Time Travel Paradoxes regularly occupy the minds of not only scientists who comprehend the possible consequences of such a movement (albeit hypothetical), but also people who are completely far from science. Surely you have argued with your friends more than once about what would happen if you see yourself in the past - like many science fiction authors, writers and directors. Today, a film starring Ethan Hawke, Time Patrol, based on a story by one of the best science fiction writers of all time, Robert Heinlein, was released. This year has already seen several successful films dealing with the theme of time, such as Interstellar or Edge of Tomorrow. We decided to speculate on what potential dangers might await the heroes of temporary sci-fi, from the murder of their predecessors to reality splits.

Text: Ivan Sorokin

The paradox of the murdered grandfather

The most common, and at the same time the most understandable of the paradoxes that overtake a time traveler. The answer to the question “what will happen if you kill your own grandfather (father, mother, etc.) in the past?” may sound different - the most popular outcome is the emergence of a parallel time sequence, erasing the culprit from history. In any case, for the temponaut himself (this word, by analogy with “cosmonaut” and “astronaut,” sometimes refers to the pilot of a time machine), this does not bode absolutely nothing good.

Movie example: The entire story of teenager Marty McFly accidentally traveling back to 1955 is built around avoiding an analogue of this paradox. Having accidentally conquered his own mother, Marty begins to literally disappear - first from photographs, and then from tangible reality. There are many reasons why the first film in the Back to the Future trilogy is an absolute classic, but one of them is how carefully the script avoids the idea of ​​potential incest. Of course, in terms of the scale of the plan, this example can hardly compare with the famous plot from Futurama, as a result of which Fry becomes his own grandfather, accidentally killing the one who was supposed to become this grandfather; As a result, this event had consequences that affected literally the entire universe of the animated series.

Pulling yourself by your hair

The second most common plot in time travel movies: by traveling to a glorious past from a terrible future and trying to change it, the hero ends up causing his own (or everyone's) troubles. Something similar can happen in a positive context: the fairytale assistant who guides the plot turns out to be the hero himself, who came from the future and ensures the correct course of events. This logic of development of what is happening can hardly be called a paradox: the so-called time loop here is closed and everything happens exactly as it should be - but in the context of the interaction of cause and effect, the human brain still cannot help but perceive this situation as paradoxical. This technique, as you might guess, is named after Baron Munchausen, who pulls himself out of the swamp.

Movie example: The space epic "Interstellar" (spoiler alert) uses a huge number of plot twists of varying degrees of predictability, but the emergence of a "closed loop" is almost the main twist: Christopher Nolan's humanistic message that love is stronger than gravity only receives its final form in at the very end of the film, when it turns out that the spirit of the bookshelf protecting the astrophysicist played by Jessica Chastain was the hero Matthew McConaughey, sending messages to the past from the depths of a black hole.

The Bill Murray Paradox

Some time ago, stories about looped time loops already became a separate subgenre of sci-fi about temponauts - both in literature and in cinema. It is not at all surprising that almost any such work is automatically compared to Groundhog Day, which over the years has come to be perceived not only as a parable about existential despair and the desire to appreciate life, but also as an entertaining study of the possibilities of behavior and self-development in extremely limited conditions. The main paradox here lies not in the very presence of the loop (the nature of this process is not always touched upon in such plots), but in the incredible memory of the temponaut (it is she who is capable of providing any movement in the plot) and the equally incredible inertia of those around him to all evidence that the position of the protagonist is truly unique.

Movie example: Detractors dubbed “Edge of Tomorrow” something like “Groundhog Day with aliens,” but in fact the script for one of the best science fiction films of the year (which, by the way, was super successful for this genre) handles its loops much more delicately. The paradox of perfect memory is bypassed here as a result of the fact that the main character records and thinks through his moves, interacting with other characters, and the problem of empathy is solved due to the fact that there is another character in the film who at some point had similar skills. By the way, the occurrence of the loop is also explained here.

Frustrated expectations

The problem of results not meeting expectations is always present in our lives - but in the case of time travel, it can hurt especially strongly. This plot device is usually used as an embodiment of the adage "Be careful what you wish for" and works according to Murphy's Law: if events can develop in the worst possible way, then they will. Since it is difficult to assume that a time traveler is able to estimate in advance what the tree of possible outcomes of his or her actions will look like, the viewer rarely doubts the plausibility of such plots.

Movie example: One of the saddest scenes in the recent rom-com Future Boyfriend goes like this: Domhnall Gleeson's temponaut tries to travel back to a time before his child was born and ends up coming home to a complete stranger. This can be corrected, but as a result of such a collision, the hero realizes that his movements along the temporary arrow are subject to more restrictions than he previously thought.

Aristotle with a smartphone

This paradox represents a special case of the popular science fiction trope of "advanced technology in a backward world" - only the "world" here is not another planet, but our own past. It is not difficult to guess what the introduction of a conventional pistol into the world of conventional batons is fraught with: the deification of aliens from the future, destructive violence, a change in the way of life in a particular community, and the like.

Movie example: Of course, the most striking example of the destructive influence of such an invasion should be the Terminator franchise: it was the appearance of androids in the USA in the 1980s that ultimately led to the emergence of the artificial intelligence Skynet, which literally destroyed humanity. Moreover, the main reason for the creation of Skynet is given by the protagonists Kyle Reese and Sarah Connor, because of whose actions the main Terminator chip falls into the hands of Cyberdyne, from whose depths Skynet eventually emerges.

The heavy lot of the rememberer

What happens to the memory of a temponaut when, as a result of his actions, the time arrow itself changes? The gigantic stress that must inevitably arise in such a case is often ignored by science fiction authors, but the ambiguity of the hero’s position cannot be ignored. There are a lot of questions here (and all of them do not have an unambiguous answer - to adequately check the answers to them you need to literally get your hands on a time machine): does the temponaut remember all the events or only part of them? Do two parallel universes coexist in the temponaut’s memory? Does he perceive his changed friends and relatives as different people? What happens if you tell people from the new timeline in detail about their counterparts in the previous timeline?

