Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

by Ananthaswamy, Anil

  So passionately that even after Schrödinger fell sick and was bedridden with a fever and cold, the host did not relent. Bohr turned up at his bedside to debate quantum physics, even as Bohr’s wife, Margrethe, took care of Schrödinger.

  The debate between Bohr and Schrödinger was a foretaste of future debates that Bohr would have with Einstein about how to think about the smallest constituents of reality (at the time, electrons and photons). It was a clash of two ways of thinking. As Walter Moore writes in his book Schrödinger: Life and Thought , “ Schrödinger was a ‘visualizer’ and Bohr was a ‘nonvisualizer,’ one thought in terms of images and the other in terms of abstractions.”

  Schrödinger left Copenhagen, but Heisenberg was still there to serve as Bohr’s debating partner. Heisenberg was now living in an attic apartment at the institute, and it was there that Bohr would turn up late at night to continue their arguments. And though the two were mostly on the same side of the debate, they still had differences: Bohr wanted to make wave-particle dualism—the idea that nature has two faces and only shows one or the other at any one time—a key component of any interpretation of reality; Heisenberg put his “ trust in the newly developed mathematical formalism,” to see what meanings it suggested, rather than presupposing any particular view of reality.

  They fretted about making sense of experiments, including the double slit. As Heisenberg would say, “ Like a chemist who tries to concentrate his poison more and more from some kind of solution, we tried to concentrate the poison of the paradox, and the final concentration was such experiments like the electron with the two holes . . . They were just a kind of quintessence of what was the trouble.”

  By the end of February 1927, their discussions at an impasse, Bohr went off to ski in Norway. Heisenberg too took time for himself. He wrote of one extraordinary night when something clarified: “ I went for a walk in the Fælledpark, which lies behind the institute, to breathe the fresh air and calm down before going to bed. On this walk under the stars, the obvious idea occurred to me that one should postulate that nature allowed only [those] experimental situations to occur which could be described within the framework of the formalism of quantum mechanics. This would apparently imply, as one could see from the mathematical formalism, that one could not simultaneously know the position and velocity of a particle.”

  Heisenberg had discovered the uncertainty principle. The formalism of quantum mechanics has pairs of observable quantities, such as the position and momentum of a particle, where trying to determine one with increasing precision means that you increase the imprecision of the values you obtain for the other. So, if you know exactly where a particle is, you have very little idea of its momentum, and vice versa. This relation extends to other pairs of quantities, such as energy and time.

  (When I visited the Niels Bohr Institute, I went up to the attic to see Heisenberg’s living quarters. His apartment was being used by builders to store air-conditioning equipment. A cartoon captioned “At home with the Heisenbergs” was stuck on the bathroom door outside the apartment, with Mrs. Heisenberg saying, “I can’t find my car keys,” and Mr. Heisenberg replying, “You probably know too much about their momentum.”)

  Bohr, meanwhile, became ever more convinced that what he called the principle of complementarity was at the heart of quantum mechanics: that wave nature and particle nature are complementary aspects of reality, and that it’s our choice of experiment that reveals one or the other, but never both at the same time. He thought that the uncertainty principle was one outcome of the broader principle of complementarity.

  Elsewhere, Einstein was growing deeply concerned about such interpretations of the quantum formalism, and building himself up toward a profound intellectual debate with Bohr, a debate that would shape the future of quantum mechanics. Einstein had a predilection for conjuring up thought experiments to make a point—and one of these involved the double-slit experiment. He brought it up at the Fifth Solvay Conference.

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  History has often portrayed Einstein and Bohr as giants in battle, slashing at each other with their respective intellectual might. But often what gets lost in the retelling is the enormous respect and affection that the two had for each other. Einstein and Bohr met for the first time in Berlin in April 1920. Impressed by Bohr, Einstein wrote to him in May, from America, beginning his letter with these words: “ Dear Mr. Bohr: The magnificent gift from the neutral world, where milk and honey still flow, gives me a welcome occasion to write to you. Not often in life has a person, by his mere presence, given me such joy as you. I understand why [Paul] Ehrenfest is so fond of you.” Bohr wrote back in June, saying, “ To meet you, and talk with you, was one of the greatest experiences I have ever had.”

