This week I have something a little bit different for you. Usually I write a fictional story every week, and a common theme in my stories is: time travel.
It’s been bothering me that I’ve never really taken the time to fully understand all the possible paradoxes involved in time travel. A long time ago I did study relativity at the University of St. Andrews in Scotland but the only true paradox we got into was the grandfather paradox. Often this is regarded as a showstopper for time travel in physics, and as the key reason why time travel to the past is probably not possible.
So in this video I’m going to discuss all the time travel paradoxes that I’ve been able to unearth. I hope you find this exploration of time travel interesting, and next week we’ll get back to regular scheduling, so to speak.
First, let’s talk about time travel to the future.
It is actually quite possible, theoretically, to travel to the future. In a sense, we’re already doing that. If you can somehow slow your own bodily processes so that you don’t experience the passing of time at the normal rate, you can accomplish true time travel into the future.
You could potentially do this by freezing yourself, if only you were able to prevent the freezing process turning your cells to mush, but the theory of relativity also predicts that time travel to the future could be accomplished by travelling somewhere at a really high speed, then returning to the point where you started.
There are ferocious technical barriers to actually accomplishing this, of course, but there is no theoretical principle that actually forbids it.
The only paradox associated with time travel to the future is the twin paradox, which is well understood—even by me—and is not actually a paradox at all. If a traveller journeys a long way from the Earth at a high speed, then turns around and comes back again, relativity tells us that less time will have passed for him than for the people who stayed on the Earth. A thousand years may have gone by on the Earth, while only some weeks have passed for the traveller. He has effectively travelled to the Earth’s future.
The name “twin paradox” arises from imagining that the traveller is one of a pair of identical twins. The traveller arrives back on the Earth to find he is younger than his twin. But isn’t the situation symmetrical, and movement relative? Can’t the twin argue that, due to symmetry and the relativity of motion, he should be younger than the traveller? That is, if motion is relative, can’t we view the stay-at-home twin as being the one who travelled, while the traveller twin actually stayed in one place?
After all, the Earth is constantly moving around the sun, and the sun is constantly in motion around the galactic centre. It’s not as though Planet Earth is somehow stationary. Actually, according to relativity, there is no such thing as stationary in an absolute sense.
However, this is simply not the case, and there is no true paradox.
The resolution of the problem doesn’t have to do with the traveler rotating to head back again—which is entirely unnecessary—nor with the traveler having to accelerate and decelerate, which may be necessary in practice but is not needed to resolve the paradox.
The simple fact is that, while there is a frame of reference—that is, a point of view—in which the Earth remains stationary the whole time, there is no single point of view in which the traveller remains stationary. If we adopt the point of view that the traveller is stationary on his outward-bound journey, then from that same point of view he is not stationary on his inward-bound journey.
While travelling away from the Earth, if the traveller argues that it’s the Earth that’s moving and not himself, then what will he think of another spaceman who’s currently following the exact route the traveller will have to take to get back to the Earth? He’s certainly not going to view that fellow as stationary.
In contrast, the people on the Earth can view themselves as existing in one single stationary frame of reference the entire time.
The traveller, in a sense, really does travel, while the Earth, leaving aside its journey around the sun, does not.
A long time ago I wrote an extensive, accurate explanation of this on the Quora website, but eventually I deleted my account there out of frustration because people kept reporting my answers and Quora kept deleting them in response to the reports. I was unfailingly polite to everyone, even in the face of considerable provocation, but the climate change people didn’t like me because I argued that there is no remotely provable mechanism by which our CO2 emissions could heat the globe by more than a degree or so, and the transgender people didn’t like me because I argued that there are only two sexes, and it’s beyond the power of science to change one into the other.
So that, along with my hundreds of my other answers, is lost.
I don’t really like politics or social issues but I do think we should all be able to speak the truth as we see it. Otherwise what’s the point in speaking at all?
Anyway, in summary, time travel to the future is theoretically possible and is paradox-free; it’s just technically difficult.
Now let’s turn to the very real paradoxes associated with time travel to the past.
If you first assume that something is possible, then you uncover paradoxes associated with that thing, sometimes that’s very illuminating. The existence of a paradox might mean that the thing you’ve hypothesised is actually impossible, but it might also mean that some common underlying assumption—that is, an assumption that underlies the way we think about reality—might be incorrect.
