The idea of a ‘doppelgänger’ (a ‘double’ of a person) is a frequent theme of science fiction. For instance, the classic television series Star Trek featured several types of doppelgänger story involving malfunctions of the ‘transporter’, the starship’s teleportation device, normally used for short-range space travel. Since teleporting something is conceptually similar to making a copy of it at a different location, one can imagine various ways in which the process could go wrong and somehow end up with two instances of each passenger – the original and the copy.

Stories vary in how similar the doppelgängers are to their originals. To share literally all their attributes, they would have to be at exactly the same location as well as looking alike. But what would that mean? Trying to make atoms coincide leads to some problematic physics – for instance, two coinciding nuclei are liable to combine to form atoms of heavier chemical elements. And if two identical human bodies were to coincide even approximately, they would explode simply because water at double its normal density exerts a pressure of hundreds of thousands of atmospheres. In fiction one could imagine different laws of physics to avoid those problems; but, even then, if the doppelgängers continued to coincide with their originals throughout the story, it would not really be about doppelgängers. Sooner or later they have to be different. Sometimes they are the good and evil ‘sides’ of the same person; sometimes they start with identical minds but become increasingly different through having different experiences.

Sometimes a doppelgänger is not copied from an original, but exists from the outset in a ‘parallel universe’. In some stories there is a ‘rift’ between universes through which one can communicate or even travel to meet one’s doppelgänger. In others, the universes remain mutually imperceptible, in which case the interest of the story (or, rather, two stories) is in how events are affected by the differences between them. For instance, the movie Sliding Doors interleaves two variants of a love story, following the fortunes of two instances of the same couple in two universes which initially differ only in one small detail. In a related genre, known as ‘alternative history’, one of the two stories need not be told explicitly because it is a part of our own history and is assumed to be known to the audience. For example, the novel Fatherland, by Robert Harris, is about a universe in which Germany won the Second World War; Robert Silverberg’s Roma Eterna is about one in which the Roman Empire did not fall.

In another class of stories, the transporter’s malfunction accidentally exiles the passengers to a ‘phantom zone’ where they are imperceptible to everyone in the ordinary world, but can see and hear them (and each other). So they have the distressing experience of yelling and gesticulating in vain to their shipmates, who are oblivious and walk right through them.

In some stories it is only copies of the travellers that are sent to a phantom zone, unbeknown to the originals. Such a story may end with the exiles discovering that they can, after all, have some effect on the ordinary world. They use that effect to signal their existence, and are rescued through a reversal of the process that exiled them. Depending on the fictional science that has been supposed, they then may begin new lives as separate people, or they may merge with their originals. The latter option violates the principle of the conservation of mass, among other laws of physics. But, again, this is fiction.

Nevertheless, there is a certain category of rather pedantic science fiction enthusiasts, myself included, who prefer the fictional science to make sense – to consist of reasonably good explanations. Imagining worlds with different laws of physics is one thing; imagining worlds that do not make sense in their own terms is quite another. For instance, we want to know how it can be that the exiles can see and hear the ordinary world but not touch it. This attitude of ours was nicely parodied in an episode of the television series The Simpsons, in which fans of a fantasy-adventure series question its star:

STAR: Next question.

FAN: Yes, over here. [Clears throat.] In episode BF12, you were battling barbarians while riding a wingèd Appaloosa, yet in the very next scene, my dear, you’re clearly atop a wingèd Arabian. Please to explain it.

STAR: Ah, yeah, well, whenever you notice something like that, a wizard did it.

FAN: I see, all right, yes, but in episode AG4 –

STAR: [firmly] Wizard.

FAN: Aw, for glayvin^* out loud!

Because that is a parody, the fan is complaining not about the story itself, but only that there is a continuity error: two horses were used at different times to play the role of a single fictional horse. Nevertheless, there are such things as flawed stories. Consider, for instance, a story about a quest to discover whether winged horses are real, in which the characters pursue that quest on winged horses. Though logically consistent, such a story would not make sense in its own terms, as an explanation. One could embed it in a context that would make sense of it – for instance, it could be part of an allegory about how people often fail to see the meaning of what is right there in front of them. But in that case any merit in the story would still depend on how the characters’ apparently nonsensical behaviour was explicable in terms of that allegory. Compare that with the explanation that ‘a wizard did it.’ Since a wizard could equally well have been said to conjure any events, in any story, it is a bad explanation; and that is why the fan is exasperated by it.

In some stories the plot is not important: the story is really about something else. But a good plot always rests, implicitly or explicitly, on good explanations of how and why events happen, given its fictional premises. In that case, even if those premises are about wizards, the story is not really about the supernatural: it is about imaginary laws of physics and imaginary societies, as well as real problems and true ideas. As I shall explain in Chapter 14, not only do all good science-fiction plots resemble scientific explanation in this way, in the broadest sense all good art does.

In that spirit, then, consider the fictional doppelgängers in the phantom zone. What enables them to see the ordinary world? Since they are structurally identical to their originals, their eyes work by absorbing light and detecting the resulting chemical changes, just as real eyes do. But if they absorb some of the light coming from the ordinary world, then they must cast shadows at the places where that light would otherwise have arrived. Also, if the exiles in the phantom zone can see each other, what light are they seeing with? The phantom zone’s own light? If so, where does it come from?

On the other hand, if the exiles can see without absorbing light, then they must be differently constituted from their originals, at the microscopic level. And in that case we no longer have an explanation of why they outwardly resemble their originals: the ‘accidental-copying’ idea will no longer do: where did the transporter get the knowledge required to build things that look and behave like human bodies, but function internally in a different way? It would be a case of spontaneous generation.

Similarly, is there air in the phantom zone? If the exiles breathe air, it can’t be the ship’s air, because they would be heard speaking or even breathing. But nor can it be a copy of the small amount of air that was in the transporter with them, because they are free to move around the ship. So there must be a whole shipful of phantom-zone air. But then what is preventing it from expanding out into space?

It seems that almost everything that happens in the story not only conflicts with the real laws of physics (which is unexceptionable in fiction), but raises problems within the fictional explanation. If the doppelgängers can walk through people, why do they not fall through the floor? In reality, a floor supports people by bending slightly. But if it were to bend in the story, it would also vibrate with their steps and set off sound waves which people in the ordinary world could hear. So there must be a separate floor and walls as well as an entire spaceship hull in the phantom zone. Even the space outside cannot be ordinary space, because if one could get back into ordinary space by leaving the ship, then the exiles could return by that route. But if there is an entire phantom-zone space out there – a parallel universe – how could a mere transporter malfunction have created that?

We should not be surprised that good fictional science is hard to invent: it is a variant of real science, and real scientific knowledge is very hard to vary. Thus few if any of the storylines that I have outlined make sense as they stand. But I want to continue with one of my own, making sure that it (eventually) does make sense.

A writer of real science fiction faces two conflicting incentives. One is, as with all fiction, to allow the reader to engage with the story, and the easiest way to do that is to draw on themes that are already familiar. But that is an anthropocentric incentive. For instance, it pushes authors to imagine ways around the absolute speed limit that the laws of physics impose on travel and communication (namely the speed of light). But when authors do that, they relegate distance to the role that it has in stories about our home planet: star systems play the same role that remote islands or the Wild West did in the fiction of earlier eras. Similarly, the temptation in parallel-universe stories is to allow communication or travel between universes. But then the story is really about a single universe: once the barrier between the universes is easily penetrable, it becomes no more than an exotic version of the oceans that separate continents. A story that succumbs entirely to this anthropocentric incentive is not really science fiction but ordinary fiction in disguise.

The opposing incentive is to explore the strongest possible version of a fictional-science premise, and its strangest possible implications – which pushes in the anti-anthropocentric direction. This may make the story harder to engage with, but it allows for a much broader range of scientific speculations. In the story that I shall tell here, I shall use a succession of such speculations, increasingly distant from the familiar, as means of explaining the world according to quantum theory.

Quantum theory is the deepest explanation known to science. It violates many of the assumptions of common sense, and of all previous science – including some that no one suspected were being made at all until quantum theory came along and contradicted them. And yet this seemingly alien territory is the reality of which we and everything we experience are part. There is no other. So, in setting a story there, perhaps what I lose in terms of the familiar ingredients of drama I shall gain in terms of opportunity to explain something that is more astounding than any fiction, yet is the purest and most basic fact we know about the physical world.

I had better warn the reader that the account that I shall give – known as the ‘many-universes interpretation’ of quantum theory (rather inadequately, since there is much more to it than ‘universes’) – remains at the time of writing a decidedly minority view among physicists. In the next chapter I shall speculate why that is so despite the fact that many well-studied phenomena have no other known explanation. For the moment, suffice it to say that the very idea of science as explanation, in the sense that I am advocating in this book (namely an account of what is really out there), is itself still a minority view even among theoretical physicists.

Let me begin with perhaps the simplest possible ‘parallel-universe’ speculation: a ‘phantom zone’ has existed all along (ever since its own Big Bang). Until our story begins, it has been an exact doppelgänger of the entire universe, atom for atom and event for event.

All the flaws that I mentioned in the phantom-zone stories derive from the asymmetry that things in the ordinary world affect things in the phantom zone but not vice versa. So let me eliminate those flaws by imagining, for the moment, that the universes are completely imperceptible to each other. Since we are heading towards real physics, let me also retain the speed-of-light limit on communication, and let the laws of physics be universal and symmetrical (i.e. they make no distinction between the universes). Moreover, they are deterministic: nothing random ever happens, which is why the universes have remained alike – so far. So how can they ever become different? That is a key question in the theory of the multiverse, which I shall answer below.

