Quantum Drama: The Prologue
An extract in celebration of the US publication of the new book by Jim Baggott and John L. Heilbron
Our drama is an episode in a long story. It has to do with the distinctly human compulsion to divide the world into domains defined by rules and expectations. Such domains, like religion and physics, can accommodate a wide range of human experience. They can also encourage fundamentalists to pursue the illusory goal of a final theory of everything belonging to the domain. Their aim is closure; to offer unassailable proof of finality and to declare that no plausible alternatives are possible. The American theorist Stephen Weinberg made clear what is at stake: ‘A final theory will be final in only one sense – that it will bring an end to a certain sort of science, the ancient search for those principles that cannot be explained by deeper principles’.
But the closure of a domain of experience ruled by a particular theory assumes the existence of criteria for unambiguously determining whether a given fact or question lies within the theory’s competence. And that, as the long story of Euclidean geometry shows, is not always easy to decide.
The domain of Euclidean plane geometry includes all figures that can be constructed with an unmarked straight edge and compass, and its ruling theory is expressed in a set of axioms assumed to be true from which everything else can be deduced. Greek geometers deduced among much else that it is possible to construct only four fundamental regular polygons. These have 3 (equilateral triangle), 4 (square), 5 (pentagon), or 15 sides. An infinite number of others can be constructed by continual bisection of the sides of any of the fundamentals. On this understanding, no construction in keeping with the axioms and the rule of edge and compass can make any other regular polygon. And yet, only 2000 years after Euclid, Carl Friedrich Gauss discovered that fundamental regular polygons with bizarre numbers of sides, such as 17, are theoretically possible.
During the same period, many Euclidean geometers believed incorrectly that the rules of their science permitted the construction of a square equal in area to a circle. They lacked the means to prove the task impossible. It took two millennia to show that pi is a transcendental number – no algebra can be devised to compute it – and the squared circle is impossible. Mathematicians opened the long-closed domain of Euclidean plane geometry to admit bizarre regular polygons and closed it again to exclude the squared circle.
Our quantum drama centres on the question whether quantum phenomena are like squared circles or bizarre regular polygons when tested by the fundamental definitions and expectations of the ‘classical’ physics that our principal actors, Niels Bohr and Albert Einstein, learned at school. The analogy to Euclidean geometry is not perfect. Physics does not confine itself to arbitrarily limited ideal types and does not stop to prove the impossibility of one theory before adopting another. Still, we believe the analogy holds. Those who dissent; those who, almost as an obligation, resist the claims of closure advanced by fundamentalists; those who stubbornly search for bizarre regular polygons, can precipitate important discoveries.
Adherents of the classical physics of Isaac Newton declared that by reducing the properties of matter to size, shape, and motion, the rival physics of René Descartes could not give a satisfactory account of gravity. Cartesians replied by attributing to Newton the concept of a gravitational force acting at a distance and rejecting it as unphysical, incomprehensible, and ‘occult’. Newton agreed with the objection but claimed that it did not apply. ‘That one body may act on another at a distance through a vacuum without the mediation of any thing else & through which their action or force may be conveyed from one to another is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it’. However, he proffered no alternative explanation: ‘I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis: and hypotheses, whether metaphysical or mechanical, have no place in experimental philosophy’.
The discomfort attendant on the admission of non-mechanical, non-local forces into physics eventually led to the introduction of field theories that incorporated elements from both earlier systems. By 1900, the president of the French Physical Society, in opening an international congress of physics in Paris, could proudly proclaim that, once again, ‘the spirit of Descartes hover[ed] over modern physics’. In our drama, Einstein plays the part of Gauss searching for bizarre regular polygons, Descartes rejecting action at a distance as unphysical and unintelligible, and Newton excluding certain sorts of ‘hypotheses’ by definition. Bohr plays the parts of the Euclidean declaring closure of his domain and the Newtonian willing to admit the unintelligible and non-intuitive in return for a consistent, quantitative account of the facts. As we will see, the instinct to reject action at a distance motivated many of the episodes in our drama.
Absurdities or, as Bohr preferred to call them, ‘irrationalities’, abounded in the forging of quantum mechanics and, for many physicists, including Bohr and Einstein, in the final product. Relative comfort with the absurd and the ambiguous measured the divide between them. Although never resolved, their disagreement prompted fruitful debates because they never lost their admiration for one another and shared the belief that physicists have a duty to discover and declare the foundations of natural philosophy. Their debates, regarded as ‘philosophical’ (and therefore irrelevant) by many physicists, did not result in experimental tests during their lifetimes, but their approaches to the problem eventually prompted a series of extraordinary experimental discoveries.
