeatedly tries to kill Hitler but always fails, this suggests that the story is about single universe time travel. Alternatively, if something happens in the story that you know did not happen in the actual 1930, for example, Hitler is severely wounded, this suggests that the story is about multiple universe time travel.

Now that you are aware of the distinction, you can be alert. Every time you watch a time travel movie, you can try to find out whether it is about multiple universe or single universe time travel. And I think that this makes such movies more fun to watch. 
(audience chuckles)
Now that we have this distinction out of the way, here is my plan for the rest of the talk. As I said, most of the talk is about single universe time travel.

I plan to first define time travel more carefully.

Then I plan to go over three time travel processes: time jumps, time slides, and wormholes.

Then I plan to address two time travel paradoxes.

And finally, I plan to examine multiple universe time travel.

From now on, and until we get to the last part, whenever I talk about time travel, you should understand me as talking about single universe time travel. I will be assuming that there is only one universe with a single timeline.

Let's start with the first task, which is to define time travel.

There are two kinds of time travel of single universe time travel. Time travel to the past, and time travel to the future. Consider first time travel to the past. This kind of time travel seems easy to define.

Something travels to the past if and only if its arrival is earlier than its departure.

 For example, if I depart today and I arrive yesterday, then I have traveled to the past.

This definition applies to anything that might travel. Not only people, but also inanimate objects, subatomic particles, light, energy, information, whatever.

Let me mention parenthetically that there is a complication.

According to the special theory of relativity, whether one event is earlier or later than another is a general relative matter. In some cases, according to one observer, your arrival is earlier than your departure, and according to another observer, your arrival is later than your departure. I'm going to ignore this complication.

In the discussion period, if you're interested, we can talk about how to define time travel in special relativity.

Consider next how to define time travel to the future.

Here is a bad definition.

Something travels to the future if and only if it's arrival is later than its departure.

By similar of the previous definition.

Now this definition is bad because according to it, any ordinary trip is time travel to the future. If you walk to school, then your arrival is later than your departure, so according to this definition, you have traveled to the future. But clearly, this is not what we mean when we talk about time travel to the future. To see what we mean, let's watch a clip from the movie, The Time Machine.

(machine whirring)
- [Voiceover] It was disconcerting to see the sun arc in less than a minute.

To see a snail race by. My flowers, flinging wide their petals to embrace the new day. 
(harp strums)
 And the hours speeding across the face of my sundial.- In this clip, the time traveler experiences, for example, his hands inside the time machine as moving at an ordinary speed, but experiences the world outside the time machine as a film running at high speed. The trip takes maybe a couple of minutes from the perspective of the traveler, but takes several days from the perspective of the world outside the machine.

Let's call the duration of the trip from the perspective of the world outside the machine, the external duration of the trip. This is the difference between the arrival and the departure time of the traveler.

Let's also call the duration of the trip from the perspective of the traveler the stopwatch duration of the trip. This is the length of time that would be measured during the trip by a properly functioning stopwatch accompanying the traveler.

What makes the trip in the clip we just watched a case of time travel to the future is the fact that the stopwatch duration of the trip, which is a couple of minutes, is shorter than the external duration of the trip, which is several days. This observation suggests the following better definition of time travel to the future.

Something travels to the future if and only if the stopwatch duration of its trip is shorter than the external duration of its trip.

Again, let me mention that parenthetically, that there is a complication. According to the special theory of relativity, different observers may disagree on how long your trip takes, so there is no such thing as the external duration of your trip. Again, I'm going to ignore this complication, which we can discuss in the question period if you're interested.

Having defined time travel, let's move to the next task, which is to go over three time travel processes. Time jumps, time slides, and wormholes.

Consider first, time jumps.

A time jump is an instantaneous trip from one moment in time to another.

For example, suppose I enter a sports car which is a time machine.

I accelerate, and then suddenly, I and the car vanish into thin air, and as a consequence, we reappear out of the blue in another space-time region.

Here is what a time jump looks like from the perspective of external observers.

