Paradoxes of Time Travel

In several previous posts, I have discussed various paradoxes that time travel could cause if it were possible. Travels to the future controlled from the past do not cause paradoxes. That they are possible is obvious, since we all travel to the future at a rate of twenty-four hours each day.

It is also possible to travel to the future if one is in a coma and later awakens; or through hibernation, if it were possible, which it is not at the moment, but it may become so someday; or by traveling through space at relativistic speeds, which would result in a time dilation that, upon returning to the starting point, translates into a journey to the future. This last procedure is not possible right now, but it could become so someday, apart from the technical difficulties of achieving it.

Time Travel and Christ’s Crucifixion

Christ crucified, wood carving
by Manuel Alfonseca Santana

If time travel were possible, the greatest incentive for travelers would be to witness firsthand famous events of the past, such as the assassination of Julius Caesar and many others. The fact that we have no record of the presence of strangers in any of these cases is a significant argument against the feasibility of time travel.

There is no doubt that one of these events, perhaps the most famous of all, would be the Crucifixion of Christ. If time travel were possible, there should have been an avalanche of visitors from future times at Golgotha ​​to witness the most important event in the history of humankind.

In fact, this idea has been used in science fiction literature. In a novella titled There Will Be Time, Poul Anderson has his protagonist travel to Jerusalem on the day of the Crucifixion to witness Christ's death. Upon arriving, he discovers a large crowd, almost all of whom are time travelers.

A New Time Travel Paradox

It is well-known that time travel into the past, and sometimes also into the future, if it were possible, could give rise to destructive paradoxes. In a previous post I offered a list of five different types of these paradoxes. Here I will explain in more detail the fourth type I mentioned there: the fact that time travel into the past and human freedom are incompatible. I will do so through a short science fiction story, divided into two scenarios.

First scenario

At 3:55 PM, my friend Max said to me, “I just invented a time machine. Do you want to see it?” Of course, I agreed.

At 3:58 PM, Max and I entered the room where the machine was located. It looked like a simple metal chair. The machinery seemed to be under the seat.

Time travel in science fiction

H.G. Wells

A few years ago, I published in this blog a series of posts about the scientific aspect of time travel, the paradoxes it could cause if it were possible (which almost certainly it is not) and proposed solutions to these paradoxes, such as the quantum multiverse, one of the most absurd theories physicists have ever concocted. In another post I talked about the scientific errors in Michael Crichton’s sci-fi novel Timeline, which tries to avoid the paradoxes in this way, but does it poorly.

Here I am going to speak about time travel from a literary point of view, as a subgenre of science fiction. In this context, it’s irrelevant that time travel may or may not be possible. We are interested in the question, because this is one of the most frequent topics in this type of literature.

Information paradoxes

Woody Allen

As I have mentioned before, time travel, if it were possible, would cause many paradoxes. In a previous post I mentioned the paradox of unsourced information, which can be summarized thus:

A time traveler who lives in time 3 knows that a person A said or did something at time 2, prior to time 3. 

The traveler goes back from time 3 to time 1, prior to time 2, where he meets A. 

While they are together, the traveler suggests person A the idea of ​​doing or saying what he knows that person will do or say in the future, which has not yet taken place. 

Whose idea was it originally? Not the traveler’s, because he learned it from the history of person A at time 3. Not from person A, because the traveler suggested the idea to person A at time 1. 

The information in question has come out of nowhere, without anyone having thought it out.

The following diagram explains it.

A model for ChatGPT

How does ChatGPT work? Suppose we ignore for the moment that ChatGPT uses an artificial neural network, and represent its algorithm in the traditional way. This algorithm can be divided into two parts:

1. Training: ChatGPT is provided with data (text files), which are used to build two data sets:
1. A list of all the words that appear in any of the texts, without repetition, regardless of their order or the number of times each one appears.
2. An array of indices to the word list, reporting the number of times a given word occurs after a series of words. For example, if the following series appears in the texts: time travel, the indices of the words travel, and time will appear in the array, followed by the index of the next word, followed by the number of times that this sequence of three words appears in the set of texts used for training.

