by Jim Baggott
Of course, we know that Newton’s laws have been superseded by Einstein’s special and general theories of relativity, which change the way we think about space, time, and mass. But these are still classical theories (in the sense that they’re not quantum theories). Take it from me that there’s nothing in relativity that should shake our confidence about Realist Proposition #3. Though they’re still very much on the surface, we have to accept that even the base concepts in our theories sometimes need to be understood at a somewhat deeper level. Space, time, and mass are real but our understanding of them in Newton’s second law of motion is only approximate. After all, scientific theories are provisional. They’re only approximately or contingently true, valid for as long as they continue to provide descriptions that are judged to be in agreement with the evidence.
Nevertheless, if I’ve managed to sow a few seeds of doubt then I’ve done my job. As we’ve already seen in Chapter 1, in quantum mechanics these doubts return with a startlingly cruel vengeance.
Now, I’ve tended to find that discussions about the interpretation of quantum mechanics can quickly get bogged down and confused on the subject of ‘reality’. There’s a tendency to conflate objective reality (Realist Proposition #1), the reality of ‘invisible’ entities like electrons (Proposition #2), and the reality of the representation of the properties and behaviour of these entities in scientific theories (Proposition #3). I’d be the first to admit that these propositions are not so cleanly separable, but I’d argue that there’s much to be gained by considering them as such.
It would seem that Proposition #3 is contingent on the acceptance of #1 and #2. It’s surely pointless to argue for a realist interpretation of a scientific representation whilst at the same time denying that stuff is real when we’re not looking at it or thinking about it, and when our only evidence for it is indirect.* But, of course, acceptance of Propositions #1 and #2 doesn’t imply acceptance of #3. We can accept #1 and #2 but still choose to reject #3. I’ve come to believe that the best way to appreciate the debate about the interpretation of quantum mechanics is to view this not as a debate about the ‘nature of reality’, as such, but as a debate about the realism (or otherwise) of our representation of reality. In essence, it’s a debate about Proposition #3.
For the sake of completeness, I want to be clear that there’s a little more to scientific realism than this.20 We need to propose further that scientific theories, interpreted realistically according to #3, meet the empirical criterion: they can be tested and either confirmed as approximately or contingently true (for now) or their predictions can be shown to be false by comparison with empirical evidence. We also need to agree that when we talk about ‘progress’ in science, we understand that this is based on successively more accurate representations, the result of sailing the Ship of Science back and forth across the sea over time, refining and tightening the relationship between our metaphysical preconceptions and the empirical data. The philosopher Hilary Putnam wrote: ‘The positive argument for realism is that it is the only philosophy that doesn’t make the success of science a miracle.’21 This is sometimes referred to as the no miracles argument.
This would seem to make for a relatively straightforward distinction between realism and empiricism (or anti-realism) at the level of representation, but let’s not be too hasty. In seeking to resolve some of the contradictions between realism and anti-realism, the philosopher John Worrall developed a philosophy derived from a position first described by mathematician Henri Poincaré. This is called structural realism. According to Worrall, scientific theories tell us only about the form or structure of reality, but they tell us nothing about the underlying nature of this reality.*
As one theory displaces another, the mathematics might change and even the interpretation of the base concepts might change, but the structure or network of relationships between physical things is preserved. In general, a better theory will accommodate all the relationships between phenomena established through the theory it has replaced. For example, the quantum mechanical description of photons preserves all the structural relationships associated with the phenomena of diffraction and interference previously described by the wave theory of light, despite the fact that the mathematical formulations of these theories are so very different.
Structural realism comes in two flavours. There’s a Kantian flavour which suggests that scientific theories are about things-as-they-appear in the form of a structure of empirical relationships. But there are, nevertheless, metaphysical things-in-themselves that are presumed to exist because, as Kant argued, there can be no appearances without anything that appears. This was largely Poincaré’s position. In another, more empiricist flavour, the structural relationships are all there is and there are no things-in-themselves. This might lead us to wonder how it is possible to establish relationships if there’s nothing to relate to, but perhaps this is really rather moot. Even if the things-in-themselves exist, we can still say nothing meaningful about them.
This kind of approach makes the realist/anti-realist distinction much less straightforward. The philosopher Ian Hacking anticipated this dilemma, and reminded us that there is more to science than theoretical representation. Science has two principal aims: theory and experiment. Theories represent, says Hacking, and experiments intervene. We represent in order to intervene, and we intervene in the light of our representations. He wrote:22
I suspect there can be no final argument for or against realism at the level of representation. When we turn from representation to intervention, to spraying niobium balls with positrons, anti-realism has less of a grip…. The final arbitrator in philosophy is not how we think but what we do.