Movie example: There is at least one example of this condition in almost every time travel movie; from the recent one, Wolverine from the last series of “X-Men” immediately comes to mind. The idea that, as a result of the success of the operation, Hugh Jackman's character will be the only one who can remember the original (extremely grim) development of events is voiced several times in the film; As a result, Wolverine is so happy to see all his friends again that memories that can traumatize even a person with an adamantium skeleton fade into the background.

Scary you #2

Neuroscientists are quite actively studying how people perceive their appearance; An important aspect of this is the reaction to twins and doubles. Typically, such meetings are characterized by an increased level of anxiety, which is not surprising: the brain ceases to adequately perceive the position in space and begins to confuse external and internal signals. Now imagine how a person must feel when he sees himself - but at a different age.

Movie example: The interaction of the main character with himself is perfectly played out in Rian Johnson’s film “Looper,” where the young Joseph Simmons is played by Joseph Gordon-Levitt in sly makeup, and the older one, who arrived from the near future, is played by Bruce Willis. Cognitive discomfort and the inability to establish normal contact is one of the important themes of the film.

Unfulfilled predictions

Your opinion about whether such events are paradoxical depends directly on whether you personally adhere to a deterministic model of the universe. If there is no free will as such, then a skilled temponaut can calmly bet huge amounts of money on various sporting events, predict the results of elections and award ceremonies, invest in shares of the right companies, solve crimes - and so on. If, as usually happens in films about time travel, the actions of a temponaut are still capable of changing the future, then the function and role of predictions based on a kind of insight from an alien from the future are as ambiguous as in the case of those predictions based solely based on logic and past experience (that is, similar to those that are used now).

Movie example: Despite the fact that “Minority Report” features only “mental” time travel, the plot of this film serves as a vivid illustration of both models of the universe: both deterministic and taking into account free will. The plot revolves around the prediction of crimes not yet committed with the help of “clairvoyants” who are able to visualize the intentions of potential killers (a situation of extreme determinism). Towards the end of the film, it turns out that visions are still capable of changing over time - accordingly, a person, to some extent, determines his own destiny.

I was yesterday to tomorrow

Most of the world's major languages ​​have several tenses to denote events that occur in the past, present, and future. But what about the temponaut, who yesterday could observe the death of the Sun, and today he is already in the company of dinosaurs? What tenses to use in speech and writing? In Russian, English, Japanese and many other languages, such functionality is simply absent - and you have to get out of it in such a way that something comical inevitably happens.

Movie example: Doctor Who, of course, belongs to the field of television, not cinema (although the list of works related to the franchise includes several television films), but it is impossible not to mention the series here. The Doctor’s confused use of different tenses became a source of mockery back in pre-Internet times, and after the revival of the series in the mid-2000s, the authors decided to deliberately emphasize this detail: now the on-screen Doctor is able to connect his non-linear perception of time with the peculiarities of the language (and at the same time laugh at the resulting phrases) .

Multiverse

The most fundamental paradox of time travel is not for nothing that it is directly related to a serious conceptual debate in quantum mechanics, based on the acceptance or rejection of the concept of the “multiverse” (that is, the collection of multiple universes). What actually needs to happen the moment you “change the future”? Do you remain yourself - or do you become a copy of yourself in a different timeline (and, accordingly, in a different universe)? Do all the timelines coexist in parallel - so that you just jump from one to another? If the number of decisions that change the course of events is infinite, then is the number of parallel universes infinite? Does this mean that the multiverse is infinite in size?

Movie example: The idea of ​​multiple parallel timelines is usually not adequately represented in films for one simple reason: writers and directors become afraid that no one will understand them. But Shane Carratt, the author of The Detonator, is not like that: understanding the plot of this film, where one non-linearity is superimposed on another, and to fully explain the movements of the characters in time requires drawing a diagram of the multiverse with intersecting timelines, is possible only after considerable effort.

Back in June, Australian researchers from the University of Queensland published an article in the journal Nature, in which they once again tried to answer the question that tormented a galaxy of theoretical physicists throughout the 20th century - whether time travel is possible. We decided to figure out what modern scientists face when trying to get to the bottom of the truth.

The so-called murdered grandfather paradox, adopted by all skeptics, until this summer was, perhaps, the main argument in the disputes between science fiction writers, physics professors and schoolchildren who had seen enough of “Back to the Future” and “Futurama”. First described in 1943 by the writer Rene Barjavel, its principle is as follows: a certain subject invents a time machine, goes back in time, finds his grandfather and kills him. As a result, for obvious reasons, the main character would never have been born, which means he would not have invented a time machine, would not have traveled through time and would not have met his ancestor. It turns out to be a vicious circle, where each subsequent action contradicts the previous one. Nevertheless, most popular science theories about time travel are based precisely on the fact that a traveler who finds himself in the past can change it, risking in his “present” all the things and events that have become familiar, but with the exception of the fact of creating a time machine and your journey itself. Thus, the representative of classic science fiction literature, Ray Bradbury, in “A Sound of Thunder” tells us about tourists who accidentally crushed a butterfly, which changed their modern world beyond recognition, but for unknown reasons, leaving them the same as before the trip.

Another opponent of the theories of time travel, or rather travel to the past, is Stephen Hawking. Among dozens of his scientific works, directly or indirectly denying the possibility of such temporary movements, he conducted an experiment, which, as he himself believes, once again proved the impossibility of the latter. In 2009, the physicist decided to throw a party. He organized everything at the highest level: buffet table, balloons, music. However, none of the guests he invited came. That's because Stephen only sent out invitations after the party was over. So, in his opinion, if it were possible to travel to the past, guests would be able to return to the past and delight him with their presence. However, the physicist did not take into account that many of the invitees would hardly want to waste their time on this kind of event, having the opportunity to see much more interesting events. Hawking also says that if such travel were possible, then we would certainly witness tourists in time, which, however, no one has seen yet. But at the same time, neither modern quantum physics nor the theory of relativity can exclude the possibility of this kind of travel.

