Niels Bohr lecturing in Iowa in the 1950s. Photo courtesy the Emilio Segrè Visual Archives/AIP


Calculate but don’t shut up

The cliché has it that the Copenhagen interpretation demands adherence without deep enquiry. That does physics a disservice

by Jim Baggott + BIO

Niels Bohr lecturing in Iowa in the 1950s. Photo courtesy the Emilio Segrè Visual Archives/AIP

Physics is important. We rely on it to provide us with valid conceptions of the nature of the physical world and how it works, conceptions that underpin almost every aspect of our technologically advanced society. At root, physics as a discipline relies on foundational theories of space and time, and of matter and light. For the most part, physicists are content to make use of foundational theories that have remained broadly unchanged for centuries. These are good enough for most practical purposes. But as they explore the physics of the very fast, or of the very small, or as they ponder the large-scale structure of the Universe, they reach for younger theories that were established only a century ago. These are quantum mechanics and Albert Einstein’s theories of relativity.

Mechanics is that part of physics concerned with stuff that moves, and quantum mechanics is the theory of the motion of matter and light at the smallest scales: the realm of molecules, atoms, subatomic particles (such as electrons), and photons, the quanta (or ‘atoms’) of light. If you want to figure out how an electron will behave as it moves in time through space, then you need to reach for quantum mechanics.

But there’s a problem.

Quantum mechanics was discovered and developed largely by European physicists in the mid- to late 1920s. As they struggled to comprehend what nature was trying to tell them, these pioneers understood only too well what they were getting themselves into. Although there had been much discussion about the philosophical interpretation of some concepts that appear in the older theory that preceded it – now called classical mechanics – the nature and structure of the new quantum mechanics begged all kinds of difficult questions about the very purpose of a scientific theory, if not the purpose of science itself. The debate became polarised around the philosophies of its two principal protagonists: Einstein and the Danish physicist Niels Bohr. The small community of quantum physicists in continental Europe formed into two distinct camps, and the Austrian-born British philosopher Karl Popper later called this divergence a schism. At the heart of the debate was the interpretation of the theory’s central concept – a mathematical object called the wave function.

The wave function was introduced in the theory as a way of accounting for the surprising experimental behaviour exhibited by quantum entities such as electrons. Under certain circumstances, this behaviour can be described in terms of electrons as familiar self-contained particles, localised as they move through space. But in different (and mutually exclusive) circumstances, the behaviour can be understood only in terms of electrons moving and spreading out through space as unfamiliar, non-localised waves. The wave function accommodates this odd duality. It has obvious wave-like properties, but also obvious particle-like properties, such as mass. It underpins a formula that assigns probabilities for any given electron existing in any one place at a particular point in time. What we might have previously judged to be physically impossible, quantum mechanics judges to be merely improbable, lending a fungible quality to reality, and challenging the truth of a universe defined by the physics that came before.

And here’s the rub. We never observe the wave function. If we push an electron through a narrow aperture, we imagine that it will diffract, spreading out in all directions in the space beyond as a wave (think of what happens to a rolling ocean wave as it squeezes through a gap in a harbour wall). If we now allow this electron to impinge on a screen covered with a photographic emulsion, we will find that the electron is detected, leaving a single bright spot at a specific point on the screen. Repeating this with more and more electrons will give us a diffraction pattern – a pattern possible only with waves – made up of a myriad of individual spots, each of which is possible only with particles. Where will the next spot appear? We have no way of knowing in advance. All we can do is use the wave function to calculate the probability that the next electron will be detected here, or there, or way over there.

What are we supposed to make of this? If we interpret the wave function realistically, as a tangible physical thing, we then have to figure out how it ‘collapses’ to produce a spot at only one location out of all the other probable locations on the screen. Such a collapse implies what Einstein in 1927 called ‘an entirely peculiar mechanism of action at a distance’ – an anathema of ghostly physical effects transmitted instantaneously across space with no apparent direct cause, now generally referred to as the ‘measurement problem’. For Einstein, the lack of any kind of physical explanation for how this is supposed to happen meant that something is missing; that quantum mechanics is in some way incomplete.

Bohr disagreed. He argued that in quantum mechanics we have hit a fundamental limit. What we observe is quantum behaviour as projected into our classical world of direct experience. As we cannot transcend this experience, we have to accept that the wave function has no physical significance beyond its relevance to the calculation of probabilities. We must be content with a ‘purely symbolic’ mathematical formalism that works. The wave function doesn’t collapse (and there’s no peculiar action at a distance) because it doesn’t actually exist, and so there is no measurement problem. In other words, all we can know is the electron-as-it-appears in different experimental arrangements. We can never know what the electron really is.

