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

by Ananthaswamy, Anil

  So a quantum system has two faces. But when does it “decide” to show one face or the other? Is that even a legitimate question? Wheeler took on the question in dramatic fashion. His thought experiment uses the Mach-Zehnder interferometer, in which we observe the photon’s particle nature when we don’t have the second beam splitter in place (D1 and D2 each click half the time) and we observe the photon’s wave nature when the second beam splitter is in place (there’s interference, and D1 clicks all the time, and D2 never does).

  Here’s what Wheeler proposed. What if we delay the choice of whether or not to put in place the second beam splitter until after the photon has gone past the first beam splitter and thus entered the interferometer? How does the photon “know” what to do inside the interferometer? At the moment it encounters the first beam splitter, let’s say there is no second beam splitter to measure the wave nature. From all we know thus far, the photon should go through either one arm or the other, as a particle. After the photon is on its way to either D1 or D2, we insert the second beam splitter and make the two paths indistinguishable. The experimental setup is now looking for the photon’s wave nature. What’s the photon to do? Suddenly decide that it has to go into a superposition of taking both paths and display interference?

  You can also do the opposite. Let the photon enter the interferometer with the second beam splitter in place—so now it is in a superposition of going through both paths, which means eventually it’ll end up at D1, not at D2. But let’s take out the second beam splitter just before the photon encounters it. If we continue thinking in terms of one path taken or both paths taken, the photon has to somehow do extreme calisthenics and appear to take only one of two paths, and thus reveal its particle nature, and end up at either D1 or D2. It’s as if the photon is going back in time and undoing what it had done. As Wheeler wrote: “ One decides whether the photon ‘shall have come by one route or by both routes’ after it has ‘already done its travel.’”

  The italicization of, or the use of scare quotes around, words and phrases like seems , knows , as if is deliberate—they highlight the fact that our classical notions and the language we use to talk about them fail us when dealing with the quantum world, at least when we limit ourselves to the standard formalism and the Copenhagen interpretation.

  When Aspect did the single photon double-slit experiment in 1985, he was aware of Wheeler’s thought experiment, and he was aware that his Mach-Zehnder setup had some of the necessary ingredients for testing Wheeler’s ideas. Still, “at that time I was not dreaming of doing the experiment,” Aspect told me.

  The reason being that the delayed-choice experiment is technically far more challenging. In Aspect’s initial experiment, each arm of the Mach-Zehnder interferometer was about 6 meters long, which is the distance from the first beam splitter to one of the detectors. A photon takes only about 20 nanoseconds to cover that distance. To trick the photon after it had entered the interferometer, Aspect’s team would have had hardly any time to either insert or remove the second beam splitter. It seemed impossible.

  Why not just increase the length of the interferometer? Say to 50 meters? That would give one about 165 nanoseconds to do the dirty deed. It’s not eternity, but not an impossibly small interval of time either.

  “I’m going to teach you something about optics,” said Aspect, and proceeded to explain why going long was not an option in 1985. Their source of single photons then was not point-like. It was as if the photons were coming out not from a pinhole but from an opening with a larger diameter. In optics experiments, you often need lenses to corral photons toward your detectors. And if the source is not point-like, the light can diverge, making it necessary to build bigger and bigger lenses, which get prohibitively expensive and technologically infeasible. “Six meters was already a problem, because my source was not exactly point-like, but I could solve it,” said Aspect. “But 50 meters was out of the question.” That would have required lenses several meters in diameter.

  Aspect had to wait twenty years before the technology caught up to where he could do Wheeler’s delayed-choice experiment just as Wheeler had intended. Other teams, meanwhile, had done versions of the experiment, but Aspect was after its essence and did not want to leave anything to interpretation. “It was clear for me in 2005 that the technology had reached a point where you can [do] an experiment which is very close to the ideal scheme of Wheeler,” he said.

  By 2005, Aspect had a source of single photons that was much more point-like, and he was able to build an interferometer with arm lengths of 48 meters—enough time to insert or remove the second beam splitter after the photon had passed the first beam splitter.

  And what they observed was that there was no fooling the photon. If the second beam splitter was not there, it behaved like a particle, otherwise it acted like a wave. It did not matter when the second beam splitter was inserted.

  Recall that the initial arguments between Bohr and Einstein as to why one cannot observe the wave nature and particle nature simultaneously had to do with Bohr’s assertion that the act of observation somehow disturbed the apparatus, smearing out the interference pattern. Complementarity was the outcome of the uncertainty principle.