At the same time, the physicist does not deny the possibility of traveling to the future. To do this, according to the professor, it is necessary to reach a speed close to the speed of light on any spacecraft. Then time on the ship, compared to time on Earth, will pass much slower. And, returning to Earth, we will see an aged world.

David Deutsch has talked about how the uncertainty principle, which governs quantum particles such as photons, may leave a lot of room for avoiding the murdered grandfather paradox.

Nevertheless, scientists from Australia at the quantum level tried to prove the inconsistency of the paradox of the murdered grandfather, with their research giving rise to new thoughts about the possibility of such travel. The authors of the experiment, Tim Ralph, Martin Ringbauer and their colleagues, claim that they have successfully simulated the behavior of a single photon, as if it had gone back in time and began to interact with its own copy from the past.

Their experiment was based on the theory of British physicist David Deutch, who in 1991, in his book “The Structure of Reality”, tries to rethink the paradox of the murdered grandfather at the quantum level, coming to a complex conclusion: time travel is possible and is something in between time travel and travel between universes. The object, traveling into the past, is divided and sent to two parallel universes. In one of them, the grandfather is actually killed, but in the other he remains safe and sound. David Deutsch has talked about how the uncertainty principle, which governs quantum particles such as photons, may leave a lot of room for avoiding the murdered grandfather paradox.

Taking as a basis Deutsch’s thoughts, which are sometimes more difficult to understand than a completely unfamiliar language, Ringbauer says that in a quantum system everything is somewhat different, since the same object in it can exist in several states at once, including in superposition.

Australian scientists have recreated at the quantum level inside closed time-like curves the behavior of a single photon in the past and present. Of course, scientists did not send a photon to the past, but only simulated it by creating a copy of its previous state and sending it to the photon of the present. During experiments, observing their behavior, Australians came to the conclusion that time travel is more than real at the quantum level. However, the practical application of the results of their experiments, at least at the atomic level, is not yet possible.

Another proponent of time travel, wormholes and quantum physics, American scientist Seth Lloyd talks about quantum teleportation. The scientist deduced the possibility of building a time machine by also studying closed timelike curves from the point of view of quantum physics. To do this, Lloyd crossed the latter with the theory of post-selection, or subsequent selection. In probability theory, it determines the possibility of one event given that another has already occurred. In quantum-level computing, post-selection means selecting the correct solution from a large number of possible ones. Next, Lloyd adds the theory of quantum teleportation to his thoughts - and the time machine is ready. Simply put, an American scientist came up with the following system at the quantum level: a quantum can teleport into the past, but a quantum cannot kill his grandfather. For example, he will buy blank cartridges in the store instead of live ones, or he will simply miss. In general, according to scientists, nature will still not allow paradoxes, but on the other hand, we have become one step closer to time travel in the form in which science fiction writers show it to us.

What happened at the Palace of Versailles in August 1901?

In August 1901, two English teachers, 55-year-old Anna Moberly and 38-year-old Eleanor Jourdain, were on vacation in France. Both women were teachers at St Hugh's College, Oxford. Anna Moberly was headmistress of the college, and Eleanor Jourdain would succeed her in this post fourteen years later. With Baedeker's tourist guides in hand, they decided to explore the Palace of Versailles, the center of political power in France until the French Revolution in 1789. They also decided to visit the Petit Trianon, a small castle built by Louis XVI for his young wife Queen Marie Antoinette, and much loved by her.

Moberly and Jourdain got a little lost while searching for the castle, and it was during this interlude that the ladies made history. They met several people dressed in 1789 period clothing and passed several structures that had not existed since 1789. Their unexpected visit 112 years into the past ended with a meeting with Marie Antoinette, sketching while sitting on the steps of the castle. Then Jourdain and Moberly suddenly found themselves once again in 1901.

Interest in this story is fueled by the unconditional authority of eyewitnesses. Very often when it comes to strange and unexplained phenomena , we hear that his witness or witnesses were famous personalities who enjoy the respect and trust of their contemporaries, therefore it is considered incredible that such people could make mistakes or invent something, and even more so, deliberately lie. The story of the Versailles time paradox is just such a case. Should we accept that this incredible event actually took place, based on the authority of Moberly and Jourdain? Whether you have heard this story before or not, it serves as a good example of how to treat incidents in which the main evidence is considered to be the testimony of a reputable eyewitness and his impeccable reputation.

Writer Nell Rose observed: “They were not deceivers; there was no benefit for them to make up this story. Moreover, this story could seriously damage their reputation.”

Moberly and Jourdain were schoolteachers, which also added to their authority in the eyes of their contemporaries. In the same way, today we believe the testimonies of pilots or astronauts who allegedly saw a UFO . Of course, a pilot will not confuse a UFO with anything, and, of course, if schoolteachers think that they have been in the past, then it is so, isn’t it? No it is not true. An authoritative witness does not necessarily have to be a deceiver - perhaps he was simply mistaken, and his perception played a cruel joke on him, or his version of what happened has reached us in an altered form. One doesn't have to question the professional credentials of Moberly and Jourdain to suggest that the story in the annals of urban legends is not a tale of time travel. in our understanding, and that everything happened exactly as the English women described. It is human nature to make mistakes - including pilots, including scientists, including English teachers.

Researchers of the Versailles time paradox have put forward two main versions of what happened to the English tourists, which in a simplified form can be stated as follows: firstly, Moberly and Jourdain accidentally wandered into the territory where the historical reconstruction was taking place, and secondly, they were at the mercy of a kind of general misconception. But in order to properly understand these explanations, you need to know who originally proposed them and why, as well as what details of this story, unknown to the general public, served as the basis for these versions. From this moment on, the Versailles time paradox turns from a curious anecdote, of which there are many, into a story completely unique in its strangeness.

