Let’s say that at noon tomorrow, time travel is invented. A brilliant scientist – let’s call him Dr. Jones – creates a machine that harnesses a huge amount of energy to tear apart the fabric of space time itself, in the process sending willing punters to any and every moment of their choosing. Better still, Dr. Jones’ machine is one without restrictions: it can send you into both the future or the past, as far as you would like to go.

If the whim took you, you could travel back to the emergence of the universe; to the assassination of JFK; to your own birth. Or, you could fling yourself into the opposite direction: you could be there for the heat death of the universe itself.

Now, let’s imagine a time traveller named Tim. Tim isn’t interested in using Dr. Jones’ newly-minted machine to watch humans invent fire, or to stand, curiously unaffected, over his own deathbed. No. Tim wants to use the machine to murder his own grandfather.

Watch physicist Brian Greene talk time travel here:

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See, Tim’s grandfather, a mean-looking bastard named Richard, was as awful as they came. Richard spent his twenties accruing notoriety as an arms dealer – he sold dirty bombs to terrorists, and machine guns to African warlords looking to slaughter women and children. From the age he could throw rocks at cats, to the very moment he died, hit by an errant rooftile shortly after conceiving Tim’s father, Richard made it his mission to make the lives of those around him hell.

So, the moment Tim learns of Dr. Jones’ time machine, he knows exactly what to do. He will travel back to Richard’s 12th birthday party, pull out a gun and shoot his own grandfather before his villainy can truly begin. He will save the suffering of thousands. He will rid the world of an unrepentant, murderous old sod of a person.

In a world in which time travel exists, it makes perfect sense that Tim could shoot anyone from the past.

But there’s the rub. How on earth can Tim kill his own grandfather? If Tim kills Richard before Tim’s own dad has even been conceived, Tim will never have existed. After all, if Richard dies at his 12th birthday party, he won’t be around to conceive Tim’s dad. He’ll be long dead by then, an infant body rotting in a grave. Sure, Tim can kill Richard after he conceives Tim’s father, but what use is that to Tim? It seems pointless to take Richard out after his evil deeds have already been committed.

So, it seems like Tim can’t kill his grandfather. And yet the question remains: what exactly is stopping him? On face value, there’s nothing restricting Tim from travelling back to Ancient Rome and taking down Caesar with an assault rifle, after all – that seems logical. In a world in which time travel exists, it makes perfect sense that Tim could shoot anyone from the past; he’s as able to do it as he is to step out of his house and shoot a random civilian. So what force is stopping Tim?

At this point, some might feel like they have a solution: perhaps they’d like to suggest that Tim shooting his grandfather creates a “new” timeline. This, after all, is the solution that Hollywood tends to utilise. So much so in fact, that you can almost imagine how this would go down in a big budget studio movie: Tim, armed to the teeth, arrives back at his grandfather’s 12th birthday party, pulls out a shotgun, shoots the baby-faced Richard… and then suddenly disappears into a cloud of acrid-smelling smoke, having essentially murdered himself out of existence.

But this is no solution. This is a fallacy, one so common that it even has its own name: the second-time around fallacy. Tim can’t create a “new” timeline by murdering his grandfather. See, in a world where time travel is possible, backwards causation is possible. That means in a time travel world, cause can follow effect, not the other way around.

Watch Neil deGrasse Tyson talk time travel:

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By means of explanation, let’s say Tim goes on a different mission: say he goes back in time and slaps his 14-year-old self on the face. In this world, before Tim even steps into the time machine, he has necessarily already been slapped in the 14-year-old face. The slapping comes first; the getting in the time machine to do the slapping – the closing of the time travel loop – happens long after.

For that reason, if Tim has successfully shot and killed Richard at Richard’s 12th birthday party, that has already happened long before Tim has even been born. All Tim is doing by stepping into the time machine is providing the cause for an effect that has already been the case.

But again, Tim necessarily can’t have shot Richard at his 12th birthday party. So what the fuck is going on here?

The above, put crudely, is the grandfather paradox. Once upon a time, it seemed like a knock-down argument against the existence of time travel. We needn’t worry about whether or not time travel might be physically possible, some philosophers thought. Such a paradox appears to prove that it’s not even logically possible.

