Christopher Nolan’s Tenet aroused a variety of emotions: from bewilderment to curiosity. For many years, prominent scientists have been talking about the theoretical possibility of time travel. However, so far humanity has not come close to realization. The leading Russian theoretical physicist Sergey Krasnikov talks about the existing theories and concepts shown in the Tenet movie.

Sergey Vladilenovich Krasnikov is a Doctor of Physical and Mathematical Sciences, a leading researcher at the Laboratory of Stellar Physics at the Pulkovo Observatory.

Sergey Vladilenovich, did you like Christopher Nolan’s film Tenet?

− I didn’t. To introduce a time machine for the sake of a couple of shots with fighting countermovers is to crack a nut with a sledgehammer. In general, I like the action genre, but, in my opinion, Tenet is a bad action movie.

From the point of view of physics, how feasible is the idea of inversion described in this movie?

− It is difficult to answer this question because the director did not present – in fact, it is not his responsibility – any specific concept one could argue for or against. He only hinted that there is time travel in his universe or rather some kind of time inversion that allows you to move into the past. However, Nolan does not develop this idea in any way but uses it as a “handout” for the viewer. And this, frankly, is annoying. The director introduces quite interesting ideas into the movie but uses them as an optional supplement. In my opinion, this somewhat devalues the whole idea.

In Interstellar, for example, I understand why a black hole was needed, the relativity of time, and so on. And in Tenet, it seems to me, there is nothing new because movies about time travel have been shot at a similar level for 50 years.

Generally, the time machine is a well-studied concept, and there is a lot to say about it, and it has already been said in various works. Why complicate the plot with the idea of inversion is beyond me.

− Does inversion occur in physics?

− No one calls it inversion, as far as I know. In fact, what Nolan calls inversion is known in physics as the reversal of the arrow of time.

In the physics of time, there is an idea of the arrow of time. For example, a cup can fall off the table and break into 1000 pieces, while the pieces cannot become a whole cup again and return to the table. And if something had evolved in time in a different direction, in other words, oriented this very arrow of time in its surrounding in the opposite direction, we would have gotten only a small part of what can be called the reversal of time.

The director obviously heard something about this phenomenon but took various incongruous elements as a basis. For example, the hero is told that when he runs back in time, the wind blows at his back. This contradicts not some high science or complex, abstruse physics, but basic common sense. And there are many such inconsistencies.

If somehow the arrow of time around the cup changed its direction, then this cup would evolve as a counter-mover. It would bounce, bringing itself together from pieces and heating up with the tea.

(Countermotion (lat. contra – against + lat. motio – movement) is the term coined by the Strugatsky brothers to describe the reverse movement in time. In the novel Monday begins on Saturday, in which the narration is conducted on behalf of Alexander Privalov, a Leningrad programmer, it is written that “Countermotion is simple movement in time in the opposite direction. Like a neutrino. But the problem is that if the parrot was a countermover, he’d be flying backward and instead of dying he’d be coming alive… But, generally, it’s a good idea. A parrot-countermover would indeed know something about space. He would be living from the future and into the past. And a countermoving Janus could not, in fact, know what happened in our “yesterday”, because it would be his “tomorrow” – Scientific Russia).

The problem is that this is not solved by exploiting the usual laws known to us, let’s say it out loud, the laws of nature. Because the direction of the arrow of time is not the matter of property of an object or a device. And not even the consequence of another known physical law. We know perfectly well why the cup breaks and the tea cools down. The second law of thermodynamics is responsible for this. What we don’t know is what caused this second law. This, as far as I know, is a completely inexplicable thing. Therefore, it is formulated as a separate law of nature, and the question of its origin remains open.

Let’s get back to the cup, around which the arrow of time is directed opposite to ours. Without figuring out why and how this happened, we will still be able to tell how the cup will evolve. This is not at all like how Nolan’s fighters behave. Simply put, when running in inversion, the wind will blow into their faces.

But the most interesting aspect is related to the interaction of an object whose arrow of time is directed in one direction, with an object in which it is directed to another. I myself have spent many months pondering this question: can a lion eat a countermover? And here everything is not so obvious.

Unfortunately, we cannot influence this phenomenon by building some devices. The laws of nature are formulated, they are symmetrical. And we are not able to influence the initial data. Can we make the cup emerge from the pieces? Theoretically, we can take all the pieces and glue them together, but this will no longer be the subject of our conversation.

Do I understand correctly that the inverse entropy that appears in Nolan’s movie violates the laws of thermodynamics and cannot exist in reality?

−I would have put it more carefully. Reverse entropy in Nolan’s interpretation cannot exist, because it is simply illogical. But can there be a place in which the arrow of time is directed opposite to ours? I would say this: no law of nature prohibits this. Just imagine a galaxy isolated enough from us, in which the arrow of time is directed opposite to ours. From our point of view, the behavior of this galaxy would be completely unnatural: all photons flying to the stars and dying in the dark. And although all the equations of motion will be observed, it will look like a complete miracle, without running around and fighting.