A great example of this is the paradox Einstein uncovered when he thought about what it would be like to travel alongside a beam of light. Einstein realised that Maxwell’s equations, which brought together everything known about electric and magnetic fields, and which predicted the existence of invisible radiation, seemed to indicate that light could only travel at a certain fixed speed. A beam of light could not appear stationary, in the same way that a moving train appears stationary from the point of view of the people in a car moving alongside the train at the same speed. According to Maxwell’s equations, light depends upon movement for its very existence.
This led Einstein to hypothesise in his famous 1905 paper on electrodynamics that the speed of light always appears the same, regardless of the speed of the observer.
Apparently unbeknownst to Einstein, this strange phenomenon had already been experimentally observed by the American physicists Albert Michelson and Edward Morley, in 1887.
Nothing else behaves like this: if you run after a ball, the speed of the ball slows relative to you, otherwise you’d never be able to catch it. Hurrying after a beam of light seems to make no difference at all; it’s always rushing ahead of you by the same relative speed.
With that in mind, it may somehow be useful to consider the paradoxes of time travel, even if we currently have no workable method of actually travelling backwards in time.
The theory of relativity arguably appears to predict that backwards time travel is actually possible, but it doesn’t give us a workable, practical method for actually doing it.
The most famous example of a time travel paradox is undoubtedly the grandfather paradox. If you could travel to the past, you could kill your own grandfather before he could even reproduce with your grandmother.
Or, if killing your ancestors doesn’t appeal, you could simply travel backwards in time and prevent your grandfather from meeting your grandmother.
In either case, how can your parents ever have been born, and how were you then able to travel backwards in time, since you can’t exist?
This is the key reason as to why many physicists consider time travel to the past to be impossible.
The name of this paradox derives from a short science fiction story by Nathaniel Schachner, called Ancestral Voices, which is out of copyright in most countries. It was originally published in a magazine called Astounding Stories in 1933.
In that story, a scientist travels backwards in time to the year 452 AD and kills one of Attila’s the Hun’s fellow Huns, who turns out to be a distant direct ancestor of the scientist’s. This causes everyone descended from this particular Hun to vanish instantly, including the scientist himself.
The resolution to the story is a little too convenient—as is the case with the resolutions to many of my own stories. In reality it’s very hard to envisage what might happen if you could kill your own ancestors.
It’s not necessary to resort to imagine tangling with your ancestors in order to understand the broader nature of the problem. You could get into your time machine and then travel backwards in time and stop yourself getting into the time machine in the first place.
If you never get into your time machine, how can you have turned up in the past to stop yourself going backwards in time?
We can even dispense with the human element altogether, and this leads us to Polchinski’s Paradox, proposed by string theorist Joseph Polchinski in 1990.
A billiard ball is fired with the correct trajectory to enter a wormhole, which transports it backwards in time. The billiard ball then collides with itself in the past, before it can enter the wormhole. So, the billiard ball never enters the wormhole and never travels backwards in time.
Then there are two billiard balls, and where did the second one even come from, if the first one did not enter the wormhole?
Some argue that this simply cannot happen, and the laws of physics must somehow forbid it—even if, according to some physicists—wormholes offer a real possibility for travelling backwards in time.
Perhaps the second copy of the billiard ball can only collide with the first in such a way that the first billiard ball still enters the wormhole. Perhaps, without the collision with its future self, it would not have entered the wormhole at all.
In this view, only self-consistent events can occur in the context of time travel. Perhaps you can meet your own grandfather, but you can’t kill him—or at least not until he’s conceived your mother or father. And perhaps that’s always what happened.
For the writer this idea offers a partial resolution of time travel paradoxes; whatever happened is always what happened, with time loops included.
This idea is known as Novikov’s self-consistency principle.
The Spanish film Timecrimes from 2007 is one of the few films about time travel that adhere to Novikov’s principle, and I would say is the best film I’ve ever seen about time travel. Along with the better-known film Looper, from 2012, which does not adhere to Novikov’s principle, it portrays a relatively realistic time machine, created by people who seem like they might actually have built a time machine.
Relativity by itself does seem to allow for backwards time travel, via so-called wormholes, which involve heavily warped spacetime, if you leave the grandfather paradox aside.
It may be that time travel to the past is possible, but Novikov’s self-consistency principle forms an additional law of nature, insisting upon only forms of backwards time-travel that do not result in outright paradox.
Igor Novikov was a Russian physicist, and the principle named after him was first formally proposed in his 1989 paper, Time machine and self-consistent evolution in problems with self-interaction.