Black holes can suddenly appear in many different astrophysical objects. Perhaps we will someday be able to discover black holes weighing from 2-3 to 100 solar masses, formed as a result of the gravitational collapse of stars. Black holes with masses of several thousand solar masses can be found at the center of massive globular star clusters; There is an opinion that supermassive black holes of several million and even billions of solar masses may be the nuclei of active galaxies, in particular radio galaxies, or such mysterious objects as quasars. At the other end of the mass scale are primordial black holes, the mass of which can take on very different values ​​in the interval limited below by a mass of about a billion tons. It has been suggested that a large amount of the invisible matter of the Universe may be contained in black holes wandering in intergalactic space. If there are many such holes, then their gravitational influence can significantly affect the course of development of the Universe.

Black holes have so often been used to “explain” a wide variety of astronomical phenomena that there is concern that they might become the only way to solve astrophysical problems. Of course, in some cases the use of ideas about black holes is quite justified.

Space-time paradoxes

Theories about time travel always remain one of the most impressive, following developments in the field of teleportation, torsion fields and antigravity.

Before Einstein, only writers spoke about time travel. In physics, it has become fashionable to think about the possibility of such movements, following Einstein. From that very moment on, the phenomenon of time travel began to be explained in terms of the action of the space-time continuum.

A corridor in time can also be formed by purely “natural” phenomena: black holes, tunnels, cosmic strings, and so on. The most likely candidate for a “corridor of time” is black holes, about the nature of which very little is still known.

A black hole is surrounded by a gravitational field in which bodies reach the speed of light. It is assumed that in the depths of a black hole - presumably at the center, at the so-called singular point - the laws of physics cease to apply, and space and time coordinates are, roughly speaking, reversed, and travel in space becomes time travel. In addition, physicists have suggested that if there are black holes that suck in everything in the impact zone, then somewhere there, in the “core” of the hole, there must be some kind of “white hole” that pushes out matter with an equally crushing force.

In the center of a black hole there is a corridor where space and time change their characteristics. However, there is one “but”: before the body reaches the zone where the laws of traditional physics cease to apply, it will be destroyed. This point of view was expressed by California Institute of Technology physicist Kip Thorne, author of the monograph “Black Holes and the Warp of Time.”

An interesting theory about methods of time travel belongs to Richard Goth, a physicist from Princeton. He suggested the existence of certain comic strings that were formed in the early stages of the formation of the universe. According to string theory, all microparticles are formed by tiny strings closed in loops and are under a monstrous tension of hundreds of millions of tons. Their thickness is much smaller than the size of an atom, but the colossal gravitational force with which they act on objects falling within their zone of influence accelerates them to colossal speed. The combination of strings or the juxtaposition of a string and a black hole can create a closed corridor with a curved space-time continuum, which could be used for time travel. There are other, less exotic ways to “cheat” time. This will be easiest for astronauts to do. Staying, for example, on Mercury for 30 years means that the astronaut will return to our planet younger than if he had remained on Earth, so how Mercury revolves around the Sun a little faster than the Earth. However, here the linear progression of time is preserved, and in its pure form this phenomenon should not be called time travel. Moreover, it has been recorded that the astronauts carried into orbit by the Shuttle are already ahead of the Earth. ” time for several nanoseconds, although, to put it mildly, they are far from the speed of light.

In addition to technical problems, physicists are also discussing possible time conflicts. The real problem that can await travelers is time paradoxes. There will be many of them, and they will all be associated with a possible impact on the course of events that have already occurred - the “grandfather paradox,” for example. Most theorists agreed that any impact on the course of something perfect creates a new, parallel reality or another “world line”, not at all not interfering with the existence of the “original”. And there will be exactly as many such “parallelities” as are necessary for the consistent existence of each of them. In general, it should be noted that reasoning, discussions and lectures about the nature of time and the possibility of time travel still remain a favorite pastime for serious physicists - a kind of intellectual fun. At one time, NASA astrophysicist Carl Sagan, in response to Stephen Hawking’s statement that if time travel were possible, we would be full of “guys from the future,” retorted that there are, there are at least a dozen ways to refute this statement.

Firstly, a time machine, for example, can only transfer to the future. Secondly, a time machine can only travel to the recent past, and we - again, for example - “too long ago.” Thirdly, our descendants from the future can only travel to those ancestors who already have a machine, and so on further, be that as it may, the hypothetical possibility of such travel remains, and the most caustic skeptics are unable to refute it. Moreover, theories are theories, but practical developments are still being carried out, and with some success.

I doubt that any phenomenon, real or fictitious, has given rise to more perplexing, tortuous, and incredibly sterile philosophical pursuits than time travel. (Some of its possible competitors, such as determinism and free will, are somehow related to the argument against time travel.) In his classic Introduction to Philosophical Analysis, John Hospers asks: “Is it logically possible to go back back in time to, say, 3000 BC. e., and help the Egyptians build the pyramids? We need to remain vigilant on this issue."

It's as easy to say - we usually use the same words when we talk about time and space - as it is easy to imagine. “Besides, H. G. Wells introduced it in The Time Machine (1895), and every reader imagines it with him.” (Hospers misremembers The Time Machine: “A man from 1900 pulls the lever of a machine and suddenly finds himself in the middle of a world several centuries earlier.”) To be fair, Hospers was something of an eccentric who was given the unusual honor for a philosopher: to receive himself one electoral vote in the election of President of the United States. But his book, first published in 1953, remained the standard for 40 years, going through 4 reprints.

IMPOSSIBLE MACHINE: In H.G. Wells' 1895 novel The Time Machine, an inventor travels 800,000 years into the future. Still from the 1960 film adaptation. Hulton Archive/Getty Images

He emphatically answers “no” to this rhetorical question. Wells-style time travel is not only impossible, but logically impossible. These are contradictions in terms. In an argument that runs for four long pages, Hospers proves this by force of persuasion.

“How can we be in the 20th century AD? e. and in the 30th century BC. e. at the same time? There is already one contradiction in this... From a logical point of view, No the opportunity to be in different centuries at the same time.” You may (and Hospers may not) pause and consider whether there is a trap hidden in that decidedly general phrase: “at the same time.” The present and the past are different times, therefore they are neither the same time nor V the same time. Q.E.D. It was surprisingly easy.