All these basic properties of my fictional world can be thought of as conditions on the flow of information: one cannot send a message to the other universe; nor can one change anything in one’s own universe sooner than light could reach that thing. Nor can one bring new information – even random information – into the world: everything that happens is determined by laws of physics from what has gone before. However, one can, of course, bring new knowledge into the world. Knowledge consists of explanations, and none of those conditions prevents the creation of new explanations. All this is true of the real world too.

We can temporarily think of the two universes as being literally parallel. Suppress the third dimension of space and think of a universe as being two-dimensional, like an infinitely flat television. Then place a second such television parallel to it, showing exactly the same pictures (symbolizing the objects in the two universes). Now forget the material of which the televisions are made. Only the pictures exist. This is to stress that a universe is not a receptacle containing physical objects: it is those objects. In real physics, even space is a physical object, capable of warping and affecting matter and being affected by it.

So now we have two perfectly parallel, identical universes, each including an instance of our starship, its crew and its transporter, and of the whole of space. Because of the symmetry between them, it is now misleading to call one of them ‘the ordinary universe’ and the other ‘the phantom zone’. So I shall just call them ‘universes’. The two of them together (which comprise the whole of physical reality in the story so far) are the multiverse. Similarly, it is misleading to speak of the ‘original’ object and its ‘doppelgänger’: they are simply the two instances of the object.

If our science-fiction speculation were to stop there, the two universes would have to remain identical for ever. There is nothing logically impossible about that. Yet it would make our story fatally flawed both as fiction and as scientific speculation – and for the same reason: it is a story of two universes, but only one history. That is to say, there is only one script about what is really there in both universes. Considered as fiction, therefore, it is really a single-universe story in a pointless disguise. Considered as scientific speculation, it describes a world that would not be explicable to its inhabitants. For how could they ever argue that their history takes place in two universes and not three or thirty? Why not two today and thirty tomorrow? Moreover, since their world has only one history, all their good explanations about nature would be about that history. That single history would be what they meant by their ‘world’ or ‘universe’. Nothing of the underlying two-ness of their reality would be accessible to them, nor would it make any more sense to them as an explanation than would three-ness or thirtyness – yet they would be factually mistaken.

A remark about explanation: Although the story so far would be a bad explanation from the inhabitants’ point of view, it is not necessarily bad from ours. Imagining inexplicable worlds can help us to understand the nature of explicability. I have already imagined some inexplicable worlds for that very reason in previous chapters, and I shall imagine more in this chapter. But, in the end, I want to tell of an explicable world, and it will be ours.

A remark about terminology: The world is the whole of physical reality. In classical (pre-quantum) physics, the world was thought to consist of one universe – something like a whole three-dimensional space for the whole of time, and all its contents. According to quantum physics, as I shall explain, the world is a much larger and more complicated object, a multiverse, which includes many such universes (among other things). And a history is a sequence of events happening to objects and possibly their identical counterparts. So, in my story so far, the world is a multiverse that consists of two universes but has only a single history.

So our two universes must not stay identical. Something like a transporter malfunction will have to make them different. Yet, as I said, that may seem to have been ruled out by those restrictions on information flow. The laws of physics in the fictional multiverse are deterministic and symmetrical. So what can the transporter possibly do that would make the two universes differ? It may seem that whatever one instance of it does to one universe, its doppelgänger must be doing to the other, so the universes can only remain the same.

Surprisingly, that is not so. It is consistent for two identical entities to become different under deterministic and symmetrical laws. But, for that to happen, they must initially be more than just exact images of each other: they must be fungible (the g is pronounced as in ‘plunger’), by which I mean identical in literally every way except that there are two of them. The concept of fungibility is going to appear repeatedly in my story. The term is borrowed from legal terminology, where it refers to the legal fiction that deems certain entities to be identical for purposes such as paying debts. For example, dollar bills are fungible in law, which means that, unless otherwise agreed, borrowing a dollar does not require one to return the specific banknote that one borrowed. Barrels of oil (of a given grade) are fungible too. Horses are not: borrowing someone’s horse means that one has to return that specific horse; even its identical twin will not do. But the physical fungibility I am referring to here is not about deeming. It means being identical, and that is a very different and counter-intuitive property. Leibniz, in his doctrine of ‘the identity of indiscernibles’, went so far as to rule out its existence on principle. But he was mistaken. Even aside from the physics of the multiverse, we now know that photons, and under some conditions even atoms, can be fungible. This is achieved in lasers and in devices called ‘atomic lasers’ respectively. The latter emit bursts of extremely cold, fungible atoms. For how this is possible without causing transmutation, explosions and so on, see below.

You will not find the concept of fungibility discussed or even mentioned in many textbooks or research papers on quantum theory, even the small minority that endorse the many-universes interpretation. Nevertheless, it is everywhere just beneath the conceptual surface, and I believe that making it explicit helps to explain quantum phenomena without fudging. As will become clear, it is an even weirder attribute than Leibniz guessed – much weirder than multiple universes for instance, which are, after all, just common sense, repeated. It allows radically new types of motion and information flow, different from anything that was imagined before quantum physics, and hence a radically different structure of the physical world.

It so happens that, in some situations, money is not only legally fungible but physically too; and, being so familiar, it provides a good model for thinking about fungibility. For example, if the balance in your (electronic) bank account is one dollar, and the bank adds a second dollar as a loyalty bonus and later withdraws a dollar in charges, there is no meaning to whether the dollar they withdrew is the one that was there originally or the one that they had added – or is composed of a little of each. It is not merely that we cannot know whether it was the same dollar, or have decided not to care: because of the physics of the situation there really is no such thing as taking the original dollar, nor such a thing as taking the one added subsequently.

Dollars in bank accounts are what may be called ‘configurational’ entities: they are states or configurations of objects, not what we usually think of as physical objects in their own right. Your bank balance resides in the state of a certain information-storage device. In a sense you own that state (it is illegal for anyone to alter it without your consent), but you do not own the device itself or any part of it. So in that sense a dollar is an abstraction. Indeed, it is a piece of abstract knowledge. As I discussed in Chapter 4, knowledge, once embodied in physical form in a suitable environment, causes itself to remain so. And thus, when a physical dollar wears out and is destroyed by the mint, the abstract dollar causes the mint to transfer it into electronic form, or into a new instance in paper form. It is an abstract replicator – though, unusually for a replicator, it causes itself not to proliferate, but rather to be copied into ledgers and into backups of computer memories.

Another example of fungible configurational entities in classical physics is amounts of energy: if you pedal your bicycle until you have built up a kinetic energy of ten kilojoules, and then brake until half that energy has been dissipated as heat, there is no meaning to whether the energy dissipated was the first five kilojoules that you had added or the second, or any combination. But it is meaningful that half the energy that was there has been dissipated. It turns out that, in quantum physics, elementary particles are configurational entities too. The vacuum, which we perceive as empty at everyday scales and even at atomic scales, is not really emptiness, but a richly structured entity known as a ‘quantum field’. Elementary particles are higher-energy configurations of this entity: ‘excitations of the vacuum’. So, for instance, the photons in a laser are configurations of the vacuum inside its ‘cavity’. When two or more such excitations with identical attributes (such as energy and spin) are present in the cavity, there is no such thing as which one was there first, nor which one will be the next to leave. There is only such a thing as the attributes of any one of them, and how many of them there are.

If the two universes of our fictional multiverse are initially fungible, our transporter malfunction can make them acquire different attributes in the same way that a bank’s computer can withdraw one of two fungible dollars and not the other from an account containing two dollars. The laws of physics could, for instance, say that, when the transporter malfunctions, then in one of the universes and not the other there will be a small voltage surge in the transported objects. The laws, being symmetrical, could not possibly specify which universe the surge will take place in. But, precisely because the universes are initially fungible, they do not have to.

It is a rather counter-intuitive fact that if objects are merely identical (in the sense of being exact copies), and obey deterministic laws that make no distinction between them, then they can never become different; but fungible objects, which on the face of it are even more alike, can. This is the first of those weird properties of fungibility that Leibniz never thought of, and which I consider to be at the heart of the phenomena of quantum physics.

Here is another. Suppose that your account contains a hundred dollars and you have instructed your bank to transfer one dollar from this account to the tax authority on a specified date in the future. So the bank’s computer now contains a deterministic rule to that effect. Suppose that you have done this because the dollar already belongs to the tax authority. (Say it had mistakenly sent you a tax refund, and has given you a deadline to repay it.) Since the dollars in the account are fungible, there is no such thing as which one belongs to the tax authority and which belong to you. So we now have a situation in which a collection of objects, though fungible, do not all have the same owner! Everyday language struggles to describe this situation: each dollar in the account shares literally all its attributes with the others, yet it is not the case that all of them have the same owner. So, could we say that in this situation they have no owner? That would be misleading, because evidently the tax authority does own one of them and you do own the rest. Could one say that they all have two owners? Perhaps, but only because that is a vague term. Certainly there is no point in saying that one cent of each of the dollars is owned by the tax authority, because that simply runs into the problem that the cents in the account are all fungible too. But, in any case, notice that the problem raised by this ‘diversity within fungibility’ is one of language only. It is a problem of how to describe some aspects of the situation in words. No one finds the situation itself paradoxical: the computer has been instructed to execute definite rules, and there will never be any ambiguity about what will happen as a result.