In fact, we have nothing to argue about with the countermovers. We live in completely different worlds, for which there are no simple laws of interaction. The total world would be much more bizarre than Nolan’s. At the same time, the adventures in it would be completely different.

When the universe originated, the initial data was such that the arrow of time was directed either in one direction or the other. To the inhabitant of the universe, for whom the arrow of time is directed towards their future from the very beginning, everything seems logical and consistent. Time for them flows from the past to the future.

And life in the universe where the arrow of time was set by the initial conditions in the opposite way would seem to our observer completely wild and unnatural. At the same time, we couldn’t say that “the laws of nature are violated there,” because all mechanics are reversible. The rain that goes upwards, the circles on water forming droplets, and the droplets flying up into the cloud would surprise the observer. They’d think it’s a miracle. But none of these “miracles” violate the laws of mechanics. According to the laws of mechanics, a stone moves symmetrically: as it falls, so it flies up. The whole miracle rests only on the given initial conditions. And why they are set this way is still unknown.

A screencap from Tenet

A screencap from Tenet


The Feynman-Wheeler theory of the one-electron universe is also mentioned in the movie. According to the theory, a positron is an electron moving backward in time. And in the movie, as I understand it, this is realized when the main character interacts with himself in inversion.

− Indeed, Nolan tried to portray this concept in this way. But to me personally, the theory of the one-electron universe seems witty, and that’s all. As far as I know, it has not been developed into a full-fledged scientific idea.

What meaning do we put into the statement that the positron moves backward in time? Is this the meaning that we attach to the words “time machine,” “time travel,” “movement in time?” I think that the movement of the electron backward in time, which Wheeler and Feynman considered, and the concept of time travel are two completely different and, in my opinion, unrelated concepts. By changing “t” to “-t” in some expressions, talking about changing the symbol of time, we will not come closer to the realization of time travel. Such formulas have nothing to do with it.

But if instead of an electron we take a complex macroscopic system, and the letter “t” denotes entropy, then (if this system behaves like an electron) we will come to the Nolan interpretation: bullets pierce the windshield before the shot.

And if we assume that the second law of thermodynamics works, and locally all laws are observed, then we come to a real time machine, the idea of which was put forward in the 1980s by Kip S. Thorne and Michael S. Morris.

What is it about?

− We are talking about some imaginary situation that we would call time travel, but which does not require manipulations with the arrow of time. The most famous variant is a time machine formed by a moving wormhole. It is thanks to this concept that interest in time machines has revived in our time.

The idea suggests that if we take two wormholes that can be made to move, then in some 4-dimensional area around the wormhole we are threatened with a violation of causality.

It was later discovered that Einstein had pondered these questions, but he did not have a ready answer. But nevertheless, he was interested in understanding what physical considerations could prohibit violations of causality.

What ideas are being considered by the scientific community today?

− It mostly comes down to what I mentioned. That is, the existence of a time machine based on geometric properties. When the concept of space-time first appeared in the 1920s, it was applied exclusively to flat space-time. It is impossible to travel faster than light in flat space-time, as well as travel to the past. For many years, this remained the generally accepted opinion. People who repeated it from time to time did not pay attention to the fact that 15 years later the General Theory of Relativity was developed, in which the geometry of our space-time looks very complicated. And in such space-time, even the very question of traveling faster than light or backward in time (these problems are closely related) becomes very non-trivial. What does it mean to travel faster than light? How can we even determine what the speed of light is if space-time is curved, and not statically curved?

Then an understanding developed that if the geometry is not static, why should topology be constant? Why not imagine that it can also change? And this, to a first approximation, is the idea of a wormhole. Many scientists, beginning with the already mentioned Wheeler, were interested in wormholes and obtained interesting results. But still, at that time it was partly marginal since quite exotic things were proposed for the appearance of features in topology.

If we talk about Thorne, he dealt with the existence of a time machine under interesting circumstances. Astronomer Carl Sagan asked him to give a scientific justification for his Contact novel. Sagan asked Thorne if there was any scientifically acceptable way to bypass the light barrier. Then Thorne began to speculate what a real wormhole might look like, and what properties it would have.

In the process of searching for an answer to Sagan’s question, Thorne, and graduate student Morris, as if in hindsight, stumbled upon an obvious fact: two wormholes moving towards each other can generate a time machine. And since such an eminent scientist became engaged in what used to be a marginal direction, it literally blossomed. And to date, much has already become clear.

A wormhole is a hypothetical astrophysical object with a distortion of space and time, which in theory makes it possible to travel through different universes

A wormhole is a hypothetical astrophysical object with a distortion of space and time, which in theory makes it possible to travel through different universes

When we talk about time travel, we somehow encounter paradoxes. And one of the most famous is the grandfather paradox. Theoretical physicist Sean M. Carroll says that such a paradox is impossible in principle and that the past in this concept cannot be changed in any way. And even if some hypothetical grandson wants to go back in time and kill his grandfather, everything will prevent him, and he will not be able to implement his terrible plan. How do you explain this paradox?