However, the point of time travel fiction is that lucky time travelers have their own clocks. Their time continues to move forward as they move into another time for the Universe as a whole. Hospers sees this, but doesn't accept it: "People can move backwards in space, but what would it literally mean to 'move backwards in time'?"

And if you continue to live, what can you do except become a day older every day? Isn't “getting younger every day” a contradiction in terms? Unless, of course, this is said figuratively, for example, “My dear, you are only getting younger every day,” where it is also accepted by default that a person, although looks younger every day, anyway getting older every day?

(He appears to be unaware of the F. Scott Fitzgerald story in which Benjamin Button does just that. Born septuagenarian, Benjamin grows younger every year, until he is infancy and oblivion. Fitzgerald recognized the logical impossibility of this. The story has a great legacy .)

Timing is obviously simple for Hospers. If you imagine that one day you were in the twentieth century, and the next day a time machine takes you to Ancient Egypt, he wittily remarks: “Isn’t there another contradiction here? The next day after January 1, 1969 is January 2, 1969. The next day after Tuesday is Wednesday (this has been proven analytically: “Wednesday” is defined as the day following Tuesday),” and so on. And he also has a final argument, the final nail in the time traveler’s logical coffin. The pyramids were built before you were born. You didn't help. You didn't even look. “This event cannot be changed,” Hospers writes. - You can't change the past. This is the key point: the past is what happened, and you cannot stop what happened from happening." It's still a textbook of analytic philosophy, but you can almost hear the author shouting:

All the royal cavalry and all the royal army could not have ensured that what happened did not happen, for this is a logical impossibility. When you say that it is logically possible for you to go back (literally) to 3000 BC. e. and help build the pyramids, you are faced with the question: did you help build the pyramids or not? When it first happened, you didn't help: you weren't there, you weren't born yet, it was before you even came on stage.

Admit it. You didn't help build the pyramids. This is a fact, but is it logical? Not every logician finds these syllogisms self-evident. Some things cannot be proven or disproved by logic. Hospers writes more quirkily than you might think, starting with the word time. And in the end he openly accepts for granted the thing he is trying to prove. “The whole so-called situation is riddled with contradictions,” he concludes. “When we say that we can imagine, we are simply playing with words, but logically words have nothing to describe.”

Kurt Gödel begs to differ. He was the leading logician of the century, a logician whose discoveries made it impossible to even think about logic in the old way. And he knew how to deal with paradoxes.

Where Hospers's logical statement sounded like "it is logically impossible to get from January 1 to any other day than January 2 of the same year," Gödel, working in a different system, expressed himself something like this:

“The fact that there is no parametric system of three mutually perpendicular planes on the abscissa axes directly follows from the necessary and sufficient condition that the vector field v in four-dimensional space must satisfy if the existence of a three-dimensional mutually perpendicular system on the field vectors is possible.

He talked about world axes in Einstein's space-time continuum. This was in 1949. Gödel published his greatest work 18 years earlier, when he was a 25-year-old scientist in Vienna. It was a mathematical proof that once and for all destroyed any hope that logic or mathematics could present a finite and constant system of axioms, clearly true or false. Gödel's incompleteness theorems were built on a paradox and are left with an even greater paradox: we certainly know that complete certainty is unattainable for us.

Walk through time: Albert Einstein (right) and Kurt Gödel during one of their famous walks. On his 70th birthday, Gödel showed Einstein calculations according to which relativity allows for cyclical time. The Life Picture Collection/Getty Images

Now Gödel was thinking about time - “that mysterious and contradictory concept, which, on the other hand, forms the basis of the existence of the world and ourselves.” Having fled Vienna after the Anschluss via the Trans-Siberian Railway, he took a job at the Princeton Institute for Advanced Study, where his friendship with Einstein, which began in the early 1930s, became even stronger. Their walks together from Fuld Hall to Alden Farm, watched with envy by their colleagues, became legendary. In his later years, Einstein confided to someone that he continued to go to the Institute mainly so that he could walk home with Gödel.

On Einstein's 70th birthday in 1949, a friend showed him an astonishing calculation: his field equations from general relativity turned out to allow for the possibility of "universes" in which time is cyclical - or, more precisely, universes in which some world lines form loops. These are “closed time lines”, or, as a modern physicist would say, closed time curves (CTCs). These are looped highways without access roads. A time curve is a set of points separated only by time: one place, different time. A closed time curve loops back on itself and therefore violates the usual rules of cause and effect: events themselves become their own cause. (The Universe itself in this case would be completely rotating, of which astronomers have found no evidence, and according to Gödel's calculations, the spin cycle would be extremely long - billions of light years - but these details are rarely mentioned.)

If the attention paid to SVKs is disproportionate to their importance or likelihood, Stephen Hawking knows why: "Scientists working in this field are forced to hide their real interest by using technical terms like SVKs, which are actually code words for time travel." . And time travel is cool. Even for a pathologically shy Austrian logician with paranoid tendencies. Almost buried in this bunch of calculations are the words of Gödel, written in seemingly understandable language:

“In particular, if P, Q are any two points on the world line of matter, and P precedes Q on this line, there is a time curve connecting P and Q on which Q precedes P, i.e., in such worlds it is theoretically possible travel into the past or otherwise change the past.”

Notice, by the way, how easy it has become for physicists and mathematicians to talk about alternative universes. “In such worlds...” writes Gödel. The title of his paper, published in the Reviews of Modern Physics, was “Solutions of Einstein's Gravitational Field Equations,” and the “solution” here is nothing more than a possible universe. “All cosmological solutions with non-zero matter density,” he writes, meaning “all possible non-empty universes.” “In this work I propose a solution” = “Here is a possible universe for you.” But does this possible universe actually exist? Do we live in it?

Gödel liked to think so. Freeman Dyson, then a young physicist at the Institute, told me many years later that Gödel often asked him: “Well, has my theory been proven?” Today there are physicists who will tell you that if the universe does not contradict the laws of physics, then it exists. A priori. Time travel is possible.