(car engine revving)

(energy whooshes)

- Look out! 
(brakes screeching)
- Now here is what a time jump looks like from the perspective of the time traveler. 
(exciting orchestral music)
 
(time machine whirs)

(energy blasts)
 
(crowd yipping)
- Indians!- We see that from the perspective of the traveler, the trip is instantaneous. One moment he is in 1955, and then suddenly, he's in 1885, faced by Indians. The stopwatch duration of the trip is zero.

Although time jumps are very popular in science fiction,

there is no known physical mechanism that corresponds to them.

How are the sudden disappearance and reappearance of the time traveler consistent with the law of conservation of mass energy?

Well, someone might propose a solution, they might say "At disappearance, the time traveler's body is converted into an equivalent amount of energy, and at reappearance, an amount of energy is converted by a reverse process into a qualitatively identical new body."

Well, this would be consistent with the law of conservation of mass energy, but my point is that no known physical process corresponds to the sudden conversion of energy in the body. So, time jumps are a merely theoretical possibility. They are not discussed in the physics literature.

Let's now move to a second kind of time travel process, which is time slides.

The idea here is that rather than jumping from one moment in time to another, you gradually slide through time. During a time slide to the past, the traveler experiences the world outside the machine as a film running backwards. Here is an example. 
(voices speaking in reverse)

(machine beeps)

(machine revs)

Note that during a time slide, the traveler continues to age. The traveler does not become younger. Time slides in science fiction are less popular than time jumps. In the philosophical literature, time slides are not considered seriously, because it is recognized that they run into a significant problem.

The clip that we just watched is in fact inconsistent. Let me explain why.

As we saw in the beginning of the clip, the machine was emptied.

And then, the time traveler climbed into it.

And then he pushed a lever, and the machine started moving backwards in time.

Suppose that he pushed the lever at noon.

As we saw, immediately before, so at 11:59 a.m., the machine was empty.

At noon, the traveler is sitting inside the machine, so the machine is not empty.

As the machine starts moving backwards in time, it goes through 11:59 am, then 11:58 am, and so on. At all those times, the traveler is still sitting inside the machine. So the machine is not empty. But we just said that at 11:59 a.m., the machine was empty. So we have a contradiction. At 11:59 a.m., the machine is both empty and non-empty.

Though that's not the end of the matter. Some people might reply,

"But in the clip we just watched, there is an inconsistency, "because the machine is not moving in space.

"So, at 11:59 a.m. the machine cannot be "both empty and non-empty at the same place."

One might think that there would be no problem if, when the traveler pushes the lever, the machine started moving in space, in addition to moving backwards in time. Because in such a case, at 11:59 a.m., there would be two copies of the machine. An empty copy moving forwards in time, and a non-empty copy moving backwards in time. And they would be at different places. So let me explain this by means of this diagram here.

At 11:59 a.m., the machine is empty. Here's the machine. It's empty, and it's not moving in space. It's moving in forwards in time, towards noon. At noon the traveler pushes the lever, and then the machine starts moving to the right in space, and starts moving backwards in time. So at 11:59 a.m., the copy of the machine with the traveler inside is to the right of the empty copy of the machine, and there's no contradiction.

That's still not the end of the matter. There's still a significant problem. Consider what an external observer sees as we get very close to noon.

First, there is an empty machine which is not moving in space. Second, there is a machine with a traveler inside, which is moving towards the left, towards the empty machine. Now as we get very close to noon, when the two machines get close enough, they don't collide, they gradually merge with each other. And when the merging is complete, at noon, the resulting single machine disappears.

But how can this be? To the extent that machines or physical bodies in general don't behave like ghosts, and so they must collide rather than merge, the physical possibility of time slides is questionable. That's why they're not really considered seriously in the literature.

Consider finally the third time travel process, by wormholes. Here it gets really interesting, because this kind of time travel is discussed very seriously by physicists.

A wormhole is like a tunnel: it is a shortcut connecting two otherwise distant space-time regions.

It has two entrances, also called mouths, which look like spheres, and the idea is the following.

You start by entering one of the mouths, which may be close to Earth, and then you go through the tunnel, and you exit the other mouth, which may be at a distant galaxy. So the trip from the one mouth to the other is very short through the tunnel, but if you went outside the wormhole, trying to reach the distant galaxy, then it would take many years. That's the idea.

