by Peter Byrne
One might still like to ask: ‘How does it work? What is the machinery behind the law?’ No one has found any machinery behind the law…. We would like to emphasize a very important difference between classical and quantum mechanics…. We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a given circumstance. Yes! physics has given up.
Richard Feynman, 19631
Fall, 1954
Beginning his second year at Princeton, Everett took only one class, Methods of Mathematical Physics. With Eugene Wigner, he studied the basic tools of quantum mechanics: vector analysis, Fourier series, and matrix algebra.
Wigner and von Neumann had been close friends and colleagues since their student days in Hungary. Both had worked for the Manhattan Project and both were foreign policy hawks. But Wigner was more deeply troubled by the foundational questions in quantum mechanics than was his friend. In fact, he questioned the reasonableness of von Neumann’s “wave collapse” postulate, and he was not happy with the “complementarity” interpretation of quantum mechanics held by Niels Bohr. Ultimately, Wigner forsook a “realist”2 approach to quantum mechanics, opting for hypostasizing human consciousness—a method soundly rejected by Everett.
Attending lectures was more or less optional for physics graduate students, but if the men3 goofed off, or proved to be intellectually incapable, they were not asked back for another term. Adhering to a self-starting regimen of lectures, private study, and discussions with teachers and peers, doctoral candidates were expected to pass a “general” examination at the end of the second year. The reward for passing was a Masters degree and a chance to write a dissertation. Given the high standards for admission (only ten percent of applicants were accepted by the physics department), most doctoral students were capable of academic success. Some, like Everett and Misner, were considered by their professors to be unusually intelligent and bound to make important discoveries.
Misner was born in Michigan in 1932. A life-long Roman Catholic, he came to the physics department by way of the University of Notre Dame. His undergraduate background in math and physics was so impressive that he was not required to take classes (although he did take a course in quantum field theory). He spent his first year working on a thorny problem in nuclear physics, (when he could break away from watching the dramatic Army-McCarthy hearings on television). But he took the time to read von Neumann’s classic textbook on quantum mechanics in the original German, as did Everett. (German had long been the prevailing language of quantum theory, and von Neumann’s textbook was not published in English until 1955.) After passing his general exam in the spring on 1954, Misner spent the summer working at Bell Labs. That fall he briefly “shopped” for a thesis advisor, selecting John Wheeler, and beginning a life-long association with him.
Left to right: Charles Misner, Hale Trotter, Niels Bohr, Hugh Everett III, David Harrison, Princeton, 1954. Alexandria Gazette
In the fall of 1954, Niels Bohr was in residence at the Institute for Advanced Study.4 Inspired by conversations with Misner, Wheeler, Bohr, and Bohr’s assistant, Aage Petersen, Everett left game theory behind for the time being. Signing on with Wheeler as his thesis advisor, Everett started to research his dissertation six months before he got his masters degree in the spring of 1955. Soaking up the formalism and philosophy of physics, and in love with paradox qua paradox, Everett chose to attack one of the deepest puzzles in quantum mechanics, the “measurement problem.” This seemingly intractable paradox was identified during the early, heady days of quantum mechanics in the 1920s. Three decades later it still stymied and stumped and frustrated those who tested their brains against it.5
Introducing the measurement problem (a little bit)
The formalism of quantum mechanics works. But why and how it works is a matter of interpretation.
In 1952, one of the founders of quantum theory, Erwin Schrödinger, (he invented the Schrödinger equation), complained about Bohr’s “anti-realist” approach to the measurement problem:
This interpretation is obsolete. There is nothing to recommend it, and it bars the understanding of what is actually going on. It obstinately refuses to take stock of the principle of superposition.6
Superposition is a property of waves. In quantum physics, particles are also waves—often described as “probability waves.” Probability waves, like water waves, can merge, or superpose. The mathematical description of a probability wave (or quantum “state”) is called a wave function, symbolized by the Greek letter psi, ψ. Schrödinger’s equation tracks the evolution of ψ through time as it combines (superposes) with other wave functions: ψx plus ψy equals ψz. But if we measure (physically interact) with the entity ψz: it seems to evaporate: leaving us staring at a piece of it, either ψx or ψy.
This is an extraordinarily counter-intuitive process; and we shall keep returning to it, searching for understanding. For the moment, think of it like this: The wave function, ψ, of an atomic particle contains all of the information about the different ways in which that particle could possibly behave. For example, the total wave function for the position of an electron lists all of the positions it could possibly assume in its environment. Each possible position on that list is a wave function. The total wave function for the electron’s position superposes (combines) the wave functions for each possible position. Conversely, this means that the total wave function can be decomposed into its constituent pieces, also wave functions. Graphed on a mathematical coordinate system, wave functions can be seen to act like ordinary waves. Where the peaks of wave functions superpose, the probability for certain positions to become definite increases. And where a wave peak meets a wave trough, probabilities cancel.7
The superposition principle asserts that, before measurement, the wave function for an electron orbiting an atomic nucleus describes the electron existing at all of its possible positions in space and time; it can be envisioned, not as having a definite orbit, but as a cloud of indefiniteness surrounding the atomic nucleus. On a graph, the superposition is represented by a single wave that sums up all of its component pieces.