An Evolving Universe: PopulScience in Book Form

CEU Ediciones has published in book form, under the title Un universo en evolución (An evolving universe), a compilation of about a hundred posts published in this blog and its Spanish version, Divulciencia, over nine years, thematically arranged. Currently this book is only available in Spanish. These are the titles of the fifteen chapters:

1. Introduction (3 posts)
2. The beginning (5 posts)
3. The standard cosmological model (9 posts)
4. The fine-tuning problem and the theories of the multiverse (7 posts)
5. The problem of time (7 posts)
6. Life on Earth and on other worlds (3 posts)
7. The evolution of life (7 posts)
8. Man (5 posts)
9. Natural and artificial intelligence (7 posts)
10. Synthetic life and artificial life (3 posts)
11. The future of man (8 posts)
12. The end of man and of the universe (4 posts)
13. Science, faith, and atheism (14 posts)
14. About science in general (17 posts)
15. Conclusion (1 article)

Julio A. Gonzalo

The book starts by a presentation by Javier Pérez Castells, and a prologue by Julio A. Gonzalo. This is a paragraph from the presentation, which has been highlighted on the back cover of the book:

Manuel Alfonseca presents us in this book with a selection of posts from his blogs arranged by topic. The guiding thread is the story of creation. Beginning with the start of the universe (where he expands more, given his experience and knowledge on this subject), going through the origin of life and evolution, ending with anthropological conceptions of the human being. After that, he turns towards the supposed conflict between science and faith, grouping together a set of posts where he answers to this false tirade. Along the way, he stops to deal with the issue of artificial intelligence, the author’s favorite subject, and devotes a good number of chapters to an optimistical look at the future, albeit not forgetting that everything, together with the story of creation, will have an end. The book concludes with a few pertinent reflections on the limits of science, today considered by many as the only source of knowledge, in the exacerbation of what we call scientism.

Most of the posts (about one hundred) that have become part of the book have been previously published on the blogs Divulciencia and PopulScience, although a few are completely new, others have been built from several consecutive original posts or from those that dealt with the same topics, and the rest, those who have passed directly from the blogs to the book, have been updated.

The same post in Spanish

Thematic Thread on Anniversaries and Organization: Previous Next

Manuel Alfonseca

The paradox of unsourced information

Ted Chiang

In a previous post in this blog I discussed the paradoxes that would take place if time travel were possible. One of them was this:

• The existence of objects without a cause, illustrated by the science fiction story Find the sculptor by Sam Mimes, which can be summarized thus: on his first trip, the inventor of the time machine jumps 100 years into the future, where he finds a statue that has been erected in his honor. He takes the statue, travels with it 100 years into the past (i.e., to the starting point of his journey), and places it in the same place where he found it, where it will remain for 100 years without anyone touching it. But who made the statue? Nobody. It is an object without a cause, that only exists during those hundred years.

Another conversation with ChatGPT

As I said in the previous post, last January I did two sessions with ChatGPT from OpenAI. In the second, my questions were directed to the following scientific topics:

• The special theory of relativity, the limit of the speed of light in a vacuum, and the possibility of traveling in time.

Throughout the session I was asking the following questions:

1. Can a particle travel at a speed greater than light?

Answer: According to the theory of relativity, as first described by Albert Einstein, nothing with mass can travel at the speed of light...

Time travel and matter transfer

C.S. Lewis

Apart from the Chronicles of Narnia, C.S. Lewis wrote a science fiction trilogy and left an unfinished fourth novel, The Dark Tower, which was published as-is after his death. In this novel, Lewis offers an argument against the possibility of time travel, not commonly advanced in this context. Usual arguments are a version of the Fermi paradox, or the enumeration of the paradoxes that could occur if it were possible to travel to the past, and in some cases also to the future.

The argument offered by C.S. Lewis consists of two parts:

Compatible, incompatible, possible, impossible

I wish to clarify the four concepts of the title, which are sometimes confused when talking about physical theories and their application:

• An event (real or imagined) can be compatible with a theory. In this case, if the event were real, it would not pose any problem for the theory, which admits in principle the possibility of that event taking place.

October the first is too late

Fred Hoyle was one of the great scientists of the 20th century, as well as one of the most controversial, due to the eccentric theories he defended. His most important scientific discovery had to do with the nucleosynthesis of elements in stars, heavier than hydrogen and helium, which are the simplest and lightest in existence. In particular, from his theory on the formation of carbon atoms, Hoyle deduced an early version of the fine-tuning problem, which made him go from atheism to a vaguely theistic position, as can be seen in this paragraph from his article The universe: past and present reflections (Engineering & Science, 1981):

Would you not say to yourself… "Some super-calculating intellect must have designed the properties of the carbon atom, otherwise the chance of my finding such an atom through the blind forces of nature would be utterly minuscule... A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."