These discoveries, which support practical applications such as quantum encryption, teleportation, and computing, came a half-century rather than two millennia after the declaration, by Bohr’s school, of the closure of the relevant theoretical domain: quantum mechanics. The pace of science has picked up since Euclid. Nonetheless, the speed with which Bohr and his school sought to close quantum mechanics, within two or three years of the discoveries on which they based their opinion, is breath-taking. Einstein and his followers objected to their overly hasty surrender of the possibility of alternatives more in keeping with an intuition grounded in classical physics. It was not a question whether light should be pictured as waves or particles, or atoms as solar systems, but of whether the microworld could be pictured at all. With enough time and talent, would it not be possible to show that the claimed failure of strict causality in the microworld was as mistaken as ruling a 17-sided regular polygon out of Euclidean geometry? Why was the move to closure on such fundamental questions so swift? Why was the opposition so ineffectual?
For answers we must invoke not only the state of science but also the social and cultural commitments and psychological motives of the participants. The first world war was a watershed for physics as for other high cultural pursuits of Western Europe. It divided the creators of quantum physics, who would stay close to classical ideas, from the creators of quantum mechanics who, with some easily explainable exceptions, began their careers with their minds full of quantum ideas. The first generation grew up between the Franco-Prussian War of 1870 and the first world war, an era of relative peace, stability, confidence, security, and the complacency associated with the Victorian era. The second generation began their careers after experiencing the anxieties and scarcities of the war and a troubled peace, and while confronting threats from the growing political appeal of fascism and communism.
Classical physics, with its emphasis on mechanical or picturable models, the all-encompassing principles of thermodynamics, and everyday notions of space, time, and causality mirrored the political and social stability of its heyday. Quantum mechanics, with its rejection of norms associated with the regime that had brought on the war and its emphasis on the uncontrollable, acausal, uncertain behaviour of the microworld, agreed well with the uncertainties of its development in the 1920s and 1930s.
Already by 1900 classical physicists had reasons to worry about foundations. They had the new experimental discoveries of X-rays, radioactivity, and the electron to absorb and their greatest theoretical achievements, electrodynamics and statistical mechanics, had encountered serious problems. Lord Kelvin, one of the great architects of classical physics, identified these problems as ‘clouds’ over the future of the discipline. The same analogy was invoked by commentators on the political scene to refer to rising socialism and nationalism, and to colonial and commercial competition, within and between the great powers. But by and large the mood of physicists and the larger society that supported them during Victorian times was optimistic and cosmopolitan. We would be hard pressed to account for a physics of the late nineteenth century distinguished by doubt and a physics of the 1920s marked by certainty.
Many of the worriers entertained the idea that physics aimed not at the fundamental truth of things, but only at an accurate description of phenomena. No doubt ‘descriptionism’, as we may call the collection of fin-de-siècle instrumentalist philosophies, was no more useful in the everyday work of scientists then than it is now. But it figured promiscuously in general talks and essays, such as the famous address that the mathematician and physicist Henri Poincaré gave at the opening of the International Congress of Physics of 1900. You should not think yourselves above librarians, Poincaré told his surprisingly receptive audience, for your theories are no more fundamental than the principles of a library catalogue and, like it, should be judged by how efficiently it accommodates new acquisitions. The most influential descriptivist for our purposes was the Austrian physicist Ernst Mach, who for a time had Einstein’s attention.
Mach taught that science built on and predicted sensory experience and that theory should attempt no more than to connect the input with the output. In its extreme version, Mach’s physics denigrated models of the world, like atoms or ethers, and gave no priority to mechanics. All reductionist schemes, all systems for referring sensory experience to the activities of hypothetical sub-microscopic particles, were inherently misleading and inconsistent with sound science. Among those who shared Mach’s criticism of atomism was the professor of theoretical physics at the University of Berlin, Max Planck. That was one reason that at the turn of the century he was working at a problem expected to yield to the combined equations of thermo- and electrodynamics without reliance on molecular theories.