Theories come and go and, Hacking argues, intervention—experiment—is the final arbitrator on vexed questions concerning reality. As we will see in what follows, deciding whether a representation conforms to Proposition #3 can be a bit of a tricky business. In such situations, we will find it helpful to reach for a further proposition to help bring us to a conclusion. Therefore, at risk of blurring Hacking’s distinction between representation and intervention, I propose to paraphrase his arguments as follows:
Realist Proposition #4: Scientific theories provide insight and understanding, enabling us to do some things that we might otherwise not have considered or thought possible.
I think of this as the ‘active’ proposition. Only by taking the representation seriously do we have a firm basis on which to act. This might take the form of a search for new empirical data, by designing, building, and performing new experiments or making new observations. This doesn’t mean that it’s impossible for a ‘passive’, anti-realist representation to engage and motivate experimentalists. But, as we will see, this happens most often because those experimentalists who care about these things tend to favour realist representations, and are generally uncomfortable with anti-realism.
I want to contrast this with the views of the anti-realist philosopher Bas van Fraassen, who in the 1970s developed a philosophy known as constructive empiricism, a less dogmatic descendant of logical positivism. Van Fraassen argues that scientific theories need only be ‘empirically adequate’. It is sufficient that the representation accommodates all the empirical data and enables some prediction, but we should avoid getting tangled up in too much metaphysics. The representation is an instrument. It passively represents, nothing more.
This, then, is the proposition of last resort. If there are arguments both ways at the level of Proposition #3, we will seek judgement based on what the representation encourages us to do. If it actively represents, then we might be inclined to accept that this is a realist representation. If it passively represents, then we might consider it to be anti-realist.
Okay. That’s enough of that.* Now, where were we?
* Readers should note that this isn’t the famous ‘Raven paradox’, devised by the positivist philosopher Carl Hempel in the 1940s. If all ravens are black, this logically implies that any (and every) non
-black object is not a raven. But, whilst we wouldn’t hesitate to accept the observation of another black raven as evidence in support of the law, we’d surely struggle to accept as supporting evidence the observation of a green apple.
* Not surprisingly, the more counterintuitive the prediction, the more scientists are likely to look twice at where the prediction comes from. It goes something like this: That’s ridiculous—how could that possibly be true? What? It is true? OMG! What’s the theory again?
* A full circle is 360°, and an arc-minute is one-sixtieth of one degree. An arc-second is then one-sixtieth of an arc-minute. So, 532 arc-seconds represents about 0.15 of a degree.
† The perihelia of other planets are also susceptible to precession caused by the curvature of spacetime, but as these planets are further away from the Sun the contributions are much less pronounced.
* This is something of a standard philosophical ploy.
* Not because I necessarily have anything against religion, mythology, incompetents, and madmen as sources of potential scientific hypotheses, but because I seriously doubt the efficacy of such an approach.
* Whether you agree with this or not, we should acknowledge that some philosophical traditions are based on the notion of rejecting (or at least remaining agnostic about) objective reality, whilst accepting that it is still possible to devise truthful representations of sensible phenomena.
* Note that structural realism is not another distinct interpretation of quantum mechanics—the question we will be addressing in this book is whether interpretations of quantum mechanics are structurally realist.
* Readers might be disappointed that I’ve nowhere mentioned philosopher Thomas Kuhn’s The Structure of Scientific Revolutions, and his notions of normal science, conducted within a paradigm, and paradigm-shifting extraordinary or revolutionary science. To be honest, these notions are not wholly relevant to my thesis in this book, though they are no less fascinating for that. Constraints of space preclude more than this footnote, although I’d encourage readers to consult a few of Kuhn’s critics—especially Popper—in Criticism and the Growth of Knowledge, edited by Imre Lakatos and Alan Musgrave, published by Cambridge University Press in 1970.
4
When Einstein Came Down to Breakfast
Because You Can’t Write a Book About Quantum Mechanics without a Chapter on the Bohr–Einstein Debate
Armed with this perspective on the business of scientific theorizing, let’s return to 1927.
Bohr’s debates with both Schrödinger and Heisenberg prompted a period of deep introspection. As we saw in Chapter 1, Schrödinger argued for a realistic interpretation of the wavefunction, in the sense of Proposition #3. For him the wavefunction was something physically meaningful and tangible; it was something that could be easily visualized, a base concept. Heisenberg favoured a much more positivist, or anti-realist interpretation of quantum mechanics. He rejected any suggestion of some kind of underlying wave nature of matter that could be easily visualized, preferring to focus instead only on what can be observed, such as the lines in an atomic spectrum, and the inherent discontinuity and uncertainty that such measurements implied. Bohr hovered between these extremes, perceiving the validity of both descriptions yet puzzled by the fact that he could find no words of his own.
After some reflection, he eventually concluded that the language of classical physics, the language of waves and particles, of causality and continuity, is quite inadequate for describing quantum phenomena. And yet, as intelligent beings experiencing a classical world, this is the only language we have.