  But the delayed-choice experiment demonstrates that complementarity is a deeper principle, deeper than probably Bohr realized. In Aspect’s 2005 experiment (the results were published in February 2007), the photon as it goes past the first beam splitter is still too far away from the location of the second beam splitter to be influenced by the decision being made at the distant location. In the language of special relativity, these two events are space-like separated, so there is no question of any disturbance due to measurement; nothing that is being done near the output stage can influence the photon. And yet, the photon shows only one face or the other.

  “Bohr’s statement that it is the measurement that determines what you observe etc. . . . should not be taken in a too naive [manner]. It is more subtle than that,” said Aspect.

  Just how subtle would become abundantly clear with an even more audacious version of the delayed-choice experiment: the so-called delayed-choice quantum eraser experiment. This is to distinguish it from Wheeler’s original idea, in which the second beam splitter is a classical, macroscopic device. It’s either there or not there. What if the experiment not only delayed the choice of whether to look for the particle nature or the wave nature of photons but allowed for that choice to be erased? What would the photon do?

  To understand the delayed-choice quantum eraser experiment involves going back, yet again, to Einstein’s objections to quantum physics. For all his work on the special and general theories of relativity and the photoelectric effect, Einstein’s most cited paper is one he wrote in 1935, identifying a weird property of quantum systems (which he would later refer to as “spooky action at a distance”). It’s a property that Schrödinger also identified in the same year, and he called it entanglement. If quantum superposition exhibited by single particles was the first mystery thrown up by quantum mechanics, then entanglement, which involves two or more particles, was something even more profound, and for Einstein, fundamentally more disturbing. Aspect calls the developments that followed—including experimental variations of the double slit that outdid even Wheeler’s thought experiments—the second quantum revolution. “[It] has to do with realizing that entanglement is dramatically different,” he said.

  4

  FROM SACRED TEXTS

  Revelations about Spooky Action at a Distance

  Nonlocality forces us to extend the conceptual toolbox we use to talk about nature’s inner workings.

  —Nicolas Gisin

  T im Maudlin can vividly recall the moment the strangeness hit him. It was more than three decades ago. He was in his senior year of college, when he came across a Scientific American article titled “The Quantum Theory and Reality” by theoretical physicist Bernard d’Espagnat. It had a rather long and unwieldly subtitle— “The Doctrine That the Wo
rld Is Made Up of Objects Whose Existence Is Independent of Human Consciousness Turns Out to Be in Conflict with Quantum Mechanics and with Facts Established by Experiment”—to go with some fifteen-odd pages of text, equations, and illustrations. Pretty heavy going. Maudlin read it thoroughly enough to be floored by the implications. “My roommates said later that they knew something was strange, because I just kept . . . holding this magazine and pacing around in circles in the room,” said Maudlin, a philosopher of science at New York University. We were sitting in the sparingly furnished living room of his New York apartment. A framed print of artwork by Croatian artist Danino Bozic graced one wall—as it does the cover of one of Maudlin’s books, The Metaphysics within Physics . Two thin, tall wooden figures—carvings made by the Nyamwezi people of Tanzania—stood in one corner. In that tastefully austere setting, Maudlin cast his mind back to the d’Espagnat article. He said he’d now take issue with some of the things that d’Espagnat wrote, but reading it then as a student, “it was clear enough that you could see something very strange was going on [with quantum mechanics], that it was a sharp enough result that you couldn’t get out of it.”

  The Scientific American article had a detailed exposition of John Bell’s 1964 paper, the very same paper that inspired Alain Aspect to embark on his experiment to settle a debate between Einstein and Bohr. In the article, d’Espagnat argued that Einstein’s ideas (enshrined in his theories of relativity) and quantum mechanics were at odds, and that Aspect’s experiment to test Bell’s theorem, which had yet to be done, would settle the issue. Einstein became aware of this tension between his theories and quantum mechanics well before almost anyone else.