Let's see what this is supposed to work. 
(machine screeching)

- Visual light source ahead. Brilliant, blue light.

Signal radiation.

(Ellie breathes deeply)
 
(energy thrumming)

It's a star.- We don't know if there are wormholes in our universe. Especially wormholes that humans could go through without being ripped apart. These are called traversable wormholes in the physics literature. However, what we definitely know is that wormholes are allowed by the general theory of relativity.

To explain how to use a wormhole to construct a time machine, I need to go first over the twin paradox.

Consider two identical twins, Peter and Paul.

One of them, Peter, stays on Earth. The other one, Paul, goes on a space trip to a distant galaxy and then comes back to Earth.

Then, the special theory of relativity predicts, and measurements have indeed confirmed, that Paul has aged less than Peter. So the twin who has gone on a spaceship and come back to Earth has aged less than the twin who stayed on Earth.

Using the terminology that I introduced earlier, we can say that the stopwatch duration of the trip is less than the external duration. And this means that the space-traveling twin has traveled to the future. Theories how to use the twin paradox to construct a wormhole time machine.

Suppose that somewhere, we have found a wormhole. To have a concrete example, suppose that one of the mouths of the wormhole is in Boston, and the other mouth is in Detroit.

Suppose also that the trip through the wormhole takes two minutes. For example, if you enter the Boston mouth at 8 a.m., and you go through the wormhole, you emerge from the Detroit mouth at 8:02 a.m. Similarly, if you enter in Detroit at 8 a.m., you'll exit in Boston at 8:02 a.m.

Now, here's the fun part. Suppose that somehow, we can move the Boston mouth. So we put it in a spaceship, we take it on a trip to a distant galaxy, and then we return it to Boston. Now, I know this sounds like science fiction, but let me assure you that this idea are seriously discussed in the most prestigious physics journals.

Then, by the reasoning of the twin paradox,

the Boston mouth has aged less than its surroundings that stayed in Boston. Remember that the twin that has gone on a spaceship and come back to Earth has aged less than the twin who stayed on Earth. So similarly, the Boston mouth that has gone on a space trip and come back to Earth, has aged less than its surroundings that stayed in Boston. Which means that time inside the Boston mouth arrives behind Boston time, which is Eastern Standard Time. For example, when in the rest of Boston, it's noon, inside the wormhole, it's earlier. It's 8:00 a.m., for example.

Now, the wormhole functions like a time machine. To see this, suppose that you start your trip in Boston at noon by entering the Boston mouth. As we just said, inside the Boston mouth it's earlier, 8 a.m. You go through the wormhole in two minutes, and you exit in Detroit at 8:02 a.m. Detroit is also in the Eastern time zone. Then, you go to the Detroit airport. You catch a 9 a.m. flight to Boston, and you arrive at 11 a.m., before your departure, which was at noon. So you have traveled to the past.

Many physicists believe that this kind of time travel is possible. Others, however, disagree.

I'm not going to enter into this debate here. I want instead to compare wormhole time travel with the other two kinds, time jumps and time slides.

In a time jump, your trajectory is discontinuous.

You suddenly disappear from one time and space, and you suddenly reappear at a different time, and maybe also a different space.

A wormhole time travel, however, or time travel through a wormhole,

has a continuous trajectory. There's no sudden disappearance or reappearance.

Moreover, as we saw, a time jump is instantaneous. Its stopwatch duration is zero. By contrast, a trip through a wormhole may be very short, but it's not instantaneous. It has a positive, non-zero stopwatch duration. As we saw, time slides also are supposed to have a positive stopwatch duration. However, during a time slide, the traveler experiences the world outside the machine as a film running backwards. By contrast, during wormhole time travel, you can hardly experience the world outside the machine. You can just see the tunnel, which is the machine, and maybe what is apparent of the tunnel.

Let's now turn to the next part of my talk, where I address two time travel paradoxes.

And let me remind you that I'm still assuming that there is only one universe with a single timeline.

A standard paradox of time travel goes roughly like this.

Suppose that time travel to the past is possible.