Diversity within fungibility is a widespread phenomenon in the multiverse, as I shall explain. One big difference from the case of fungible money is that in the latter case we never have to wonder about – or predict – what it would be like to be a dollar. That is to say, what it would be like to be fungible, and then to become differentiated. Many applications of quantum theory require us to do exactly that.

But first: I suggested temporarily visualizing our two universes as being next to each other in space – just as some science-fiction stories refer to doppelgänger universes as being ‘in other dimensions’. But now we have to abandon that image and make them coincide: whatever that ‘extra dimension’ was supposed to denote, it would make them non-fungible.^* It is not that they coincide in anything, such as an external space: they are not in space. An instance of space is part of each of them. That they ‘coincide’ means only that they are not separate in any way.

It is hard to imagine perfectly identical things coinciding. For instance, as soon as you imagine just one of them, your imagination has already violated their fungibility. But, although imagination may baulk, reason does not.

Now our story can begin to have a non-trivial plot. For example, the voltage surge that happens in one of the two universes when the transporter malfunctions could cause some of the neurons in a passenger’s brain to misfire in that universe. As a result, in that universe, that passenger spills a cup of coffee on another passenger. As a result, they have a shared experience which they do not have in the other universe, and this leads to romance – just as in Sliding Doors.

The voltage surges need not be ‘malfunctions’ of the transporter. They could be a regular effect of the way it works. We accept much larger unpredictable jolts during others forms of travel such as flying or bronco-riding. Let us imagine that a tiny surge is produced in one of the universes whenever the transporter is operated in both, but that it is too small to be noticeable unless measured with a sensitive voltmeter, or unless it nudges something that happens to be on the brink of changing but would recede from the brink if not nudged.

In principle, a phenomenon could appear unpredictable to observers for one or more of three reasons. The first is that it is affected by some fundamentally random (indeterministic) variable. I have excluded that possibility from our story because there are no such variables in real physics. The second, which is at least partly responsible for most everyday unpredictability, is that the factors affecting the phenomenon, though deterministic, are either unknown or too complex to take account of. (This is especially so when they involve the creation of knowledge, as I discussed in Chapter 9.) The third – which had never been imagined before quantum theory – is that two or more initially fungible instances of the observer become different. That is what those transporter-induced jolts bring about, and it makes their outcomes strictly unpredictable despite being described by deterministic laws of physics.

These remarks about unpredictable phenomena could be expressed without ever referring explicitly to fungibility. And indeed that is what multiverse researchers usually do. Nevertheless, as I have said, I believe that fungibility is essential to the explanation of quantum randomness and most other quantum phenomena.

All three of these radically different causes of unpredictability could in principle feel exactly the same to observers. But, in an explicable world, there must be a way of finding out which of them (or which combination of them) is the actual source of any apparent randomness in nature. How could one find out that it is fungibility and parallel universes that are responsible for a given phenomenon?

In fiction, there is always the temptation to introduce inter-universe communication for this purpose, making the universes no longer ‘parallel’. As I have said, that would really make it a single-universe story – but we might try to disguise that fact by saying that such communication is difficult. For example, it might be that there is a way of adjusting the transporter in either universe so that it produces a voltage surge in the other. Then one could use it to transmit a message there. But we could imagine that this is very expensive, or dangerous, so that the ship’s regulations limit its use. ‘Personal communication’ with one’s own doppelgänger is especially prohibited. Nevertheless, one crew member illicitly ignores this prohibition during the night watch, and is startled to receive a message ‘have married sonak.’ We know, but the character does not, that this marriage is a knock-on effect of the coffee-spilling incident which was itself a knock-on effect of the voltage surge in the other universe. Then the transmission ends and no more such messages are received. We know – but again the character does not – that this is because the illicit use of the equipment has been detected in the other universe and stricter safeguards have been implemented. The story could then explore what might happen when the crew member acts upon that startling message.

How should one react to the news that one’s doppelgänger has married? Should one seek out the spouse’s doppelgänger in one’s own universe – whom one has never even met personally, let alone formed a romantic relationship with? Or whom, in the time-honoured tradition of love stories, one finds annoying. It can’t do any harm. Or can it?

Ideas originating in the other universe are at least as fallible as those in ours; and if they are difficult to obtain, that makes error-correction harder. Knowledge-creation depends on error-correction. So perhaps the message would have continued ‘already regretting it’. Or perhaps Sonak had just turned up in the transporter room in the other universe, making it impossible to send that warning. Or perhaps the couple are happy at the moment, but will shortly have a disastrous break-up resulting in divorce. In all those cases, that inter-universe communication, far from being helpful, could cause a doubling of the number of disastrous marriage decisions made by the two instances of that crew member.

More generally, the news that your doppelgänger seems happy having made a particular decision in the other universe does not imply that you will be happy if you make the ‘corresponding’ decision. Once there are differences between the universes (and without such differences news from the other universe is not news), there is no good reason to expect the outcome of a decision to be unaffected by them. In one universe, you met because of an accidental shared experience; in the other, because you have illegally used the ship’s equipment. Can that affect the happiness of a marriage? Perhaps not, but you can only know that if you have a good explanatory theory of which factors affect the outcomes of marriages and which do not. And if you have such a theory, then perhaps you have no need to be skulking in transporter rooms.

Still more generally, the benefit of inter-universe communication would be, in effect, that it permits new forms of information processing. In the fictional case I have described, since the two universes have been identical until quite recently, communicating with one’s other-universe counterpart achieves the same effect as running a computer simulation of an alternative version of a period of one’s own life, without having to know all the relevant physical variables explicitly. This computation is infeasible in any other way, and could be helpful in testing explanatory theories of how various factors affect outcomes. Nevertheless, it is no substitute for thinking of those theories in the first place.

Therefore, if such communication is a scarce resource, a more efficient way of using it might be to exchange the theories themselves: if your doppelgänger solves a problem and tells you the solution, then you can see for yourself that it is a good explanation even if you have no way of knowing how your doppelgänger arrived at it.

Another efficient use of inter-universe communication might be to share the work of a lengthy computation. For instance, the story might be that some crew members have been poisoned and will die within hours unless the antidote is administered. To find the antidote requires computer simulations of the effects of many variants of a drug. So the two instances of the ship’s computer can each search half the list of variants, thus running through the full list in half the time. When the cure is found in one universe, its number in the list can be transmitted to the other universe, the result can be checked there, and the crew in both universes are saved. Again, evidence that there is computer power accessible in this way through the transporter would be evidence that there really was a computer out there, performing different calculations from one’s own. Reflecting on the details (about what the doppelgängers breathe and so on) would then let the inhabitants know that the other universe as a whole was a real place with similar structure and complexity to their own. So their world would be explicable.

Since there is no inter-universe communication in real quantum physics, we shall not allow it in our story, and so that specific route to explicability is not open. The history in which our crew members are married and the one in which they still hardly know each other cannot communicate with each other or observe each other. Nevertheless, as we shall see, there are circumstances in which histories can still affect each other in ways that do not amount to communication, and the need to explain those effects provides the main argument that our own multiverse is real.

After the universes in our story begin to differ inside one starship, everything else in the world exists in pairs of identical instances. We must continue to imagine those pairs as being fungible. This is necessary because the universes are not ‘receptacles’ – there is nothing to them apart from the objects that they contain. If they did have an independent reality, then each of the objects in such a pair would have a property of being in one particular universe and not the other, which would make them non-fungible.

Typically, the region in which the universes are different will then grow. For instance, when the couple decide to marry, they send messages to their home planets announcing this. When the messages arrive, the two instances of each of those planets become different. Previously only the two instances of the starship were different, bur soon, even before anyone broadcasts it intentionally, some of the information will have leaked out. For instance, people in the starship are moving differently in the two universes as a result of the marriage decision, so light bounces off them differently and some of it leaves the starship through portholes, making the two universes slightly different wherever it goes. The same is true of heat radiation (infra-red light), which leaves the starship through every point on the hull. Thus, starting with the voltage happening in only one universe, a wave of differentiation between the universes spreads in all directions through space. Since information travelling in either universe cannot exceed the speed of light, nor can the wave of differentiation. And since, at its leading edge, it mostly travels at or near that speed, differences in the head start that some directions have over others will become an ever smaller proportion of the total distance travelled, and so the further the wave travels the more nearly spherical it becomes. So I shall call it a ‘sphere of differentiation’.

Even inside the sphere of differentiation, there are comparatively few differences between the universes: the stars still shine, the planets still have the same continents. Even the people who hear of the wedding, and behave differently as a result, retain most of the same data in their brains and other information-storage devices, and they still breathe the same type of air, eat the same types of food, and so on.

However, although it may seem intuitively reasonable that news of the marriage leaves most things unchanged, there is a different commonsense intuition that seems to prove that it must change everything, if only slightly. Consider what happens when the news reaches a planet – say, in the form of pulse of photons from a communication laser. Even before any human consequences, there is the physical impact of those photons, which one might expect to impart momentum to every atom exposed to the beam – which will be every atom in something like that half of the surface of the planet which is facing the beam. Those atoms would then vibrate a little differently, affecting the atoms below through interatomic forces. As each atom affected others, the effect would spread rapidly through the planet. Soon, every atom in the planet would have been affected – though most of them by unimaginably tiny amounts. Nevertheless, however small such an effect was, it would be enough to break the fungibility between each atom and its other-universe counterpart. Hence it would seem that nothing would be left fungible after the wave of differentiation had passed.

