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

by Ananthaswamy, Anil

  The paper did see the light of day in 1993 in another somewhat less prestigious journal, but the idea gained prominence when Roger Penrose wrote about it in his 1994 book, Shadows of the Mind . Given that Elitzur and Vaidman worked in Israel, Penrose rather cheekily suggested that the experiment could be coopted for building what he called the “Shabbos switch,” to help those of the Jewish faith observe Shabbat, which starts just before sunset on Friday and ends after sunset on Saturday. During this period, strict adherents are not supposed to light a fire or even turn on appliances. Penrose’s Shabbos switch could help someone turn on appliances without actually doing it. Imagine replacing the bomb in the Elitzur-Vaidman experiment with your finger. Half the time, a photon entering the interferometer will hit your finger, and nothing happens. But one-quarter of the time, a photon will go through the other path, thus not interact with your finger, and reach detector D2, which could then flip a switch and turn on an appliance. “ Surely . . . it can be no sin to fail to receive the photon that activates the switch!” wrote Penrose.

  Jokes aside, interaction-free experiments highlight the disturbing conceptual questions thrown up by notions of collapse. When there’s a live bomb in one arm of the interferometer, standard quantum mechanics says that the wavefunction of the photon collapses—making the photon act like a particle and go through one arm or the other. Half the time, the photon meets the bomb and blows the whole thing up. The other half of the time, it takes the bomb-free path, which allows us to infer the presence of a bomb in the other arm. But nothing interacted with the bomb. What does collapse mean in this context?

  The collapse of a wavefunction has built into it the two elements that bothered Einstein: randomness and action at a distance, with the latter concerning him much, much more than the lack of determinism. In the standard formalism, when a wavefunction collapses, we can only assign probabilities to the outcomes of the collapse. The outcome is inherently random. Also, when the wavefunction involves two or more particles that have interacted at some point, meaning they are entangled, then the collapse of the wavefunction due to a measurement on one particle affects the entangled partners instantaneously—making the influence nonlocal. “Collapse has nonlocality and randomness,” Vaidman told me. “This is the only phenomenon in quantum mechanics which has these two properties.” Just like Einstein, Vaidman is bothered by such a theory. He’d rather see an alternative take shape. “I think a theory without action-at-a-distance and without randomness is a much better theory.”

  For Vaidman, interaction-free measurements are the clearest indication that any theory that invokes a measurement-induced collapse of the wavefunction cannot be the correct theory. He’s not the only one to think so. Coming up with alternative interpretations or theories to explain the experimental observations has consumed the minds of a small subset of quantum theorists, a trend that began with Einstein and his insistence that there must be a theory that is both local and realistic. While Einstein’s particular desire for a local realistic theory or local hidden variable theory has been refuted by the experiments done by Clauser, Aspect, Zeilinger, and others, there are alternatives very much in the running and, some would say, gaining ground, because the simple Mach-Zehnder interferometer and, by extension, the double-slit experiment continue to produce glaring paradoxes.

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  Lucien Hardy, whom we met in the prologue, was a PhD student in the early 1990s when he saw a preprint of the Elitzur-Vaidman bomb paper. This was before the days of the arXiv Internet server (where authors these days upload their preprints for everyone to read)—you got to read a preprint if it was sent to you. “Fortunately, they had sent a preprint to my supervisor, Euan Squires, and Euan showed me this preprint, and we both got very excited,” Hardy told me.

  In the Elitzur-Vaidman thought experiment, the bomb is itself a classical device. What if, thought Hardy, the bomb is quantum mechanical? What would constitute a quantum mechanical explosion? Once the thought entered his mind, it didn’t take him long to devise an experiment with two Mach-Zehnder interferometers, in which an explosion happens when a negatively charged electron meets its positively charged anti-particle, a positron.

