'The Doctor has his own museum?' Martha blinked at that idea.

'A monument to his adventures and accomplishments,' said the android. 'Built by the grateful Reldeenii people after he saved them from a neuro-parasite invasion.' The lenses shimmered and the robot projected a holographic 'skin' over its metal form, and Martha found herself looking at a mirror image. Then it juddered and changed into various different versions of her. There she was in the lab coat she wore as a medical student. In some kind of all-black military outfit, with short hair. Dressed like a Victorian housemaid. In a s.p.a.cesuit. 'Stop!' she shouted, and the image flicked back to its earlier setting. 'Why do you look like me?'

'I am an exhibit. I represent Martha Jones.' She c.o.c.ked her head. 'I'm sorry. They made me come here. I was stolen from the museum. They reprogrammed me. I didn't have a choice but to tell you all those things.'

Martha struggled to hold all the questions she had in her thoughts, and went for the most important. 'Who did this?'

'If you won't go of your own accord, they'll have to take steps,' said the android. 'A more permanent solution. They didn't want to do that, in case it disrupted the timeline even more. But now they have no choice!' Her duplicate grabbed her hand. 'I didn't want this to happen, Martha! I'm programmed to be just like you. I didn't want you to get hurt...'

The dark stone wall behind the android rippled, and it began to peel back as forces from across time pushed their way into the damp cavern.

'You have to run!' cried the android.

'That time has pa.s.sed,' said a hissing, breathy voice, from a mouth with far too many teeth. A hulking, muscular figure came into existence, a monster with blue-grey flesh and a huge head that was sharp like the prow of a ship. It had dead eyes, doll-like black marbles that radiated malice. All over its body were cybernetic implants and embedded armour plates, and a long, finned tail trailed lazily behind it. If a shark could walk and talk, this was how it would look. 'You would not delete yourself from the Doctor's timeline willingly,' it gurgled, flexing clawed hands. 'So you will be undone here instead.'

The sonic screwdriver didn't work. It usually works, the Doctor said to himself. He could do so many clever things with the tool, and he was sure he'd got it right this time. Use the sonic to project solid-wave sound echoes off the basalt rock walls, confuse the targeting system of the drone, make it stumble, cause a cave-in and bury it. Good plan. Great plan. Brilliant plan.

If it had worked, of course. But instead, the machine saw right through the sonic illusions he created and came smashing its way toward him, and this time it had plasmatic flame-throwers and bone-seeker microdarts with his name on them.

'Time for Plan B!' he shouted, and ran away in big splashy steps with an angry robot octopus on his heels.

'Get lost, mackerel-face!' Martha shouted.

The shark-man was fast, and it was all she could do to keep out of the reach of the glistening talons on the end of its fingers.

'You merely prolong the inevitable,' it hissed. 'The Karadax will see victory at your end, human. Your absence is the key-point. Without you, the Doctor fails.'

'Stop-' began the android, but the Karadax warrior shoved it away.

'We calculated for centuries,' said the creature. 'Found the exact moment. Laid our plans.'

'Why?' Martha shot back.

'The Doctor!' roared the Karadax. 'Again and again, the Time Lord has thwarted our plans for conquest! So we drilled into the deep past, searching for the perfect time to strike. Through you, human. We will change our own defeats into victories. We rewrite history!'

Martha saw an opening and broke into a run but the warrior slapped her back with a heavy blow that shocked the air from her lungs. She landed hard on the sandbank, groaning in pain.

As Martha looked up, the shark-man loomed over her, his too-wide mouth yawning open to reveal row after row of dagger-tip teeth. 'The journey from the future was long,' he said. 'It made me hungry.'

'No!' Martha heard the shout in her own voice, and suddenly she was watching herself attack the Karadax, a different Martha Jones grabbing the alien's dorsal fin and punching him in his gill-slits. The warrior spun around, and the museum android's holographic skin winked out, but the Karadax could not dislodge the machine's implacable grip. 'Overloading holo-matrix!' she cried.

Martha had to cover her eyes as a powerful electrostatic charge blazed out of the robot's core and shocked through the Karadax's twitching body. She smelled cooked fish and the shark-man released a bellow of agony as sparks collected around the implants fixed to his flesh.

Finally, the android dropped, but the Karadax was still wailing, beating at itself as it were trying to put out flames. Then at once, the ground beneath the alien's feet rippled and he fell into nothingness with a tortured screech, disappearing from sight.

'What... just happened?' Martha staggered to the exhibit-droid's side.

'I short-circuited his temporal recall module,' explained the machine. 'Sent him back to his origin point in the far future.' Her voice was slurred and full of static. 'At considerable cost to myself. Power levels dropping. Shutdown imminent. I am sorry, Martha Jones. I am programmed to be like you. I wanted to be... You.'

'You think I'm that brave?' said Martha, in a small voice.