We can also look at the grandfather paradox in a slightly different way. Take, for example, the Hitler paradox. We travel backwards in time to kill Hitler, before he got started with his whole disturbing project. But then, in the future, there’s no Hitler, so why would anyone have gone backwards in time to kill him, since he no longer exists?
Killing Hitler would therefore have to be forbidden by Novikov’s principle.
Backwards time travel finds its greatest paradoxes in interactions between the time traveller and the events that led to him to travelling backwards in time.
The “Meeting Yourself” paradox broadly considers what happens when a time traveller meets his past self. The grandfather paradox is example of this, as is a form of the bootstrap paradox.
Suppose you develop instructions for building a time machine, and you travel backwards in time and take those instructions to your past self, who then builds the very time machine that you then use to travel backwards in time.
I tackle this idea in my story Letters from the Future, in which an amateur scientist sends notes back to his past self that facilitate his invention of a time machine.
The question is, where did the knowledge of how to build the time machine actually come from?
Without a time machine, the inventor cannot meet his past self nor send messages to his past self, so the time machine cannot exist.
It seems as though these letters have no ultimate cause. The whole process has no way to get started, or in other words, to bootstrap itself, where the term bootstrap arises from the impossible idea of pulling yourself upwards via straps attached to your own boots.
Even if one alters the past in the most minimal way possible, the butterfly effect comes into play. Tiny changes in the past may well result in very large changes in the future. If, for example, on the day that Hitler was conceived, Hitler’s mother had had a headache—perhaps occasioned only by something small, like one cup of coffee too many or too few—the entire Nazi regime and the second world war might never have happened.
In general, the effects of small things seem to cascade over time into large changes; this is predicted both by classical physics and by computer models of physical processes, such as the weather, as Edward Lorenz discovered in 1961.
It then seems like any alteration to the past could easily produce changes that violate Novikov’s self-consistency principle, unless Novikov’s principle is a fundamental law of nature which the universe somehow enforces.
If Novikov’s principle really is a law of nature, we would expect backwards time travel to lead to various forms of predestination paradox. These aren’t true logical paradoxes, but they seem counter intuitive.
Sticking with the Hitler example, you might go back in time to kill Hitler, only to find, following the self-consistency principle, that your actions actually lead to the rise of Hitler.
If Novikov’s principle is really a fundamental law of the universe, then whatever happened in the past was, in a way, predestined to happen; at least in the sense that you can’t change it. Any attempt to change the past must only lead to the exact same things happening that have already happened.
Causal loops in general seem problematic for time travel, although the idea of self-consistency partially resolves their paradoxical nature. When time travel is involved, a sequence of events can cause itself. A causes B which causes A, and it’s unclear how the whole thing could have got started.
But then, let’s not forget, it’s unclear how the entire universe got started.
Consider the Münchhausen trilemma. This illustrates the impossibility of ultimately proving anything using logic alone.
Logic is a process of reasoning, which must always rest on certain axioms.
If you then try to use logic to prove your axioms, you will require other axioms.
There are three ways out of his, and none of them would be considered satisfactory by a logical positivist.
Either we must commit to an infinite regress of axioms, or else we must accept axioms that prove themselves in a circle, or else we must adopt the dogmatic approach and insist that our axioms are true without any further proof being needed.
We have here three forms of argument: circular, regressive and dogmatic.
The fictional Baron Munchausen after whom the trilemma is named, pulled himself and his horse out of a bog by his own hair: a form of bootstrapping.
A solution to a problem involving infinite regress satisfies few. Perhaps the Earth is supported by four elephants sitting on a giant turtle, but what is the turtle standing on? Does anyone really want an infinite tower of animals?
Perhaps we are made of atoms which are made of neutrons and protons, which are made of quarks, but what are quarks made of? Tiny strings, perhaps, and what are they made of?
The temptation, for scientists, religious believers and frustrated parents is always to fall back on a dogmatic argument: it just is. Superstrings aren’t made of anything else, and neither is God.
The alternative is some form of circular argument, where a thing causes itself. Perhaps even time is circular, with no beginning, and the future eventually leads to the past. But then the question remains: how did the whole thing get started, and without dogmatism, it’s impossible to answer.
Given that the universe itself seems altogether impossible, and certainly should not exist, arguments against causal loops in general seem weakened.
We can never state the ultimate cause of anything at all without resorting to dogmatism.
