Paradoxes of time travel

Science fiction - the theoretical possibility of time travel entails many logical paradoxes. If we ever want to realize this fantasy, we will have to answer these paradoxes as well * From Galileo, Issue No. 66

By: Marius Cohen, "Galileo"

Stories dealing with time travel have always been among the most fascinating in science fiction, starting with Mark Twain's classic writings, "Yankee in King Arthur's Court" and H.G. Wells "The Time Machine", to contemporary stunt-heavy films such as Spielberg's "Back to the Future". One of the main motifs in stories like this is the way in which the actions of the time travelers (the chrononauts) in the distant past affect their reality in the present.

In some stories, the smallest change made in the past causes far-reaching changes in the present, with a classic example of this being Isaac Asimov's book, "The End of Time", while in others, the changes in the past fit perfectly with the events of the present without causing any change in reality. Whether or not time travel is ever possible, we can perform a few simple thought experiments to discover the surprises that such travel might hold. But first we will review the theoretical possibilities through which modern physics can bring us even a small step closer to the greatest adventure of all.

Time travel - theories and technological limitations

The possibilities for time travel can be divided into two types: travel to the future and travel to the past, if only due to the fact that we already know that travel to the future is possible. Modern physics knows two ways to slow down time in a given system (which is equivalent to speeding up time outside the system): one, based on Einstein's special theory of relativity, is through flight at a very high speed (far beyond the speeds within our reach today), and the second, based on the theory of Its general relativity is through staying in an extremely strong gravitational field.

To travel in time to the future all we have to do is go on a fast flight through space, and if possible also spend some time in the vicinity of an occasional black hole. We have all the theoretical knowledge to return to Earth precisely for the celebrations of the next millennium, or at any other date chosen. The only limitation is a technological limitation, and even though it is a significant limitation, partly due to the enormous amounts of energy needed for such an operation, we can assume that in the distant future we may have the means to do so.

Another way, perhaps even more practical, to reach the future, is by the method of the circle dwellers: sleep. We are now technologically close to the ability to freeze humans for an almost unlimited period (cryonics, during this period, until they are thawed at a desired point in the future, the metabolism in their bodies will be completely suspended, and upon awakening they will find themselves at the same biological age at which they were frozen (with a feeling of: "What, 300 years have already passed?!").

longer life

It is possible that already in the foreseeable future people will ask to go through the process, in the hope that they will wake up in a better world, with a medical option for a longer life (and maybe also with a savings plan that will generate handsome profits over the years). Today, the technological knowledge for this is still in its infancy, but this method is already being used to freeze incurable patients who have died a clinical death, and who have coordinated their freezing in advance, in the hope that in the future it will be possible to safely thaw them and cure them with more advanced means than those available to medicine today.

And what are the theoretical possibilities to move in time to the past? First, it is possible that the phenomenon occurs by itself at the subatomic level. Richard Feynman, the well-known physicist and Nobel laureate, showed that it is not possible to fundamentally differentiate between a particle charged with a negative electric charge and a particle with a positive electric charge moving backwards in time (and vice versa), and that both descriptions are physically equivalent. Physicist John Wheeler, who was Feynman's teacher and colleague, even raised the possibility that maybe there is only one electron in the entire universe, moving relentlessly back and forth in time, thus creating the impression that there are countless electrons and positrons...

Another possibility at the subatomic level is obtained from the special theory of relativity, which perhaps allows for the theoretical existence of particles moving at super-light speed (tachyons), and which therefore also move backwards in time. No one has yet succeeded in discovering tachyons, and even though in the meantime theoretical considerations have also been raised against their existence, there are physicists who are still looking for them. If we do succeed in finding tachyons and harnessing them for our use, we will not be able to move in time ourselves, but we may be able to use them to maintain intertemporal communication by passing messages to the past (when returning an answer to the future will be possible, for example, by publishing an ad in a daily newspaper).

The first to propose a theoretical way to travel in real time was the mathematician Kurt Gadel, who discovered that the equations of general relativity make it possible, in the event that the entire universe revolves around itself, thus sweeping space-time with it, to return to the past by circling the universe. As of today there is no evidence that the universe rotates around itself, but even if it does, it seems that in the visible range we will not be able to circle the entire universe in a reasonable amount of time to perform the scientific experiment.