At point t1 T talks to himself in the past.
At t2, T boards a rocket to travel back in time.
Let t1=1950, t2=1974.

Not the most original start, but Dwyer is a philosopher who publishes in Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, a far cry from Tall Tales. However, Dwyer is well prepared in this area:

“There are many stories in science fiction that revolve around certain people using complex mechanical devices to travel back in time.”

In addition to reading stories, he also reads philosophical literature, starting with Hospers' proof of the impossibility of time travel. He thinks Hospers is simply mistaken. Reichenbach is also mistaken (this is Hans Reichenbach, author of the book “The Direction of Time”), as is Čapek (Milic Čapek, “Time and Relativity: Arguments for the Theory of Becoming”). Reichenbach argued for the possibility of meetings with oneself - when the “young self” meets the “old self”, for which “the same event occurs a second time,” and although this seems paradoxical, there is logic in it. Dwyer disagrees: “It is talk like this that has created such confusion in the literature.” Capek draws diagrams with “impossible” Gödel world lines. The same can be said about Swinburne, Withrow, Stein, Horowitz (“Horowitz certainly creates his own problems”), and even about Gödel himself, who misrepresent his own theory.

According to Dwyer, they all make the same mistake. They imagine that a traveler can change the past. This is impossible. Dwyer can come to terms with other difficulties of time travel: reverse causation (effects precede causes) and multiplication of entities (travelers and their time machines meeting their counterparts). But not with this one. “Whatever time travel implies, changing the past is impossible in it.” Consider an old T who travels through a Gödel loop from 1974 to 1950 and meets a young T there.

This meeting, of course, is recorded twice in the traveler's memory; if young T's reaction to meeting himself can be fearful, skeptical, joyful, etc., old T, in turn, may or may not remember his feelings when in his youth he met a person who called himself the same person in the future . Now, of course, it would be illogical to say that T can do something to young T because his own memory tells him that it did not happen to him.

Why can't T go back and kill his grandfather? Because he didn't. It's so simple. Except, of course, things are never that simple.

Robert Heinlein, who created many Bob Wilsons in 1939 punching each other before explaining the mysteries of time travel, returned to the paradoxical possibilities again 20 years later in a story that surpassed its predecessors. It was entitled "You're All Zombies" and published in Fantasy and Science Fiction after a Playboy editor rejected it because the sex in it made him sick (this was 1959). The story has a transgender subplot, a bit progressive for the era, but necessary to perform the equivalent of a quadruple axel in time travel: the main character is his own mother, father, son and daughter. The title is also a joke: "I know where I came from - but where did all you zombies come from?"

A paradox made real: In some ways, a time travel loop is similar to a spatial paradox, such as this one created by artist Oskar Ruthersvard.

Can anyone beat this? In purely quantitative terms, of course. In 1973, David Gerrold, as a young television writer on the short-lived (and later long-running) Star Trek, published his novel Dubbed, about a student named Daniel who receives the Time Belt from the mysterious "Uncle Jim" along with instructions. Uncle Jim convinces him to keep a journal, which turns out to be handy because life quickly becomes confusing. We soon find it hard to keep track of the accordion-wide cast of characters, including Don, Diana, Danny, Donna, ultra-Don and Aunt Jane - all of whom (as if you didn't know it) are one person on a twisting rollercoaster of time.

There are many variations on this theme. The number of paradoxes is increasing almost as fast as the number of time travelers, but when you take a closer look, they turn out to be the same. It's all one paradox in different costumes to suit the occasion. It is sometimes called the shoelace paradox, after Heinlein, whose Bob Wilson dragged himself into the future by his own shoelaces. Or the ontological paradox, the riddle of being and becoming, also known as “Who’s Your Daddy?” People and objects (pocket watches, notebooks) exist without reason or origin. Jane from You're All Zombies is her own mother and father, begging the question of where her genes came from. Or: in 1935, an American stockbroker finds Wells's time machine ("polished ivory and bright nickel") hidden in the palm leaves of the Cambodian jungle ("mysterious land"); he presses the lever and travels to 1925, where the car is polished and hidden in palm leaves. This is its life cycle: a closed ten-year time bend. “But where did it come from in the first place?” - the broker asks the yellow-robed Buddhist. The sage explains to him like a fool: “There was never any ‘originally’.”

Some of the most clever loops involve simply information. "Mr. Buñuel, I had a movie idea for you." A book about how to build a time machine comes from the future. See also: paradox of predestination. Trying to change something that needs to happen somehow helps it happen. In The Terminator (1984), a cyborg assassin (played with a strange Austrian accent by 37-year-old bodybuilder Arnold Schwarzenegger) goes back in time to kill a woman before she gives birth to a child destined to lead a resistance movement in the future; after the failure of a cyborg, debris remains that makes its creation possible; and so on.

In a sense, of course, the paradox of predestination appeared several thousand years before time travel. Laius, hoping to break the prophecy of his murder, leaves the infant Oedipus in the mountains to die, but unfortunately his plan backfires. The idea of ​​a self-fulfilling prophecy is old, although the name is new, coined by sociologist Robert Merton in 1949 to describe a very real phenomenon: “a false definition of a situation that causes new behavior that turns the original false belief into reality.” (For example, a warning about a gasoline shortage leads to panic buying, resulting in a gasoline shortage.) People have always wondered if they could escape their fate. Only now, in the era of time travel, do we ask ourselves whether we can change the past.

All paradoxes are time loops. They all force us to think about cause and effect. Can the effect precede the cause? Of course not. Obviously. A-priory. “A cause is an object followed by another...” Repeated David Hume. If your child gets a measles vaccine and then has a seizure, the vaccine may have caused the seizure. The only thing everyone knows for sure is that the seizure was not the cause of the vaccine.