There are other arguments against backwards time travel which, while perhaps not appealing to everyone, carry weight with those of us who haven’t adopted science as our religion, at least not in its most materialistic version.
After Einstein developed the theory of relativity, the mathematician Hermann Minkowski showed that relativity could be understood in terms of a four-dimensional geometry. This involves the three dimensions of space with which we are all familiar—which we could think of as up-down, left-right and backwards and forwards—plus the addition of time as an additional pseudo-spatial dimension.
In this scheme, either the three dimensions of space or, more conventionally, the single time dimension, must be multiplied by the square root of minus one. The purpose of this whole shenanigans is to turn relativistic physics into a question of geometry.
The idea of time as the fourth dimension led some to take the idea very literally. The universe then becomes a four-dimensional structure in which the past, present and future are all simultaneously present.
But this isn’t, in truth, predicted by the theory of relativity. It’s only an assumption made in order to work with relativity geometrically. It fails to incorporate quantum physics, which, in important respects, removes linear predictability from physics, retaining it only at the statistical level.
The human eye is capable of perceiving even a single photon under the right conditions, and the behaviour of a single photon is not deterministically predictable, according to quantum physics. Physics does not, in fact, lead to a view of the future as necessarily predetermined. That so many people think it does, is, I think, a case of wishful thinking.
Without deterministic physics, categories of causation seem to become possible that defy any strict predictability, and cannot even always be subject to statistical analysis, and this unsettles many people.
A million subatomic particles behave in aggregate in a predictable way, but a single particle may affect, ultimately, the whole world, and its behaviour cannot be predicted.
The question of whether or not modern physics can be said to “allow room”, so to speak, for free will, is a huge topic. I’ve gone over all the arguments against free will quite carefully, and I find none of them at all convincing. But that’s a topic for a different video.
Instead of getting off on a tangent, let’s ask—if free will really does exist—what does this means for time travel to the past?
Suppose a person—let’s call him George—gets into a time machine and travels a week into the past. Then he goes to meet his former self. So now, there’s two of them.
Two distinct naming conventions are possible for the two Georges, if we want to distinguish them. Looking at the situation from the point of view of the original, past version of George, the George who travels backwards in time is another George, whom we could call George 2 or George B. The original George is then George 1 or George A.
This is the naming scheme used in the Spanish film Timecrimes, where a man named Hector travels backwards in time, becoming Hector 2 in the process.
On the other hand, we could view the situation from the perspective of the George who travels backwards in time. The George he encounters in the past, who is a past version of himself, would then be George 2, while the time traveller is George 1.
I’ll go here with the first naming convention; by travelling into the past, George becomes George 2. His original self in the past is George 1.
If we apply Novikov’s principle, it seems that George 1 now must get into the time machine after a week has passed, otherwise where did George 2 even come from?
But then George 1 seems to not have free will. He cannot choose to change his mind, even if George 2 begs him not to get into the machine for some reason. For that matter, it seems George 2 cannot prevent George 1 from getting into the machine by any means. He can neither kill him nor deter him.
I explore a scenario like this in my story Time Machine: A Terrible Idea.
There seems to be a conflict here between free will and Novikov’s principle.
Some people argue that the conflict is more apparent than real, since after all, free will is not the freedom to do absolutely anything; we are all subject to the laws of physics, and here is, perhaps, simply another law of physics that we are forced to obey under relevant circumstances.
But it is hard to see exactly why George 1 would have to get into the machine, and why George 2 wouldn’t be able to stop him. What form, exactly, would the intervention of the universe take?
If Novikov’s principle does not apply, then another interesting problem arises. Suppose George 1 does not get into the time machine, after meeting George 2. Then, from the moment that George 2 appears, there are two Georges, and always will be—at least till one of them dies, and even then the matter of which they are composed will still exist, even if decomposition radically changes its form.
This raises the question of whether, if the time machine can duplicate matter, another copy of George isn’t created every single time George gets into the machine, potentially creating a vast army of Georges.
Surely there was a point in time when George really had not created the machine, and could have chosen not to bother creating the machine. At that point there was only one George. Then George decides, of his own free will, to build the time machine, and he gets into it and travels back a week in time. Now the past seems to have been changed, and we have a whole week during which there were, in fact, two Georges.
Why wouldn’t yet another George be created, and a new version of the past be created with three Georges, if George gets into the time machine again?
