The third type of story would have seen the TARDIS travel 'sideways' in time. An early example is The Edge of Destruction (1964), but the sideways kind of story was pretty much abandoned as a result of the huge success of the Daleks. Gradually, the show became more about battling monsters. By 1967, even stories set in Earth's history had sci-fi monsters lurking in them.

There's another example of a sideways story from the first twelve months of the series. In Planet of Giants (1964), the TARDIS doors open just as it is landing and because of what the Doctor calls 's.p.a.ce pressure' he and his friends are miniaturised. They've landed in a garden in England, apparently in the (then) present day.

Planet of Giants is not the last time the Doctor is miniaturised. It happens again in The Invisible Enemy (1977), The Armageddon Factor (1979), Let's Kill Hitler and The Wedding of River Song (2011), and Into the Dalek (2014). In each story, things that are normally harmless such as a cat, a virus or antibodies suddenly become dangerous because our heroes are so much smaller. The process was even used as a weapon. Between Terror of the Autons (1971) and Planet of Fire (1984), the Master frequently killed people by miniaturising them though when he accidentally miniaturised himself, it didn't kill him.

If we really could miniaturise ourselves and survive we'd find the micro-world very strange indeed. For one thing, the molecules of the air around us would be proportionately larger, so we would feel the air as thicker, warmer and more viscous. It would be a little like walking through a heated swimming pool. Just as humans can float in water, small creatures find it easier to fly because the syrupy air helps to support them. Just as we can dive safely from a diving board into deep water, small creatures can safely tumble from great heights because the air cushions their fall. Maybe next time the Doctor and his friends are miniaturised they could have a go at flying.fn1 When we've seen the Doctor miniaturised, he and his friends can still recognise and interact with the world around them: in Planet of Giants, they mountaineer into a kitchen sink, light a match the size of a battering ram and help to catch a full-sized murderer. But go smaller, and the world is unrecognisable and very strange indeed.

At our normal scale, we can use everyday laws of physics to work out how things relate to one another. For example, if someone throws a ball, we can work out how to catch it from the amount of force used to throw it, its speed and the direction it's going in. We often work all that out in our heads without even realising: when a ball is thrown to us, we catch it. A skilled cricketer (such as the Fifth Doctor) can do more, judging the movement of the ball just right to hit it with a bat and send it to a good spot on the cricket pitch.

But at a much smaller scale, things don't move like a cricket ball. Take light, for example. As we saw in Chapter 2, light moves at 299,792,458 metres per second, but to understand how it moves and predict its movements like we can with a cricket ball we need to know what it's made of and how that stuff behaves.

What is light made of? The smallest possible amount of any physical ent.i.ty is called a quantum (from the Greek word for 'how much'). Quantum mechanics is the science of working out how quanta behave. It usually comes into effect on a very small scale of less than 100 nanometres a nanometre is one billionth of a metre; there are a million nanometres in a millimetre and is extremely strange. It doesn't help that light sometimes behaves like a particle (that is, like a very, very small cricket ball) called a photon and sometimes it behaves like a wave of energy. But is it a particle or a wave? Oddly, it can be either or both at the same time. Scientists call this strange property of quantum mechanics 'wave-particle duality'. Sometimes, quantum particles are even able to pa.s.s through solid barriers in a process called 'tunnelling' (which doesn't actually involve tunnelling at all). The weird behaviour of matter and energy at quantum scales is so far removed from everyday experience that it is very hard to visualise even for physicists. Richard Feynman, who won the n.o.bel Prize for his work in physics, once said: 'I can safely say that n.o.body understands quantum mechanics.'

In this chapter, we're interested in just one small part of quantum mechanics: the so-called uncertainty principle. Objects on the quantum scale are so small that we can't measure them without affecting them, which in turn affects the measurement that we're trying to make. In 1927 German physicist Werner Heisenberg explained that the more precisely we know where a particle is, the less precisely we can know how fast it is moving and vice versa. We can never be entirely certain about every single detail of a particle or a system of particles and there's no such thing as an independent observer the observer is always inextricably involved in the process that he or she is trying to observe.

