The Copenhagen Confusion

Despite all the popular media attention given to fantastical interpretations of quantum mechanics which invoke the existence of multiple, parallel universes, according to a survey published in 2016, the Copenhagen interpretation remains the most favoured.

What I found even more fascinating is that the 2016 survey, conducted by Sujeevan Sivasundaram and Kristian Hvidtfelt Nielsen at Aarhus University in Denmark, included questions which allowed them to go beyond this simple statement of preference and to assess what respondents thought they meant by the ‘Copenhagen interpretation’. The answers reveal a world of confusion, leading the authors to conclude: ‘However, when one regards the results of the survey, it shows that the resurgence the topic [quantum foundations] has been undergoing in recent times still has not had an impact on the participants being familiar with foundational concepts. This is seen from the answers to the questions concerning Bell’s inequality and the measurement problem, where a minority of the participants had a proper grasp of these topics’ (emphasis added).

To a certain extent this confusion is understandable. The rot set in with the very first exchange between Albert Einstein and Niels Bohr at the Solvay conference in October 1927, and the confusion has grown ever since. That there isn’t a single ‘Copenhagen interpretation’ doesn’t help. Anyone who has tried to study Bohr’s writings on the subject knows to keep handy a ready supply of headache tablets. The Copenhagen interpretation is accused (rightly) of dogmatism, but often for the wrong reasons. And, to be frank, in seeking to demonize it, some commentators have been guilty of (I believe) deliberately misinterpreting what it says.

The survey question that caught my attention is this: ‘What characterizes the Copenhagen interpretation of quantum mechanics?’ Respondents were allowed multiple choices, but ‘The collapse of the wavefunction upon measurement’ was the most popular, polling 116 votes (77%). In this post I hope to explain why respondents were wrong to choose this, and why its popularity betrays a profound confusion on these important foundational questions.

In an effort to bring clarity, I’m going to over-simplify (but hopefully not too much). The Bohr-Einstein debate involved a clash of philosophical positions. The bizarre nature of the quantum formalism begs all kinds of fundamental questions about its meaning, and especially the meaning of its central concept – the quantum wavefunction. Bohr’s principle of complementarity can be articulated in the language of classical waves and of particles, or as descriptions in which the physics evolves smoothly and continuously and energy is conserved (an electron ‘orbits’ an atomic nucleus but we can’t say where it is at any moment in time), or discontinuously in a space-time framework (the particulate electron is ‘here’). These descriptions are not contradictory, they are complementary. According to Bohr what we cannot do is go beneath these descriptions and say what the electron is at all times in all circumstances.

This and the variants of the Copenhagen interpretation due to Bohr and Werner Heisenberg are essentially anti-realist. This doesn’t mean that they deny objective reality or the reality of ‘invisible’ microscopic entities (such as electrons), although Heisenberg was guilty of a degree of subjectivism that is often (wrongly) levelled at Bohr. It means that the wavefunction shouldn’t be taken as a literal representation of the real physical states of real physical quantum things. Bohr referred to application of the quantum formalism as a ‘purely symbolic procedure’, and is famously quoted as saying: ‘There is no quantum world. There is only an abstract quantum physical description’.

The Copenhagen interpretation obliges us to resist the temptation to ask: But how does nature actually do this? Like emergency services personnel at the scene of a tragic accident, Bohr advises us to move along, as there’s nothing to see here. And there lies the rub: for what is the purpose of a scientific theory if not to aid our understanding of the physical world? We want to rubberneck at reality. The simplest way to do this in quantum mechanics is to take the wavefunction more literally and realistically.

And this is what Einstein did in 1927. Electrons pushed one at a time through a small hole at O in a screen S (see the figure below) will eventually produce a pattern on the photographic film P consistent with the diffraction of a classical ‘electron wave’. But each electron is detected as a single particle, registering as a single point on the film. Einstein offered two conceptions of this experiment. In the first, the wavefunction represents a collection or ensemble of electrons and the probability that any individual electron will strike the film at any specific place is given by the modulus-square of the wavefunction.

In his second conception, Einstein imaged that the wavefunction describes each individual electron, whose probability of detection at a specific place on the film is also given by the modulus-square of the wavefunction. But Einstein did not consider the choice between these conceptions to be a matter of taste. For him, the second conception could not stand. It violated relativity and common sense. It ‘… assumes an entirely peculiar mechanism of action at a distance, which prevents the wave continually distributed in space from producing an action in two places on the screen’. This would later become widely known as ‘spooky action at a distance’.

But we should quickly note that all this talk about being ‘distributed in space’ and ‘physical action’ betrays the fact that these concerns are based on a realistic interpretation of the wavefunction of the electron. According to Bohr, between its generation and detection we can say nothing at all about what each electron is up to. Quantum mechanics allows us to predict where each electron might be detected on the screen, but says nothing about how it gets there. What’s quite fascinating is that Einstein was attacking a position that Bohr wasn’t actually defending. No real surprise that Bohr responds: ‘I feel myself in a very difficult position because I don’t understand what precisely is the point which Einstein wants to [make]. No doubt it is my fault’.