The measurement problem arises when a scientist employs a scientific instrument, such as a Geiger counter, to register the position of a particle. Instead of finding the particle in the multiple positions documented by the superposed wave function, the scientist finds it confined to a single position (as a result of measuring it); he would be astonished to find it in more than one position!
This is the mystery: when we measure the position of an atomic particle we record it as existing in a definite place, not in all of the many places it occupies according to its smoothly evolving wave function. The emergence of a single position from the set of all physically possible positions is inexplicable; it creates a logical discontinuity, a gap, a fissure, an interruption in the flow of the Schrödinger equation: it creates a problem.
In the early years of quantum theory, leading physicists decided that the Schrödinger equation just does not apply to atomic systems at the moment they come into contact with measuring devices (or our brains). But the equation instantly reapplies to the system subsequent to a measurement or observation, they said. Shortly after Bohr arrived in Princeton, Everett had his own brain storm: he decided to treat the Schrödinger equation as uninterrupted—as correctly describing physical reality as continuous, not broken—and then see what happened. And in doing so, he challenged the most powerful person in quantum physics: Bohr.
Enter Bohr
During Bohr’s lifetime, he was lionized as a teacher, a philosopher, and a founder of quantum physics. In the half century since his death, hagiography has given way to more critical analysis. One historian, Mara Beller, portrayed him as caring more about preserving his personal prestige than searching for scientific truth. Other researchers assert that his actual part in developing the Copenhagen interpretation of quantum mechanics—which is usually thought to be Bohr’s in
tellectual baby—has been obscured by “mythology.”8 Nonetheless, it is a fact that Bohr decisively shaped how quantum physics was and is presented—not only to physicists, but to the world at large—as an exact science troubled by paradoxes that can be dismissed for all practical purposes. And in his thesis Everett equated Bohr’s philosophy with the Copenhagen interpretation.9
Young Niels Bohr, date unknown.
Old Bohr, circa 1959.
Niels Henrik David Bohr was born in 1885 in Copenhagen to a closely knit, upper middle-class, scientific family. His father, Christian, was a professor of physiology (and later, the rector) at the University of Copenhagen. His brother, Harald, was a famous soccer player and an accomplished mathematician. After receiving his doctoral degree from the University of Copenhagen, Bohr studied in England with the leading atomic physicists of the day, J. J. Thompson and Ernest Rutherford.
In 1913, he claimed his pedestal in the pantheon of physics by explaining why an electron continuously orbiting an atomic nucleus does not radiate energy and fall into the nucleus in a fraction of a second, as was required by conventional electromagnetic theory and Newton’s laws of motion. Using a physical constant that Max Planck had introduced in 1900, the “quantum of action,” Bohr correctly theorized that electrons orbit in discrete energy levels (“shells”) surrounding the nucleus, while seeming to “jump” from one orbit to another—without passing through the space between—as the atom emits or absorbs radiation.
Although Bohr could not explain why the elementary particle behaved in this odd, discontinuous manner, his insight helped shatter the “classical” paradigm of physics. Impressed by his achievement, the Danish government appointed him the first professor of theoretical physics in the history of Denmark. He established the Institute for Theoretical Physics in 1921 in Copenhagen with funding from the government and the Carlsberg Foundation. He won a Noble Prize for Physics in 1922 for his work modeling the atom; and his institute quickly became an international locus of research in quantum mechanics.
Pipe-chewing, avuncular, and ruthlessly inquisitive, Bohr was involved in most of the important discoveries in nuclear physics made during the 1920s and early 30s. He mentored the young genius, Werner Heisenberg, as he birthed the uncertainty principle. He drove Schrödinger to distraction with penetrating questions about wave mechanics. He argued endlessly with Einstein about the probabilistic nature of quantum mechanics.
And he addressed the measurement paradox by artificially partitioning the universe between the microscopic world ruled by the Schrödinger equation and the macroscopic world governed by the “classical” laws of motion and electromagnetism.