But we are not very good at understanding why. The first person we know to have attempted to analyze cause and effect using logical reasoning was Aristotle, who created levels of complexity that have caused confusion ever since. He distinguished four distinct types of causes, which can be called (allowing for the impossibility of translation between millennia): action, form, matter and purpose. In some of them it is difficult to recognize the reasons. The efficient cause of sculpture is the sculptor, but the material cause is the marble. Both are needed for the sculpture to exist. The final reason is purpose, that is, for example, beauty. From a chronological point of view, final causes usually come into play later. What was the cause of the explosion: dynamite? spark? robber? safe hacking? Such thoughts seem petty to modern people. (On the other hand, some professionals believe that Aristotle's vocabulary was woefully primitive. They would not like to discuss causation without mentioning immanence, transcendence, individuation, and arity, hybrid causes, probabilistic causes, and causal chains.) In any case, we It is worth remembering that nothing, upon closer examination, has a single, unambiguous, indisputable cause.

Would you accept the assumption that the reason for the existence of the stone is the same stone a moment earlier?

“It seems that all reasoning about establishing a fact is based on relations Causes and Effects" states Hume, but he realized that these reasonings were never easy or certain. Is it the sun that causes the stone to heat up? Is insult the cause of someone's anger? Only one thing can be said for sure: “The cause is an object followed by another...” If the effect not necessary follows from the cause, was it even a cause? These debates echo through the corridors of philosophy, and continue to echo despite Bertrand Russell's attempt in 1913 to settle the matter once and for all, for which he turned to modern science. “It is strange that in advanced sciences such as gravitational astronomy the word ‘cause’ never appears,” he wrote. Now it's the philosophers' turn. “The reason physicists have given up looking for causes is that, in fact, there are none. I believe that the law of causation, like much that is heard among philosophers, is just a relic of a bygone era, surviving, like the monarchy, only because it was mistakenly considered harmless.”

Russell had in mind the hyper-Newtonian view of science described a century earlier by Laplace - a bonded universe - in which everything that exists is bound together by the mechanisms of physical laws. Laplace spoke of the past as reason future, but if the whole mechanism chugs along as one, why should we think that any single gear or lever will be more causal than any other part? We may think that the horse is the reason the cart moves, but this is simply a prejudice. Whether you like it or not, the horse is also completely defined. Russell observed, and he was not the first to do so, that when physicists write their laws in mathematical language, time has no predetermined direction. “The law makes no difference between the past and the future. The future “determines” the past in the same sense in which the past “determines” the future.”

“But,” we are told, “you cannot influence the past, whereas you can, to a certain extent, influence the future.” This view is based on the very errors of causality that I wanted to get rid of. You can't make the past different from what it was - that's right... If you already know what it was, there's obviously no point in wishing it were different. But you also cannot make the future other than it will be... If it happens that you know the future - for example, in the case of an approaching eclipse - it is as useless as wishing the past to be different.

But for now, contrary to Russell, scientists are greater slaves to causality than anyone else. Cigarette smoking causes cancer, although no single cigarette causes any specific cancer. Burning oil and coal causes climate change. A mutation in a single gene causes phenylketonuria. The collapse of an aged star causes a supernova explosion. Hume was right: “All speculation about the establishment of facts seems to be based on relations Causes and Effects" Sometimes that's all we talk about. Lines of causality are everywhere, long and short, clear and blurred, invisible, intertwined and inevitable. They all go in the same direction, from the past to the future.

Let's say that one day in 1811, in the city of Teplitz in northwestern Bohemia, a man named Ludwig wrote notes on a line of music in his notebook. On an evening in 2011, a woman named Rachel blew a horn in Boston's Symphony Hall, with the famous effect of vibrating the air in the room, generally at a rate of 444 vibrations per second. Who can deny that, at least in part, writing on paper caused fluctuations in the atmosphere two centuries later? Using physical laws, it would be difficult to calculate the path of influence of the molecules of Bohemia on the molecules in Boston, even taking into account Laplace's mythical "mind that has a concept of all forces." At the same time, we see an unbroken causal chain. A chain of information, if not matter.

Russell did not end the discussion when he declared the principles of causality to be relics of a bygone era. Not only do philosophers and physicists continue to butt heads over cause and effect, they have added new possibilities to the mix. Retrocausality, also known as backward causation or retrochronal causation, is now on the agenda. Michael Dummett, a prominent English logician and philosopher (and reader of science fiction), appears to have started this movement with his 1954 paper, “Can Effect Precede Cause?”, followed 10 years later by his less cautious paper, “Making the Past Realized.” . Among the questions he raised was this: Suppose a man hears on the radio that his son's ship has sunk in the Atlantic Ocean. He prays to God that his son will be among the survivors. Did he commit sacrilege when he asked God to undo what had been done? Or is his prayer functionally identical to the prayer for his son's future safe journey?

What, against all precedent and tradition, can inspire modern philosophers to consider the possibility that effects can precede causes? The Stanford Encyclopedia of Philosophy offers this answer: “Time travel.” That's right, all the paradoxes of time travel, and murder, and birth, grow out of retro-causality. Effects cancel their causes.

The first main argument against the causal order is that a temporal order in which temporally backward causation is possible is possible in cases like time travel. It seems metaphysically possible that a time traveler enters a time machine at the moment t1, in order to get out of it at some earlier moment t0. And this seems nomologically possible, after Gödel proved that there are solutions to Einstein's field equations that resolve closed paths.

But time travel doesn't exactly rid us of all questions. “Many incoherences may be encountered here, including the incoherence of changing what has already been corrected (by bringing up the past), the ability to kill or not kill one's own ancestors, and the ability to create a causal loop,” the encyclopedia warns. Writers bravely risk a couple of incoherences. Phillip K. Dick set clocks backwards in Backward Time, as did Martin Amis in Time's Arrow.

It seems like we really are traveling in circles.

