The Beginning of Infinity

by David Deutsch

  The Schrödinger equation, when applied to the case of an individual particle, described a wave moving through space. But Schrödinger soon realized that for two or more particles it did not. It did not represent a wave with multiple crests, nor could it be resolved into two or more waves; mathematically, it was a single wave in a higher-dimensional space. With hindsight, we now know that such waves describe what proportion of the instances of each particle are in each region of space, and also the entanglement information among the particles.

  Although Schrödinger’s and Heisenberg’s theories seemed to describe very dissimilar worlds, neither of which was easy to relate to existing conceptions of reality, it was soon discovered that, if a certain simple rule of thumb was added to each theory, they would always make identical predictions. Moreover, these predictions turned out to be very successful.

  With hindsight, we can state the rule of thumb like this: whenever a measurement is made, all the histories but one cease to exist. The surviving one is chosen at random, with the probability of each possible outcome being equal to the total measure of all the histories in which that outcome occurs.

  At that point, disaster struck. Instead of trying to improve and integrate those two powerful but slightly flawed explanatory theories, and to explain why the rule of thumb worked, most of the theoretical-physics community retreated rapidly and with remarkable docility into instrumentalism. If the predictions work, they reasoned, why worry about the explanation? So they tried to regard quantum theory as being nothing but a set of rules of thumb for predicting the observed outcomes of experiments, saying nothing (else) about reality. This move is still popular today, and is known to its critics (and even to some of its proponents) as the ‘shut-up-and-calculate interpretation of quantum theory’.

  This meant ignoring such awkward facts as (1) the rule of thumb was grossly inconsistent with both theories; hence it could be used only in situations where quantum effects were too small to be noticed. Those happened to include the moment of measurement (because of entanglement with the measuring instrument, and consequent decoherence, as we now know). And (2) it was not even self- consistent when applied to the hypothetical case of an observer performing a quantum measurement on another observer. And (3) both versions of quantum theory were clearly describing some sort of physical process that brought about the outcomes of experiments. Physicists, both through professionalism and through natural curiosity, could hardly help wondering about that process. But many of them tried not to. Most of them went on to train their students not to. This counteracted the scientific tradition of criticism in regard to quantum theory.

  Let me define ‘bad philosophy’ as philosophy that is not merely false, but actively prevents the growth of other knowledge. In this case, instrumentalism was acting to prevent the explanations in Schrödinger’s and Heisenberg’s theories from being improved or elaborated or unified.

  The physicist Niels Bohr (another of the pioneers of quantum theory) then developed an ‘interpretation’ of the theory which later became known as the ‘Copenhagen interpretation’. It said that quantum theory, including the rule of thumb, was a complete description of reality. Bohr excused the various contradictions and gaps by using a combination of instrumentalism and studied ambiguity. He denied the ‘possibility of speaking of phenomena as existing objectively’ – but said that only the outcomes of observations should count as phenomena. He also said that, although observation has no access to ‘the real essence of phenomena’, it does reveal relationships between them, and that, in addition, quantum theory blurs the distinction between observer and observed. As for what would happen if one observer performed a quantum-level observation on another, he avoided the issue – which became known as the ‘paradox of Wigner’s friend’, after the physicist Eugene Wigner.

  In regard to the unobserved processes between observations, where both Schrödinger’s and Heisenberg’s theories seemed to be describing a multiplicity of histories happening at once, Bohr proposed a new fundamental principle of nature, the ‘principle of complementarity’. It said that accounts of phenomena could be stated only in ‘classical language’ – meaning language that assigned single values to physical variables at any one time – but classical language could be used only in regard to some variables, including those that had just been measured. One was not permitted to ask what values the other variables had. Thus, for instance, in response to the question ‘Which path did the photon take?’ in the Mach–Zehnder interferometer, the reply would be that there is no such thing as which path when the path is not observed. In response to the question ‘Then how does the photon know which way to turn at the final mirror, since this depends on what happened on both paths?’, the reply would be an equivocation called ‘particle–wave duality’: the photon is both an extended (non-zero volume) and a localized (zero-volume) object at the same time, and one can choose to observe either attribute but not both. Often this is expressed in the saying ‘It is both a wave and a particle simultaneously.’ Ironically, there is a sense in which those words are precisely true: in that experiment the entire multiversal photon is indeed an extended object (wave), while instances of it (particles, in histories) are localized. Unfortunately, that is not what is meant in the Copenhagen interpretation. There the idea is that quantum physics defies the very foundations of reason: particles have mutually exclusive attributes, period. And it dismisses criticisms of the idea as invalid because they constitute attempts to use ‘classical language’ outside its proper domain (namely describing outcomes of measurements).

  Later, Heisenberg called the values about which one was not permitted to ask potentialities, of which only one would become actual when a measurement was completed. How can potentialities that do not happen affect actual outcomes? That was left vague. What caused the transition between ‘potential’ and ‘actual’? The implication of Bohr’s anthropocentric language – which was made explicit in most subsequent presentations of the Copenhagen interpretation – was that the transition is caused by human consciousness. Thus consciousness was said to be acting at a fundamental level in physics.