However, although we can never have precise knowledge about the exact state of every particle in a system, we can still work out the probability of how the system will behave. In 1926, Austrian physicist Erwin Schrdinger came up with an equation that can be used to predict the behaviour of particles in terms of probabilities.

An odd consequence of Schrdinger's equation is that, although it describes the behaviour of particles, it treats them as though they are waves the same wave-particle duality that we saw with photons of light. In our everyday experience, a particle can only be in one place at once, while a wave can be spread out over a wider area more strongly present in some places than others, but not confined to a single position. If we fire a particle such as an electron at a sheet of metal that has two holes in it, we might expect the electron to pa.s.s through one hole or the other, but not through both. But in Schrdinger's treatment the wave-like electron has a particular probability of pa.s.sing through each of the holes and its behaviour on the far side of the metal sheet is a combination of these probabilities as if it had pa.s.sed through both. This might seem like a very odd way for a particle to behave, but experiments have shown time and time again that this is exactly what particles like electrons, protons and neutrons really do in real life.

Wave-particle duality is a very strange thing to imagine but it is the basis of technologies such as the laser, the atom bomb and the DVD player so every time you watch an episode of Doctor Who on DVD you're demonstrating that the weird behaviour of the quantum realm is real. We might be happy to accept that a DVD player relies on the weirdness of subatomic particles, but wave-particle duality on the quantum scale also has some rather disturbing implications for objects in the everyday world implications which have troubled physicists for almost a hundred years.

Particles and waves behave in a characteristic manner ...

Particles that pa.s.s through the slits build up a pattern of impacts that matches the two slits.

As waves that pa.s.s through the slits radiate outwards, they overlap. Where a crest of one meets a trough of the other, they cancel out. Where a crest meets a crest, they amplify each other. We detect a distinctive, stripy interference pattern.

... But experiments show that light (made of photons) and subatomic particles such as electrons and protons can show properties of both

When we fire individual electrons at the slits, they build up a stripy pattern, just like that created by the interference of waves.

But if we try to observe the same electrons pa.s.sing through one or other of the slits, they change their behaviour and behave like particles as if caused by the act of observation itself!

Schrdinger himself was very worried about this. In a series of letters to Albert Einstein, he described an imaginary 'thought experiment' which showed how the weirdness of tiny quantum particles might translate into weirdness on a larger, everyday scale. Schrdinger's equation treats quantum particles as if they exist in a mixture of all their possible states, right up until the particle's state is measured. So a radioactive atomic nucleus, which has a particular probability of decaying over time, will exist in both a 'decayed' and an 'undecayed' state until an observation is made at which point it will settle into either one state or the other.

In Schrdinger's thought experiment, a cat is placed in a box along with a bottle of poison gas. The bottle is connected to an atom of a radioactive element that using Schrdinger's equation has a fifty per cent chance of decaying in one hour. If it decays, the bottle will open, the poison gas will escape and the imaginary cat will die. If it doesn't decay, the imaginary cat will be fine.

Of course, once the hour has pa.s.sed and the lid is opened, we'll know whether the cat has survived. But, according to quantum mechanics, until the box is opened the atom is both undecayed and decayed, the bottle is both closed and open, and Schrdinger's imaginary cat is both alive and dead.

The idea of a cat being both alive and dead at the same time might be hard to swallow, but physicists have come up with several different ways of explaining what this might actually mean some of which are rather strange themselves.

In 1957, American physicist Hugh Everett III suggested that every time a quantum system is observed, forcing it to choose one state out of many possibilities, different universes split off one for each of the possible outcomes of the observation. In the case of the cat, two almost identical universes would be created: one where the cat is dead and the other where it's alive. All we do in opening the box is discover which of those two universes is the one we exist in. Physicists disagree on whether this idea is realistic but it certainly seems to have influenced the Doctor Who story Inferno (1970).