If Novikov’s principle is real, there is only one version of the past, and it’s the version in which George builds the time machine and uses it to travel backwards in time. The only version of the past week that ever exists is the version in which there are two Georges. George could never have not decided to build the machine, and he could never choose to not travel backwards in time after he’s built it. For that one week, there were always two Georges.
If Novikov’s principle does not apply, an alternative possibility is that every time George travels backwards in time, a new version of the past is created.
This is the possibility I envisaged in my last story, Mountain Loop. In that story, Novikov’s principle initially seems to apply—but then, to obtain a satisfactory ending, I decided to ditch it completely.
It’s brilliantly explored in the 2009 British horror film, Triangle, which also makes excellent and horrifying use of the matter duplication aspect of time travel.
In contrast, the equally-brilliant Spanish film Timecrimes from 2007 seems to envisage a form of time travel in which Novikov’s principle perhaps does apply.
Physicists have long struggled to explain the bizarre laws of quantum mechanics, which were originally devised to explain atomic spectra, but which seem as though they should apply to ordinary life at the macroscopic scale, and yet—as illustrated by the Schrödinger’s Cat thought experiment—seemingly don’t.
It’s a funny thing about interpretations of quantum mechanics that, while none of them are provably correct, people tend to gravitate strongly to one or the other of them.
One popular interpretation is the many worlds hypothesis, which takes various forms, none of them fully worked-out.
This hypothesises that every time a quantum observation is made, whether under conscious supervision or not, the universe branches into two or more copies. Everything that can happen, does happen, according to this theory. It’s only a question of what happens in which universe.
If this is actually true, then clearly a universe (or class of universes) could exist in which George invents a time machine, but never encounters his past self. Right up until George actually gets into the time machine, perhaps only this universe exists.
When George travels through time and becomes George 2, another universe then comes into being in which George 2 meets George 1.
The two universes simply have different pasts.
If we accept that time travel is possible—which of course, for the moment, it isn’t, as far as we know—then it seems as though we either have to commit to the idea that somehow George is always going to get into his time machine, or else we are faced with multiple different pasts somehow existing.
The grandfather paradox is resolved either by removing free will somewhat from the picture, so that you simply can’t kill your own grandfather, or else by multiple universes allowing you to travel from one universe, where your grandfather has descendants, to another universe where you can kill your grandather, who then has no descendants in that universe.
You could try to argue that the universe where you kill your grandfather and the one where you don’t are the same universe, with different pasts.
But consider the universe where you do kill your grandfather. How, in this universe, did you go on to create the time machine? You can’t, because you are never born. Instead, you appeared at a certain point in time and, for unknown reasons, killed a man.
Yet you still remember the universe in which you were actually born. Perhaps you can still go back to that universe, but only by building another time machine and this time using it to prevent yourself from killing your grandfather. Bearing in mind the butterfly effect, this seems unlike to precisely restore the universe you fondly remember, but it might restore something very close to it, if you take care to prevent the killing with a minimum of fuss.
Whether we should say that these different pasts belong to the same universe or different parallel universes is perhaps a little bit unclear. Perhaps they were once the same universe, then they diverged when you went back in time and killed your grandfather.
Were two separate copies of everyone and everything brought into being at that point?
This is exactly the kind of thing that the many worlds interpretation of quantum mechanics envisages, and it definitely seems extravagant and, for most of us, a little unbelievable.
There’s one final paradox that I’d like to mention.
This is sometimes called the Fermi Paradox, since the Italian physicist Enrico Fermi once asked, “Where is everybody?”
He was referring to aliens but he could as well have been referring to time travellers. If, in the future, time travel to the past is invented, then where are all the time travellers now?
If what we might call the “many worlds” theory of time travel is correct, then the answer is that they are in a parallel universe.
Stephen Hawking once joked that he had held a party for time travellers, where he sent out the invitations after the party instead of before, but no-one showed up. His point being that it doesn’t seem as though there are any time travellers from the future around us.
No-one, as far as is known, has a credible plan for building a time machine, nor anything close to one. The closest physicists seem to have got is that apparently the theory of general relativity permits wormholes to exist in which spacetime loops back on itself—but the creation of such a wormhole would require far more energy than any human being is ever likely to control and the wormhole would likely crush anything that enters it, so that doesn’t seem very useful, nor practicable.
The best argument I can come up with in favour of backwards time travel is simply to vaguely assert that surely “everything is possible if only we knew how”.
That’s not a hill I want to die on.
But it is interesting to speculate about.