The golden rules of science fiction and my own work

Isaac Asimov

These are, according to Isaac Asimov, the two golden rules of good science fiction:

1.      Any scientific claim (even a prediction) must always be compatible with current science. It would not, therefore, be good science fiction a novel where the squaring of the circle with a ruler and compass was achieved, because it has been shown mathematically that this is impossible. Or traveling through space at a speed greater than that of light, without using some scientific trick that makes it possible to achieve it, such as going through the world of tachyons.

2.      Predicting social consequences is better than predicting technical advances. Thus, in a hypothetical novel written in the nineteenth century, predicting the parking problem would be much better than just predicting the car. An example of this kind of good science fiction, mentioned by Asimov in this regard, is Robert Heinlein's short story Solution Unsatisfactory, written in 1941, which not only predicted the atomic bomb as a means of ending World War II (in which the United States were not yet taking part), but also predicted the subsequent equilibrium between the great powers and the permanent threat of a war of extermination.

To be exact, these two laws are my elaborations of what Asimov wrote in two popular articles published in The Magazine of Fantasy and Science Fiction: Future? Tense! (1965) and O Keen Eyed Peerer into the Future (1974). To be even more exact, Asimov's laws were three and, similarly to his three laws of Robotics, he called them the three laws of Futurics.

Science and Science Fiction: mutual influences in the 20th century

H.G. Wells

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Halfway between the 19th and 20th centuries, the British H.G. Wells also practiced the literature of scientific prediction, although his predictions are usually longer-term than Verne's, more remote from the technique of his time, so very few have come to be carried out. We still don't have The Time Machine and can't see it anywhere near. We cannot make artificial men by vivisecting animals (The Island of Doctor Moreau). Nor can we make ourselves invisible (The invisible man). And fortunately the Martians have not invaded us (The War of the Worlds). In 1938, a radio dramatization of this novel by Orson Welles caused a mass panic in the United States. Despite the boom in science fiction at the time, the public was still as credulous as when it had been fooled a century earlier by the articles in the Sun.

Wells also wrote (of course) about a trip to the moon and populated our satellite with intelligent giant ants, although the procedure to make the trip is more imaginative than, and as impractical as Verne's. But his great scientific foresight success is the novel The World set free (1913), which not only anticipated the atomic bomb, but also influenced its practical realization, stimulating Leo Szilard's research on the neutron chain reaction. Although Wells also made a tremendous mistake in this novel, by predicting in 1913 that the First World War would start in 1956. But as he said a few years later: [I have] always been... a rather slow prophet. You can also see my review of this book in Goodreads.

What does mathematics say about time travel?

On September 21st, an article on time travel by Germain Tobar and Fabio Costa was published in the scientific magazine Classical and Quantum Gravity. This article has been given considerable coverage by the mass media. The article argues that time travel would be possible if certain mathematical restrictions were fulfilled that would eliminate the paradoxes. In a previous post in this blog I explain those paradoxes and their different types.

In relation to this we must distinguish two different things:

1. What the article actually says: it only mentions the grandfather paradox (the time traveler who returns to the past to kill his grandfather as a child, which would make his own existence impossible), and specifies a mathematical equation that supposedly prevents it, without making the traveler's freedom of action totally impossible. The equation is this:

Timeline

Poster of the film based on Timeline

In 1999, Michael Crichton published his novel Timeline, a typical science fiction novel about time travel, whose plot can be summarized as follows:

A research company has developed a procedure to travel into the past. Using it, they sent to 14th century France, in the midst of the 100 Years War, a history professor who is conducting archaeological studies in ruins near the medieval fortress of La Roque. His collaborators, who do not know what is happening, find among the ruins a call for help from the professor, which when subjected to carbon-14 dating turns out to come from the 14th century. Picked up by the company that sponsors their studies, they are sent into the past to save the professor, who cannot return on his own.

In another post in this blog, I discussed the paradoxes that can be caused by traveling into the past, and various procedures invented by scientists and writers to escape them. In the novel, Crichton mentions two:

Travelling to the past?