In many ways, the other Earth seen in Inferno is very similar to our own, but there are also some startling differences. Britain is ruled by a dictator, the royal family have been executed, and a mining project is run by nightmare versions of the Doctor's friends in UNIT. For example, 'Brigade Leader' (rather than Brigadier) Lethbridge-Stewart is a coward who tries more than once to kill the Doctor. Presumably (though not stated in the story), at some point in history this world diverged from our own perhaps when Britain chose whether to fight the n.a.z.is in the Second World War. Later Doctor Who stories explored more 'similar-but-different' versions of the Earth: in Battlefield (1989), there's an Earth where King Arthur is real and the Doctor is Merlin, and in Rise of the Cybermen (2006), there's an Earth where the Doctor's friend Rose Tyler never existed except as a dog.

If this 'many worlds' interpretation of quantum mechanics is correct, there must be an infinite number of universes, each with its own version of Earth. In this 'multiverse', there's a universe for every possible outcome of every possible choice. As we'll see in Chapter 6, the multiverse might explain how time travel and changing history are possible. But at present we can't really test the idea of the multiverse scientifically, which has led some physicists to argue that it isn't a scientific idea at all since science is all about testing our ideas against evidence.

However, a related idea does make predictions that might one day be tested. String theory argues that all of the particles which make up the universe are really the result of the vibration of extremely tiny one-dimensional objects called 'strings'. Atomic physics takes place on scales of about 1 nanometre that is, a millimetre divided by 1,000,000. The strings in string theory are a lot smaller than that. They're thought to exist at the scale of a millimetre divided by 62,500,000,000,000,000,000,000,000,000,000 what's called the Planck length, named after physicist Max Planck.

If string theory is right, it should be possible to detect 'string harmonics', with a tell-tale distribution of heavy copies of the sub-atomic particles with which we're familiar. But to do so, we'd need a particle accelerator machine many times more powerful than the Large Hadron Collider at CERN which, at about 2.8 billion, is one of the most expensive scientific instruments ever built. It seems unlikely that such a machine will be built any time soon.

A more practical test may be the way the behaviour of these tiny strings (if they exist) has affected the structure of the universe on much larger scales. Some physicists have suggested that strings might sometimes get stretched to sizes big enough to be detected using telescopes. So far, no evidence has been found to either support or disprove string theory, but particle physicists and cosmologists are still actively searching.

But why is string theory related to the idea of other universes? To make the equations of string theory work, it needs more than the four dimensions we're used to the three dimensions of height, width and depth plus the dimension of time. Different ideas about string theory suggest different numbers of dimensions: M-theory (physicists can't agree whether the 'M' stands for magic, mystery or matrix) requires eleven dimensions while bosonic string theory requires twenty-six.

So why don't we see these extra dimensions? It's possible that they are 'rolled up' very tightly so that they're invisible to objects on the scale of human beings. Depending on how tightly the dimensions are coiled, it might still be possible for smaller objects like atoms to be 'pushed' into them in which case they would seem to disappear from our familiar three-dimensional world, though they would still exist. In The Stones of Blood (1978), the Doctor discovers a s.p.a.ceship hovering above a stone circle but hidden from view because it's in 'hypers.p.a.ce' (which the Doctor and his companion Romana both describe as 'a theoretical absurdity'). Could hypers.p.a.ce in Doctor Who simply be a way of shunting large objects sideways into string theory's extra dimensions?

Other types of universe in Doctor Who seem to be more self-contained. In Full Circle (1980), the TARDIS ends up in E-s.p.a.ce, a s.p.a.ce-time continuum separate from our own universe but with planets and star systems of its own. In the following story, State of Decay, we're told E-s.p.a.ce is smaller than our own N-s.p.a.ce a 'pocket universe'. In The Doctor's Wife (2011), the TARDIS leaves our universe to reach the world called House. Again, that might be in a separate, smaller pocket universe, though the Doctor suggests it's more complicated than that:

'So we're in a tiny bubble universe, sticking to the side of the bigger bubble universe?'

'Yeah. No. But if it helps, yes... Not a bubble, a plughole. The universe has a plughole and we've just fallen down it.'