In the XNUMXs, Roy Kerr, a mathematician from New Zealand, showed that spinning black holes also sweep space-time with them, and about a decade later physicist Frank Tipler used Kerr's work to propose the theoretical possibility of time travel by flying near a massive spinning black hole. at high speed.

wormholes

Another theoretical way to move from one place-time to another place-time was proposed by the physicists Kip Thorne and John Wheeler, who proposed using a wormhole for this purpose: the spontaneous formation of a kind of tunnel, which under certain conditions can connect two different points in space-time. Although the size of a wormhole is not supposed to allow the passage of matter or even light through it, and in addition to that the phenomenon is supposed to be unstable, several theoretical proposals have already been put forward on how to stabilize a wormhole and how to enlarge it in such a way that it can be passed through. But even if it turns out that this can indeed be done, the amount of energy needed for such an operation will prevent this technology from being applicable in the foreseeable future.

Another possible time machine, which would combine principles from general relativity and quantum theory, was proposed by the Israeli physicist Prof. Yakir Aharonov. Such a machine will be based on a cell made of a material with extremely high gravity (relativistic effect), inside which the time traveler will be found, and through advanced technology the volume of the cell will change so that it will be a superposition of several different volumes (quantum effect). Such a time machine, if it were to operate, would do so on a probabilistic basis, and it would be impossible to know in advance what time the Chrononaut would move to (if at all). Of course, the technology to implement this method is also far from being applicable today.

Another technological problem, which will be faced by the designers of any time machine, is the fact that it will also have to be a space machine! And this is for the simple reason that the earth moves in space at a high and complex speed due to its movement around itself, its movement around the sun, the movement of the sun around the center of our galaxy, and the movement of the galaxy in the universe. Hence, our time-machine will also be required to move through space like a spaceship for everything, and what is no less important: to be very precise in its stopping point in space-time (so that it does not get stuck in a concrete wall or fall from a height of 4 stories).

Paradoxes of time travel

The various paradoxes related to time travel can basically be divided into two types: paradoxes of inconsistent reality, in which the time travel creates an alternative reality, different from the reality that preceded this journey, resulting in a logical contradiction, and in contrast paradoxes of consistent reality, in which the actions of the time travelers do not change reality, but violate the principle of causality.

The grandmother (or grandfather) paradox

The Grandmother Paradox is probably the most well-known paradox of time travel. It describes a time traveler who goes back to the past before his parents were born, and kills his maternal grandmother. Since his grandmother was killed before she could give birth to his mother, he himself was never born, so he cannot go back to the past to kill his grandmother. But if the grandmother remains alive, she does give birth to his mother, and so he himself was born, and when the time comes he returns to the past and...

If our time-traveler had killed someone else, it is possible that upon his return to the present he would have discovered in a local newspaper archive an article from the distant past about the mysterious death he himself caused only a few hours earlier. It is also possible that this article was probably there all these years without him knowing about it, so in practice he did not cause any change in reality. Killing the grandmother, on the other hand, creates an endless loop of jumps between two alternate realities, each of which ultimately contradicts its own possibility of existence.

Another version of this paradox (which is less violent than the previous one), describes a scientist, who returns in his time machine to the immediate past, and convinces himself not to use it (preferably by talking, but to be safe you can also bring handcuffs). If our scientist is indeed convinced and does not activate the time machine, he can no longer return to the immediate past to prevent himself from using the machine...

The causality paradox

We have already seen that returning to the past does not necessarily bring about a change in reality, and that the actions of the time-traveler in the past may be an integral part of the reality of his time. But even if the consistency of reality is preserved, the actions of the time-traveler may violate the principle of causality, according to which the cause precedes the cause (if I bruise my hand and feel pain, then the pain, caused by the blow I received, will appear after the blow and not before it. If I feel pain In my hand even before I got hurt I would know for sure that something else caused the pain).

To see how this principle can be violated, let's imagine that the time traveler returns to a time when his parents have not yet met, and knowing that without his help they will never meet, he intervenes and brings them together. The reality that is created is indeed completely consistent, but the concept of causality is fatally damaged: the time traveler was born thanks to the fact that his parents met, but his parents met thanks to the fact that he brought them together! So what came before what? What is the reason and what is the motive?