Bohr concludes his remarks with the observation: ‘I may not have understood, but I think the whole thing lies [therein that the] theory is nothing else [but] a tool for meeting our requirements and I think it does’.

But the seeds of confusion were now already sown. If the (realistically-interpreted) wavefunction starts out ‘distributed in space’ and ends up at a single point then it is presumed to ‘collapse’. Whilst it is possible to find references to an equivalent phrase – the ‘reduction of the wave packet’ – in Heisenberg’s 1929 Chicago lectures, this is used to critique a purely wave description. The ‘collapse of the wavefunction’ was never part of the Copenhagen interpretation because the wavefunction isn’t interpreted realistically. The only thing that happens when an electron is detected on a screen in the context of Copenhagen is that we gain knowledge of the position of the electron.

The collapse of the wavefunction is more appropriately associated with John von Neumann’s quantum theory of measurement, included in his text Mathematical Foundations of Quantum Mechanics, first published (in German) in 1932, although von Neumann doesn’t actually use this phrase. Instead he distinguishes two kinds of quantum process. Process 2 is the smooth, continuous evolution of a quantum system as described by quantum mechanics. Process 1 is the discontinuous ‘projection’ of the system into a single measurement outcome (such as a single spot on the screen). At the moment of measurement, von Neumann postulates that we abandon process 2 in favour of process 1.

What’s quite remarkable is how von Neumann’s theory would become conflated with the Copenhagen interpretation and summarised under the heading of ‘the measurement problem’. In the Copenhagen interpretation, all measurements are classical and the notion of ‘quantum measurement’ doesn’t arise. There is no such thing as the ‘measurement problem’ in the Copenhagen interpretation. No matter how deep you dig, you’ll struggle to find any reference to von Neumann’s theory in Bohr’s writings. In Niels Bohr’s Times, Abraham Pais describes an entry he found in one of his old notebooks pertaining to a lecture delivered by Bohr in November 1954. The entry reads: ‘[Bohr] thinks that the notion “quantum theory of measurement” is wrongly put’. A 1980 article by the philosopher Paul Teller opens with a question and an observation: ‘Why does Bohr nowhere discuss the projection postulate? He has the courtesy to cast at least a few disparaging words at some other notions for which he has no use, such as quantum logic. But he will not even admit the projection postulate as a subject for discussion’. Indeed, why would an anti-realist interpretation (which insists that the use of a quantum description at classical scales is wholly inappropriate) require a quantum theory of measurement?

So how did the conflation arise? I’m confident there isn’t a straightforward answer to this question. But I’d like to draw your attention to an article published in the journal Physics Today in 1970, by Bryce DeWitt. It is titled ‘Quantum Mechanics and Reality’.

DeWitt’s search for a quantum theory of gravity had led him to the Wheeler-DeWitt equation which, when applied to the entire universe, implies a ‘universal wavefunction’. He perceived a problem. The Copenhagen interpretation appears to place special emphasis on the process of measurement and the role of an observer (it doesn’t, but never mind) and, as there can be nothing and nobody outside the universe to collapse such a wavefunction, he rejected Copenhagen in favour of Hugh Everett III’s ‘relative state’ formulation, which he re-invented (with Everett’s blessing) as the many worlds interpretation of quantum mechanics.

Let’s be clear. DeWitt was seeking an interpretation in which the wavefunction is to be interpreted realistically, and the ‘measurement problem’ is a real problem in need of a solution. That in itself should be sufficient reason to reject Copenhagen, but no. DeWitt invents what he clearly believes is a stronger argument by conflating Copenhagen with the collapse of the wavefunction: ‘According to the Copenhagen interpretation of quantum mechanics, whenever a [wavefunction] attains a form like that in equation 5 [a superposition of wavefunctions pertaining to measurement] it immediately collapses’. This sentence appears in a section titled ‘The Copenhagen collapse’. Incidentally, in his PhD thesis Everett is careful to distinguish von Neumann’s theory from Copenhagen. His thesis is based rather on a rejection of von Neumann’s projection postulate (process 1). He dismisses the Copenhagen interpretation separately, as ‘safe from contradiction’ but ‘overcautious’. ‘We do not believe the primary purpose of theoretical physics is to construct “safe” theories at severe cost in the applicability of their concepts, which is a sterile occupation’. Well, okay, but all I’d say is that this is a bit rich coming from the proponent of an alternative interpretation which spawns a structure so heavily burdened by its metaphysics, in which its central concept is not susceptible to empirical test, that it is likewise ‘safe from contradiction’.