'I-I know it,' the android stuttered. 'What I said before. S-some of it was not true, some of it was. I must tell you what's to come.'

'No!' Martha shook her head firmly. 'Don't. That would be rewriting history, wouldn't it? And we shouldn't mess with that.' She paused, thinking. 'I don't need to know my future, I trust the Doctor. That's enough for me.'

'Yes,' said the android, the light in her eyes fading. 'You are going to be... Brilliant...'

And then Martha was alone.

The Doctor burst into the cavern where he had left Martha, with the octopoid a heartbeat behind him, and he instantly had the sense that he was missing something. For starters, there was a robot of some kind lying on the rocks, that he was sure hadn't been there when he'd left, and Martha looked like she was fit to burst into tears.

'You all right?' he offered.

But before she could answer, the war machine crashed into the gap in the rocks and gave a furious howl. The cavern entrance was too narrow for it to fit through, and it began clawing at the sides, breaking off bits of black rock, trying to widen the gap. Its oval body squeezed forward, the bright blue sensor grid flashing cold light across the chamber.

'Tell me later!' the Doctor said. 'The box! I need it right now, tell me you've still got it!'

Martha blinked like she was shaking off a trance and then looked around. 'I had it... I must have dropped it when... I mean...' Something caught her eye and she dashed across the cavern. 'Here it is!'

He watched her s.n.a.t.c.h up the little plastic box floating atop the sloshing water and his hearts sank, both at once. 'Please do not say you got the contents wet! If you got it wet, we are in a lot of trouble!' He ducked as the octopoid managed to get a single tentacle into the cavern and whip it around.

She fished out the old sock and held it like it was a dead rat. 'Why did you give me this?'

The Doctor grabbed it, a grin blooming on his face. 'You trust me, don't you?'

'Yes,' she said, a little warily.

He bounded away toward the drone. 'Karadax technology is very good stuff, but it does have a weak point. It doesn't react well to certain kinds of dry, organic, non-conductive materials...' He got to the 'head' of the oval body and stared right at it. 'Like, for example, if you stuff a smelly old sock into one of their very delicate sensor grids.' The Doctor did exactly that, and the octopoid let out a howl of distorted sound that was almost a cry of pain.

It staggered backwards, tentacles reaching up to pluck at the grid and failing to dislodge the errant footwear. Something important deep inside the machine sizzled unpleasantly and all life fled from the drone. The machine skidded into a deep pool and sank silently beneath the surface.

'Done,' he said, with a smirk, brushing imaginary dust from his fingers. 'Hmm. That was a bit harder than I thought it would be, actually. From now on, I'll keep a closer eye on the Karadax. Come back every hundred years in case they're trying anything else unpleasant, and put a stop to it.' The Doctor turned around and fell into a hug as Martha grabbed him. 'Oh. Um. OK.'

She gave him a squeeze, then let go. 'Glad I could help.'

He looked around, frowning. 'Did, uh, something happen while I was gone?'

A smile crossed Martha's face. 'Nothing you need to worry about. Just you and me, being brilliant.'

That made him grin again. 'Yeah, I suppose we were!' he said. 'Come on, then. Back to the TARDIS. Stuff to do. Things to see.'

'History to make,' she added.

He offered her his hand. 'You got that right, Martha Jones.'

'I have seen you change time, I have seen you break any rule you want.'

'I know when I can; I know when I can't.'

Clara Oswald and the Twelfth Doctor, Dark Water (2014)

Even as you read this sentence, you are travelling in time. We're all time travellers, moving at a constant rate of one second per second, each of us growing steadily older. The trick would be to move at a different speed from everybody else either faster into the future or back into the past.

Surprisingly, we can already travel into the future to a small degree. Einstein's Special and General Theories of relativity predicted that relative velocity and gravity can both alter the rate at which we experience the pa.s.sage of time compared to observers moving at different speeds or experiencing a different gravitational field from us. This process is called 'time dilation'. In Chapter 1, we saw proof of Einstein's theory, in which he correctly predicted the position of the planet Mercury given the warping of s.p.a.ce-time by the Sun. Today, modern technology gives us many examples of relativistic time dilation in action.

When we send craft into s.p.a.ce, differences in gravity and velocity affect the amount of time which pa.s.ses for them, relative to us back here on Earth. The clocks on s.p.a.cecraft travelling to low Earth orbit have been shown to run very slightly slower than clocks on the planet's surface. Clocks on satellites circling Earth run very slightly faster than clocks on the ground. The differences are only fractions of a second, but if the navigation systems in our cars and mobile phones which use satellites as a reference are to work properly, this difference in time must be taken into account. Because that means keeping track of very slight variations, satellite navigation systems usually keep correct time to about a 10,000,000th of a second.