Whatever the true nature of the electron-in-itself, the behaviour it exhibits is conditioned by the kinds of experiments we choose to perform. These, by definition, are experiments requiring apparatus of classical dimensions, resulting in effects sufficiently substantial to be observed and recorded in the laboratory, perhaps in the form of tracks in a cloud chamber, or the series of spots on an exposed photographic plate which build up to an interference pattern, as we saw in Figure 4.
So, a certain kind of experiment will yield effects that we interpret, using the language of classical physics, as electron diffraction and interference. We conclude that in this experiment the electron is a wave. Another kind of experiment will yield effects which we interpret in terms of the trajectories and collisions of localized electrons. We conclude that in this experiment the electron is a particle. Bohr reasoned that these experiments are mutually exclusive. We cannot conceive an experiment to demonstrate both types of behaviour simultaneously, not because we lack the ingenuity, but because such an experiment is simply inconceivable.
What we get is a quantum world composed of shadows cast by our classical apparatus (think Plato’s cave). We can see the electron’s wave shadows or we can see its particle shadows. But because we are unable to construct apparatus in anything other than classical dimensions we cannot see what the electron really is: we can never discover anything about the electron-in-itself. What we are left to deal with is a fundamental wave–particle duality, a quantum world whose shadows are consistently different when we choose to cast them in different ways, using different classical apparatus.
Bohr sought to resolve this dilemma by declaring that these very different, mutually exclusive behaviours are not contradictory, they are instead complementary. They are different shadow projections of the same objectively real things-in-themselves.
So, where does this leave Bohr on Proposition #3? This is a good question. Although Bohr was infamously obscure in many of his writings on the subject, and he was much less staunchly empiricist than Heisenberg, on balance I believe it is fair to conclude that Bohr adopted a generally anti-realist interpretation of the wavefunction. Although it’s a bit of a stretch to provide only one Bohr quote in support of this conclusion (especially as this is not even a direct quote), I’ve nevertheless always found this rather telling. He is quoted as saying:1
There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.
If indeed he ever said it, much has been written about Bohr’s quoted use of the phrase ‘There is no quantum world’, as it seems to suggest that he denied the existence of an objective reality (Proposition #1). I believe this is nonsense, and entirely characteristic of a debate that oversimplifies questions concerning ‘reality’. I attach much greater significance to ‘Physics concerns what we can say about nature’. Bohr’s quote is all about the representation.
This kind of anti-realism is quite subtle. What Bohr is actually saying is that we’re fundamentally limited by the classical nature of our apparatus and our measurements, and the language of classical waves and particles we use to describe what we see. It’s therefore pretty pointless to speculate about the reality or otherwise of elements of the ‘abstract quantum physical description’, including the wavefunction, as we have absolutely no way of discovering anything about them.2
Heisenberg was initially resistant to Bohr’s notion of complementarity, as it gave equal validity to the wave description associated with his rival Schrödinger. As their debate became more bitter and personalized, Wolfgang Pauli was called to Bohr’s institute in Copenhagen in early June 1927 to calm things down and broker a peace. With Pauli’s help, Bohr and Heisenberg agreed to an uneasy reconciliation.
Among the key ingredients in the resulting interpretation of quantum mechanics are Bohr’s notion of wave–particle complementarity, the uncertainty principle, and Born’s quantum probability. It goes without saying that, as far as these physicists were concerned, by 1927 quantum mechanics was already a complete theory, and there was nothing more to be added.
What was remarkable was the zeal with which the disciples of this new quantum orthodoxy embraced and preached the new gospel. Heisenberg spoke and wrote of the ‘Kopenhagener Geist der Quantentheorie’; the ‘Copenhagen spirit’ of quantum theory.3 Thi
s has become known as the Copenhagen interpretation although, strictly speaking, there was never really a single ‘interpretation’ that all its advocates bought into. Like scripture, everybody had their own personal views on what it meant.
Einstein didn’t like it at all.
The stage was set for a great debate about the quantum representation of reality. This commenced at the fifth Solvay congress in Brussels, part of a series of invitation-only international conferences on physics supported by the wealthy Belgian industrialist and philanthropist Ernest Solvay. This was the first time the protagonists had an opportunity to gather together, face to face. Born and Heisenberg delivered a joint lecture, declaring that quantum mechanics is a complete theory, ‘whose fundamental physical and mathematical assumptions are no longer susceptible of any modification’.4 Schrödinger then delivered a lecture on wave mechanics. And, following an interruption to allow participants the opportunity to attend a competing conference that had been organized in Paris, Bohr presented a lecture on complementarity.
Then Einstein stood to raise an objection. He was concerned by the implications of physical events which we would now interpret as the collapse of the wavefunction. Look back at Figure 5. Before measurement, the electron wavefunction is distributed across the screen, with a probability of being found in any location where the square of the wavefunction is non-zero—Figure 5a. After measurement, we learn that the electron is ‘here’, in a single location—Figure 5b. However, Einstein now pointed out, we also learn simultaneously that the electron is definitely not ‘there’, where ‘there’ can be any location on the screen where we might have expected to find it.
