The Beginning of Infinity

by David Deutsch

  I do want to make one indirect comment on the Socratic problem, though: we habitually underestimate the difficulty of communication – just as Socrates does at the end of the dialogue, when he assumes that each party to a debate necessarily knows what the other is saying, and Plato increasingly gets the wrong end of the stick. In reality, the communication of new ideas – even mundane ones like directions – depends on guesswork on the part of both the recipient and the communicator, and is inherently fallible. Hence there is no reason to expect that the young Plato, just because he was intelligent and highly educated, and by all accounts a near-worshipper of Socrates, made the fewest mistakes in conveying Socrates’ theories. On the contrary, the default assumption should be that misunderstandings are ubiquitous and that neither intelligence nor the intention to be accurate is any guarantee against them. It could easily be that the young Plato misunderstood everything that Socrates said to him, and that the older Plato gradually succeeded in understanding it, and is therefore the more reliable guide. Or it could be that Plato slipped ever further into misinterpretation, and into positive errors of his own. Evidence, argument and explanation are needed to distinguish between these and many other possibilities. It is a difficult task for historians. Objective knowledge, though attainable, is hard to attain.

  All this holds as much for knowledge written down as for knowledge spoken in person. So there would still be a ‘Socratic problem’ even if Socrates had written books. Indeed, there is such a problem in regard to the prolific Plato, and sometimes even in regard to living philosophers. What does the philosopher mean by such and such a term or assertion? What problem is the assertion intended to solve, and how? These are not themselves philosophical problems. They are problems in the history of philosophy. Yet nearly all philosophers, especially academic ones, have devoted a great deal of their attention to them. Courses in philosophy place great weight on reading original texts, and commentaries on them, in order to understand the theories that were in the minds of various great philosophers.

  This focus on history is odd, and is in marked contrast to all other academic disciplines (except perhaps history itself). For example, in all the physics courses that I took at university, both as an undergraduate and as a graduate student, I cannot recall a single instance where any original papers or books by the great physicists of old were studied or were even on the reading list. Only when a course touched upon very recent discoveries did we ever read the work of their discoverers. So we learned Einstein’s theory of relativity without ever hearing from Einstein; we knew Maxwell, Boltzmann, Schrödinger, Heisenberg and so on only as names. We read their theories in textbooks whose authors were physicists (not historians of physics) who themselves may well never have read the works of those pioneers.

  Why? The immediate reason is that the original sources of scientific theories are almost never good sources. How could they be? All subsequent expositions are intended to be improvements on them, and some succeed, and improvements are cumulative. And there is a deeper reason. The originators of a fundamental new theory initially share many of the misconceptions of previous theories. They need to develop an understanding of how and why those theories are flawed, and how the new theory explains everything that they explained. But most people who subsequently learn the new theory have quite different concerns. Often they just want to take the theory for granted and use it to make predictions, or to understand some complex phenomenon in combination with other theories. Or they may want to understand nuances of it that have nothing to do with why it is superior to the old theories. Or they may want to improve it. But what they no longer care about is tracking down and definitively meeting every last objection that would naturally be made by someone thinking in terms of older, superseded theories. There is rarely any reason for scientists to address the obsolete problem-situations that motivated the great scientists of the past.

  Historians of science, in contrast, must do precisely that – and they encounter much the same difficulties as the historians of philosophy who address the Socratic problem. Why, then, do scientists not encounter these difficulties when learning scientific theories? What is it that allows such theories to be communicated through chains of intermediaries with such apparent ease? What has happened to the ‘difficulty of communication’ that I stressed above?

  The first, seemingly paradoxical, half of the answer is that, when they learn a theory, scientists are not interested in what the theory’s originator, or anyone else along the chain of communication, believed. When physicists read a textbook on the theory of relativity, their immediate objective is to learn the theory, and not the opinions of Einstein or of the textbook’s author. If that seems strange, imagine, for the sake of argument, that a historian were to discover that Einstein wrote his papers only as a joke, or at gunpoint, and was actually a lifelong believer in Kepler’s laws. This would be a bizarre and important discovery about the history of physics, and all the textbooks about that would have to be rewritten. But our knowledge of physics itself would be unaffected, and physics textbooks would not need any change at all.

  The second half of the answer is that the reason why the scientists are trying to learn the theory, and also why they have such disregard for faithfulness to the original, is that they want to know how the world is. Crucially, this is the same objective that the originator of the theory had. If it is a good theory – if it is a superb theory, as the fundamental theories of physics nowadays are – then it is exceedingly hard to vary while still remaining a viable explanation. So the learners, through criticism of their initial guesses and with the help of their books, teachers and colleagues, seeking a viable explanation, will arrive at the same theory as the originator. That is how the theory manages to be passed faithfully from generation to generation, despite no one caring about its faithfulness one way or the other.

  Slowly, and with many setbacks, the same is becoming true in non-scientific fields. The way to converge with each other is to converge upon the truth.

  11

  The Multiverse

  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.