  The setup is essentially two interferometers placed side by side (see next page). The first one is for electrons: a source shoots electrons one at a time into the interferometer, which have the choice of taking path a- or b- (“-” here denotes the electron’s negative charge). The second one is for positrons, which can go along a+ or b+. The interferometers are arranged such that path b- of the electron and path b+ of the positron cross just before they hit their respective fully reflecting mirrors. The whole setup, in principle, is built to exacting standards, so that if an electron and a positron leave their respective sources at exactly the same time, and if the electron happens to take path b- and the positron path b+, then the two particles will encounter each other at the point where their paths intersect. This is a recipe for an explosion: a particle and its anti-particle when brought together will annihilate into pure energy.

  Let’s start by analyzing the electron interferometer, while ignoring its positron counterpart. We know that electrons are going to act like waves, so all of them will end up in detector C- (“C” for constructive, “-” for negative charge), while none will reach D-. Similarly, if you consider only the positron interferometer, independent of the electrons, all the positrons will reach C+, and none will reach D+.

  But put them side by side as shown, and suddenly, the wave nature of the electrons and positrons sometimes disappears. That’s because we now have a which-way detector built into the configuration of the two interferometers: it’s the equivalent of having a live bomb in one arm of each interferometer.

  First, let’s tackle cases when the electrons and positrons behave like waves. For an electron, this happens when the positron goes through path a+. In this situation, there’s no impediment to the electron’s progress through its interferometer, so it’ll be in a superposition of taking paths a- and b-, and consequently ends up at detector C-. Similarly, when an electron takes path a-, the corresponding positrons will end up at C+.

  But there are times when the electrons and positrons will act like particles. Take the case of the positron going through path b+. For the electron interferometer, the positron’s presence in path b+ is the same as having a detector in path b-, so the electron is going to act like a particle and take path a- or path b- with equal probability. If it takes b-, then the electron encounters the positron and annihilates. But if it takes a-, then at the final beam splitter, it’s going to go to either C- or D-. When it was acting like a wave, the electron would never go to D-. So if an electron makes it to D-, it’s a signal that there was a positron in path b+. An electron is able to “sense” the presence of a positron without actually encountering it—an interaction-free measurement.

  Since the two interferometers are symmetric, you get the same result if you analyze the positron side of things. If an electron is in path b-, then a positron can end up at either C+ or D+; if a positron makes it to D+, it signifies there was an electron in path b-.

  Hardy was not done, however. The mathematical formalism, he showed, predicts that one-sixteenth of the time, on average, D+ and D- will click simultaneously. So if you did the experiment a million times, this will happen about 62,500 times. And this presents a paradox.

  Here’s why. From the point of view of an electron, if D- clicks, it means that a positron was in path b+. From the positron’s perspective, if D+ clicks, an electron was in path b-. So, when D+ and D- go off together, it means that the electron was in b- and the positron in b+, at least according to classical logic. Which, recall, is the original recipe for an annihilation. But in these one-sixteenths of the cases, there is no annihilation: the electron makes it to D- and the positron to D+, without an attendant explosion.

  If all this feels a bit like gedanken mumbo jumbo, and you cry out, “Surely, this can’t happen in a real lab experiment,” you would be wrong.
A nearly exact replica of this experiment, using photons and their polarizations, was done by Dirk Bouwmeester at the University of California at Santa Barbara and his colleagues. They used photons because technology doesn’t exist to do the experiment with electrons and positrons.

  Hardy’s paradox is real. But the paradox arises because we are talking and thinking classically of space and time, of particles taking this or that path, and reaching this or that detector. Nature has its own inimitable way of doing things.

  D+ and D- go off simultaneously sometimes because, according to the formalism of quantum mechanics, the particles are somewhat entangled just before they hit their respective final beam splitters. What’s even more astonishing is that the entanglement is between an electron and a positron that came from different sources. In the previous experiments, when two photons were entangled, they had been emitted by the same atom, or had in some way interacted and gotten entangled. Not so in this case.