The problem concerned the properties of radiation maintained at a constant temperature inside a cylindrical porcelain vessel closed apart from a small hole. This construction made it a good approximation to an ideal ‘black body’, which can absorb and emit radiation of all frequencies. The setup may seem arcane in theory and far from useful, but it turned out to touch on fundamental questions and to have practical application in the then new industry of electric lighting. When the vessel is heated, its interior glows like a furnace, red, orange, bright yellow, brilliant white, depending on the temperature. Planck’s problem was to find a ‘radiation law’ to describe the colour distribution (the intensity of radiant energy at each frequency) as a function of temperature and frequency. He failed to find one that agreed with experiment until he made what amounted to the assumptions that radiation in the container could exchange energy with its walls only through discrete amounts or quanta of energy, and that these permissible amounts had to be proportional to the frequency of the radiation participating in the exchange.
Being a theorist, Planck sought a theory that would allow for the quanta. In what he later described as an act of desperation, he turned to atomistic ideas that gave him what he needed. They not only appeared to ground his theory but also enabled him to deduce reliable information about the size of atoms. With this achievement, Planck contributed to the accumulating evidence supportive of atomism, for example, radioactivity and Brownian motion, and to the vigorous contemporary discussion of its status. Should physicists regard the atomic theory as a mere tool for describing an increasing range of phenomena or a discovery of the real, true, objective state of matter? Theories of radioactive decay and the initial successes of the nuclear model favoured atomism. Paradoxes in the behaviour of X-rays and gas molecules favoured a physics of description, even of contrary descriptions. The confusion of fundamental issues that would confound quantum mechanics were joined long before its invention.
The first two acts of our drama centre on issues brought up in arguments between Einstein and Bohr and their primary followers. Act I covers the generation born before 1900 and runs to the invention of quantum mechanics in 1925/6. The invention was the accomplishment primarily of young men who embarked on their careers after the catastrophic war that made a watershed in physics as in most other sectors of high European culture. Bohr and Einstein belonged to the previous generation. They established the positions from which they began their debate while making the contributions for which they received Nobel prizes in the early 1920s.
Act II opens with the debate prompted by the invention of quantum mechanics, beginning at the fifth Solvay conference held in Brussels in 1927. The Act continues with the consolidation of the ‘Copenhagen spirit’ (the approach of Bohr’s school) and ends with the effort to spread its insights into psychology, biology, and thinking in general. World war then again intervened to change the situation fundamentally. With the mobilization and Americanization of physics, interest in fundamental problems plummeted. Questions that were centrally important to Bohr and Einstein vanished from the agenda.
Discussion revived through opposition to the Copenhagen spirit among mavericks centred at Princeton, where Einstein lived and worked until his death in 1955. By then a few of his leftist followers took on the challenge of reopening the supposedly closed matter of interpretation. Eventually they devised crucial experiments that, as some of them anticipated, would decide against Bohr. This is the matter of Act III, during which Bohr, as an international senior statesman of science, was busy with other things. He died in 1962 before techniques had developed to enable the crucial experiments. These and the surprising developments to which they gave rise occupy Act IV.
The entry into our drama of experimentalists precipitated a shift in emphasis. Although overtly in pursuit of an answer to the eternal question of closure, their efforts exposed a bizarre regular quantum polygon that resided, previously only glimpsed, within the domain of quantum mechanics. It is called entanglement. The practical demonstration of entanglement over large distances sponsored new technological developments that may yet transform our world.
The questions at the heart of our quantum debate remain open. Followers of Bohr continue to hold that quantum theory in its present form is final, and the quantum-mechanical domain closed. Followers of Einstein continue to search for evidence that will undermine the claim to finality or support a Cartesian challenge to the occult action at a distance that entanglement appears to imply. Their opposition, which rests on conflicting ideas about the ultimate purpose of science, has been fruitful and inspirational; full of ‘deep human interest’ even to Bohr’s bulldog Léon Rosenfeld, who had little sympathy for Einstein. It is a mistake, made in many accounts of the debate, academic, popular, past, and recent, to credit one side or the other with following the only true path. The motion was, and continues to be, necessarily zigzag, dialectical, reciprocal.
Galileo informed the world that ‘[Physics] is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth’. And even with them. The physicist’s calculations begin by translating a problem from ordinary language into symbols, continue by manipulating the symbols according to the applicable algebra, and end by translating the results into ordinary language for discussion or experimentation. During the manipulation the symbols may come to relate to ordinary language in new ways unperceived by the algebraist. One way of describing the consequences is confusion. A more fruitful elucidation calls attention to the multivalent content of a symbol, not all of which may be present to the algebraist’s mind.