Then, I can enter a time machine, travel back to 1975,

meet my younger self, who is at the time a 10-year-old boy,

point a loaded gun at the boy, and then it seems that I can kill the boy. I can kill my younger self. But on the other hand, I cannot kill my younger self, because of course, he grew up to become me. So, we have contradiction. If time travel to the past is possible, then I both can and cannot kill my younger self. Or so the paradox goes. I don't agree, as you will see.

Let's call this the retro-suicide paradox.

A well-known variant is the grandfather paradox. Which asks whether I can kill my paternal grandfather at the time before my father was conceived.

Let me first make the follow point in response to this paradox.

If time travel is uncontrollable, then I cannot kill my younger self. To explain what I mean by uncontrollable time travel, let's watch a clip from the movie The Time Traveler's Wife.

- It's because I am. I've come back to this night from the future. I'm a time traveler.- Oh my god, you are out of your mind.

- It started when I was six years old. I have fits. I disappear. I travel through time. I've come to this night from the year 2003. What year is this?

- 1995, I don't like this.

- I get dislocated in time, I never know when it's going to happen or where I'm going to end up. I have to break and enter, steal clothes from the first person I see.- In this clip, the time traveler cannot control anything. He cannot control when his trips start.

He cannot control where he goes, or when. He cannot control whether he goes to the past or to the future, or how long he stays there. He can't even take anything with him. He travels naked, and he always has the problem of finding clothes wherever he arrives. This is uncontrollable time travel.

Let's contrast this with a kind of time travel in the next clip.

- You can spare a cigar, I trust, Doctor.

Now, let us imagine that this cigar is the time traveler.

Now in front of him is the lever which controls movement. Forward pressure sends the machine into the future. Backward pressure, into the past. And the harder the pressure, the faster the machine travels.- In this clip, the time traveler can control when his trips start, can control at what future or past moment he goes, can control how quickly he gets there, or how long he stays there. This is controllable time travel.

If time travel is uncontrollable, or at least if I have no control over my destination time, then I cannot travel back to 1975, even if I do end up traveling to 1975. Why? Because to say that I can do something is to say that I have a corresponding ability. But if traveling through time is something that just happens to me, as in the movie we just watched, then I don't have a corresponding ability. So if I do end up traveling to 1975, it will not be as a result of my ability. It will be instead as a result of forces beyond my control, just like The Time Traveler's Wife clip.

So, if time travel is uncontrollable, then I cannot travel to 1975 or to any other time, and there's no reason to say I can kill my younger self, and there's no paradox. The paradox relies on two lines of reasoning, which have contradictory conclusions. One line of reasoning with the conclusion that I can kill my younger self, and another line of reasoning with the conclusion that I cannot kill my younger self. My point is that if time travel is uncontrollable, then the first line of reasoning fails. It's false that I can travel back to the past and kill my younger self. And so, there is no contradiction, and there is no paradox.

So let's move on to controllable time travel, for which the paradox is still with us.

From now on, I'm going to talk about controllable time travel. Let's assume that I can choose my destination time, so I can travel back to 1975 or to any other time I choose, and I can kill my younger self. The paradox, as I said, arises because the result's a line of reasoning that says that I cannot kill myself. And now I want to distinguish two versions of the paradox, which correspond to two ways of grounding the claim that I cannot kill my younger self.

According to the wide paradox, I cannot kill my younger self because my killing him would change the past, and I cannot change the past. According to the narrow paradox, I cannot kill my younger self because my killing him is impossible, and I cannot do something impossible. Why is it impossible that I kill my younger self? Because he grew up to become me. So if I kill him, he must be somehow resurrected. And resurrection, I assume, is impossible in the sense of contradicting the laws of physics.

Now, why the labels wide and narrow?

Here's a crucial point. If my inability to change the past were the whole story,

then my inability to kill my younger self would be on a par with my inability to do anything inconsistent with the actual past. For example, with my inability to kill Hitler. To kill Hitler would also be to change the past, given that he was not killed by me. But we are not inclined to treat these cases equally. It seems that there is something especially problematic when my target is my younger self, rather than anyone else.

Similarly, for the grandfather paradox.

It seems essential to assume that the time of the contemplated murder is before my father's conception. But this assumption would be inessential if my inability to change the past was the whole story. Because killing my grandfather, even after my father's conception, would still change the past. So it seems that the wide paradox is missing something. By contrast, in the narrow paradox, the fact that my target is my younger self rather than anyone else does play a special role. Because as I said, the idea is that my killing him is impossible, because resurrection is impossible. By contrast, no similar impossibility attaches to my killing Hitler, for example.

