The Beginning of Infinity

by David Deutsch

  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 thirty-ness – 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 le
dgers 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.