These two opposite intuitions reflect the ancient dichotomy between the discrete and the continuous. The above argument – that everything in the sphere of differentiation must become different – depends on the reality of extremely small physical changes – changes that would be many orders of magnitude too small to be measurable. The existence of such changes follows inexorably from the explanations of classical physics, because in classical physics most fundamental quantities (such as energy) are continuously variable. The opposing intuition comes from thinking about the world in terms of information processing, and hence in terms of discrete variables such as the contents of people’s memories. Quantum theory adjudicates this conflict in favour of the discrete. For a typical physical quantity, there is a smallest possible change that it can undergo in a given situation. For instance, there is a smallest possible amount of energy that can be transferred from radiation to any particular atom. The atom cannot absorb any less than that amount, which is called a ‘quantum’ of energy. Since this was the first distinctive feature of quantum physics to be discovered, it gave its name to the field. Let us incorporate it into our fictional physics as well.

Hence it is not the case that all the atoms on the surface of the planet are changed by the arrival of the radio message. In reality, the typical response of a large physical object to very small influences is that most of its atoms remain strictly unchanged, while, to obey the conservation laws, a few exhibit a discrete, relatively large change of one quantum.

The discreteness of variables raises questions about motion and change. Does it mean that changes happen instantaneously? They do not – which raises the further question: what is the world like halfway through that change? Also if a few atoms are strongly affected by some influence, and the rest are unaffected, what determines which are the ones to be affected? The answer has to do with fungibility, as the reader may guess, and as I shall explain below.

The effects of a wave of differentiation usually diminish rapidly with distance – simply because physical effects in general do. The sun, from even a hundredth of a light year away, looks like a cold, bright dot in the sky. It barely affects anything. At a thousand light years, nor does a supernova. Even the most violent of quasar jets, when viewed from a neighbouring galaxy, would be little more than an abstract painting in the sky. There is only one known phenomenon which, if it ever occurred, would have effects that did not fall off with distance, and that is the creation of a certain type of knowledge, namely a beginning of infinity. Indeed, knowledge can aim itself at a target, travel vast distances having scarcely any effect, and then utterly transform the destination.

In our story, too, if we wanted the transporter malfunction to have a significant physical effect at astronomical distances, it would have to be via knowledge. All those torrents of photons streaming out of the starship and carrying, intentionally or unintentionally, information about a wedding will have a noticeable effect on the distant planet only if someone there cares about the possibility of such information enough to set up scientific instruments that could detect it.

Now, as I have explained, our imaginary laws of physics which say that a voltage surge happens ‘in one universe but not the other’ cannot be deterministic unless the universes are fungible. So, what happens when the transporter is used again, after the universes are no longer fungible? Imagine a second starship, of the same type as the first and far away. What happens if the second starship runs its transporter immediately after the first one did?

One logically possible answer would be that nothing happens – in other words, the laws of physics would say that, once the two universes are different, all transporters just work normally and never produce a voltage surge again. However, that would also provide a way of communicating faster than light, albeit unreliably and only once. You set up a voltmeter in the transporter room and run the transporter. If the voltage surges, you know that the other starship, however far away, has not yet run its transporter (because, if it had, that would have put a permanent end to such surges everywhere). The laws governing the real multiverse do not allow information to flow in that way. If we want our fictional laws of physics to be universal from the inhabitants’ point of view, the second transporter must do exactly what the first one did. It must cause a voltage surge in one universe and not in the other.

But in that case something must determine which universe the second surge will happen in. ‘In one universe but not the other’ is no longer a deterministic specification. Also, a surge must not happen if the transporter is run only in the other universe. That would constitute inter-universe communication. It must depend on both instances of the transporter being run simultaneously. Even that could allow some inter-universe communication, as follows. In the universe where a surge has once happened, run the transporter at a prearranged time and observe the voltmeter. If no surge happens, then the transporter in the other universe is switched off. So we are at an impasse. It is remarkable how much subtlety there can be in the apparently straightforward, binary distinction between ‘same’ and different’ – or between ‘affected’ and ‘unaffected’. In the real quantum theory, too, the prohibitions on inter-universe communication and faster-than-light communication are closely connected.

There is a way – I think it is the only way – to meet simultaneously the requirements that our fictional laws of physics be universal and deterministic, and forbid faster-than-light and inter-universe communication: more universes. Imagine an uncountably infinite number of them, initially all fungible. The transporter causes previously fungible ones to become different, as before; but now the relevant law of physics says, ‘The voltage surges in half the universes in which the transporter is used.’ So, if the two starships both run their transporters, then, after the two spheres of differentiation have overlapped, there will be universes of four different kinds: those in which a surge happened only in the first starship, only in the second, in neither, and in both. In other words, in the overlap region there are four different histories, each taking place in one quarter of the universes.

Our fictional theory has not provided enough structure in its multiverse to give a meaning to ‘half the universes’, but the real quantum theory does. As I explained in Chapter 8, the method that a theory provides for giving a meaning to proportions and averages for infinite sets is called a measure. A familiar example is that classical physics assigns lengths to infinite sets of points arranged in a line. Let us suppose that our theory provides a measure for universes.

Now we are allowed storylines such as the following. In the universes in which the couple married, they spend their honeymoon on a human-colonized planet that the starship is visiting. As they are teleporting back up, the voltage surge in half those universes causes someone’s electronic notepad to play a voice message suggesting that one of the newlyweds has already been unfaithful. This sets off a chain of events that ends in divorce. So now our original collection of fungible universes contains three different histories: in one, comprising half the original set of universes, the couple in question are still single; in the second, comprising a quarter of the original set, they are married; and in the third, comprising the remaining quarter, they are divorced.

Thus the three histories do not occupy equal proportions of the multiverse. There are twice as many universes in which the couple never married as there are universes in which they divorced.

Now suppose that scientists on the starship know about the multiverse and understand the physics of the transporter. (Though note that we have not yet given them a way of discovering those things.) Then they know that, when they run the transporter, an infinite number of fungible instances of themselves, all sharing the same history, are doing so at the same time. They know that a voltage surge will occur in half the universes in that history, which means that it will split into two histories of equal measure. Hence they know that, if they use a voltmeter capable of detecting the surge, half of the instances of themselves are going to find that it has recorded one, and the other half are not. But they also know that it is meaningless to ask (not merely impossible to know) which event they will experience. Consequently they can make two closely related predictions. One is that, despite the perfect determinism of everything that is happening, nothing can reliably predict for them whether the voltmeter will detect a surge.

The other prediction is simply that the voltmeter will record a surge with probability one-half. Thus the outcomes of such experiments are subjectively random (from the perspective of any observer) even though everything that is happening is completely determined objectively. This is also the origin of quantum-mechanical randomness and probability in real physics: it is due to the measure that the theory provides for the multiverse, which is in turn due to what kinds of physical processes the theory allows and forbids.

Notice that when a random outcome (in this sense) is about to happen, it is a situation of diversity within fungibility: the diversity is in the variable ‘what outcome they are going to see’. The logic of the situation is the same as in cases like that of the bank account I discussed above, except that this time the fungible entities are people. They are fungible, yet half of them are going to see the surge and the other half not.

In practice they could test this prediction by doing the experiment many times. Every formula purporting to predict the sequence of outcomes will eventually fail: that tests the unpredictability. And in the overwhelming majority of universes (and histories) the surge will happen approximately half the time: that tests the predicted value of the probability. Only a tiny proportion of the instances of the observers will see anything different.

Our story continues. In one of the histories, the newspapers on the astronauts’ home planets report the engagement. They fill many column-inches with reports about the accident that brought the astronauts together and so on. In the other history, where there is no astronaut-engagement news, one newspaper fills the same space on the page with a short story. It happens to be about a romance on a starship. Some of the sentences in that story are identical to sentences in the news items in the other history. The same words, printed in the same column in the same newspaper, are fungible between the two histories; but they are fiction in one history and fact in the other. So here the fact/fiction attribute has diversity within fungibility.

The number of distinct histories will now increase rapidly. Whenever the transporter is used, it takes only microseconds for the sphere of differentiation to engulf the whole starship, so, if it is typically used ten times per day, the number of distinct histories inside the whole starship will double about ten times a day. Within a month there will be more distinct histories than there are atoms in our visible universe. Most of them will be extremely similar to many others, because in only a small proportion will the precise timing and magnitude of the voltage surge be just right to precipitate a noticeable, Sliding Doors-type change. Nevertheless, the number of histories continues to increase exponentially, and soon there are so many variations on events that several significant changes have been caused somewhere in the multiversal diversity of the starship. So the total number of such histories increases exponentially too, even though they continue to constitute only a small proportion of all histories that are present.

Soon after that, in an even smaller but still exponentially growing number of histories, uncanny chains of ‘accidents’ and ‘unlikely coincidences’ will have come to dominate events. I put those terms in quotation marks because those events are not in the least accidental. They have all happened inevitably, according to deterministic laws of physics. All of them were caused by the transporter.

Here is another situation where, if we are not careful, common sense makes false assumptions about the physical world, and can make descriptions of situations sound paradoxical even though the situations themselves are quite straightforward. Dawkins gives an example in his book Unweaving the Rainbow, analysing the claim that a television psychic was making accurate predictions:

There are about 100,000 five-minute periods in a year. The probability that any given watch, say mine, will stop in a designated five-minute period is about 1 in 100,000. Low odds, but there are 10 million people watching the [television psychic’s] show. If only half of them are wearing watches, we could expect about 25 of those watches to stop in any given minute. If only a quarter of these ring in to the studio, that is 6 calls, more than enough to dumbfound a naive audience. Especially when you add in the calls from people whose watches stopped the day before, people whose watches didn’t stop but whose grandfather clocks did, people who died of heart attacks and their bereaved relatives phoned in to say that their ‘ticker’ gave out, and so on.