After all, the world follows logical laws. To imagine that we might live in a fundamentally illogical world is such a big bullet to bite, many thinkers were happy to give up on the idea of time travel in order to preserve it.

Many – but not all. This is where the philosopher David Lewis came in. A great mind with a striking array of interest areas, Lewis loved ruminating on the apparent paradoxes others saw in time travel. And unlike so many others, he had a neat resolution to the puzzling grandfather paradox.

Listen to a talk by philosopher David Lewis here:

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Here’s how he put it. According to Lewis, Tim can shoot his grandfather, but he necessarily doesn’t. That’s a lot to unpack, so let’s start first with that word ‘can’. What does it mean? Well, it refers to a little pool of facts that are all true in respect to each other – the technical term is that they are ‘compossible’ with each other. So, it is true Tim can buy a gun; it is true Tim can pull a trigger; it is true that Tim can travel back in time. These things are all true in and of themselves. And, more than that, they are true in relation to each other; they are all compossible. No one of these facts is impossible in the context of the others.

However, let’s add another fact into this pool: that Tim can murder his grandfather. This is where the problem arises. Tim murdering his grandfather is not compossible with Tim being able to travel back in time. Suddenly, two facts start negating each other. After all, if Tim had succeeded in killing his grandfather, he wouldn’t be around to get into the time machine. He wouldn’t even exist. He would be a non-entity; a curiously unimaginable thing. So he can’t both kill his grandfather, and travel back in time.

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So. What does this all actually mean? It means that Tim can indeed get into a time machine and travel back to Richard’s 12th birthday party. It means he can take a gun with him. It means he can raise that gun, point it directly and the young Richard, and fire the shot. But it also means that he must necessarily miss. Let’s try and imagine it. Let’s say that just as Tim’s about to take out his young grandfather, he slips on a banana peel, and unloads a clip into the ceiling. He fails.

This is Lewis’ solution to the grandfather paradox. And to some then – and still some now – it seems utterly, unreservedly bonkers. After all, sure, it’s somewhat believable that Tim’s first assassination attempt might fail. But let’s not forget: he’s got a fucking time machine.

Tim has unlimited opportunities to go back and re-attempt to kill Richard at that party. Sure, he might slip on a banana peel the first time. But then he can simply get back in his time machine, re-arm himself in the present, and return to the party, looking out for banana peels this time. But even then, this second attempt must necessarily fail.

Tim has unlimited opportunities to go back and re-attempt to kill Richard at that party.

You can stretch this example as far as you want: push it to the very boundaries of what seems to make logical sense. Hell, Tim can even hire a small army, give ‘em each an assault rifle, take them back to Richard’s 12th, line them up in a circle around Richard, and get them to pull the trigger at exactly the same time – and even in this case, every single one of them will fail.

This is the part some philosophers don’t want to swallow. This, they argue, is Lewis testing the very limits of credibility and sense. But again, some is not all, and the logician Nicholas J. J. Smith has a neat response to these objections in his excellently-titled paper ‘Bananas Enough For Time Travel?’

Watch a guest lecturer with philosopher David Lewis here:

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As Smith outlines it, the cries of illogicality only come when we read the story the wrong way around. So let’s do exactly that. Here’s the wrong way to read the story of Tim and his mercenaries: something has had to stop Tim from murdering his grandfather. A force – maybe chance – has come to Richard’s rescue. This force has placed a banana peel under the foot of every mercenary. And it has done this because it has been required that Richard must not die.

This version of the story is wrong for a simple reason; it doesn’t take into account backwards causation. After all, it’s not only that the banana peels have saved Richard’s life; it’s that the banana peels have themselves been required to allow Tim and his mercenaries to step into the time machine in the first place. If the banana peels weren’t there, Tim would have successfully killed his grandfather, and if he had done that, he wouldn’t be able to amass an army of mercenaries and step into a time machine. The banana peels have made Tim standing there in the past possible in the first place.

Which, of course, is still totally fucking bizarre. But, as Lewis himself put it, it’s not really such a stretch to imagine that a world with time travel in it might just well be a little bonkers.

Some arguments in this feature were previously made (albeit in a different form) in the paper The Apparent Paradoxes of Time Travel by Joseph Earp.