Amy Pond and the Eleventh Doctor, The Doctor's Wife (2011)

It seems that in Doctor Who the physics of these other universes can be different to ours. On the TARDIS scanner, E-s.p.a.ce seems to have a greenish tinge compared to the blackness of our own N-s.p.a.ce, and according to K-9 its smallness makes it easier for the TARDIS to move a short distance within it. In The Three Doctors (19721973), the Doctor and Jo travel through a black hole to a universe of antimatter 'where all the known physical laws cease to exist'. This is rather different from current ideas of what might really happen inside a black hole, but we'll find out more about these strange objects in Chapter 4.

Conditions in our universe could present physical problems to creatures from anywhere else. In Flatline (2014), the Doctor says that the Boneless are 'from a universe with only two dimensions' and must learn to move about in three. Einstein's General Theory of Relativity tells us that in a universe with fewer than three s.p.a.ce dimensions the force of gravity would not be able to operate, which might explain why the 2D Boneless initially find our own universe so challenging to get around in.

Like the Boneless struggling with our universe, we, too, struggle to understand how the universe might exist with more than the four dimensions that we're used to. Again, General Relativity hints at how weird things might get: in a universe with more than three s.p.a.ce dimensions, gravity would be weaker, stars would not be able to hold on to their planets and life as we know it might be impossible.

The very first episode of Doctor Who suggests that if we don't understand how other dimensions operate, we can barely understand the universe at all. In An Unearthly Child (1963), the Doctor's granddaughter, Susan Foreman, is a pupil at Coal Hill School. Her science teacher sets her what he thinks is a simple problem using three dimensions A, B, C. But Susan gets upset, arguing that it's impossible to solve the problem without using the dimensions D and E as well. 'You can't simply work on three of the dimensions,' she insists, claiming that the additional dimensions required are 'time' and 's.p.a.ce'. By 's.p.a.ce' perhaps she means the extra s.p.a.ce dimensions predicted by string theory? If so, young Gallifreyans clearly like to make their maths problems as complicated as possible.

However, the way different universes are described in Doctor Who is not always very consistent. In Flatline, the Doctor describes the Boneless as 'creatures from another dimension'. In this sense the world we know is an intersection of four different dimensions: one of width, one of depth, one of height and one of time. However, in Battlefield, too, the Doctor says the knights are from 'another dimension' and 'another universe'. Does he mean that 'dimension' in Doctor Who is another word for 'universe'?

The initials 'TARDIS' come from Time And Relative Dimension In s.p.a.ce, and the Doctor claims that 'dimensional engineering' is the reason the TARDIS is bigger on the inside than on the outside. In The Robots of Death (1977), he explains to Leela that its 'insides and outsides are not in the same dimension'. In Frontios (1984) and Father's Day (2005), the exterior of the TARDIS is separated from the interior as if they're two different realms, connected by a door.

Or perhaps 'dimension' and 'universe' have subtly different meanings in Doctor Who. In Hide (2013), the Doctor refers to the alien world as both a 'pocket universe' (like E-s.p.a.ce) and 'another dimension', but corrects Clara when she calls it a 'parallel universe'. In geometry, lines are parallel if they do not touch or intersect, so perhaps in Doctor Who a parallel universe is one that doesn't branch off from ours but simply exists alongside it something we'll discuss more in Chapter 6.

In 2003, physicist Max Tegmark suggested that there might be four different types of multiverse. The first, a Level I Multiverse, is anywhere in our universe further than 46 billion light years from Earth. That distance is the furthest that we can see into the universe, so anything beyond it is effectively cut off from us.

In Level II, our entire universe is just one of a number of distinct bubbles inside a greater whole like E-s.p.a.ce and N-s.p.a.ce in Doctor Who. In Level III, there are universes for 'every conceivable way that the world could be' universes branching out from each other as choices lead to different outcomes, such as Schrdinger's dead and alive cats or the consequences of Donna's choice to turn left or right in Turn Left (2008), which we'll discuss more in Chapter 6.

