'It's like in the films. You step on a b.u.t.terfly, you change the future of the human race.'

'Tell you what, then, don't step on any b.u.t.terflies. What have b.u.t.terflies ever done to you?'

'What if, I don't know, what if I kill my grandfather?'

'Are you planning to?'

'No.'

'Well, then.'

Martha Jones and the Tenth Doctor, The Shakespeare Code (2007)

In fact, the Doctor does change history. He frequently claims that time can be rewritten. When he visits the past, the future that is, the time we live in now is always at risk. In Pyramids of Mars (1975), the Doctor and Sarah battle the alien Sutekh who wants to kill all life on Earth in the year 1911. Sarah says that they already know Sutekh will lose because she is from 1980. The Doctor sets the controls of the TARDIS for 1980, which they find a desolate, ravaged world because they've not yet defeated Sutekh. Sarah agrees that they have to go back and finish the fight.

Does the Doctor cause paradoxes? We saw in Chapter 5 that in Day of the Daleks (1972) he changes an event in the present day to stop the Daleks conquering Earth in the future. He only changed history because people from the future told him what to do. Surely if he changes things, they never existed to be able to come back and tell him?

One possibility to explain what happens is that the new future the Doctor creates is something like the alternative worlds we talked about in Chapter 3. Imagine time as the letter I. The future is at the top, the past at the bottom. The TARDIS travels back in time from the future to halfway down the I. There, the Doctor makes a change and creates an alternative world: turning the I into a Y. He doesn't stop the original future existing altogether, he branches off from it. Some physicists argue that this might get around there being a paradox.

Doctor Who stories such as Father's Day (2005) or Turn Left (2009) show us other Earths, but make a point that these are branches created by the Doctor's companions (Rose saves her dad's life; Donna doesn't turn right on a particular day). In both stories, history must be put back on course, the alternative branch destroyed.

The trouble with branching history is that such an idea is very hard for us to test scientifically. Does it at least match the evidence in Doctor Who? The problem is that the Doctor never tells us exactly how time travel works. We know from River Song that he lies, but he's also vague on detail. He gives a good explanation in The Waters of Mars (2009), but begins by telling us that he's not sure if it's right.

'I mean, it's only a theory, what do I know, but I think certain moments in time are fixed. Tiny, precious moments. Everything else is in flux, anything can happen, but those certain moments, they have to stand. This base on Mars with you, Adelaide Brooke, this is one vital moment. What happens here must always happen.'

The Tenth Doctor, The Waters of Mars (2009)

In Kill the Moon (2014), the Doctor seems able to see how the future changes just by closing his eyes. He never needs to look up what counts as a fixed moment and what doesn't he seems somehow to feel it. In City of Death (1979), he and the Time Lady Romana are able to feel changes made to time, while in the 1996 television movie Doctor Who (1996), the Eighth Doctor can glimpse people's future just by having a good look at them. But perhaps his understanding is based less on the physics of whether it's actually possible to change history or not, and more on the moral case for whether or not it is right.

'You have heard the charge against you, that you have repeatedly broken our most important law of non-interference in the affairs of other planets. What have you to say? Do you admit these actions?'

'I not only admit them, I am proud of them.'

A Time Lord and the Second Doctor, The War Games (1969)

The Time Lords put the Doctor on trial twice in The War Games (1969) and The Trial of a Time Lord (1986). On both occasions, evidence is presented on screens as if the jurors are watching TV.

We're told in The Trial of a Time Lord that this evidence was recorded by the TARDIS. That's interesting because it implies how the TARDIS ought to be used. We know TARDISes are designed to disguise themselves, blending in with their surroundings. (The Doctor's TARDIS is stuck in the shape of a police box, but if its Chameleon Circuit was working properly, it would change its shape wherever it landed.) If Time Lords can blend in with their surroundings un.o.btrusively, it suggests they can visit other worlds and times without making any change. They never risk stepping on b.u.t.terflies and thus changing the whole of the future.

The charge against the Doctor is that he's been irresponsible. If it's all right for Time Lords to travel through time and s.p.a.ce and observe what's going on, the problem with what the Doctor does must be that he's not content to merely watch. He steps out of the TARDIS the implication being that even just doing that changes the initial conditions of wherever he turns up, and so changes history to at least some degree.