  So if we hold on to local realism—the bedrock of classical physics—and give a local description in terms of particles taking actual paths, then we end up with Hardy’s paradox. But let go of local realism and we are faced with an unavoidable conclusion: “Quantum theory is nonlocal,” said Hardy. His paper, as it happened, was published in 1992 in physics’ premier journal, Physical Review Letters (which had rejected Elitzur and Vaidman in 1991); the irony is that Hardy’s work was inspired by the Elitzur and Vaidman paper that was yet to see the light of day in a peer-reviewed journal. In his paper, Hardy acknowledged the Israeli duo’s paper as a “Tel Aviv Report, 1991.” In 1994, physicist David Mermin wrote that Hardy’s thought experiment to demonstrate nonlocality is “ simpler and more compelling” than tests of Bell’s theorem: “[It] stands in its pristine simplicity as one of the strangest and most beautiful gems yet to be found in the extraordinary soil of quantum mechanics.”

  The experiments in this chapter illustrate the counterintuitive nature of the quantum world, even more so than the wave-particle duality we encountered earlier. But what will become clear in the forthcoming chapters is that phrases and words like wave-particle duality , nonlocality , spooky action at a distance , superposition of being here and there , the randomness of nature , nondeterminism —these are ways of thinking about what’s happening in the quantum realm when the mathematical formalism is interpreted according to the Copenhagen interpretation. Other interpretations, sometimes with different formalisms, sometimes just reinterpretations of the same formalism, give us a very different view of the quantum underworld.

  At the heart of the formalisms is the wavefunction. What do we make of it? Does it merely represent our knowledge about the quantum world, making it epistemic? Or is it something real (as potentially evidenced by interaction-free measurements, which suggest that it’s the wavefunction that’s “sensing” the bomb, for example), making the wavefunction a key ingredient of reality and part of the ontology of the world? And regardless of whether it’s ontological or epistemic, what does one make of the wavefunction’s collapse?

  As successful as quantum mechanics is as a theory—and it’s by far the most successful physical theory we have—such questions continue to haunt those who ponder the very essence of reality. For them, some of whom are gray-haired, it’s not enough to harness quantum mechanics to build better technology, to “shut up and calculate,” as the saying goes. Among the earliest thinkers looking for a deeper description of reality, of course, were Einstein and de Broglie. After them, the first physicist to seriously tackle the conceptual difficulties of the Copenhagen interpretation by formulating a hidden variable theory was an American physicist who briefly worked alongside Einstein at Princeton before he was hounded out of an America steeped in McCarthy-era paranoia.

  6

  BOHMIAN RHAPSODY

  Obvious Ontology Evolving the Obvious Way

  There’s an entirely different way of understanding all this stuff (a way of being absolutely deviant about it, a way of being polymorphously heretical against the standard way of thinking, a way of tearing quantum mechanics all the way down and replacing it with something else).

  —David Albert

  I t’s no small irony that one of the strongest moves against the Copenhagen interpretation was made by a student of Robert Oppenheimer. Best known to the world as the scientific director of the Manhattan Project, the US effort to build the atomic bomb, Oppenheimer was a strong proponent of Niels Bohr’s view of the quantum world. He founded the first school of theoretical physics in the United States and taught quantum mechanics at the University of California, Berkeley, where “ Bohr was God and Oppie was his Prophet.” A young David Bohm came to do his PhD with Oppenheimer and was probably deeply influenced by Oppenheimer’s evangelism of Bohr’s ideas. But there was already a hint of a rebel in Bohm’s behavior.

  World War II was devastating countries, and America was building the bomb. Bohm became a member of the Communist Party and got involved with union activities—which meant that he could not get the security clearance necessary to defend his thesis, which was on a topic considered sensitive enough to be classified. Eventually, Bohm got his PhD, but only after Oppenheimer reassured UC Berkeley that his student’s thesis deserved a degree without the customary defense.

  Soon after he got his PhD, Princeton University gave Bohm a job (after all, he was one of the brightest of the crop of young American theorists, and “ probably Oppenheimer’s best student at Berkeley” ). Bohm began teaching quantum physics. But soon his past caught up with him. In 1949, the House Un-American Activities Committee subpoenaed him to appear before Congress and talk about his and his colleagues’ communist connections. Bohm refused, and pleaded the Fifth. This was contempt of Congress: Bohm was indicted, arrested, but then released on bail. A court subsequently acquitted him, but the damage was done. Princeton suspended him and barred his access to university facilities, and when his contract came up for renewal in 1951, they demurred.