As this example shows, the fact that certain circumstances can explain other events without being in any way involved in causing them is very familiar despite being counter-intuitive. The ‘naive’ audience’s mistake is a form of parochialism: they observe a phenomenon – people phoning in because their watches stopped – but they are failing to understand it as part of a wider phenomenon, most of which they do not observe. Though the unobserved parts of that wider phenomenon have in no way affected what we, the viewers, observe, they are essential to its explanation. Similarly, common sense and classical physics contain the parochial error that only one history exists. This error, built into our language and conceptual framework, makes it sound odd to say that an event can be in one sense extremely unlikely and in another certain to happen. But there is nothing odd about it in reality.

We are now seeing the interior of the spaceship as an overwhelmingly complex jumble of superposed objects. Most locations on board are packed with people, some of them on very unusual errands, and all unable to perceive each other. The spaceship itself is on many slightly different courses, due to slightly different behaviours of the crew. Of course we are ‘seeing’ this only in our mind’s eye. Our fictional laws of physics ensure that no observer in the multiverse itself would see anything like that. Consequently, on closer inspection (in our mind’s eye), we also see that there is great order and regularity in that apparent chaos. For instance, although there is a flurry of human figures in the Captain’s chair, we see that most of them are the Captain; and although there is a flurry of human figures in the Navigator’s chair, we see that few of them are the Captain. Regularities of that kind are ultimately due to the fact that all the universes, despite their differences, obey the same laws of physics (including their initial conditions).

We also see that any particular instance of the Captain only ever interacts with one instance of the Navigator, and one instance of the First Officer; and those instances of the Navigator and First Officer are precisely the ones that interact with each other. These regularities are due to the fact that the histories are nearly autonomous: what happens in each of them depends almost entirely on previous events in that history alone – with transporter-induced voltage surges being the only exceptions. In the story so far, this autonomy of the histories is rather a trivial fact, since we began by making the universes autonomous. But it is going to be worth becoming even more pedantic for a moment: what exactly is the difference between the instance of you that I can interact with and the ones that are imperceptible to me? The latter are ‘in other universes’ – but, remember, universes consist only of the objects in them, so that amounts only to saying I can see the ones that I can see. The upshot is that our laws of physics must also say that every object carries within it information about which instances of it could interact with which instances of other objects (except when the instances are fungible, when there is no such thing as ‘which’). Quantum theory describes such information. It is known as entanglement information.^*

So far in the story we have set up a vast, complex world which looks very unfamiliar in our mind’s eye, but to the overwhelming majority of the inhabitants looks almost exactly like the single universe of our everyday experience and of classical physics, plus some apparently random jiggling whenever the transporter operates. A tiny minority of the histories have been significantly affected by very ‘unlikely’ events, but even in those the information flow – what affects what – is still very tame and familiar. For instance, a version of the ship’s log that contains records of bizarre coincidences will be perceptible to people who remember those coincidences, but not to other instances of those people.

Thus the information in the fictional multiverse flows along a branching tree, whose branches – histories – have different thicknesses (measures) and never rejoin once they have separated. Each behaves exactly as if the others did not exist. If that were the whole story, that multiverse’s imaginary laws of physics would still be fatally flawed as explanations in the same way that they have been all along: there would be no difference between their predictions and those of much more straightforward laws saying that there is only one universe – one history – in which the transporter randomly introduces a change in the objects that it teleports. Under those laws, instead of branching into two autonomous histories on such occasions, the single history randomly does or does not undergo such a change. Thus the entire stupendously complicated multiverse that we have imagined – with its multiplicity of entities including people walking through each other and its bizarre occurrences and its entanglement information – would collapse into nothing, like the galaxy in Chapter 2 that became an emulsion flaw. The multiverse explanation of the same events would be a bad explanation, and so the world would be inexplicable to the inhabitants if it were true.

It may seem that, by imposing all those conditions on information flow, we have gone to a lot of trouble to achieve that very attribute – to hide, from the inhabitants, the Byzantine intricacies of their world. In the words of Lewis Carroll’s White Knight in Through the Looking Glass, it is as if we were

…thinking of a plan

To dye one’s whiskers green,

And always use so large a fan

That they could not be seen.

Now it is time to start removing the fan.

In quantum physics, information flow in the multiverse is not as tame as in that branching tree of histories I have described. That is because of one further quantum phenomenon: under certain circumstances, the laws of motion allow histories to rejoin (becoming fungible again). This is the time-reverse of the splitting (differentiation of history into two or more histories) that I have already described, so a natural way to implement it in our fictional multiverse is for the transporter to be capable of undoing its own history-splitting.

If we represent the original splitting like this

where X is the normal voltage and Y is the anomalous one introduced by the transporter, then the rejoining of histories can be represented as

In an interference phenomenon, differentiated histories rejoin.

This phenomenon is known as interference: the presence of the Y-history interferes with what the transporter usually does to an X-history. Instead, the X and Y histories merge. This is rather like the doppelgängers merging with their originals in some phantom-zone stories, except that here we do not need to repeal the principle of the conservation of mass or any other conservation law: the total measure of all the histories remains constant.

Interference is the phenomenon that can provide the inhabitants of the multiverse with evidence of the existence of multiple histories in their world without allowing the histories to communicate. For example, suppose that they run the transporter twice in quick succession (I shall explain in a moment what ‘quick’ means):

An interference experiment

If they did this repeatedly (with, say, different copies of the transporter on each occasion), they could soon infer that the intermediate result could not be just randomly X or Y, because if it were then the final outcome would sometimes be Y (because of ), while in fact it is always X. Thus the inhabitants would no longer be able to explain away what they see by assuming that only one, randomly chosen, value of the voltage is real at the intermediate stage.

Although such an experiment would provide evidence that multiple histories not only exist but affect each other strongly (in the sense that they behave differently according to whether the other is present or absent), it does not involve inter-history communication (sending a message of one’s choice to the other history).

In our story, just as we did not allow splitting to happen in a way that would allow communication faster than light, so we must ensure the same for interference. The simplest way is to require that the rejoining take place only if no wave of differentiation has happened. That is to say, the transporter can undo the voltage surge only if this has not yet caused any differential effects on anything else. When a wave of differentiation, set off by two different values X and Y of some variable, has left an object, the object is entangled with all the differentially affected objects.

Entanglement

So our rule, in short, is that interference can happen only in objects that are unentangled with the rest of the world. This is why, in the interference experiment, the two applications of the transporter have to be ‘in quick succession’. (Alternatively, the object in question has to be sufficiently well isolated for its voltages not to affect its surroundings.) So we can represent a generic interference experiment symbolically as follows:

If an object is unentangled, it can be made to undergo interference by something acting on it alone.

(The arrows ‘’ and ‘’ represent the action of the transporter.) Once the object is entangled with the rest of the world in regard to the values X and Y, no operation on the object alone can create interference between those values. Instead, the histories are merely split further, in the usual way:

In entangled objects, further splitting happens instead of interference.

When two or more values of a physical variable have differently affected something in the rest of the world, knock-on effects typically continue indefinitely, as I have described, with a wave of differentiation entangling more and more objects. If the differential effects can all be undone, then interference between those original values becomes possible again; but the laws of quantum mechanics dictate that undoing them requires fine control of all the affected objects, and that rapidly becomes infeasible. The process of its becoming infeasible is known as decoherence. In most situations, decoherence is very rapid, which is why splitting typically predominates over interference, and why interference – though ubiquitous on microscopic scales – is quite hard to demonstrate unambiguously in the laboratory.

Nevertheless, it can be done, and quantum interference phenomena constitute our main evidence of the existence of the multiverse, and of what its laws are. A real-life analogue of the above experiment is standard in quantum optics laboratories. Instead of experimenting on voltmeters (whose many interactions with their environment quickly cause decoherence), one uses individual photons, and the variable being acted upon is not voltage but which of two possible paths the photon is on. Instead of the transporter, one uses a simple device called a semi-silvered mirror (represented by the grey sloping bars in the diagrams below). When a photon strikes such a mirror, it bounces off in half the universes, and passes straight through in the other half, as shown on next page:

Semi-silvered mirror

The attributes of travelling in the X or Y directions behave analogously to the two voltages X and Y in our fictitious multiverse. So passing through the semi-silvered mirror is the analogue of the transformation above. And when the two instances of a single photon, travelling in directions X and Y, strike the second semi-silvered mirror at the same time, they undergo the transformation , which means that both instances emerge in the direction X: the two histories rejoin. To demonstrate this, one can use a set-up known as a ‘Mach–Zehnder interferometer’, which performs those two transformations (splitting and interference) in quick succession:

Mach–Zehnder interferometer

The two ordinary mirrors (the black sloping bars) are merely there to steer the photon from the first to the second semi-silvered mirror.

If a photon is introduced travelling rightwards (X) after the first mirror instead of before as shown, then it appears to emerge randomly, rightwards or downwards, from the last mirror (because then, happens there). The same is true of a photon introduced travelling downwards (Y) after the first mirror. But a photon introduced as shown in the diagram invariably emerges rightwards, never downwards. By doing the experiment repeatedly with and without detectors on the paths, one can verify that only one photon is ever present per history, because only one of those detectors is ever observed to fire during such an experiment. Then, the fact that the intermediate histories X and Y both contribute to the deterministic final outcome X makes it inescapable that both are happening at the intermediate time.