S.Augustin, by Louis Comfort Tiffany
Lightner Museum

In his Confessions (Book XI, chapter 14), St. Augustine wrote these words, still valid today:

What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.

In the current situation of our scientific and philosophical knowledge, we still don’t know what time is.

·         For classical philosophy and Newton’s science, time is a property of the universe. Therefore, time would be absolute.

·         For Kant, time is an a priori form of human sensibility (i.e. a kind of mental container to which our sensory experiences adapt).

·         For Einstein, time is relative to the state of repose or movement of each physical object. There is, therefore, no absolute time.

·         For the standard cosmological theory, there is the possibility to define an absolute cosmic time for every physical object, measuring the time distance since the Big Bang to the present.

·         For the A theory of time (using J. McTaggart’s terminology) the flow of time is part of reality. The past no longer exists. The future does not yet exist. There is only the present. If the A theory is correct, travel to the past is impossible, because you cannot travel to what does not exist.

·         For the B theory of time, the flow of time is an illusion. Past, present and future exist simultaneously, but for each of us the past is no longer directly accessible, and the future is not yet accessible. Einstein adopted the B philosophy of time. In a condolence letter written to someone who had lost a beloved person, he wrote the following:

The distinction between past, present and future is only a stubbornly persistent illusion.

Is physics losing touch with reality?

In his famous posthumous book The Discarded Image, published in 1964, a few months after his death, C.S. Lewis shows he is ahead of his time by predicting a situation that today, when it has become usual in physics, gives a rather bad forecast for the future of this science. Let’s look at a relevant quote:

The mathematics are now the nearest to the reality we can get. Anything imaginable, even anything that can be manipulated by ordinary (that is, non-mathematical) conceptions, far from being a further truth to which mathematics were the avenue, is a mere analogy, a concession to our weakness. Without a parable, modern physics speaks not to the multitudes. Even among themselves, when they attempt to verbalise their findings, the scientists begin to speak of this as ‘making models’... Sometimes [the models] illustrate this or that aspect of [reality] by an analogy. Sometimes, they do not illustrate but merely suggest, like the sayings of the mystics... By accepting [an expression such as] the ‘curvature of space’ we are not ‘knowing’ or enjoying ‘truth’ in the fashion that was once thought to be possible.

A mathematical model for time travel

Welcome for time travellers

On May 2 2017, Newsweek published an article with this title:

Time travel is mathematically possible with mind-boggling model

You may well imagine that, with that title, the article will rather fall into the category of sensationalist papers on seemingly scientific issues. Indeed, in a quick reading of this article I have detected the following inaccuracies:

1. The title does not make clear the difference between a theoretical possibility of traveling in time and building a time machine. That is, the different between theory and practice. What Ben Tippett has developed is a purely theoretical mathematical model.
2. It presents the idea as something new which puts an end to a string of failures and disappointing calculations. Space-time loops, however, are known to be compatible with the general theory of relativity since quite a long time ago. In 1992, for instance, Stephen Hawking came to the conclusion that it would not be possible to use them without negative energy, something that is not known to exist. In 2005, the Israeli Amos Ori proposed a procedure that would not require it, consisting of spinning around an empty toroid region surrounded by a sphere containing enormous amounts of matter (e.g. a black hole). This is not so different from what is being proposed now.

Can time travel paradoxes be avoided?

Cover of Fantastic SciFi with a
Porges story (The Shadowsmith)

In a science fiction story written in 1962 by Arthur Porges, entitled The rescuer, the inventors of a time machine discover that a man has entered the machine to travel back in time. To stop him, they destroy the machine with the man inside. When they are tried for murder and destruction of valuable property, they explain:

This man had taken with him a repeating rifle and five thousand rounds of ammunition. His intention was to arrive at Golgotha in time to rescue Jesus Christ from the Roman soldiers. In short, to prevent the crucifixion. And with a modern rifle, who can say he wouldn’t succeed? And then what?... What of the effect on the future, the entire stream of history, secular as well as religious?

The story is an excellent example of the paradox of predestination mentioned in a previous article, with several more that make us doubt the possibility of time travel. But is there no way to avoid the paradoxes? Is it possible to devise a theory that would remove them making time travel feasible, at least in principle? There have been several attempts to achieve this.