  This mutual admiration underpinned their relationship, despite their strong disagreements over quantum mechanics.

  Their friendly salvos were fired in earnest at the Fifth Solvay Conference in Brussels. This was a grand battle of ideas, the likes of which occur infrequently enough in science to be etched in cultural memory as moments that changed our understanding of our place in the universe. Sometimes the individuals debating have been separated by the intervening centuries, as was the case with Copernicus, who in the sixteenth century argued against the Greek astronomer and mathematician Ptolemy’s ancient theory that Earth is at the center of the solar system. Copernicus put the sun at the center. Sometimes, it’s one person’s fight against an emerging consensus, as was the case in the 1950s with English astronomer Fred Hoyle’s increasingly isolated stand for a steady-state universe, when theory and evidence were both pointing to an expanding cosmos that began in a big bang. And at times, the antagonists debated the nature of scientific progress itself, as happened between philosophers Karl Popper and Thomas Kuhn. Popper, impressed by Einstein’s work on relativity, argued that science progresses in increments; scientists come up with hypotheses to explain phenomena, hypotheses that they then try their best to falsify. Kuhn would be influenced by the goings-on at the Fifth Solvay Conference and argued that science mostly moves along in the manner suggested by Popper, with scientists working within an accepted paradigm, until anomalies—things that cannot be explained within the current way of thinking—pile up, bringing science to the brink of crisis, causing an upheaval and a dramatic paradigm shift.

  The debates at the Fifth Solvay Conference set the stage for just such a shift. Bohr, Heisenberg, and Pauli were making a case for what eventually came to be called the Copenhagen interpretation of quantum mechanics. According to them, the only aspects of reality that you could know about were those that were allowed by the formalism. For example, you could ask about the probability of finding an electron somewhere, but you couldn’t ask what path it took to get there, because there is nothing in the math that captures an electron’s path. It’d take another five years for the math to become sophisticated, thanks to John von Neumann, but the new view of reality was taking hold. Taken at its most extreme, the Copenhagen interpretation is anti-realist: it denies any notion of reality that exists independent of observation. More important, the proponents were claiming that the mathematical formalism is complete, and that there is nothing more to say about reality.

  This was, of course, a massive shift in our way of thinking. Until then, our theories said something concrete about a natural world that exists regardless of observation. Einstein, a realist, argued that the mathematical formalism of quantum mechanics was incomplete and did not paint a full picture of reality.

  The Solvay Conference was being held at the Institute of Physiology in the heart of Brussels. “ However, with all the participants staying at the Hotel Metropole, it was in its elegant art deco dining room that the keenest arguments took place . . . The acknowledged master of the thought experiment, Einstein would arrive at breakfast armed with a new proposal that challenged the uncertainty principle and with it the much-lauded consistency of the Copenhagen interpretation. The analysis would begin over coffee and croissants. It con
tinued as Einstein and Bohr headed to the Institute of Physiology, usually with Heisenberg, Pauli and Ehrenfest trailing alongside. As they walked and talked, assumptions were probed and clarified before the start of the morning session . . . During dinner back at the Metropole, Bohr would explain to Einstein why his latest thought experiment had failed to break the limits imposed by the uncertainty principle. Each time Einstein could find no fault with the Copenhagen response, but they knew, said Heisenberg, ‘in his heart he was not convinced.’”

  At the center of one of their mind games was the double-slit experiment. Einstein imagined an electron that first passes through a single slit, and then encounters a double slit, and eventually ends up somewhere at the center of the far screen. In Einstein’s original thought experiment, the single slit could move up and down, while the double slit was fixed, but physicists since then have reimagined the setup with the single slit held in place, and the double slit as the one that can move up or down as it’s buffeted by the particles going through the slits. While conceptually identical to Einstein’s imagined apparatus, the newer version is easier to grasp.