In 1927, Bohr declared that all talk of the quantum world must, on pain of incomprehensibility, be couched in the language of classical physics. He modeled the universe philosophically as a unity and struggle of mutually exclusive phenomena and called it “complementarity.” And his philosophy was integrated into what eventually became known as the Copenhagen interpretation of quantum mechanics.10
Years later, Bohr’s assistant, Petersen wrote:
The word ‘reality’ is also a word, a word which we must learn to use correctly…. In Bohr’s view, the core of the problem of knowledge is in our separation between subject and object…. In physics, if anywhere, we keep ourselves outside the description…. [T]he meaning of a message depends on where the partition between subject and object is placed … The quantum physical regularities responsible for the stability and specific properties of thing can be neither formulated nor explained in the framework of causality. But, as Bohr predicted, these regularities can be encompassed in a frame that is an extension or generalization of the causal description.11
As the Second World War broke out in Europe, Bohr partnered with Wheeler to make an important theoretical discovery about nuclear fission that advanced the creation of the first atom bomb. During the early years of the war, he visited Los Alamos and worked on the bomb trigger. But as D-Day approached, ruminating on the likelihood of post-war nuclear proliferation, Bohr obtained a private meeting with British Prime Minister, Winston Churchill and, a few weeks later, with the American president, Franklin D. Roosevelt. He urged them to create an “open world” by sharing the fruits of atomic research with the Russians. Unimpressed by this appeal to reason, Churchill declared that the Dane’s hair was excessively long and unruly and suggested, unsuccessfully, that he be detained as a communist sympathizer.12
It was not easy to talk with Bohr, especially as he aged. He was hard to hear and legendarily obtuse. His complicated sentences hung fire in mid-air while he paused to light and relight his trademark briar. He paced slowly, inexorably in circles, while mumbling almost incomprehensibly and giving, Wheeler said, “the appearance of a man thinking deeply, very deeply, with his deep thoughts struggling to find expression.”13 And although Bohr was a profound thinker, his pronouncements on the interpretation of quantum mechanics were often more oracular than explanatory.
During the post-war years, Bohr, with the prestige and resources of his institute behind him, was the most prominent figure in physics, next to Einstein. His favor could make a man’s career, and his disfavor could stifle it. As he grew older, he drew his personal circle of physicists ever more protectively about himself. His long-time assistant and collaborator, Leon Rosenfeld, in particular, became almost fanatical in his devotion to shielding Bohr’s complementarity from attack by young Turks like Everett and Bohm.
Bohr was in residence at the Institute for Advanced Study in Princeton for four months. He enjoyed talking with Einstein, Wigner, von Neumann, Wheeler, and Oppenheimer, while meeting a new generation of physicists. Harvey Arnold recalls seeing Bohr, Petersen, and Everett walking the quad at the Graduate College deep in conversation.
On November 16, Bohr lectured at the Graduate College. Everett and Misner were there. Bohr’s biographer, Abraham Pais, a physicist at the Institute for Advanced Study, noted in his diary:
Lecture by Bohr. He thinks that the notion ‘quantum theory of measurement’ is wrongly put.14
Aage Petersen summed up Bohr’s approach to the measurement problem:
There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physicists is to find out how nature is. Physics concerns what we can say about nature.15
Bohr’s point was both rhetorical and pragmatic. He was not denying that atomic particles exist. But he believed that we can only experience this world through the medium of experiment. For instance, when an alpha particle flies off a radioactive metal to interact with a Geiger counter, that tiny event is amplified by the machine into an observable, classical result: a click, a beep, a needle pointing to a number on a dial. The unseen quantum event corresponds to a classical event. As Bohr put it,
Quantum mechanics represents a reformulation of classical mechanics adapted to the existence of the quantum of action.16
In short, Bohr urged physicists to forgo trying to describe or interpret the world in purely quantum mechanical terms. We are doomed to be forever ignorant of the inner workings of the quantum world, he insisted, so we must speak only of what we can know: experimental results. And these results can only be expressed in a language of classical physics, as a generalization of the mechanics of the “quantum of action.” In other words, out of epistemological necessity, classical physics must explain quantum physics, not the reverse. Everett was of the opposite opinion: he theorized that the universe is fundamentally quantum mechanical. Quantum physics explains classical physics, said Everett, pulling Bohr’s theory of knowledge inside out, claiming that the wave function represents physical reality itself, not simply our knowledge of reality.
A slosh or two of sherry
While tape recording their conversation during an alcohol-soaked party at Everett’s home a quarter century later, Misner asked his old pal, “How did you get on to, ah, weird quantum mechanics?”
EVERETT:
Oh, it was becau
se of you and Aage Petersen. One night at the Graduate College after a slosh or two of sherry, as you might recall. You and Aage were starting to say some ridiculous things about the implications of quantum mechanics and I was having a little fun joshing you and telling you some of the outrageous implications of what you said, and, ah, as we had a little more sherry and got a little more potted in the conversation—don’t you remember, Charlie? You were there!’
MISNER:
I don’t remember that evening actually, but I do remember that Aage Petersen was around—that’s entirely possible.
EVERETT:
You had too much sherry…. Well, anyway, the whole business started with those discussions, and my impression is I went to Wheeler then later and said, ‘Hey, how about this, this is the thing to do … there is an obvious inconsistency in the [quantum] theory.’
MISNER:
It is strange that he would be so interested in it—all in all, because it certainly went against the normal tenets of his great master, Bohr.
EVERETT:
Well, he still feels that way a little bit.
MISNER:
He was preaching this idea that you ought to just look at the equations and if there were the fundamentals of physics, why you followed their conclusions and give them a serious hearing. He was doing that on these solutions of Einstein’s equations like wormholes and geons.