This is an empiricist, ‘antirealist’, or (to some) an ‘instrumentalist’ interpretation, which judges a theory to be largely meaningless except as an instrument to connect together our empirical experiences. Such an antirealist theory doesn’t necessarily deny the existence of an objective reality (we can happily continue to assume that the Moon is still there even if nobody looks at it or thinks about it), nor does it necessarily deny the reality of unobserved electrons, however we imagine them. But it does deny a direct and exact correspondence between the wave function and the things that the wave function purportedly describes. The formalism appears simply to encode our experiences of quantum phenomena in ways that allow us to calculate the probability that this or that will happen next. Quantum mechanics is complete, and we just need to get over it.

This, in essence, is the Copenhagen interpretation of quantum mechanics, named for the location of Bohr’s Institute for Theoretical Physics in Denmark. It is most closely associated with Bohr, whose writings on the subject are famously obscure to the point of impenetrability, though we will see below that this interpretation comes in different flavours and some care is required. As the US-born British physicist David Bohm explained in a 1987 interview: ‘The main point was whether you could get a unique description of reality. And Einstein took the ordinary view of a scientist that you could, and Bohr said you couldn’t … [Einstein] didn’t accept that Bohr’s approach could be taken as final, and Bohr insisted that it was.’ In a letter to Erwin Schrödinger in May 1928, Einstein called it a ‘tranquilising philosophy’.

The popular reading of subsequent history suggests that Bohr emerged the victor in the debate, browbeating the presumed-senile Einstein into submission, and the Copenhagen interpretation became a dogmatic orthodoxy. The Northern Irish physicist and quantum dissident John Stewart Bell was one of only a few physicists of the time prepared to push back against this orthodoxy, writing in 1981: ‘Making a virtue of necessity, and influenced by positivistic and instrumentalist philosophies, many came to hold not only that it is difficult to find a coherent picture but that it is wrong to look for one – if not actually immoral then certainly unprofessional.’

This reading was the basis for a column in Physics Today magazine in April 1989 by N David Mermin, a professor at Cornell University. He was concerned with attitudes towards quantum mechanics and how these had evolved from generation to generation of physics students in the US. Though few of his generation were likely to brood at length about what it all meant, Mermin expressed some personal discomfort with the Copenhagen interpretation. He wrote: ‘If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be “Shut up and calculate!”.’ Mermin’s meme would go on to become part of modern quantum folklore.

‘Shut up and calculate’ is the perfect foil, tantamount to declaring enough is enough

More years passed. Some commentators began to hint that ‘Shut up and calculate’ had actually been coined not by Mermin but by the charismatic US physicist Richard Feynman. In a follow-up column for Physics Today published 15 years later, Mermin was able to convince himself that it was indeed he who first used the phrase in the context of quantum foundations. He was also in no doubt about who was to blame, as he drew on

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.

The phrase has since become deeply embedded in the literature on quantum foundations, repeated in academic papers and in popular articles and books. It has become a handy put-down, an easy slight, a catchy synonym, summarising in just four words everything that is wrong with a dogmatic, orthodox interpretation that insists there is nothing more to be understood from a supremely successful theory of physics that – to many – leaves just too many unanswered questions. For those seeking to push a preferred realist alternative, such as Sean Carroll in his bestselling popular book Something Deeply Hidden (2019), ‘Shut up and calculate’ is the perfect foil, tantamount to declaring enough is enough, demanding that we look again.

But this doesn’t quite add up.

If, as Mermin suggests, those Harvard teachers berating him in the late 1950s were indeed ‘agents of Copenhagen’, this would imply that they had studied the literature (especially Bohr) and had fully signed up to the Copenhagen orthodoxy. But, despite what a superficial reading of history might imply, the ‘Copenhagen interpretation’ didn’t actually exist as such until the mid-1950s (try typing ‘Copenhagen interpretation’ into Google’s Ngram Viewer). And this version of Copenhagen is largely an invention of the German physicist Werner Heisenberg, seeking rehabilitation with the international physics community after the war. Heisenberg’s interpretation differed from Bohr’s in many key respects, particularly in the former’s willingness to admit a substantial subjective element.