In the real multiverse, there is no need for the transporter or any other special apparatus to cause histories to differentiate and to rejoin. Under the laws of quantum physics, elementary particles are undergoing such processes of their own accord, all the time. Moreover, histories may split into more than two – often into many trillions – each characterized by a slightly different direction of motion or difference in other physical variables of the elementary particle concerned. Also, in general the resulting histories have unequal measures. So let us now dispense with the transporter in the fictional multiverse too.

The rate of growth in the number of distinct histories is quite mind-boggling – even though, thanks to interference, there is now a certain amount of spontaneous rejoining as well. Because of this rejoining, the flow of information in the real multiverse is not divided into strictly autonomous subflows – branching, autonomous histories. Although there is still no communication between histories (in the sense of message-sending), they are intimately affecting each other, because the effect of interference on a history depends on what other histories are present.

Not only is the multiverse no longer perfectly partitioned into histories, individual particles are not perfectly partitioned into instances. For example, consider the following interference phenomenon, where X and Y now represent different values of the position of a single particle:

How instances of a particle lose their identity during interference. Has the instance of the particle at X stayed at X or moved to Y? Has the instance of the particle at Y returned to Y or moved to X?

Because these two groups of instances of the particle, initially at different positions, have gone through a moment of being fungible, there is no such thing as which of them has ended up at which final position. This sort of interference is going on all the time, even for a single particle in a region of otherwise empty space. So there is in general no such thing as the ‘same’ instance of a particle at different times.

Even within the same history, particles in general do not retain their identities over time. For example, during a collision between two atoms, the histories of the event split into something like this

and something like this

So, for each particle individually, the event is rather like a collision with a semi-silvered mirror. Each atom plays the role of the mirror for the other atom. But the multiversal view of both particles looks like this

where at the end of the collision some of the instances of each atom have become fungible with what was originally a different atom.

For the same reason, there is no such thing as the speed of one instance of the particle at a given location. Speed is defined as distance travelled divided by time taken, but that is not meaningful in situations where there is no such thing as a particular instance of the particle over time. Instead, a collection of fungible instances of a particle in general have several speeds – meaning that in general they will do different things an instant later. (This is another instance of ‘diversity within fungibility’.)

Not only can a fungible collection with the same position have different speeds, a fungible group with the same speed can have different positions. Furthermore, it follows from the laws of quantum physics that, for any fungible collection of instances of a physical object, some of their attributes must be diverse. This is known as the ‘Heisenberg uncertainty principle’, after the physicist Werner Heisenberg, who deduced the earliest version from quantum theory.

Hence, for instance, an individual electron always has a range of different locations and a range of different speeds and directions of motion. As a result, its typical behaviour is to spread out gradually in space. Its quantum-mechanical law of motion resembles the law governing the spread of an ink blot – so if it is initially located in a very small region it spreads out rapidly, and the larger it gets the more slowly it spreads. The entanglement information that it carries ensures that no two instances of it can ever contribute to the same history. (Or, more precisely, at times and places where there are histories, it exists in instances which can never collide.) If a particle’s range of speeds is centred not on zero but on some other value, then the whole of the ‘ink blot’ moves, with its centre obeying approximately the laws of motion in classical physics. In quantum physics this is how motion, in general, works.

This explains how particles in the same history can be fungible too, in something like an atomic laser. Two ‘ink-blot’ particles, each of which is a multiversal object, can coincide perfectly in space, and their entanglement information can be such that no two of their instances are ever at the same point in the same history.

Now, put a proton into the middle of that gradually spreading cloud of instances of a single electron. The proton has a positive charge, which attracts the negatively charged electron. As a result, the cloud stops spreading when its size is such that its tendency to spread outwards due to its uncertainty-principle diversity is exactly balanced by its attraction to the proton. The resulting structure is called an atom of hydrogen.

Historically, this explanation of what atoms are was one of the first triumphs of quantum theory, for atoms could not exist at all according to classical physics. An atom consists of a positively charged nucleus surrounded by negatively charged electrons. But positive and negative charges attract each other and, if unrestrained, accelerate towards each other, emitting energy in the form of electromagnetic radiation as they go. So it used to be a mystery why the electrons do not ‘fall’ on to the nucleus in a flash of radiation. Neither the nucleus nor the electrons individually have more than one ten-thousandth of the diameter of the atom, so what keeps them so far apart? And what makes atoms stable at that size? In non-technical accounts, the structure of atoms is sometimes explained by analogy with the solar system: one imagines electrons in orbit around the nucleus like planets around the sun. But that does not match the reality. For one thing, gravitationally bound objects do slowly spiral in, emitting gravitational radiation (the process has been observed for binary neutron stars), and the corresponding electromagnetic process in an atom would be over in a fraction of a second. For another, the existence of solid matter, which consists of atoms packed closely together, is evidence that atoms cannot easily penetrate each other, yet solar systems certainly could. Furthermore, it turns out that, in the hydrogen atom, the electron in its lowest-energy state is not orbiting at all but, as I said, just sitting there like an ink blot – its uncertainty-principle tendency to spread exactly balanced by the electrostatic force. In this way, the phenomena of interference and diversity within fungibility are integral to the structure and stability of all static objects, including all solid bodies, just as they are integral to all motion.

The term ‘uncertainty principle’ is misleading. Let me stress that it has nothing to do with uncertainty or any other distressing psychological sensations that the pioneers of quantum physics might have felt. When an electron has more than one speed or more than one position, that has nothing to do with anyone being uncertain what the speed is, any more than anyone is ‘uncertain’ which dollar in their bank account belongs to the tax authority. The diversity of attributes in both cases is a physical fact, independent of what anyone knows or feels.

Nor, by the way, is the uncertainty principle a ‘principle’, for that suggests an independent postulate that could logically be dropped or replaced to obtain a different theory. In fact one could no more drop it from quantum theory than one could omit eclipses from astronomy. There is no ‘principle of eclipses’: their existence can be deduced from theories of much greater generality, such as those of the solar system’s geometry and dynamics. Similarly, the uncertainty principle is deduced from the principles of quantum theory.

Thanks to the strong internal interference that it is continuously undergoing, a typical electron is an irreducibly multiversal object, and not a collection of parallel-universe or parallel-histories objects. That is to say, it has multiple positions and multiple speeds without being divisible into autonomous sub-entities each of which has one speed and one position. Even different electrons do not have completely separate identities. So the reality is an electron field throughout the whole of space, and disturbances spread through this field as waves, at the speed of light or below. This is what gave rise to the often-quoted misconception among the pioneers of quantum theory that electrons (and likewise all other particles) are ‘particles and waves at the same time’. There is a field (or ‘waves’) in the multiverse for every individual particle that we observe in a particular universe.

Although quantum theory is expressed in mathematical language, I have now given an account in English of the main features of the reality that it describes. So at this point the fictional multiverse that I have been describing is more or less the real one. But there is one thing left to tidy up. My ‘succession of speculations’ was based on universes, and on instances of objects, and then on corrections to those ideas in order to describe the multiverse. But the real multiverse is not ‘based on’ anything, nor is it a correction to anything. Universes, histories, particles and their instances are not referred to by quantum theory at all – any more than are planets, and human beings and their lives and loves. Those are all approximate, emergent phenomena in the multiverse.

A history is part of the multiverse in the same sense that a geological stratum is part of the Earth’s crust. One history is distinguished from the others by the values of physical variables, just as a stratum is distinguished from others by its chemical composition and by the types of fossils found in it and so on. A stratum and a history are both channels of information flow. They preserve information because, although their contents change over time, they are approximately autonomous – that is to say, the changes in a particular stratum or history depend almost entirely on conditions inside it and not elsewhere. It is because of that autonomy that a fossil found today can be used as evidence of what was present when that stratum was formed. Similarly, it is why, within a history, using classical physics, one can successfully predict some aspects of the future of that history from its past.

A stratum, like a history, has no separate existence over and above the objects in it: it consists of them. Nor does a stratum have well-defined edges. Also, there are regions of the Earth – for instance, near volcanoes – where strata have merged (though I think there are no geological processes that split and remerge strata in the way that histories split and remerge). There are regions of the Earth – such as the core – where there have never been strata. And there are regions – such as the atmosphere – where strata do form but their contents interact and mix on much shorter timescales than in the crust. Similarly, there are regions of the multiverse that contain short-lived histories, and others that do not even approximately contain histories.

However, there is one big difference between the ways in which strata and histories emerge from their respective underlying phenomena. Although not every atom in the Earth’s crust can be unambiguously assigned to a particular stratum, most of the atoms that form a stratum can. In contrast, every atom in an everyday object is a multiversal object, not partitioned into nearly autonomous instances and nearly autonomous histories, yet everyday objects such as starships and betrothed couples, which are made of such particles, are partitioned very accurately into nearly autonomous histories with exactly one instance, one position, one speed of each object in each history.

That is because of the suppression of interference by entanglement. As I explained, interference almost always happens either very soon after splitting or not at all. That is why the larger and more complex an object or process is, the less its gross behaviour is affected by interference. At that ‘coarse-grained’ level of emergence, events in the multiverse consist of autonomous histories, with each coarse-grained history consisting of a swathe of many histories differing only in microscopic details but affecting each other through interference. Spheres of differentiation tend to grow at nearly the speed of light, so, on the scale of everyday life and above, those coarse-grained histories can justly be called ‘universes’ in the ordinary sense of the word. Each of them somewhat resembles the universe of classical physics. And they can usefully be called ‘parallel’ because they are nearly autonomous. To the inhabitants, each looks very like a single-universe world.