  For decades, various versions of all that were taught as fact – vagueness, anthropocentrism, instrumentalism and all – in university physics courses. Few physicists claimed to understand it. None did, and so students’ questions were met with such nonsense as ‘If you think you’ve understood quantum mechanics then you don’t.’ Inconsistency was defended as ‘complementarity’ or ‘duality’; parochialism was hailed as philosophical sophistication. Thus the theory claimed to stand outside the jurisdiction of normal (i.e. all) modes of criticism – a hallmark of bad philosophy.

  Its combination of vagueness, immunity from criticism, and the prestige and perceived authority of fundamental physics opened the door to countless systems of pseudo-science and quackery supposedly based on quantum theory. Its disparagement of plain criticism and reason as being ‘classical’, and therefore illegitimate, has given endless comfort to those who want to defy reason and embrace any number of irrational modes of thought. Thus quantum theory – the deepest discovery of the physical sciences – has acquired a reputation for endorsing practically every mystical and occult doctrine ever proposed.

  Not every physicist accepted the Copenhagen interpretation or its descendants. Einstein never did. The physicist David Bohm struggled to construct an alternative that was compatible with realism, and produced a rather complicated theory which I regard as the multiverse theory in heavy disguise – though he was strongly opposed to thinking of it in that way. And in Dublin in 1952 Schrödinger gave a lecture in which at one point he jocularly warned his audience that what he was about to say might ‘seem lunatic’. It was that, when his equation seems to be describing several different histories, they are ‘not alternatives but all really happen simultaneously’. This is the earliest known reference to the multiverse.

  Here was an eminent physicist joking that he might be considered mad. Why? For claiming that his o
wn equation – the very one for which he had won the Nobel prize – might be true.

  Schrödinger never published that lecture, and seems never to have taken the idea further. Five years later, and independently, the physicist Hugh Everett published a comprehensive theory of the multiverse, now known as the Everett interpretation of quantum theory. Yet it took several more decades before Everett’s work was even noticed by more than a handful of physicists. Even now that it has become well known, it is endorsed by only a small minority. I have often been asked to explain this unusual phenomenon. Unfortunately I know of no entirely satisfactory explanation. But, to understand why it is perhaps not quite as bizarre and isolated an event as it may appear, one has to consider the broader context of bad philosophy.

  Error is the normal state of our knowledge, and is no disgrace. There is nothing bad about false philosophy. Problems are inevitable, but they can be solved by imaginative, critical thought that seeks good explanations. That is good philosophy, and good science, both of which have always existed in some measure. For instance, children have always learned language by making, criticizing and testing conjectures about the connection between words and reality. They could not possibly learn it in any other way, as I shall explain in Chapter 16.

  Bad philosophy has always existed too. For instance, children have always been told, ‘Because I say so.’ Although that is not always intended as a philosophical position, it is worth analysing it as one, for in four simple words it contains remarkably many themes of false and bad philosophy. First, it is a perfect example of bad explanation: it could be used to ‘explain’ anything. Second, one way it achieves that status is by addressing only the form of the question and not the substance: it is about who said something, not what they said. That is the opposite of truth-seeking. Third, it reinterprets a request for true explanation (why should something-or-other be as it is?) as a request for justification (what entitles you to assert that it is so?), which is the justified-true-belief chimera. Fourth, it confuses the nonexistent authority for ideas with human authority (power) – a much-travelled path in bad political philosophy. And, fifth, it claims by this means to stand outside the jurisdiction of normal criticism.

  Bad philosophy before the Enlightenment was typically of the because-I-say-so variety. When the Enlightenment liberated philosophy and science, they both began to make progress, and increasingly there was good philosophy. But, paradoxically, bad philosophy became worse.

  I have said that empiricism initially played a positive role in the history of ideas by providing a defence against traditional authorities and dogma, and by attributing a central role – albeit the wrong one – to experiment in science. At first, the fact that empiricism is an impossible account of how science works did almost no harm, because no one took it literally. Whatever scientists may have said about where their discoveries came from, they eagerly addressed interesting problems, conjectured good explanations, tested them, and only lastly claimed to have induced the explanations from experiment. The bottom line was that they succeeded: they made progress. Nothing prevented that harmless (self-)deception, and nothing was inferred from it.