In both trials, the Doctor's defence rests on the fact that he battles evil, defeats monsters and improves the lot of the people he meets. He is changing things implicitly, he is changing history for the better.

Both times the Time Lords concede the point and allow the Doctor to continue his adventures. After The War Games, they exile him to Earth but at a time when Earth will need his help, and even then they send the Doctor on specific missions to alien worlds, too. In Genesis of the Daleks (1975), the mission they send him on is explicitly to change history: they want the Doctor to stop the Daleks ever being created. (We'll discuss this, and time travel being used as a weapon, in Chapter 9.) The issue in Genesis of the Daleks and more broadly in Doctor Who is not whether history can be changed but whether it should be. That seems to match another important law of the Time Lords:

'The First Law of Time expressly forbids him to meet his other selves.'

Time Lord Chancellor, The Three Doctors (19721973)

This First Law of Time is presumably to prevent earlier incarnations of the Doctor learning information from or about their future selves that would create a paradox. Yet exceptions can be made: in The Three Doctors, the Chancellor is overruled and the Time Lords themselves send the First and Second Doctors to a.s.sist the Third. In fact, when the Doctor meets his other selves in The Three Doctors, The Five Doctors (1983) and The Day of the Doctor (2013), it's because Gallifrey itself is in danger. The Time Lords might have laws about changing history, but the only way the Doctor can save his own people is to ignore their rules. (In The Day of the Doctor, it seems the Doctor forgets his encounters with his future selves, which solves the problems of paradox.) Despite all these potential problems some scientists think that there might just be a way of travelling into the past, but this involves one of the strangest ideas in physics: a wormhole.

Wormholes are effectively a 'shortcut' in s.p.a.ce-time, linking two otherwise distant parts of the universe. Although they are predicted by some branches of theoretical physics, no one knows if they actually exist certainly scientists have yet to find any convincing evidence for them. If wormholes do occur in nature they're likely to be extremely small and only last for a tiny fraction of a second, but some physicists have speculated that it might just be possible to stabilise one and expand it to a size that a person or even a s.p.a.ceship might fit through. As well as providing a shortcut through s.p.a.ce, such a wormhole might also provide a means of travelling back and forth through time.

The wormhole creates a shortcut between two parts of s.p.a.ce-time, A and B, linking them in both s.p.a.ce and time. An object travelling through the wormhole from A would arrive at B much more quickly than if it had travelled through conventional s.p.a.ce.

Imagine that two physicists manage to create a useable wormhole in their laboratory. By stepping into one end of the wormhole, they can emerge instantaneously at the other end, which is on the far side of the lab. This is fun, but not particularly useful. Now the first physicist takes one end of the wormhole and places it inside a s.p.a.ceship, leaving the wormhole's other end in the laboratory. Bidding farewell to her colleague she pilots the s.p.a.ceship out into the depths of the cosmos, travelling at ninety-nine per cent of the speed of light.

Back in the lab, her colleague tracks the s.p.a.cecraft through a powerful telescope. After watching for a hundred years, this physicist is now very old. But on the s.p.a.cecraft, ninety-nine light years from Earth, things look rather different. Travelling at such a colossal speed, time on board has been pa.s.sing at a vastly different rate and, while one hundred years have pa.s.sed on Earth, only ten years have elapsed on the s.p.a.cecraft. The first physicist is just ten years older than when she left home and so is the end of the wormhole which she has carried with her.

This is where the strange properties of wormholes could become useful for time travel. The two ends of the wormhole remain directly linked to each other in s.p.a.ce, forming a shortcut between the laboratory and the s.p.a.ceship. But they are also linked to each other in time. The end of the wormhole on board the s.p.a.cecraft is now ten years old, and is connected to the end of the wormhole back in the lab when it was also just ten years old. By stepping into the wormhole on board the ship, the first physicist will emerge back in the lab, but only ten years after she left it. She has effectively travelled ninety years into her past. She could even join her colleague who would also only be ten years older at his telescope and see her s.p.a.ceship, still only partway through its journey. The two physicists could then step back through the wormhole and emerge instantaneously on the distant s.p.a.cecraft, just moments after the first physicist left it, ninety years in the future.