Lastly, in Level IV universes, even the laws of physics can be different and anything might happen. In Battlefield (1989), the Doctor says the Arthurian knights come from 'another dimension' and 'sideways in time from another universe' one where magic seems to be real. That suggests the other Earth where King Arthur is real has its own laws of physics, different to our own. If all possibilities are played out somewhere, then there's a universe where Doctor Who is real all of it, even the bits that are contradictory or silly and another universe where you are the Doctor, and another where you're a Dalek.

Perhaps there are even more than these four levels of universe. In 2011, physicist Brian Greene suggested nine different types. There might be many more. It's ironic, isn't it? Trying to understand the very smallest size of matter has led to fundamental questions about how the universe works at the very biggest scale.

Double trouble In 2003, physicist Max Tegmark argued that even in our universe there's a good chance that physical circ.u.mstances repeat themselves, so that there are distant worlds where copies of you and me live copies of our lives. He called this a Level I Multiverse. In Doctor Who, we've seen several people who look just like Doctors or companions. (This list does not include robots or creatures who disguise themselves as Doctors or companions.) * Steven Taylor looks just like tourist Morton Dill seen in The Chase (1965) * The Brigadier looks just like s.p.a.ce Security Service agent Bret Vyon seen in The Daleks' Master Plan (19651966) * The First Doctor looks just like the sixteenth-century Abbot of Amboise seen in The Ma.s.sacre of St Bartholomew's Eve (1966) * The Second Doctor looks just like dictator Ramn Salamander seen in The Enemy of the World (1968) * Harry Sullivan looks just like Lieutenant John Andrews seen in Carnival of Monsters (1973) * The first Romana looks just like Princess Strella of Tara seen in The Androids of Tara (1978) * The second Romana chooses to look just like Princess Astra of Atrios in Destiny of the Daleks (1979) * Nyssa looks just like a woman from 1925, Ann Talbot seen in Black Orchid (1982) * The Sixth Doctor looks just like Maxil, Commander of the Chancellery Guard on Gallifrey seen in Arc of Infinity (1983) * Torchwood's Gwen Cooper looks just like Victorian servant Gwyneth seen in The Unquiet Dead (2005) * Martha Jones looks just like her cousin Adeola Oshodi seen in Army of Ghosts (2006) * Amelia Pond looks just like the Soothsayer seen in The Fires of Pompeii (2008) * The Twelfth Doctor looks just like marble merchant Lobus Caecilius seen in The Fires of Pompeii (2008), and that might be on purpose (as we'll discuss in Chapter 15) * The Tenth Doctor looks just like a human copy of himself created by regeneration energy seen in Journey's End (2008) * Clara Oswald looks just like a number of people the Doctor has met throughout his life, including s.p.a.ce traveller Oswin Oswald seen in Asylum of the Daleks (2012) * Danny Pink looks just like time traveller (and Danny's relation) Orson Pink seen in Listen (2014), which we'll discuss more in Chapter 11.

fn1 In The Armageddon Factor, Drax suggests that the miniaturised Doctor should 'fly over' and close the TARDIS door. This Time Lord ability to fly is only mentioned once again in the series in City of Death (1979). Perhaps Drax is only joking there are lots of occasions when being able to fly would have got the Doctor out of difficulty, such as when he's hanging from a radio telescope at the end of Logopolis (1981), so it seems odd that he doesn't use this ability more often.

'It's time to leave the airlock, if you dare.' The s.n.a.t.c.h of tune went around Tobbs's head, just as it did whenever he entered the airlock, turned the dog lever and opened the exterior hatch. It was a tune from the olden days, hundreds of years old, and those probably weren't even the right words. And now he'd have it looping around in his head for the rest of the EVA. If only he knew what the next line was.

He reached outside, gripped a handrail in his thickly padded gloved hand and swung through the hatchway. Ahead of him stretched a horizontal ladder of more handrails, leading across the rust-red panelling. Above him lay a night sky of infinite blackness, speckled with a billion points of unwavering light. Although, of course, out in s.p.a.ce, concepts like up and down were a matter of personal choice. Tobbs made a conscious effort to think of the star-dotted firmament as 'up' and began to float along the ladder, one handrail at a time.