Microscopic events which are accidentally amplified to that coarse-grained level (like the voltage surge in our story) are rare in any one coarse-grained history, but common in the multiverse as a whole. For example, consider a single cosmic-ray particle travelling in the direction of Earth from deep space. That particle must be travelling in a range of slightly different directions, because the uncertainty principle implies that in the multiverse it must spread sideways like an ink blot as it travels. By the time it arrives, this ink blot may well be wider than the whole Earth – so most of it misses and the rest strikes everywhere on the exposed surface. Remember, this is just a single particle, which may consist of fungible instances. The next thing that happens is that they cease to be fungible, splitting through their interaction with atoms at their points of arrival into a finite but huge number of instances, each of which is the origin of a separate history.

In each such history, there is an autonomous instance of the cosmic-ray particle, which will dissipate its energy in creating a ‘cosmic-ray shower’ of electrically charged particles. Thus, in different histories, such a shower will occur at different locations. In some, that shower will provide a conducting path down which a lightning bolt will travel. Every atom on the surface of the Earth will be struck by such lightning in some history. In other histories, one of those cosmic-ray particles will strike a human cell, damaging some already damaged DNA in such a way as to make the cell cancerous. Some non-negligible proportion of all cancers are caused in this way. As a result, there exist histories in which any given person, alive in our history at any time, is killed soon afterwards by cancer. There exist other histories in which the course of a battle, or a war, is changed by such an event, or by a lightning bolt at exactly the right place and time, or by any of countless other unlikely, ‘random’ events. This makes it highly plausible that there exist histories in which events have played out more or less as in alternative-history stories such as Fatherland and Roma Eterna – or in which events in your own life played out very differently, for better or worse.

A great deal of fiction is therefore close to a fact somewhere in the multiverse. But not all fiction. For instance, there are no histories in which my stories of the transporter malfunction are true, because they require different laws of physics. Nor are there histories in which the fundamental constants of nature such as the speed of light or the charge on an electron are different. There is, however, a sense in which different laws of physics appear to be true for a period in some histories, because of a sequence of ‘unlikely accidents’. (There may also be universes in which there are different laws of physics, as required in anthropic explanations of fine-tuning. But as yet there is no viable theory of such a multiverse.)

Imagine a single photon from a starship’s communication laser, heading towards Earth. Like the cosmic ray, it arrives all over the surface, in different histories. In each history, only one atom will absorb the photon and the rest will initially be completely unaffected. A receiver for such communications would then detect the relatively large, discrete change undergone by such an atom. An important consequence for the construction of measuring devices (including eyes) is that no matter how far away the source is, the kick given to an atom by an arriving photon is always the same: it is just that the weaker the signal is, the fewer kicks there are. If this were not so – for instance, if classical physics were true – weak signals would be much more easily swamped by random local noise. This is the same as the advantage of digital over analogue information processing that I discussed in Chapter 6.

Some of my own research in physics has been concerned with the theory of quantum computers. These are computers in which the information-carrying variables have been protected by a variety of means from becoming entangled with their surroundings. This allows a new mode of computation in which the flow of information is not confined to a single history. In one type of quantum computation, enormous numbers of different computations, taking place simultaneously, can affect each other and hence contribute to the output of a computation. This is known as quantum parallelism.

In a typical quantum computation, individual bits of information are represented in physical objects known as ‘qubits’ – quantum bits – of which there is a large variety of physical implementations but always with two essential features. First, each qubit has a variable that can take one of two discrete values, and, second, special measures are taken to protect the qubits from entanglement – such as cooling them to temperatures close to absolute zero. A typical algorithm using quantum parallelism begins by causing the information-carrying variables in some of the qubits to acquire both their values simultaneously. Consequently, regarding those qubits as a register representing (say) a number, the number of separate instances of the register as a whole is exponentially large: two to the power of the number of qubits. Then, for a period, classical computations are performed, during which waves of differentiation spread to some of the other qubits – but no further, because of the special measures that prevent this. Hence, information is processed separately in each of that vast number of autonomous histories. Finally, an interference process involving all the affected qubits combines the information in those histories into a single history. Because of the intervening computation, which has processed the information, the final state is not the same as the initial one, as in the simple interference experiment I discussed above, namely , but is some function of it, like this:

A typical quantum computation. Y1…Y_many are intermediate results that depend on the input X. All of them are needed to compute the output f (X) efficiently.

Just as the starship crew members could achieve the effect of large amounts of computation by sharing information with their doppelgängers computing the same function on different inputs, so an algorithm that makes use of quantum parallelism does the same. But, while the fictional effect is limited only by starship regulations that we may invent to suit the plot, quantum computers are limited by the laws of physics that govern quantum interference. Only certain types of parallel computation can be performed with the help of the multiverse in this way. They are the ones for which the mathematics of quantum interference happens to be just right for combining into a single history the information that is needed for the final result.

In such computations, a quantum computer with only a few hundred qubits could perform far more computations in parallel than there are atoms in the visible universe. At the time of writing, quantum computers with about ten qubits have been constructed. ‘Scaling’ the technology to larger numbers is a tremendous challenge for quantum technology, but it is gradually being met.

I mentioned above that, when a large object is affected by a small influence, the usual outcome is that the large object is strictly unaffected. I can now explain why. For example, in the Mach–Zehnder interferometer, shown earlier, two instances of a single photon travel on two different paths. On the way, they strike two different mirrors. Interference will happen only if the photon does not become entangled with the mirrors – but it will become entangled if either mirror retains the slightest record that it has been struck (for that would be a differential effect of the instances on the two different paths). Even a single quantum of change in the amplitude of the mirror’s vibration on its supports, for instance, would be enough to prevent the interference (the subsequent merging of the photon’s two instances).

When one of the instances of the photon bounces off either mirror, its momentum changes, and hence by the principle of the conservation of momentum (which holds universally in quantum physics, just as in classical physics), the mirror’s momentum must change by an equal and opposite amount. Hence it seems that, in each history, one mirror but not the other must be left vibrating with slightly more or less energy after the photon has struck it. That energy change would be a record of which path the photon took, and hence the mirrors would be entangled with the photon.

Fortunately, that is not what happens. Remember that, at a sufficiently fine level of detail, what we crudely see as a single history of the mirror, resting passively or vibrating gently on its supports, is actually a vast number of histories with instances of all its atoms continually splitting and rejoining. In particular, the total energy of the mirror takes a vast number of possible values around the average, ‘classical’ one. Now, what happens when a photon strikes the mirror, changing that total energy by one quantum?

Oversimplifying for a moment, imagine just five of those countless instances of the mirror, with each instance having a different vibrational energy ranging from two quanta below the average to two quanta above it. Each instance of the photon strikes one instance of the mirror and imparts one additional quantum of energy to it. So, after that impact, the average energy of the instances of the mirror will have increased by one quantum, and there will now be instances with energies ranging from one quantum below the old average to three above. But since, at this fine level of detail, there is no autonomous history associated with any of those values of the energy, it is not meaningful to ask whether an instance of the mirror with a particular energy after the impact is the same one that previously had that energy. The objective physical fact is only that, of the five instances of the mirror, four have energies that were present before, and one does not. Hence, only that one – whose energy is three quanta higher than the previous average – carries any record of the impact of the photon. And that means that in only one-fifth of the universes in which the photon struck has the wave of differentiation spread to the mirror, and only in those will subsequent interference between instances of that photon that have or have not hit the mirror be suppressed.

With realistic numbers, that is more like one in a trillion trillion – which means that there is only a probability of one in a trillion trillion that interference will be suppressed. This is considerably lower than the probability that the experiment will give inaccurate results due to imperfect measuring instruments, or that it will be spoiled by a lightning strike.

Now let us look at the arrival of that single quantum of energy, to see how that discrete change can possibly happen without any discontinuity. Consider the simplest possible case: an atom absorbs a photon, including all its energy. This energy transfer does not take place instantaneously. (Forget anything that you may have read about ‘quantum jumps’: they are a myth.) There are many ways in which it can happen but the simplest is this. At the beginning of the process, the atom is in (say) its ‘ground state’, in which its electrons have the least possible energy allowed by quantum theory. That means that all its instances (within the relevant coarse-grained history) have that energy. Assume that they are also fungible. At the end of the process, all those instances are still fungible, but now they are in the ‘excited state’, which has one additional quantum of energy. What is the atom like halfway through the process? Its instances are still fungible, but now half of them are in the ground state and half in the excited state. It is as if a continuously variable amount of money changed ownership gradually from one discrete owner to another.

This mechanism is ubiquitous in quantum physics, and is the general means by which transitions between discrete states happen in a continuous way. In classical physics, a ‘tiny effect’ always means a tiny change in some measurable quantities. In quantum physics, physical variables are typically discrete and so cannot undergo tiny changes. Instead, a ‘tiny effect’ means a tiny change in the proportions that have the various discrete attributes.

This also raises the issue of whether time itself is a continuous variable. In this discussion I am assuming that it is. However, the quantum mechanics of time is not yet fully understood, and will not be until we have a quantum theory of gravity (the unification of quantum theory with the general theory of relativity), so it may turn out that things are not as simple as that. One thing we can be fairly sure of, though, is that, in that theory, different times are a special case of different universes. In other words, time is an entanglement phenomenon, which places all equal clock readings (of correctly prepared clocks – or of any objects usable as clocks) into the same history. This was first understood by the physicists Don Page and William Wooters, in 1983.