If a wormhole used in this way can allow travel both backwards and forwards through time, what about the grandfather paradox? Could the first physicist travel back to the lab and prevent the wormhole from ever being created, thus preventing her from travelling back in the first place, thus preventing her from preventing the wormhole and so on into an infinite paradoxical loop?

Luckily, time travel by wormhole seems to come with its own in-built paradox prevention mechanism. Because the two ends of the wormhole are always linked to each other in time, you could never enter one end to emerge from the other before the wormhole itself was created. The physics of the wormhole would also stop you from meeting past and future versions of yourself. Because the physicist has to move her end of the wormhole through s.p.a.ce before she can use it to travel back in time, when she gets round to making her trip back in time to the lab, her past self has already left on the s.p.a.ceship.

Perhaps something like that is happening in Doctor Who. We know that the Doctor's people, the Time Lords, are one of the oldest civilisations in the universe. They invented time travel long before everyone else as we've already seen, the Doctor claims in The Satan Pit (2006) that his people 'practically invented black holes'. Perhaps the first black hole is like the end of the wormhole fixed in the lab. When the Doctor visits us in what we think of as the present day, to him it is the far future like the wormhole on the s.p.a.cecraft. He can still head back through the tunnel to his own time, but his own time is slowly moving forward in time.

That might explain why the Doctor's encounters with his own people occur in the same order for both him and them. It doesn't even need to be encounters on Gallifrey itself. The Master is, like the Doctor, a time traveller, and yet usually when they meet they refer to the events of their previous meeting and it's the same previous meeting for both of them. For example, in The King's Demons (1983), the Doctor says that he last saw the Master trapped on the planet Xeriphas in Time-Flight (1982). The Master explains that he found the robot Kamelion on Xeriphas and used it to escape.

Compare that to the Doctor's meetings with River Song, which don't happen in the same order for both of them. Whenever they meet, they need to work out where in each other's timelines they are.

'Right then, where are we? Have we done Easter Island yet?'

'Er, yes! I've got Easter Island.'

'They worshipped you there. Have you seen the statues?'

River Song and the Eleventh Doctor, The Impossible Astronaut (2011)

If there was any chance that the Master in The King's Demons had not yet experienced the events of Time Flight because they remained in his future surely the Doctor would not dare to mention Xeriphas, for fear of giving the Master an advantage when he eventually gets there. Instead, the Doctor takes it for granted that he and the Master experience events in the same order.

If that's generally what happens, there are exceptions. In The Five Doctors the story immediately following The King's Demons the Master meets four incarnations of the Doctor all at once. The first three Doctors are all meeting him out of sequence.

There's also evidence that the Doctor can sometimes travel back into Gallifrey's past or to before the Time Lords invented time travel. In Listen (2014), the TARDIS lands in a shack where Clara meets the Doctor when he was a child. This moment is clearly way back in the Doctor's past, long before any previous story set on Gallifrey. We may also have seen time travel capable of reaching back to the very start of the universe. In Terminus (1983), fuel from a time-travelling s.p.a.ce station is jettisoned and explodes, and the Doctor concludes that it might have caused the Big Bang the beginning of time and s.p.a.ce as we know it.

In Doctor Who, it therefore seems possible to travel back to a time before the first time machine or wormhole is invented. Maybe, one day in the future, we will understand how.

The Doctor, all silver hair and belligerent eyebrows, had promised Clara Rome; so far, he'd given her several miles of uninhabited Germanic forest, which he'd irritably pointed out was still a part of the Roman Empire so, broadly speaking, was more or less what she'd asked for.

Clara had disagreed, but as she looked down into a valley cut in half by a vast, winding river, she was glad she had the chance to see her world like this. Like the forest behind her, it felt so much wilder, grander, than the Earth she knew. Even the air seemed to taste different.

'Aurochs,' said the Doctor, pointing at a great herd of animals grazing by the river. 'Extinct hundreds of years before your century, but you can find them all over Europe just now.'

'They look like really big cows,' Clara said.

'They are.'

'Are they dangerous?' she asked. Their horns were over two feet long, and she really didn't fancy being on the wrong end of a charge.