'Nearly there,' crackled Locklear's voice in his helmet. 'Outage in aft hull, section twelve. Spreading to sections ten to fourteen.' That was unusual. A localised power failure was a familiar occurrence in interstellar s.p.a.ce, hence why a lowly third-cla.s.s engineer had been a.s.signed to investigate. The a.s.sumption was that it was the result of the ship being struck by a piece of debris and only warranted direct observation because the failure had also blacked out the exterior cameras and the sensor array. For a power failure to expand was seriously out of the ordinary.

Tobbs felt a flutter of excitement in his stomach, thinking of congratulatory handshakes and well-earned bonuses. Maybe, when he was hero of the hour, he'd even get up the courage to ask Thelesa out to dinner. He maintained a steady speed, grasping each rung and propelling himself forward. According to extra-vehicular protocol, he should've been tethering and decoupling a safety line to each rail, but this was an emergency and, besides, he could always use his jet if needed.

The line of the song kept going round his head as he reached the end of the ladder. The aft section was hidden out of sight below the side of the hull. Tobbs hauled himself over the edge, and the sloping aft hull rose into view. He held his breath, the only noise the hiss of static.

The hull was in absolute blackness. His headlamp lit up a number of plates scattered over its surface. The plates were dome-shaped, like flattened cones, as white as bone and covered in ridges.

'What can you see?' said Locklear. 'Tobbs. Report.'

Tobbs realised he'd been holding his breath. 'It's not an impact. It looks like, mad as this sounds, organic material.'

'Organic? Specify.'

Tobbs drifted closer. The plates were sh.e.l.ls. This was an undiscovered life form. They'd probably be named after him.

'I'm not sure,' said Tobbs. 'They look like sea life. Barnacles. s.p.a.ce barnacles.'

Something moved. Tobbs leaned forward, his nose almost touching the gla.s.s of his helmet. One of the sh.e.l.ls ejected a cloud of dust. Then, as it was caught in the glow of his headlamp, it detached itself from the hull and floated silently upwards. Tobbs could make out glittering, gossamer tentacles undulating beneath its sh.e.l.l.

'They seem to respond to light,' said Tobbs. Hearing his own words back through his earphones, his voice sounded full of wonder. 'Like it's waking them up.'

'Report on hull damage,' said Locklear. 'Outage in sector eleven.'

'Can't see any damage, but there's too many of them, they must be covering the cameras.' Tobbs swung his headlamp back and forth. Was it his imagination or was the light fading?

'Return to airlock,' said Locklear.

'What?' said Tobbs. One of the barnacles rose up before him, so close he could reach out and touch it.

'We're picking up a power loss on your life support-' Locklear's voice was buried in static, then the radio fell silent.

Tobbs checked his life support. The row of indicator lights just below his eye line flashed. He switched to back-up, and the lights lit up, then began flashing again.

Tobbs looked up, just in time to see the underside of one of the barnacles as it rushed towards him, its tentacles twirling, lights pulsing up and down the gla.s.s-like filaments. It hit the front of his helmet, clasping onto the gla.s.s. Tobbs could see its squashed, fleshy innards.

He reached up to pull it away. His heavily padded fingers could barely grip and he couldn't wrench it off; the angle was wrong and it had excreted some form of glue.

'Request a.s.sistance,' said Tobbs, forgetting that his radio had stopped working. 'Request a.s.sist-'

Something hard and hefty slammed into his back. Then something hit his left arm, sticking fast. Then more and more of the barnacles smacked into him until he was encrusted in a ball of the creatures. He couldn't see anything through his helmet. All he could see were the indicator lights going out one by one.

Then he heard a terrible, high-pitched squeaking. Cracking. The sound of breaking gla.s.s.

His last thought was that he would never find out the next line of the song.

'Tobbs, respond! Respond!'