  Consider an electron that goes through the single slit, then through the double slit, and then lands at the center of the far screen. Using Einstein’s analysis, if the electron went through the lower slit, then it’d have had to change directions and move upward to get to the center of the screen. This would impart a downward kick to the slit itself. And if the electron went through the upper slit, it’d impart an upward kick to the slit. So, by measuring the momentum transfer, one should be able to tell which slit the electron went through, said Einstein. His point was that even though one observes the interference pattern, which demonstrates the electron’s wave nature, measuring the slit’s momentum tells us about the electron’s path on its way to the far screen, thus revealing its particle nature. The two aspects of reality are not mutually exclusive, he claimed, and the fact that quantum mechanics did not have the formalism to capture that fact meant that it was somehow incomplete.

  Bohr was stumped for a bit, but soon came back with a retort (in addition to coming up with the drawings that involved bolting the apparatus to a base and other practical things). He pointed out that if the slit can move when the electron passes through, and if we can measure the momentum transfer with precision, then we’ll have imprecise knowledge about its location (thanks to Heisenberg’s uncertainty principle). Now, if you do the calculations of where the electrons land on the far screen, taking into account the uncertainty about the slit’s position, it turns out the interference pattern gets smudged. Trying to find out which slit the electron went through, by allowing the slits to move, destroys its wave nature. We can see the electrons either as particles or as waves, not both at the same time.

  This was, of course, a thought experiment. There was no way to implement such an exquisitely engineered experiment in the 1920s, to get information about the particle’s path without destroying the particle. It’d take almost a century of effort to carry out a variation of this thought experiment. It turns out that Bohr was right in this regard: it’s impossible to dupe nature. (However, physicists and historians reading Bohr’s writings would point out later that Bohr’s arguments were somewhat inscrutable, so one should be circumspect about unqualified claims that “Bohr was right”—nonetheless, as experimental evidence goes, it went against Einstein on this count.) The experiment also showed that complementarity is a seemingly more powerful principle than maybe even Bohr imagined.

  Such victories in hand, Bohr and company started giving concrete shape to the Copenhagen interpretation and its anti-realist view of nature. In the double-slit experiment, the Copenhagen interpretation makes no claim as to the path of the particle through the apparatus and, some would say, even denies that such a path exists.

  Einstein and Bohr continued sparring over what quantum mechanics was telling us about reality. Was quantum physics the whole story? Was the mathematical formalism that described the statistical behavior of the subatomic world a complete description of reality? Or was there a hidden reality that the math wasn’t capturing? Bohr metaphorically shrugged his massive shoulders and insisted there was no hidden reality.

  Bohr, for his part, kept returning to the double-slit experiment to make philosophical points, sometimes infuriating his audience. Hendrik Casimir, a young physicist who had come to work with Bohr, wrote about a conversation with Bohr and Danish philosophers Harald Høffding and Jørgen Jørgensen. They were all at the Carlsberg mansion (the erstwhile residence of the founder of the Carlsberg brewery). Bohr was talking about the double-slit experiment done with electrons. Someone quipped, “ But the electron must be somewhere on its road from source to observation screen.” Bohr pointed out that the answer depends on what one means by the phrase to be . An exasperated Jørgensen retorted: “One can, damn it, not reduce the whole of philosophy to a screen with two holes.”

  But Bohr wasn’t being flippant. What does it mean to be something in the quantum realm? Opinions differ dramatically. And the experiment with two holes, despite Jørgensen’s protestations, remains at the center of these historic, differing scientific and philosophical arguments.

  3

  BETWEEN REALITY AND PERCEPTION

  Doing the Double Slit, One Photon at a Time

  The electron, as it leaves the atom, crystallises out of Schrödinger’s mist like a genie emerging from his bottle.