DeWitt no doubt believed that in order to gain the attentions of physicists and other interested readers, he needed to tell a story in which Bohr, Heisenberg, and the Copenhagen interpretation are the villains, and Einstein and Erwin Schrödinger are heroes of the ‘realist resistance’. The modern folk-historical telling of the Bohr-Einstein debate paints Bohr as a dogmatic bully, browbeating the senile Einstein as the physics community looks on, cheering from the side-lines. But it’s doubtful that Bohr was any more dogmatic than any other Nobel laureate, and if Einstein’s insistence on a God free of a gambling addiction was not dogmatic in its turn, what was it?

There might be a sense in which Bohr’s complementarity swept unquestioned across the centres of physics in continental Europe, but English physicists such as Paul Dirac were essentially unmoved (you’ll find no mention of complementarity in Dirac’s The Principles of Quantum Mechanics, first published in 1930). There was little doubting the extraordinary successes of the theory and attentions inevitably shifted from debates about its meaning to more practical concerns related to its application. For example, post-war experimental studies of the hydrogen atom had thrown the quantum physics of the electron into crisis. But these were technical problems in need of practical solutions and J. Robert Oppenheimer approached the 1947 Shelter Island conference, in which American theorists strove to find these solutions, much as he had chaired technical committees at Los Alamos. Solutions had indeed emerged, through the invention of new mathematical techniques, not from endless philosophical nit-picking over meaning.

By 1949 the Copenhagen interpretation had become synonymous with general indifference or disinterest. Physicists who didn’t care to trouble themselves with questions of interpretation would wave in the direction of the standard student textbooks and just shrug their shoulders. And American scientific hegemony after the second world war ensured that these standard textbooks, such as Quantum Mechanics, by Leonard Schiff (greatly influenced by Oppenheimer) carried often-garbled versions of Bohr’s complementarity and the Copenhagen line on measurement. Schiff’s text would go on to inform the teaching of quantum mechanics throughout North America, Europe, and Asia, through three editions spanning twenty years. It did nothing to satisfy the curiosity of the young John Bell, in his final year of undergraduate study at The Queen’s University in Belfast.

The Copenhagen interpretation had become a dogma not through acceptance of reasoned philosophical arguments, but by default. In a 1987 interview, David Bohm explained it this way: ‘… everybody plays lip service to Bohr, but nobody knows what he says. People then get brainwashed into saying Bohr is right, but when the time comes to do their physics, they are doing something different.’

Here’s N. David Mermin, writing about his experiences as a research student studying quantum mechanics in the 1950s, in the journal Physics Today in 2004, in which he recalls:

… vivid memories of the responses my conceptual inquiries elicited from my professors – whom I viewed as agents of Copenhagen – when I was first learning quantum mechanics as a graduate student at Harvard, a mere 30 years after the birth of the subject. ‘You’ll never get a PhD if you allow yourself to be distracted by such frivolities,’ they kept advising me, ‘so get back to serious business and produce some results.’ ‘Shut up,’ in other words, ‘and calculate.’ And so I did, and probably turned out much the better for it. At Harvard, they knew how to administer tough love in those olden days.

Mermin has admitted to me in private correspondence that his professors were simply indifferent to philosophy, and only in this sense did he view them as ‘agents of Copenhagen’. ‘They had no interest in understanding Bohr, and thought that Einstein’s distaste for [quantum mechanics] was just silly… It was a very unphilosophical time.’

There can be no doubt that the slow-to-reawaken interest in foundational questions raised by Bohm and Bell (and others) has uncovered some remarkable phenomena that might have otherwise gone unnoticed, and has helped to establish the wholly new disciplines of quantum information and quantum computing, efforts recognised through the award of the 2022 Nobel prize in physics. But we should not overlook the simple fact that all the experimental studies of the last 50 years have failed to establish the superiority of any realist interpretation or extension of quantum mechanics. The matter of interpretation remains undecided. No doubt this failure will not shake the firm realist convictions of some commentators. For many years, on balance I have preferred Einstein’s realism and have championed Bell’s rejection of the Copenhagen ‘orthodoxy’ (I still do). But in recent years I have developed real doubts. Like the great philosopher Han Solo, I’ve got a very bad feeling about this.

I encourage readers with an interest in these questions to go beyond the superficial treatments that can be found in some popular science books, and (alas) in student textbooks. Dig a little deeper. As Sivasundaram and Nielsen imply in their paper, become more familiar with the foundational concepts. Learn a little more about the philosophy of the subject, and make up your own mind. I believe your efforts will be greatly rewarded, not least through a better appreciation of one of the most dramatic debates in the entire history of science.

As the philosopher Don Howard notes, the Bohr-Einstein debate: ‘… was not a clash between a dogmatic bully and a senile old man. Theirs was a clash between two determined seekers after truth. They both knew that a deep truth was to be discovered where separability and entanglement came into conflict’.

Jim Baggott is a freelance science writer and a co-author with John Heilbron of Quantum Drama: From the Bohr-Einstein Debate to the Riddle of Entanglement, to be published by Oxford University Press in April 2024.

This essay is an edited version of an essay with the same title first posted on my behalf by my good friend Massimo Pigliucci in June 2020.

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@JimBaggott