In this full version of the quantum multiverse, how is our science-fiction story to continue? Almost all the attention that the quantum theory has attracted, from physicists, philosophers and science-fiction authors alike, has focused on its parallel-universes aspect. That is ironic, because it is in the parallel-universe approximation that the world most resembles that of classical physics, yet that is the very aspect of quantum theory that many people seem to find viscerally unacceptable.

Fiction can explore the possibilities opened up by parallel universes. For instance, since our story is a romance, the characters may well wonder about their counterparts in other histories. The story could compare their speculations with what we ‘know’ happened in the other histories. The character whose spouse’s unfaithfulness was revealed by a ‘random’ event might wonder whether that event provided a lucky escape from what was a doomed marriage anyway. Are they still married in the history in which the unfaithfulness was not subsequently revealed? Are they still happy? Can it be true happiness if it is ‘based on a lie’? As we see them speculating on these matters, we see the ‘still married’ history and know the (fictional) fact of the matter.

They might also speculate about less parochial issues. The story could say that their sun is part of a cluster of dozens of stars, all within a sphere of a few light-weeks’ radius. This has puzzled their scientists for decades, since the composition of the stars shows that they originated from far and wide and became gravitationally bound through a series of very unlikely coincidences. In most universes, these scientists calculate, life cannot evolve in such dense star clusters, because there are too many collisions. So in most universes that contain humans there are no fleets of starships visiting inhabited star systems one after another. They have been trying to discover a mechanism by which the proximity of nearby stars might somehow precipitate the formation of intelligent life, but they have failed. Should they consider it just an astronomically unlikely coincidence? But they do not like leaving things unexplained. Something must have selected them, they conclude. It did. Those people are not just a story. They are real, living, thinking human beings, wondering at this very moment where they came from. But they will never find out. In that one respect, they are unlucky: they were indeed selected by coincidence. Another way of putting that is that they were selected by the very story that I am now telling about them. All fiction that does not violate the laws of physics is fact.

Some fiction in which the laws of physics appear to be violated is also fact, somewhere in the multiverse. This involves a subtle issue about how the multiverse is structured – how histories emerge. A history is approximately autonomous. If I boil some water in a kettle and make tea, I am in a history in which I switched on the kettle and the water became gradually hotter because of the energy being poured into it by the kettle, causing bubbles to form and so on, and eventually hot tea forms. That is a history because one can give explanations and make predictions about it without ever mentioning either that there are other histories in the multiverse where I chose to make coffee instead or that the microscopic motion of the water molecules is slightly affected by parts of the multiverse that are outside that history. It is irrelevant to that explanation that a small measure of that history differentiates itself during that process and does other things. In some tiny sliver of it, the kettle transforms itself into a top hat, and the water into a rabbit which then hops away, and I get neither tea nor coffee but am very surprised. That is a history too, after that transformation. But there is no way of correctly explaining what was happening during it, or predicting the probabilities, without referring to other parts of the multiverse – enormously larger parts (i.e. with larger measures) – in which there was no rabbit. So that history began at the transformation, and its causal connection with what happened before that cannot be expressed in history terms but only in multiverse terms.

In simple cases like that, there is a ready-made approximative language in which we can minimize mention of the rest of the multiverse: the language of random events. This allows us to acknowledge that most of the high-level objects concerned still behaved autonomously except for being affected by something outside themselves – as when I am affected by the rabbit. This constitutes some continuity between a history and a previous history from which it split, and we can refer to the former as a ‘history that has been affected by random events’. However, this is never literally what has happened: the part of that ‘history’ prior to the ‘random event’ is fungible with the rest of the broader history and therefore has no separate identity from it: it is not separately explicable.

But the broader of those two histories still is. That is to say, the rabbit history is fundamentally different from the tea history, in that the latter remains very accurately autonomous throughout the period. In the rabbit history I end up with memories that are identical to what they would be in a history in which water became a rabbit. But those are misleading memories. There was no such history; the history containing those memories began only after the rabbit had formed. For that matter, there are also places in the multiverse – of far larger measure than that one – in which only my brain was affected, producing exactly those memories. In effect, I had a hallucination, caused by random motion of the atoms in my brain. Some philosophers make a big issue of that sort of thing, claiming that it casts doubt on the scientific status of quantum theory, but of course they are empiricists. In reality, misleading observations, misleading memories and false interpretations are common even in the mainstreams of history. We have to work hard to avoid fooling ourselves with them.

So it is not quite true that, for instance, there are histories in which magic appears to work. There are only histories in which magic appears to have worked, but will never work again. There are histories in which I appear to have walked through a wall, because all the atoms of my body happened to resume their original courses after being deflected by atoms in the wall. But those histories began at the wall: the true explanation of what happened involves many other instances of me and it – or we can roughly explain it in terms of random events of very low probability. It is a bit like winning a lottery: the winner cannot properly explain what has just happened without invoking the existence of many losers. In the multiverse, the losers are other instances of oneself.

The ‘history’ approximation breaks down completely only when histories not only split but merge – that is to say, in interference phenomena. For example, there are certain molecules that exist in two or more structures at once (a ‘structure’ being an arrangement of atoms, held together by chemical bonds). Chemists call this phenomenon ‘resonance’ between the two structures, but the molecule is not alternating between them: it has them simultaneously. There is no way of explaining the chemical properties of such molecules in terms of a single structure, because when a ‘resonant’ molecule participates in a chemical reaction with other molecules, there is quantum interference.

In science fiction, we have a mandate to speculate, even to levels of implausibility that would make for quite bad explanations in real science. But the best explanation of ourselves in real science is that we – sentient beings in this gigantic, unfamiliar structure in which material things have no continuity, in which even something as basic as motion or change is different from anything in our experience – are embedded in multiversal objects. Whenever we observe anything – a scientific instrument or a galaxy or a human being – what we are actually seeing is a single-universe perspective on a larger object that extends some way into other universes. In some of those universes, the object looks exactly as it does to us, in others it looks different, or is absent altogether. What an observer sees as a married couple is actually just a sliver of a vast entity that includes many fungible instances of such a couple, together with other instances of them who are divorced, and others who have never married.

We are channels of information flow. So are histories, and so are all relatively autonomous objects within histories; but we sentient beings are extremely unusual channels, along which (sometimes) knowledge grows. This can have dramatic effects, not only within a history (where it can, for instance, have effects that do not diminish with distance), but also across the multiverse. Since the growth of knowledge is a process of error-correction, and since there are many more ways of being wrong than right, knowledge-creating entities rapidly become more alike in different histories than other entities. As far as is known, knowledge-creating processes are unique in both these respects: all other effects diminish with distance in space, and become increasingly different across the multiverse, in the long run.

But that is only as far as is known. Here is an opportunity for some wild speculations that could inform a science-fiction story. What if there is something other than information flow that can cause coherent, emergent phenomena in the multiverse? What if knowledge, or something other than knowledge, could emerge from that, and begin to have purposes of its own, and to conform the multiverse to those purposes, as we do? Could we communicate with it? Presumably not in the usual sense of the term, because that would be information flow; but perhaps the story could propose some novel analogue of communication which, like quantum inference, did not involve sending messages. Would we be trapped in a war of mutual extermination with such an entity? Or is it possible that we could nevertheless have something in common with it? Let us shun parochial resolutions of the issue – such as a discovery that what bridges the barrier is love, or trust. But let us remember that, just as we are at the top rank of significance in the great scheme of things, anything else that could create explanations would be too. And there is always room at the top.

Fungible Identical in every respect.

The world The whole of physical reality.

Multiverse The world, according to quantum theory.

Universe Universes are quasi-autonomous regions of the multiverse.

History A set of fungible universes, over time. One can also speak of the history of parts of a universe.

Parallel universes A somewhat misleading way of referring to the multiverse. Misleading because the universes are not perfectly ‘parallel’ (autonomous), and because the multiverse has much more structure – especially fungibility, entanglement and the measures of histories.

Instances In parts of the multiverse that contain universes, each multiversal object consists approximately of ‘instances’, some identical, some not, one in each of the universes.

Quantum The smallest possible change in a discrete physical variable.

Entanglement Information in each multiversal object that determines which parts (instances) of it can affect which parts of other multiversal objects.

Decoherence The process of its becoming infeasible to undo the effect of a wave of differentiation between universes.

Quantum interference Phenomena caused by non-fungible instances of a multiversal object becoming fungible.

Uncertainty principle The (badly misnamed) implication of quantum theory that, for any fungible collection of instances of a physical object, some of their attributes must be diverse.

Quantum computation Computation in which the flow of information is not confined to a single history.

The physical world is a multiverse, and its structure is determined by how information flows in it. In many regions of the multiverse, information flows in quasi-autonomous streams called histories, one of which we call our ‘universe’. Universes approximately obey the laws of classical (pre-quantum) physics. But we know of the rest of the multiverse, and can test the laws of quantum physics, because of the phenomenon of quantum interference. Thus a universe is not an exact but an emergent feature of the multiverse. One of the most unfamiliar and counter-intuitive things about the multiverse is fungibility. The laws of motion of the multiverse are deterministic, and apparent randomness is due to initially fungible instances of objects becoming different. In quantum physics, variables are typically discrete, and how they change from one value to another is a multiversal process involving interference and fungibility.