The Scientific Secrets of Doctor Who

by Simon Guerrier

  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 entity 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 pass 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 Nobel Prize for his work in physics, once said: ‘I can safely say that nobody 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 Schrödinger came up with an equation that can be used to predict the behaviour of particles in terms of probabilities.

  An odd consequence of Schrödinger’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 pass through one hole or the other, but not through both. But in Schrödinger’s treatment the wave-like electron has a particular probability of passing 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 passed 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 pass through the slits build up a pattern of impacts that matches the two slits.

  As waves that pass 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 passing through one or other of the slits, they change their behaviour and behave like particles – as if caused by the act of observation itself!

  Schrödinger 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. Schrödinger’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 Schrödinger’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 Schrödinger’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 passed 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 Schr
ödinger’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 Nazis 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 spaceship hovering above a stone circle but hidden from view because it’s in ‘hyperspace’ (which the Doctor and his companion Romana both describe as ‘a theoretical absurdity’). Could hyperspace 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-Space, a space-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-Space is smaller than our own N-Space – 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-Space seems to have a greenish tinge compared to the blackness of our own N-Space, and – according to K-9 – its smallness makes it easier for the TARDIS to move a short distance within it. In The Three Doctors (1972–1973), 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 space 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 space 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 ‘space’. By ‘space’ perhaps she means the extra space 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 Space, 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-Space) 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-Space and N-Space 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 Schrödinger’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.