“The recent revival of wormhole physics has led to a very disturbing observation,” wrote Matt Visser, a mathematician and cosmologist from New Zealand in 1994 in the journal Nuclear Physics B (an offshoot of Nuclear Physics devoted to “theoretical, phenomenological and experimental high-energy physics, quantum theory fields and statistical systems"). The "revival" of wormhole physics appears to be well established, although these supposed tunnels through spacetime were (and remain) entirely hypothetical. The troubling observation was: "If traversable wormholes exist, they seem to be quite easy to turn into time machines." The observation is not only disturbing, but disturbing in the highest degree: "This extremely disturbing state of affairs stimulated Hawking to proclaim his insight into chronological protection."

Hawking is, of course, Stephen Hawking, the Cambridge physicist who had already become the most famous physicist alive, partly because of his decades-long battle with amyotrophic lateral sclerosis, partly because of his popularization of some of the thorniest problems in cosmology. It's not surprising that he was attracted to time travel.

“The Chronology Security Hypothesis” was the title of a paper he wrote in 1991 for the journal Physical Review D. He explained his motivation this way: “It was proposed that an advanced civilization might have the technology to distort space-time into closed time curves, such that would allow travel into the past." Suggested by whom? An army of science fiction writers, to be sure, but Hawking cited physicist Kip Thorne (another of Wheeler's protégés) at Caltech, who was working with his graduate students on "wormholes and time machines."

At a certain point, the term “sufficiently developed civilization” became stable. For example: if we humans cannot do this, will a sufficiently advanced civilization be able to? The term is useful not only for science fiction writers, but also for physicists. Thus, Thorne, Mike Morris and Ulvi Yurtsever wrote in Physical Review Letters in 1988: “We begin with the question: Do the laws of physics allow a sufficiently advanced civilization to create and maintain wormholes for interstellar travel?” It's no surprise that 26 years later, Thorne became executive producer and scientific consultant for the film Interstellar. “It is conceivable that an advanced civilization could pull a wormhole out of the quantum foam,” they wrote in that 1988 paper, and they included an illustration with the caption: “Space-time diagram for turning a wormhole into a time machine.” They imagined wormholes with holes: a spaceship could enter one and exit another in the past. It is logical that they brought up a paradox as a conclusion, only this time it was not the grandfather who died in it:

“Could an evolved being capture Schrödinger's cat alive at an event P (collapse its wave function to a living state) and then go back in time through a wormhole and kill the cat (collapse its wave function to a dead state) before it reaches P? »

They didn't give an answer.

And then Hawking intervened. He analyzed the physics of wormholes, as well as paradoxes (“all sorts of logical problems that arise from the ability to change history”). He considered the possibility of avoiding paradoxes "by some modification of the concept of free will," but free will is rarely a comfortable topic for a physicist, and Hawking saw a better approach: he proposed the so-called security chronology hypothesis. It took a lot of calculations, and when they were ready, Hawking was convinced: the very laws of physics protect history from possible time travelers. Regardless of what Gödel believes, they should not allow closed time curves to arise. “There appears to be a force protecting chronology,” he wrote in a rather fantastical manner, “that prevents the occurrence of closed time curves and thus makes the universe safe for historians.” And he completed the article beautifully - he could have done it in the Physical Review. He didn't just have a theory - he had "proof":

“There is also compelling evidence for this hypothesis in the form of the fact that we are not being swept away by hordes of tourists from the future.”

Hawking is one of those physicists who knows time travel is impossible, but also knows it's interesting to talk about. He notes that we are all time traveling into the future at a rate of 60 seconds per minute. He describes black holes as time machines, recalling that gravity slows down the passage of time in a certain place. And he often tells the story of a party he threw for time travelers - he only sent invitations after the event itself. “I sat and waited for a very long time, but no one came.”

In fact, the idea of ​​the chronology security hypothesis was in the air long before Stephen Hawking gave it a name. Ray Bradbury, for example, put it in his 1952 story about time-traveling dinosaur hunters: “Time does not allow such confusion - for man to meet himself. When the threat of such events arises, Time moves aside. Like a plane falling into an air pocket.” Notice that Time is the active subject here: Time does not allow, and time moves aside. Douglas Adams offered his own version: “Paradoxes are just scar tissue. Time and space themselves heal their wounds around them, and people simply remember as meaningful a version of the event as they need.”

Maybe it's a little like magic. Scientists prefer to refer to laws of physics. Gödel believed that a healthy, paradox-free universe is only a matter of logic. “Time travel is possible, but no one can kill themselves in the past,” he told a young visitor in 1972. “Originality is often neglected. Logic is very strong." At some point, protecting the chronology became part of the ground rules. It has even become a cliché. In her 2008 short story "The Region of Dissimilarity," Rivka Galchen takes all of these concepts for granted:

"Science fiction writers have come up with similar solutions to the Grandfather's Paradox: murderous grandsons inevitably run into some obstacle—non-working guns, slippery banana skins, their own conscience—before carrying out their impossible deed."

“The region of dissimilarity” is from Augustine: “I felt myself far from You, in the region of dissimilarity” - in regione dissimilitudinis. He does not fully exist, like all of us, chained to a moment in space and time. “I contemplated other things below You, and I saw that they are not completely there, and they are not completely not.” Remember, God is eternal, but we are not, much to our regret.

The narrator Galchen makes friends with two older men, maybe philosophers, maybe scientists. It doesn't say exactly. These relationships are not clearly defined. The narrator feels that she herself is not very accurately defined. Men speak in riddles. “Oh, time will tell,” says one of them. And also: “Time is our tragedy, the matter through which we have to wade in order to become closer to God.” They disappear from her life for a while. She keeps an eye on the obituaries in the newspapers. An envelope mysteriously appears in her mailbox - diagrams, billiard balls, equations. She remembers the old joke: "Time flies like an arrow, but fruit flies love bananas." One thing becomes clear: everyone in this story knows a lot about time travel. A fateful time loop - the same paradox - begins to emerge from the shadows. Some rules are explained: “contrary to popular films, traveling to the past does not change the future, or rather, the future has already been changed, or rather, things are even more complicated.” Fate seems to be gently pulling her in the right direction. Can anyone escape fate? Remember what happened to Lai. All she can say is: “Certainly our world is governed by rules still foreign to our imagination.”