− I agree with Carroll. Indeed, it is impossible to change the past, as well as the future. And this is not a deep conclusion, this is a completely trivial consideration. If you can change something by returning, as you think, to the past, then this is no longer a time machine, and you are not in the past, but in another world.

Left: Diagram of the "grandfather paradox". In addition to the area that makes up the time machine, time is directed from the bottom up.Right: A simplified version of the same paradox. The plane is cut along the dashed segments and the upper side of each cut is glued to the lower side of the other

Left: Diagram of the "grandfather paradox". In addition to the area that makes up the time machine, time is directed from the bottom up.

Right: A simplified version of the same paradox. The plane is cut along the dashed segments and the upper side of each cut is glued to the lower side of the other

Provided by S. Krasnikov

And what if there are no other worlds?

− Good. Imagine a world in which causality is violated, and there is a time machine. Will the grandson succeed in killing his grandfather? If the grandson is vicious enough and crack shot enough, why not? In fact, there is no paradox, there is confusion about how to explain the constant failures of the grandson?

Here I am proud to have formulated an explanation. It depends on which of the two varieties of the paradox we are discussing. The first is about a world where a time machine already exists, where a grandson lives, who grows up and decides: “I’ll kill my grandfather.” This is one story.

The second situation is when you have a wormhole at your disposal, but there is no time machine yet. The grandson grows up and decides: “I’ll kill someone.” He creates a time machine out of the wormhole, enters it, finds himself at the moment when he just entered the time machine, and shoots. These two paradoxes are different in that in the first case you have violence against free will. That is, for some reason the grandson cannot kill the grandfather, and we do not understand why. In the second case, all decisions about the murder were made at a time when there was no time machine yet. So, there is nothing specifically anthropogenic in this case. A grandson can be replaced with any other person or a robot. And it has nothing to do with free will.

Therefore, these paradoxes are solved in different ways. The paradox of the always-existing grandson (the first case) is solved very simply. To begin with, life inside a time machine is no picnic. It is quite possible that ordinary matter cannot exist there at all. But then you will say: “But there is a possibility that humanity will emerge there. It’s very small, but it’s there.” I’ll agree: “Okay, but what is the probability that a bloodthirsty grandson will arise in this universe?” You’ll say: “Negligible, but not zero.” I’ll say: “And since you admit that the existence of a grandson we need is extremely unlikely, then why to be surprised that we could not find one.” There is a whole chapter dedicated to this in my book, so the details can be found there. In this case, it is important to understand that there is actually no paradox. There is only a strange situation that does not arise independently. It is created by the one who asks the question. Simply put, we took a set of implausible assumptions and got an implausible consequence. That’s how it should be.

And what about the second case?

− Let me clarify that no matter how you influence the geometry of our universe, you cannot force it to form a time machine. It may or may not emerge. So, you sharpened the knife, loaded the gun, prepared with all your might. You took wormholes, moved their mouths towards each other to go there immediately when the wormhole appears, and it appears a year later and in a different place.


− And, moreover, it is provable.


− I’m generally very proud of this since I formulated and proved a geometric theorem. The bottom line is that if there were no closed time-like curves until some point, then they do not have to appear later.

Tell us more about the Krasnikov tube that you proposed and about further additions by scientists who subsequently proposed a model consisting of two tubes.

− In fact, I always tried to avoid the two-tube model. You use two tubes if you want to make a time machine yourself. But imagine that you are a simple pragmatic cosmonaut who wants to return from his expedition as soon as possible but does not want the emergence of parasitic time machines with bloodthirsty brothers. So, the Krasnikov tube is a kind of geometric phenomenon that allows for “faster-than-light” travel without violating causality. Imagine that you are flying on an ordinary photon spaceship, whose engine distorts the space-time behind you. Your device is moving fast, but not faster than light. After studying a star in a distant galaxy, you decide to go back in time. For example, you left in 2000. And from the point of view of an earthly observer, you find yourself in a distant galaxy in the year 3000. Using the Krasnikov tube, you eventually return to 2001. You don’t create causal loops, as it would be if you went back to 1999, but in a sense, you exceed the speed of light. Although locally you have never moved faster than light anywhere.

How is this implemented?

− Of course, this is a purely theoretical model. And with the current development of technology, it is not possible to implement it.

While you are flying on your ship from one star to another, along the way you blow up stars, “twist” and “tie” space-time. That is, you involve very powerful forces. According to Einstein’s equations, where strong fields, high densities, and high pressures are formed, the geometry of space-time changes. Hypothetically speaking, one can imagine that while you were flying, you twisted space-time so that, relatively speaking, a tunnel was formed, which, upon returning, allows you to cover distances in a short time.

Will humanity ever be able to create such spacecraft or time machines?

− As it turned out, we can’t deal with a simple virus, and here we talk about blowing up stars. Of course, humanity will not be able to create such a mechanism. After all, this would require fantastically large resources. But can the further development of science and technology lead to something alternative, but more realistic? - I hope so.

− And how did you become interested in the theories of time and eventually developed your own?

− Thanks to books. The first thing I learned to read were fairy tales, and the second was science fiction.

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