We would see a greater effect of time dilation on longer and faster journeys into s.p.a.ce. The closer to the speed of light a s.p.a.cecraft travelled, the more time would dilate. For example, imagine a very fast s.p.a.cecraft is sent out to explore s.p.a.ce travelling at ninety-nine per cent of the speed of light. The astronauts would return to Earth after experiencing the pa.s.sing of ten years on board the ship but they would discover that on Earth one hundred years had pa.s.sed. (In the Doctor Who story Aliens of London (2005), the Doctor thinks he and Rose have been away for twelve hours, but they discover that for people on Earth it has been twelve months. However, this isn't the result of time dilation but of the Doctor making a mistake.) The astronauts on their s.p.a.cecraft and the people on Earth wouldn't feel time pa.s.sing any quicker or slower. Their local experience of time would remain the same. This is because, as Einstein said, time is relative: you only notice the difference when you compare different clocks moving at different speeds. (This seems to be fundamental to the TARDIS, the initials of which stand for Time And Relative Dimension In s.p.a.ce.) The astronauts in our example would effectively be travelling a hundred years into the Earth's future while using up only ten years of their own lives effectively jumping ninety years ahead of where they'd be if they'd stayed at home. The faster their s.p.a.cecraft could fly, the further into the future it could take them. In Chapter 4, we saw how the extreme gravity close to a black hole has a similar effect, slowing the local pa.s.sage of time while time outside pa.s.ses at its usual rate, potentially allowing an astronaut to fast-forward into the future.

So travelling forwards in time is certainly possible if somewhat risky. But is it possible to travel in the opposite direction, backwards into the past? After all, if you can only go forwards into the future then time travel is a one-way trip and you could never return to your own time. But if we can go back in time, that begs an intriguing question: is it possible to change history?

When Doctor Who began, the Doctor was quite clear that we couldn't change history. As he told his companion, Barbara:

'But you can't rewrite history! Not one line! ... What you are trying to do is utterly impossible. I know, believe me, I know.'

The First Doctor, The Aztecs (1964)

That might be interpreted as the Doctor saying that we can, technically, change history but we ought not to. However, later the same year the point was made more explicitly. In The Reign of Terror (1964), Barbara and Ian see Napoleon years before he becomes emperor of France. Ian wonders what would have been the result had they written Napoleon a letter telling him some the things due to happen to him. The Doctor's granddaughter Susan explains that, 'It wouldn't have made any difference, Ian. He'd have forgotten it, or lost it, or thought it was written by a maniac.'

The implication is that they physically cannot change history. If they try to, circ.u.mstance will conspire to stop them. As Barbara says, 'I suppose if we'd tried to kill him with a gun, the bullet would have missed him.'

Some physicists agree that circ.u.mstance or some force of nature would stop you changing history. One argument given for why we can't change history is the so-called 'grandfather paradox'. The idea is that you go back in time to a point before your grandfather had children. You shoot and kill your grandfather, so he never has children which means one of your parents now never existed. That means you never existed, either. However, if you never existed, you can't have gone back in time to kill your grandfather so he was never shot. But if he was never shot, he had children and grandchildren, and that includes you. Which means you're able to go back in time and shoot him... We go round and round in a loop.

A paradox isn't only created by killing someone. In Dark Water (2014), Clara asks the Doctor to change history and save the life of Danny Pink. The Doctor has to say no.

'If I change the events that brought you here, you will never come here and ask me to change those events. Paradox loop. The timeline disintegrates. Your timeline.'

The Twelfth Doctor, Dark Water (2014).

Note that he doesn't just say no because a paradox would be created, but because that paradox would destroy Clara. So in Doctor Who, it is possible to create paradoxes, but they have deadly consequences which we'll discuss more in Chapter 9.

It's thought that paradoxes might even be created by tiny changes to history. In 1961, the American meteorologist Edward Lorenz used a computer programme to predict the weather. This involved entering a series of numbers describing the initial conditions, then letting the computer work out what those initial conditions would lead to. One of the numbers to be entered was 0.506127 but to save time Lorenz rounded it up to 0.506. He was then amazed to discover that this small change in just one of the initial conditions produced a radically different prediction of the weather.

This phenomenon became known as the 'b.u.t.terfly effect' named after the idea that a b.u.t.terfly flapping its wings could eventually trigger the circ.u.mstances which lead to a hurricane on the other side of the world. It's not that the b.u.t.terfly causes the hurricane, but without the b.u.t.terfly, the initial conditions are different so the complex chain of events leads to something else perhaps a nice sunny day.

The weather is just one of a number of systems that can be ma.s.sively affected by small changes in initial conditions. Since these systems can be so complex that they appear chaotic, attempts to understand them better are known as 'chaos theory'. Chaos theory suggests that even a tiny change in history could be catastrophic for the world as we know it.

In Doctor Who, the Doctor doesn't seem too worried about this. When he takes Martha Jones back in time to meet Shakespeare, Martha asks about changing history.