Make no mistake, the physicists of the 1950s understood that there was an orthodox interpretation. But what was known only vaguely from the early 1930s as the Kopenhagener Geist (the Copenhagen ‘spirit’ – Heisenberg again) was far from widely shared by US physicists. Harvard’s Percy Williams Bridgman had developed his own firmly empiricist philosophy of science, called operationalism, in 1927. Bridgman’s student Edwin Kemble, the first American to write a doctoral dissertation on quantum mechanics, had no need of the Copenhagen spirit. Neither did the Americans Edward Condon and Philip Morse, who wrote the first English-language textbook on quantum mechanics, published in 1929 (they referred questions on interpretation to Bridgman’s book The Logic of Modern Physics).

It’s possible that the only entry point for the Copenhagen spirit into mainstream physics in the US during this period came from J Robert Oppenheimer’s lectures on quantum mechanics at Berkeley in the 1930s. But although Oppenheimer would later evangelise Bohr’s philosophy, at the time he delivered these lectures his understanding of Bohr was filtered through Wolfgang Pauli, with whom Oppenheimer had worked in Zurich in the late 1920s, and who had published his own text on quantum mechanics in the Handbuch der Physik in 1933.

Oppenheimer’s lectures informed Leonard Schiff’s student textbook Quantum Mechanics, first published in 1949, which would be used to teach quantum mechanics throughout North America, Europe and Asia, through three editions spanning 20 years. Schiff’s treatment of interpretation and problems related to measurement was rudimentary at best, and did nothing to satisfy the curiosity of the young Bell, in his final year of undergraduate study at Queen’s University in Belfast. In fact, according to Andrew Whitaker’s biography of Bell, it led him to conclude that Bohr was ‘annoyingly vague, and, indeed, [Bell] felt that, for Bohr, lack of precision seemed to be a virtue’.

But such observations relate only to the minority of physicists in the US who remotely cared about aspects of the philosophy of science and the interpretation of quantum mechanics; it appears that the majority just didn’t care at all.

Unlike in Europe, theoretical physics in universities of the prewar US was not the lofty preserve of a few exalted specialists, able to exert influence through the unquestionable authority of an academic hierarchy, until death. Physics departments in the US were more inclusive, collaborative and inherently democratic, with theorists working directly alongside their experimentalist colleagues. Their hierarchies and reward structures favoured theorists who engaged in experiments, and who could perform the theoretical calculations that were becoming increasingly difficult for the experimentalists to perform for themselves. On meeting Oppenheimer for the first time, the experimentalist Arthur Compton was impressed, judging him to be a model US theorist: ‘one of the very best interpreters of the mathematical theories to those of us who were working more directly with the experiments’.

This practical mindset extended to the students, most of whom had, according to the Dutch-born physicist Samuel Goudsmit, ‘at one time or another taken the family car apart and had put it together again’. Such ‘hands-on’, ‘can-do’ instincts fit comfortably within a culture that, from the 19th into the 20th century in the US, reputedly paid less attention to philosophy than any other country in the civilised world, and which had continued to foster, in the words of the historian Richard Hofstadter, a deep-seated anti-intellectualism, ‘a resentment and suspicion of the life of the mind and of those who are considered to represent it; and a disposition constantly to minimise the value of that life’.

The dominance of a more philosophically inclined European physics was soon to be ended by an avalanche of discoveries in nuclear physics in a time of impending war, the forced emigration of leading European physicists, and an allied atom bomb programme that at the time cost $2 billion and would of urgent necessity prize application above all else. It would be the bolder, brasher, more empirical ‘hands-on’ style of US theoretical physics that would come to dominate the postwar world.

The success of the Manhattan Project led to a postwar boom in student enrolments at university physics departments in the US. With most students electing to study physics as a means to a more financially rewarding end, the student body became noticeably less curious, more narrowminded and conformist. As the science historian David Kaiser puts it, physics in the US became ‘suburbanised’. Those students inclined to seek research careers in academia or the national laboratories relied on federal money and the major sources of funds, especially the US Atomic Energy Commission and the US Department of Defense, were ‘mission-oriented’. Even the National Science Foundation sought to avoid granting funding requests judged to lie outside mainstream physics. None encouraged the investigation of foundational questions. Research advisers, many already inclined towards empiricism or plain indifference, sought to steer their students towards projects more likely to attract funding, and so more likely to provide a firm basis on which to build careers as ‘professional calculating physicists’.

The dominance of US postwar science meant that such attitudes were inevitably exported back to Europe, and they continue to this day. In April 2018, I was invited to talk about Quantum Reality (2020), a new popular book I was then working on about the interpretation of quantum mechanics, at a dinner hosted by the Royal Society in London. After dinner, I was approached by a number of esteemed fellows who took the trouble to explain to me that ‘nobody cares about this’.