  —Arthur Eddington

  T he 2014 Nobel Prize winner for chemistry, Stefan Hell, during his Nobel banquet speech, recalled the 1933 Nobel Prize winner Erwin Schrödinger as saying, “ It is fair to state that we are not going to experiment with single particles any more than we will raise dinosaurs in the zoo.”

  Hell, speaking eighty-one years after Schrödinger’s comment, quipped, “ Now, ladies and gentlemen, what do we learn from this? First. Erwin Schrödinger would never have gone on to write Jurassic Park . . . Second. As a Nobel Laureate you should say ‘this or that is never going to happen,’ because you will increase your chances tremendously of being remembered decades later in a Nobel banquet speech.”

  The reference to dinosaurs and Schrödinger’s skepticism of single-particle experiments came up when I met Alain Aspect, a French experimental physicist at the Institut d’Optique in Palaiseau, a suburb of Paris. Aspect, in fact, pioneered some of the first experiments done with single photons, including the first-ever double-slit experiment done by sending single photons through the apparatus. It was a pivotal moment in the more than half-a-century-long story of quantum physics, one that gave credence to all the theorizing that had come before, while laying the foundation for similar, more sophisticated experiments to come.

  When we met more than twenty-five years after he had announced the results of his pioneering experiments, Aspect spoke as an elder statesman of quantum physics; the combination of his French-accented English and luxurious, graying mustache reminded me of the fictional detective Hercule Poirot in Agatha Christie mysteries (with apologies to Aspect; Poirot, of course, is Belgian).

  In the early 1970s, Aspect finished his master’s degree and went to Cameroon, Africa, to teach schoolchildren, as part of his mandatory French military service. While in Cameroon, his mind was on physics. He couldn’t shake the feeling that there was something lacking in what he had learned. All the physics he had been taught—things like optics, electromagnetism, and thermodynamics—dealt with the classical, continuous, and deterministic world of Newton, Maxwell, and Einstein. He knew little about the physics of the microscopic quantum world of particles and atoms. When he heard talk of how an atom jumps from one energy level to another by emitting or absorbing a photon of light, he couldn’t understand how. “I knew I was missing something,” he said.

  So, Aspect bought a newly published book, simply titled Quantum Mechanics (one that would become a highly regarded textbook, and one of the authors of which, Claude Cohen-Tannoudji, would become Aspect’s PhD thesis advisor and would also win the
Nobel Prize in 1997). Aspect read the book from cover to cover, or as he put it, “from page one to, I don’t know, page 1,300.” He was hooked.

  When he returned to France in 1974, Aspect came upon a decade-old paper by John Bell, a Northern Irish physicist working at CERN (European Organization for Nuclear Research), the particle physics lab near Geneva, Switzerland. Bell wasn’t yet famous for his 1964 paper, which contained a theorem that is now regarded as his signature contribution. When Aspect read the paper, which he did in a two-hour sitting, he said to himself, “This is unbelievable . . . it’s fantastic.” He realized that Bell’s paper offered a way of resolving an argument over the nature of reality that had so consumed Einstein and Bohr (others had realized it too, but for young Aspect it was a revelation).

  Bell’s ’64 theorem made it possible to experimentally address the question posed by Einstein: were there local hidden variables to describe properties of quantum systems that weren’t there in the standard formalism of quantum mechanics, variables that in Einstein’s opinion would turn quantum mechanics into a complete description of reality? The word local refers to elements of reality that cannot influence each other any faster than the speed of light: local variables are bits of mathematics in our theories that represent this reality, and hidden local variables refer to variables that are, well, absent from the formalism. Bell was particularly interested in locality. While some physicists had already done experiments based on Bell’s ideas, the results weren’t conclusive. In Aspect’s eyes, these experiments had failed to come close to the ideal experiment demanded by Bell’s theorem. He felt he could do a better job.