  Gradually, though, empiricism did begin to be taken literally, and so began to have increasingly harmful effects. For instance, the doctrine of positivism, developed during the nineteenth century, tried to eliminate from scientific theories everything that had not been ‘derived from observation’. Now, since nothing is ever derived from observation, what the positivists tried to eliminate depended entirely on their own whims and intuitions. Occasionally these were even good. For instance, the physicist Ernst Mach (father of Ludwig Mach of the Mach–Zehnder interferometer), who was also a positivist philosopher, influenced Einstein, spurring him to eliminate untested assumptions from physics – including Newton’s assumption that time flows at the same rate for all observers. That happened to be an excellent idea. But Mach’s positivism also caused him to oppose the resulting theory of relativity, essentially because it claimed that spacetime really exists even though it cannot be ‘directly’ observed. Mach also resolutely denied the existence of atoms, because they were too small to observe. We laugh at this silliness now – when we have microscopes that can see atoms – but the role of philosophy should have been to laugh at it then.

  Instead, when the physicist Ludwig Boltzmann used atomic theory to unify thermodynamics and mechanics, he was so vilified by Mach and other positivists that he was driven to despair, which may have contributed to his suicide just before the tide turned and most branches of physics shook off Mach’s influence. From then on there was nothing to discourage atomic physics from thriving. Fortunately also, Einstein soon rejected positivism and became a forthright defender of realism. That was why he never accepted the Copenhagen interpretation. I wonder: if Einstein had continued to take positivism seriously, could he ever have thought of the general theory of relativity, in which spacetime not only exists but is a dynamic, unseen entity bucking and twisting under the influence of massive objects? Or would spacetime theory have come to a juddering halt like quantum theory did?

  Unfortunately, most philosophies of science since Mach’s have been even worse (Popper’s being an important exception). During the twentieth century, anti-realism became almost universal among philosophers, and common among scientists. Some denied that the physical world exists at all, and most felt obliged to admit that, even if it does, science has no access to it. For example, in ‘Reflections on my Critics’ the philosopher Thomas Kuhn wrote:

  There is [a step] which many philosophers of science wish to take and which I refuse. They wish, that is, to compare [scientific] theories as representations of nature, as statements about ‘what is really out there’.

  Imre Lakatos and Alan Musgrave, eds., Criticism and the Growth of Knowledge (1979)

  Positivism degenerated into logical positivism, which held that statements not verifiable by observation are not only worthless but meaningless. This doctrine threatened to sweep away not only explanatory scientific knowledge but the whole of philosophy. In particular: logical positivism itself is a philosophical theory, and it cannot be verified by observation; hence it asserts its own meaninglessness (as well as that of all other philosophy).

  The logical positivists tried to rescue their theory from that implication (for instance by calling it ‘logical’, as distinct from philosophical), but in vain. Then Wittgenstein embraced the implication and declared all philosophy, including his own, to be meaningless. He advocated remaining silent about philosophical problems, and, although he never attempted to live up to that aspiration, he was hailed by many as one of the greatest geniuses of the twentieth century.

  One might have thought that this would be the nadir of philosophical thinking but unfortunately there were greater depths to plumb. During the second half of the twentieth century, mainstream philosophy lost contact with, and interest in, trying to understand science as it was actually being done, or how it should be done. Following Wittgenstein, the predominant school of philosophy for a while was ‘linguistic philosophy’, whose defining tenet was that what seem to be philosophical problems are actually just puzzles about how words are used in everyday life, and that philosophers can meaningfully study only that.

  Next, in a related trend that originated in the European Enlightenment but spread all over the West, many philosophers moved away from trying to understand anything. They actively attacked the idea not only of explanation and reality, but of truth, and of reason. Merely to criticize such attacks for being self-contradictory like logical positivism – which they were – is to give them far too much credence. For at least the logical positivists and Wittgenstein were interested in making a distinction between what does and does not make sense – albeit that they advocated a hopelessly wrong one.

  One currently influential philosophical movement goes under various names such as postmodernism, deconstructionism and structuralism, depending on historical details that are unimportant here. It claims th
at because all ideas, including scientific theories, are conjectural and impossible to justify, they are essentially arbitrary: they are no more than stories, known in this context as ‘narratives’. Mixing extreme cultural relativism with other forms of anti-realism, it regards objective truth and falsity, as well as reality and knowledge of reality, as mere conventional forms of words that stand for an idea’s being endorsed by a designated group of people such as an elite or consensus, or by a fashion or other arbitrary authority. And it regards science and the Enlightenment as no more than one such fashion, and the objective knowledge claimed by science as an arrogant cultural conceit.

  Perhaps inevitably, these charges are true of postmodernism itself: it is a narrative that resists rational criticism or improvement, precisely because it rejects all criticism as mere narrative. Creating a successful postmodernist theory is indeed purely a matter of meeting the criteria of the postmodernist community – which have evolved to be complex, exclusive and authority-based. Nothing like that is true of rational ways of thinking: creating a good explanation is hard not because of what anyone has decided, but because there is an objective reality that does not meet anyone’s prior expectations, including those of authorities. The creators of bad explanations such as myths are indeed just making things up. But the method of seeking good explanations creates an engagement with reality, not only in science, but in good philosophy too – which is why it works, and why it is the antithesis of concocting stories to meet made-up criteria.