In 1967 the physicist Feinberg postulated the existence of particles capable of traveling at speeds greater than that of light, tachyons . Four years later Bendford, Book and Newcomb studied the consequences of this fact from the so-called Tolman paradox -enunciated in 1917- where it is shown that sending signals faster than light implies communicating with the past, as in the novel science fiction Chronoscape by Gregory Bendford himself or in the horror magician John Carpenter’s film The Prince of Darkness .
Let’s imagine that we play with a tachyon frisbee. We see how our friend makes the movement of throwing it to us and seconds later, while we see that the image of the frisbee travels towards us, we find it in our hands! Going faster than light, which brings its image to the retina after hitting the frisbee, it arrives before it. Even more. The sequence of images that we would see would be: first the one of 5 meters, then the one of 15, followed by the ones of 30, 45… until the last one would be the one of the frisbee coming out of the hand of our friend. The frisbee reaches our hand before leaving.
This, of course, implies serious paradoxes. For example, imagine that both Cervantes and Jorge Manrique own a tachyon telephone. Cervantes writes Don Quixote, he reads it to Manrique and he copies it and publishes it. Historically, Don Quixote appears many years before Cervantes was born, but the style, the language belongs to Cervantes. How can a book be printed before it is written?
More subtle paradoxes appear if we deal with events dependent on each other. Imagine that Mamen and Esther have inherited such telephones, but now the messages arrive with only an hour delay: if a message is sent at three, it will be received at two. They both decide that Mamen will send a message at three if she hasn’t received one from Esther before at one . On the other hand, Esther will send one a little after two if she has received the one from Mamen at two. Will Esther send the message? In this case the cause lies in the future. Whether Esther sends her message at two depends on whether Mamen sends hers at three. And the most paradoxical thing, Mamen will do it if she doesn’t receive Esther’s: the communication will happen if it doesn’t take place .
temporal paradoxes
Time travel means a complete break in causality . Surprisingly, there is no law that prohibits the existence of time machines, named by physicist Kip S. Thorne as Closed Time Curves (CTC). The absurdities are served and science fiction has taken them to surprising extremes. The most common is to travel into the past and modify history, as in the classic matricide paradox . We have an example in Philip K. Dick’s raving novel The Man in the High Castle recounts Hitler’s victory in World War II due to massive interruptions in the time stream. In Terry Gilliam’s film Twelve Monkeys , the protagonist, Bruce Willis, is sent back in time to prevent the destruction of civilization. He doesn’t get it and the story remains unchanged.
The contradictions of these trips in time are innumerable. If in the movie Terminator the cyborg had killed the mother of the leader of the revolution, then it would not have been necessary to send any robot from the future. And if they had not sent him, the mother would not have died and the child would have been born. To overcome such paradoxes, the physicists Novikov, Thorne, Morris, Friedmann, Echeverría, Klinkhammer and Yurstever proposed, in 1990, the principle of self-coherence : the Universe allows the existence of time machines as long as the Universe is globally self-coherent. If you decide to kill your mother, you won’t be able to do it: the gun will jam, or the shot will miss…
The Self-Coherence Principle saves us from such contradictions, but it does not prevent ambiguity. For example, in Michael Moorcock’s novel Behold the Man, a very religious man travels to the time of Jesus Christ only to discover, to his astonishment, that he did not exist. His time machine is destroyed and he involuntarily begins to reproduce the Gospel narratives, becoming the proclaimed Messiah. In Find the Sculptor by Sam Mines, a scientist travels to the future only to discover that a statue has been dedicated to him. He steals it, taking it to his time… and that is the statue they use to honor him. Who carved it? The Self-Coherence Principle leaves a bitter aftertaste in the mouth. We can create information out of nothing!
In this sense, the two most insane stories are the product of two incredible science-fiction minds: Robert A. Heinlein and Fredrick Brown. In All of You Zombies by Heinlein the central character of the story, thanks to a time machine and a sex change operation, is his own father and mother . Brown poses the following experiment: imagine that we send a metal cube 5 minutes into the past. The time sequence turns out to be a cube that appears out of nowhere and five minutes later we put it in the machine to send it past. Now, what would happen if we decided NOT to do it? Brown solves it in a brilliant way: the whole universe disappears and only the cube remains.
A self-coherent but ambiguous universe
The existence of CTCs and the self-coherence principle allow the existence of multiple histories that are compatible with the laws of physics, and therefore equally possible. This was demonstrated by two young physicists, Echeverria and Klinkhammer, studying the so-called Polchinski paradox : Carlos goes to see his girlfriend. Passing by a telephone booth someone, identical to him, comes out of some bushes in front of her and pushes him into the booth. What he doesn’t know is that the supposed booth is a time machine and it suddenly appears out of the bushes five minutes before he walked by, so he sees himself coming down the road! Then he thinks: “enough of impersonation!” and decides to push his other self into the cabin… For his girlfriend, who is waiting for him at home, this event is no different from another in which nothing had happened to Carlos when he passed the cabin.
Echeverria and Klinkhammer demonstrated that the time machine allows the existence of an infinite number of possibilities for the same story . This debunks classical physics. For her, for example, there is only one possible trajectory for the movement of a billiard ball; however with a time machine there are infinite, all equally valid.
Does this lead us to insoluble paradoxes? No. Klinkhammer and Thorne have found, applying quantum mechanics (the part of physics that studies atoms and the subatomic world), that each of these trajectories has a certain probability of happening . It is not possible to say which of them will occur, but some will have more possibilities than others. Thus, if a certain trajectory of a billiard ball has a 48% chance of occurring and another has a 52% chance, out of a hundred times we hit it with the cue 48 will go one way and 52 will go another.
The parallel universes to the rescue
Physicists who do not like this kind of probabilistic games solve the problem with the (mis)known parallel universes hypothesis , developed by Everett in 1957 and completed by DeWitt in 1970. Although it was devised to solve a difficulty related to the mechanics quantum -the so-called measurement problem-, a certain analogy with the problem that concerns us has been found. According to her, the entire universe splits in two every time she is faced with an alternative. If red or black can come up on the roulette wheel, the universe will split in two; one comes out red and the other black, saving the problem of ambiguity. In this way, the time traveler dedicates himself to moving through the different branches of the tree of Universes. The traveler can kill his mother and nothing happens: he has simply entered a branch of the Universe in which he was not born . Perhaps the best example of this type of travel is found in the novel by the incredible Fredrick Brown Universo de Locos . The protagonist jumps from one Universe to another where in one he is an employee, in another he is the boss, in another he has married an imposing blonde, in another…
Still, scientists like Stephen Hawking are not happy with any of these solutions. For Hawking, there must be a kind of temporary censorship, called Chronological Protection , which prevents the appearance and creation of time machines. Using quantum arguments, Hawking suspects that if a device were to become a time machine, a series of instabilities would appear and circulate through it and destroy it. Calculations made by Kip Thorne and Eanna Flanagan seem to agree with Hawking, but they are not conclusive.
The paradox of matricide weighs like a slab. Hawking’s most powerful argument against time machines is that if they could be built today we would be practically overrun with tourists from the future. With characteristic humor, Hawking asserts that this conjecture keeps the world safe for historians.
Perhaps Herbert George Wells ‘s Time Machine can never be built and we cannot have Time in his Hands .
Or maybe yes.
References:
Gott, JR (2003) Time travel, Tusquets Publishers
