The Beginning of Infinity

by David Deutsch

  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 di
screteness 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.