  But Bohm hadn’t been sitting on his hands. In 1951, he published one of the most lucid textbooks on quantum mechanics, Quantum Theory , in which he elegantly explained the Copenhagen viewpoint (the book was a result of his pedagogical efforts at Princeton). It was also the book in which Bohm reformulated the Einstein-Podolsky-Rosen (EPR) thought experiment, crystallizing its essence better than Einstein himself. After the book came out, Bohm and Einstein met and discussed quantum mechanics, a discussion that played a key role in Bohm’s evolving views about the nature of reality.

  But before he could do that, his career took a turn for the worse. When his contract at Princeton wasn’t renewed, Bohm knew his days as an academic in the United States were numbered. He moved to Brazil in October 1951, where a coterie of former Princeton graduates got him an academic appointment at the University of São Paolo, with recommendations from no less than Einstein and Oppenheimer. Bohm was looking forward to collaborating with physicists in Europe, but those hopes were dashed when the US State Department confiscated his passport. Bohm was now officially in exile in Brazil and he would stay there until 1955, when he would leave for Israel.

  In the meantime, Bohm published a paper that challenged the anti-realist stance of the Copenhagen crowd. It seemed to come out of the blue, but in hindsight, his 1951 textbook contained hints of his radical ruminations. In the book, he openly discussed the idea of hidden variables. Using the laws of thermodynamics to make his point, he argued that the reason why we have to deal with probabilities of outcomes in thermodynamics is because we don’t have complete knowledge of the properties of, say, the underlying molecules of some gas. Variables that capture these properties would constitute hidden variables. Could the probabilities that arise in quantum theory—for example the probability of finding an electron here or there—be similarly the outcome of not knowing enough about variables that capture the properties of some hidden layer of reality?

  Even though he raised these issues in the book, Bohm wasn’t yet convinced that the Copenhagen interpretation ne
eded rethinking. “ Until we find some real evidence for a breakdown [of quantum theory] . . . it seems, therefore, almost certainly of no use to search for hidden variables. Instead, the laws of probability should be regarded as fundamentally rooted in the very structure of matter,” he wrote. So Bohm, while pondering heresies, was still espousing Bohr’s views in his book (the way Zeilinger still does). In fact, Bohm’s book was not “ only orthodox in the Copenhagen sense but one of the clearest and fullest, most penetrating and critical presentations of the Copenhagen view ever published.” He even went so far as to say that the “ general conceptual framework of the quantum theory cannot be made consistent with the assumption of hidden variables.” He used the EPR result to make his case. As Einstein, Podolsky, and Rosen had pointed out, their thought experiment suggested that under assumptions of locality, both the momentum and position of two entangled particles would have clearly defined values—but this would contradict the uncertainty principle, which Bohm called “ one of the most fundamental deductions of the quantum theory.”

  Therefore, Bohm concluded, “ no theory of . . . hidden variables can lead to all of the results of the quantum theory.”

  But all that changed a year later. In 1952, Bohm published his seminal paper in Physical Review , titled “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables.” (The paper acknowledges only one person: “The author wishes to thank Dr. Einstein for several interesting and stimulating discussions.”) It was the first and clearest example of a theory that Bohm himself had said could not be conceived. It also implicitly showed that John von Neumann had been wrong: it was possible to come up with a theory with hidden variables that could explain experimental observations in quantum physics and recover realism and determinism.

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  It’s in the nature of the debate about quantum theory that the proponents of the Copenhagen view are not particularly vocal. They don’t have to be. They have history on their side. Niels Bohr, Werner Heisenberg, Wolfgang Pauli, and many other giants of theoretical physics have already argued the case for the Copenhagen interpretation. But for some theorists thinking about the foundations of quantum mechanics, it’s far from a done deal. They have to, however, raise their voices to make themselves heard, and they are usually far more passionate than the adherents to the orthodoxy. Sheldon Goldstein is no exception.