A simple case is ‘frequency’. Its root meaning of number of recurrences in a given time is familiar, in both concept and quantity, from the 440 air pulses per second by which an orchestra tunes itself. The same concept is applied to visible light, although its frequency is ten billion times that of sound and the ‘ether’ that was supposed to carry its vibrations does not exist. Representing both by the same symbol, nu, has obvious perils as well as the potential fruitfulness of ambiguity. Here are two examples. The discovery and clarification of the ambiguity of nu as the frequency with which an electron traverses its orbit and nu as the frequency of the light so generated, were fundamental to Bohr’s quantized atom. And the unresolved contradiction between nu as light frequency and nu as measure of light energy was fundamental to posing and elucidating the ‘wave-particle duality’.
We give these examples to emphasize the power and advertise the dangers of symbolic representations that, in the end, must be translated into ordinary language. Bohr expressed the situation more perfectly than he realized when, unintentionally substituting Danish metaphor for English idiom, he declared that we are ‘hanging in’ (for ‘dependent on’) language. In this uncomfortable posture quantum physicists generated many apparent paradoxes, which prompted Bohr to invent his far-reaching and often-contested doctrine of complementarity. Its chief opponent was Einstein.
Galileo was only half right in saying that no one can understand the book of nature who cannot read its mathematical symbols. We believe, as did Bohr and Einstein, that the foundational concepts in physics can be understood without mastering its argot. All that is required is the attention necessary to acquire unfamiliar ideas. We have used a few mathematical symbols, however, to avoid ambiguity and circumlocution, and occasionally history and brevity have demanded a short equation, like E = mc-squared. These belong to the rhetoric of our subject just as ‘ex nihilo nihil fit’ (nothing comes from nothing) does to philosophy, cosmology, and the kitchen. The symbol h (Planck’s constant) designates a quantum quantity; phrases like E = hnu and delta-q.delta-p is approximately h express physical constructs, mathematical relations, and slogans that drive our drama.
In the hope that it might be useful to an understanding of our approach to the drama, we end this prologue with a few words about what each of us brings to our collaboration. Jim Baggott’s fascination with quantum mechanics, awakened while an undergraduate in 1975, spilled over to obsession some twelve years later with the discovery that using quantum mechanics is by no means the same as understanding it. He has written several books about it for a general audience, the first published in 1992. An encounter with John led him to suggest a collaboration on Quantum Drama. We decided to try to write a book that captures the deeper riddles of the subject and humanizes the people who created and struggled with them.
John Heilbron was lucky enough to participate as a graduate student in a project to interview physicists active in the early days of quantum physics and to collect and microfilm their correspondence. He lived in Copenhagen in 1962/3 and met Bohr and other physicists associated with the mainstream interpretations of quantum physics, among them Werner Heisenberg, Pascual Jordan, Oskar Klein, and Léon Rosenfeld. After immersion in the science of early modern times he returned to the 20th century to write a brief biography of Bohr and, at Jim's suggestion, to collaborate in exploring the sequel to the story of quantum physics that he began to study in Copenhagen sixty years ago.
Fantastic post! Most notable for me:
"It is a mistake, made in many accounts of the debate, academic, popular, past, and recent, to credit one side or the other with following the only true path. The motion was, and continues to be, necessarily zigzag, dialectical, reciprocal."
As I will be writing over the next couple of weeks, the dialectical tools are implicit for any given perspective whose lens and subsequent feature are distributive, ie. map & location. The call "to be objective" is especially pronounced as the implication is one of "suppressing" whatever urge might arise or showing "restraint." Whatever unit or measure and even the process being described are readily deferred elsewhere with a notable lack of precision. The lens, and the salient features that rise to meet it, imply some insalient tool that is, as far as I can tell, always the opposite whenever lens and feature are both distributive or dialectical. An example of the latter would be an artist who must anticipate some dialectical set of influences within some media, and they must also implement that vision sufficiently, requiring real world skills that are only as sufficient as the body is fluently distributed and coordinated.
Cheers!
Wonderful introduction ... We're still in the early part of the puzzle. As it turns out this is part of a longer story / puzzle involving determinism, computability, understanding, chaos, complexity ... we're just at the 'baby-talk' stage of learning the actual language of reality. Great writing, great discussion, keep pressing forward ... much more enlightenment to be had ...we're only about a century or so into the puzzle ...