It was this ‘dogma of indifference’ that Mermin had experienced as a student in the late 1950s, and which he had retrospectively identified as a preference for the Copenhagen interpretation. Foundational questions were judged to belong in a philosophy class, and there was no place for philosophy in physics. As he explained to me in December 2019, his professors were ‘just indifferent to philosophy. Full stop. Quantum mechanics worked. Why worry about what it meant?’

The exploration of seemingly pointless philosophical issues can have profound practical consequences

In a quick follow-up discussion with me in July 2021, Mermin confessed that he now regrets his choice of words. Already by 2004 he had ‘come to hold a milder and more nuanced opinion of the Copenhagen view’. He had accepted that ‘Shut up and calculate’ was ‘not very clever. It’s snide and mindlessly dismissive.’ But he also felt that he had nothing to be ashamed of ‘other than having characterised the Copenhagen interpretation in such foolish terms’.

So, at what point did it become fashionable to gather together all the ills of quantum mechanics – all those conundrums that arise only in realist interpretations – and bundle them into a demonised version of the antirealist Copenhagen interpretation? The motives are fairly obvious. It’s hard to criticise a vague and amorphous culture of indifference in anything other than the most general terms and, in any case, such indifference is an issue for the sociology of science, not its content. Those more inquisitive physicists and philosophers looking to develop a more realist alternative interpretation needed a better foil, a more meaningful straw man to knock down.

And here was Bohr’s notorious obscurity and a handy, dogmatic, orthodox interpretation, a dogma that was not inspired by Bohr, but that was nevertheless inescapably associated with him. ‘Everybody pays lip service to Bohr,’ Bohm explained in 1987, ‘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.’ Overlook (or ignore) its fragmented nature and questionable paternity, and the ‘Copenhagen interpretation’ is a great platform on which to build your counterarguments, or deepen discontent in order to foment your revolution. Or sell a few more books.

One of my favourite examples of this trend is an article by the US theorist Bryce DeWitt published in 1970 in Physics Today: ‘According to the Copenhagen interpretation of quantum mechanics,’ he wrote, ‘whenever a [wave function] attains a [certain form pertaining to measurement] it immediately collapses.’ DeWitt was seeking to validate an alternative reality based on the idea of ‘many worlds’, and no doubt his contrived version of Copenhagen helped him to breed discontent with the prevailing orthodoxy.

The timing is about right. The work of Bohm in the late 1950s, and Bell in the ’60s, had, by the early ’70s, led to another extraordinary conclusion. A so-called ‘locally real’ interpretation of quantum mechanics in which entities like photons or electrons are assumed to have intrinsic properties all along – and not just at their point of observation or measurement – makes predictions that differ from ‘ordinary’ quantum mechanics. It was realised that these predictions could be tested experimentally. Such tests have been performed at regular intervals ever since, with ever-increasing sophistication and precision, confirming that, despite how reasonable they might seem, all locally real interpretations are quite wrong. These experiments have, nonetheless, spawned entirely new disciplines – of quantum information and quantum computing – demonstrating that exploration of seemingly pointless philosophical issues can have profound practical consequences.

The deliberate conflation typified by DeWitt’s article has led to a world of confusion. In a 2016 survey of physicists, conducted by Sujeevan Sivasundaram and Kristian Hvidtfelt Nielsen at Aarhus University in Denmark, it was found that just a minority of physicists truly understood the meaning of the Copenhagen interpretation or the foundational concepts of quantum mechanics – based on the idea of a probabilistic universe, in which a particle is neither here nor there until measured, described by the wave function itself. In fact, only a minority of respondents had a proper grasp of the measurement problem that launched the field.

Mermin should be forgiven for following a trend that, by 1989, was entrenched in the quantum cultural mindset. I did much the same in my first book on quantum mechanics, published in 1992. We have both since learned to be more circumspect; we have to acknowledge that a dogma of indifference to philosophical questions was at least as much to blame for the rejection of foundational enquiry as anything Bohr might have said. Of course, the first to give expression to a meme such as ‘Shut up and calculate’ can claim no ownership over it and cannot control how others will use it. Irrespective of the historical rights and wrongs, those who continue to use it as a term of abuse directed at the Copenhagen interpretation are perfectly at liberty to do so.

But there is a growing number of commentators who are both familiar with the history and prepared to call this out. The purpose of this essay is to help you do the same.