Unfortunately, I only have the time to address the wide paradox. We can talk about the narrow paradox in the discussion period if you want.

As I said, the wide paradox relies on the claim that I cannot change the past.

To response to the wide paradox, I will argue that an ability to change the past is not incoherent.

Let's see why.

Suppose that there is now a wormhole mouth standing right here next to me. And the wormhole leads back to 1930. So, by entering the wormhole, the wormhole mouth, I can travel to 1930.

Suppose for a moment that I'm not very adventurous, I choose to ignore the wormhole mouth, and I never visit 1930.

Well, this doesn't mean that I cannot. Really, I can, the wormhole mouth is right here standing next to me. There are plenty of things that I can do but I choose not to do.

Since I can visit 1930, but I don't, I can change the past.

Well, this is not to say, when I say that I can change the past, is not to say that I can bring it about that there is a first past in which I don't visit 1930, and there's a second past in which I do visit 1930. That's not what I'm saying. I agree that this would be incoherent. What I'm saying instead is that I can change the past in the sense that I can bring about a past different from the actual past. And this I can do, just as I can change the future. For example, I can right now interrupt this talk and walk out of the room in the next minute. I will not do it, but my point is that I can.

In the actual future, I don't leave the room. But I can bring about the future in which I leave the room. And in this sense, I can change the future. I can bring about the future different from the actual future. Similarly, I can change the past in the following sense. I can bring about the past different from the actual past. If I were to enter the wormhole mouth, it's not that the past would chance retroactively. Rather, it would never have been what it actually is, and it would have always been something different.

To clarify, I'm not saying that I will change the past. I'm saying that I can, although I would clearly not. To conclude, an ability to change the past, properly understood, is not incoherent. So the fact that controllable time travel requires an ability to change to the past does not show that controllable time travel is impossible. This is my proposed resolution of the wide paradox.

Finally, let's turn to the last part of the talk, which I think is actually the most interesting one, in which I examine multiple universe time travel.

To remind you, the idea is that there are multiple universes. For example, there is a universe in which I am a biologist. Or, more precisely, there is a universe in which I have a counterpart who's a biologist.

Let's go back to my plan to travel to 1930 and kill Hitler.

Given what I have said so far in this talk, I realize that my plan should not be to travel to 1930 in our universe. Why? Because in our universe, Hitler was not killed in 1930. So if I go there and try to kill him, I will fail. So, I have instead the plan of traveling to 1930 in a different universe, and killing Hitler, or rather, his counterpart, in that universe.

But here is a problem with my plan. There are countless universes, or so the idea goes.

In some of these universes, our whole solar system does not even exist in 1930. There is instead a black hole in its place.

So, if it is a random matter to which universe I arrive,

then I may end up in the middle of a black hole.

But who wants to risk that. So, to have a safe kind of multiple universe time travel, let's assume that when I travel to 1930 in a different universe, then things look there like the actual universe. For example, if Hitler still exists there, or rather, his counterpart, and he has done up to that time, the things that Hitler has done in the actual universe. So the assumption here is that whenever one travels from one universe to another, the two universes are parallel until the time of one's arrival. And by parallel, I mean that they have qualitatively identical pasts. Which means that exactly similar people exist in the past of the two universes, and they do exactly similar things.

Well, let's call this the fundamental assumption of multiple universe time travel.

There are many time travel stories and movies which deviate from this fundamental assumption. They show time travelers who travel to different universe, which has a past slightly different or even very different from the actual past, from the past of our universe. I'm not saying that there is anything wrong with these stories. What I'm saying instead, that that kind of time travel is like playing Russian roulette, you may end up in the middle of a black hole and get killed. So in the rest of the talk, I'm going to talk only about the kind of multiple universe time travel for which the fundamental assumption is true. Whenever you travel to another universe, it is guaranteed that until the time of your arrival, the past of that universe is indistinguishable from the past of your departure universe.

So, suppose the fundamental assumption is true, and in the year of 2018 of our universe, I enter a time machine.