The Knowledge Paradox (or "Free Meal")

The knowledge paradox is a special case of the causality paradox. Let's imagine a time-traveler who takes with him the scores of Beethoven's Ninth Symphony, travels to the composer's time, hands him the scores, and authorizes him to publish the piece as his own. As a result, Beethoven publishes the Ninth Symphony, and the whole world gets to enjoy it throughout the generations. Here, too, a completely consistent reality is obtained, but there is now in the world a work of splendor that no one has written! The time traveler certainly did not do this, since the work had already existed for generations, while Beethoven did not write it because he received it from someone else.

Another version of the paradox of knowledge describes a young physicist who aspires to invent a time machine, but has no idea how to even begin the job. One day he meets an elderly man, who identifies himself as an older version of himself, and who gives him precise instructions on how to build the long-awaited time machine. Our physicist follows the instructions he received with great precision, and spends his life pleasantly traveling in time (when he tries not to cause significant changes in the past, and of course avoids meeting his grandmother). In the twilight of his days, the physicist realizes that he must return to the days of his choice to guide himself in the construction of the time machine, otherwise none of this happened and will not happen. So who invented the time machine?

On the same conceptual basis, we can imagine that scientists transfer a number of small mammals to the end of the dinosaur era, and these mammals become, in the end, the ancestors of today's mammals. Or, another sophisticated possibility, which is based on Robert Heinlein's story, "All You Zombies": a time-traveler, whose baby was adopted by a foster family from an orphanage, takes with her a baby born out of wedlock, and leaves Her on the doorstep of the same orphanage where she grew up.

The baby grows up to be herself and continues the loop that has no beginning and no end... and perhaps the greatest "free lunch" ever practiced is that of Lee and Gott, who proposed the possibility that the entire universe is a consequence of itself in a closed space-time curve.

The weathering paradox

This paradox is based on the paradox of knowledge. Let's say our time traveler takes Leonardo da Vinci's Mona Lisa with him this time, goes back in time, and hands it over to the artist a few weeks before he actually started working on it. The artist is enthusiastic about the painting and presents it as his original work. Without a doubt a "free meal". However, in this case the problem is even more complicated: the painting is already several hundred years old when the time traveler decides to take it to the past, and therefore when the artist receives it in his hands, the painting is already quite ancient.

From the moment the painting reaches Da Vinci until the moment the time traveler sets off (that is, to the past), a few more hundreds of years go by, then a few more hundreds of years until the "next" cycle, and so on and so forth. In fact, it is likely that the painting that reaches the artist's hands will end up being so faded, that it will not impress him at all. It can be assumed that over the years the painting is repeated and renovated, but even a painting that is renovated countless times wears out in the end, if only because of the fabric's resistance to the ravages of time. This paradox creates, of course, an inconsistent reality, since the wear and tear of the painting will prevent it from being handed over to the artist, who will then paint it himself, and thus the whole process will be possible "again"...

And some more thought experiments

Suppose I have a working time machine at my disposal. It is now 12.00:14.00, and I decide that at 13.00:13.00 I will send back to the past, let's say at 14.00:XNUMX, my wristwatch. Towards XNUMX:XNUMX p.m., a bold idea occurs to me: I decide that if the watch does appear at the said time, then at XNUMX:XNUMX p.m. I will not send it over as I had originally planned, but if, on the other hand, my wristwatch does not appear at that time, I will carry out the task as planned.

Assuming the time machine works, what will really happen? Will the clock appear or not appear at the said time? Either option leads to a logical contradiction.

For this experiment there is also a version of consistent reality: as before, at 12.00:14.00 I decide that at 13.00:14.00 I will send my watch back to the past, to XNUMX:XNUMX. The clock does appear at the appointed time, and at XNUMX, so as not to cause an inconsistent reality (which could possibly lead to disastrous results for the entire universe, as the matter is sometimes presented in science fiction films) I am sending towards... the same clock! (And I don't remove my original wristwatch from my wrist for a single moment during the experiment. In fact, it's possible that I even forgot it at home...) A situation was created, therefore, where for a period of an entire hour I had in my possession a perfect copy of my wristwatch - Out of nowhere!

Marius Cohen is a PhD student in the Department of Philosophy at Ben-Gurion University