I travel to 1930 in another universe, in which Hitler or rather his counterpart exists, and still plans to do a lot of awful things, and suppose further that I kill him.

Now the point that I want to explain is that there is no way I will go back to 2018 in our universe. There's no way I will go back to where I came from.

Why? Well, let's call our universe, universe #1. And the universe in which I kill Hitler, universe #2.

If I travel from universe #2 to 2018 in universe #1, then, by the fundamental assumption, the past of the two universes, the past of 2018 in the two universes will be the same. That's what the fundamental assumption says. If you travel from one universe to another, then the two universes will have the same past up to the time of your arrival. So, if I travel from universe #2 to 2018 in universe #1, the past of 2018 will be the same in the two universes. But the past of 2018 is not the same in the two universes. In universe #2, Hitler dies in 1930, but in universe #1, Hitler does not die in 1930. So, I will not travel back from universe #2 to 2018 in universe #1.

If the fundamental assumption is true, then multiple universe time travel is a one-way ticket. There's no return.

To summarize, if the fundamental assumption is false, then multiple universe time travel is like playing Russian roulette. But if the fundamental assumption is true, then multiple universe time travel is a one-way ticket.

But now suppose that I want a one-way ticket.

Suppose I'm not happy, I don't like our universe, a universe in which the Holocaust occurred. I want to live in different universe, in which the Holocaust does not occur. So, when I kill Hitler in 1930 in universe #2, suppose I travel to the future of that universe, 2018 in that universe. And suppose further that things are indeed much better in that universe. Suppose that the world is a much more peaceful and civilized place in universe #2 than in universe #1 in 2018.

Should I be happy then? Not necessarily. The problem is that in universe #2, I'm a stranger. I have no family, no job, no place to live.

Some time travel stories try to avoid this problem by assuming that I do have a family and a job, only better than what I had in the original universe. Let's see an example from the movie Back to the Future. 
(gentle orchestral music)
 
(Marty exhales deeply)

- How 'about a ride, Mister?

- Jennifer. Oh, are you a sight for sore eyes. Let me look at ya.

- Marty, you're acting like you haven't seen me in a week.

- I haven't. 
(audience chuckles)

- In this movie, Marty travels first from 1985 to 1955, and then some things happen there which did not happen in the actual 1955. For example, his mother, who is at that time a young girl, starts falling in love with him. So clearly, he has reached 1955 in a different universe, not in his departure universe. And then he travels to 1985, and he finds things there much better than in the original 1985. For example, in the clip we just watched, he's realizing that he has a much better car than what he had in the original 1985.

Now the problem is that this car does not belong to him. 
(audience laughs)
 When did he acquire it, and when was it given to him? Presumably, it was given to his counterpart in universe #2. Let's call him Marty #2. And while, in fact, in the clip we just watched, Jennifer says, "You act like you haven't seen me in a week." So clearly, she's not his girlfriend, she's the girlfriend of his counterpart, whom she has been seeing in the last week.

The movie has the flaw that we never see the counterpart.

He must mysteriously disappear when the time traveling Marty appears. 
(audience chuckles)
 If we had seen the counterpart, then the problem that I'm raising would have been obvious. Which is that in universe #2, the time traveling Marty is a stranger. He has no family, no car, no girlfriend.

So, to summarize.

Multiple universe time travel is either like playing Russian roulette, or is a one-way ticket to a universe in which you are a stranger.

To conclude, here are three take-home lessons that I hope you will remember from this talk. First, there are many kinds of time travel: multiple universe versus single universe time travel, uncontrollable versus controllable time travel, time travel by time jumps, time slides, or wormholes.

Second, some kinds of time travel deserve more serious attention than others. As we saw, time jumps and time slides, although popular in science fiction, run into problems, and so they are not considered seriously by physicists. By contrast, as I said, wormhole time machines are discussed seriously in leading physics journals.

Third, the paradoxes of time travel do not show time travel to be impossible. I argue, for example, that an ability to change the past is not incoherent. I did not fully defend this third conclusion because I did not have the time to go over all time travel paradoxes. But we can talk more about the paradoxes in the discussion period, if you're interested.

I'm done. 
(audience applauds)