  To make his case at the 1927 Solvay Conference, Einstein took the case of a particle going through a hole in a screen. With characteristic humility, he “ first apologized for not having gone deeply into quantum mechanics.” Then, with characteristic insight, he gave an astute analysis of what was puzzling him. According to the formalism, the particle’s wavefunction goes through the hole, diffracts, and spreads out semi-spherically, and one can calculate the probability of finding the particle at any one location on the surface of this spreading hemisphere. Now, let’s say a detector at some distance from the hole detects the particle. This is the same as saying that the spread-out wavefunction collapses upon measurement. If one interprets the wavefunction as a complete description of the state of the particle and as a description of what’s actually happening (and not merely a statement about our state of knowledge, or lack thereof, of reality), then it seems that the particle, which was itself spread out, gets localized. If so, Einstein made the point that this localization, or the unequivocal appearance of the particle at one location, is happening simultaneously with the indisputable disappearance of the particle from all other locations. It’s a violation of the principle of locality, which says that if something is happening in one region of spacetime, it cannot influence something else happening in another region of spacetime any faster than the speed of light. The collapse of the wavefunction, in this way of thinking about it, is instantaneous and patently nonlocal. Even this early in the history of quantum mechanics, Einstein was aware that this seeming nonlocality, which implied simultaneity of actions, was in conflict with his own theory of special relativity.

  But a more seminal analysis was to come from Einstein and two colleagues. To Einstein’s chagrin, the world learned of this not through the usual channels of scientific discourse but via an almost tabloid-like report in The New York Times .

  EINSTEIN ATTACKS QUANTUM THEORY screamed the headline on May 4, 1935. According to The New York Times , Einstein and his two younger collaborators, Boris Podolsky and Nathan Rosen, had shown that quantum mechanics wasn’t complete and that it needed augmenting.

  Einstein found out that Podolsky had leaked information about their upcoming paper some two weeks in advance of its publication in Physical Review , and Einstein complained to the Times , saying, “ I deprecate advance publication of any announcement in regard to . . . [scientific] matters in the secular press.” (Decades later, physicist David Mermin would quip, “ If The New York Times is the secular press, it follows that the sacred text is the Physical Review .”)

  Nonetheless, the elegant four-page-long paper, published on May 15, 1935, was a slowly unfolding seismic event whose aftershocks continue to shake up quantum physics to this day. Known as the EPR paper in the literature (for Einstein-Podolsky-Rosen), it had its roots in a teatime conversation between Einstein and Rosen about the quantum state of two particles after they have interacted with each other. It turns out that post-interaction, there is no separate wavefunction to describe each particle; rather, they are described with one, joint wavefunction. The particles are said to be entangled. Einstein figured that entangled particles would allow him to strengthen his argument about the incompleteness of quantum theory. Despite his seeming defeat at the hands of Bohr at the Fifth Solvay Conference, giving the round to the Copenhagen interpretation, Einstein was far from done debating Bohr.

  Central to the EPR argument is the assumption that nature is local. It seems a pretty intuitive idea, but it took Einstein’s theory of general relativity to bring locality into sharp focus. Before Einstein, Newton had obfuscated locality by suggesting that gravitational influences were instantaneous. In Newtonian gravity, if the sun were to somehow disappear, the Earth would be immediately influenced by the changes in the gravitational field. Einstein’s general relativity showed that gravity is the outcome of the warping of spacetime by the presence of matter (the way a heavy ball placed on a taut sheet of rubber dents the sheet), and any changes to the curvature of spacetime caused by matter can propagate only at the speed of light. So it will take Earth about eight minutes to notice the absence of the sun’s gravitational pull, were it to disappear. Locality is essential to Einstein’s relativity.

  Besides locality, Einstein had long held dear the idea of “realism” and it showed up in the EPR paper, which begins with these words: “Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves.”

  For Einstein, the real world exists independent of our observations.

  Realism can be sharpened to a statement about our physical theories, to argue that variables in the theories correspond to actual physical reality. Completeness of a theory, in this regard, depends on it having enough relevant variables to capture all of physical reality (for example, variables for a particle’s position and momentum, which would allow us to calculate its trajectory, if a particle has one, that is).

  And indeed, one of the arguments EPR used to make their point that quantum mechanics is incomplete involved a somewhat complicated thought experiment that required measuring the position and momentum of entangled particles. Sixteen years later, in 1951, physicist David Bohm would illustrate the EPR argument using a simpler thought experiment. With hindsight, it’s easier to understand the issue using Bohm’s clearer example.

  Imagine a particle with zero spin that decays into two identical particles that move away from each other. The conservation of angular momentum dictates that the particles must be spinning in opposite directions, so that the total spin still adds up to zero. Assume that the particles, A and B, are moving away from each other along the X-axis (the left-right direction on this page). Quantum mechanics says that the two particles are entangled in their spin.

  Let’s first take particle A. If you were to measure the spin of the particle along the X direction, you can predict only the probability of the outcome. It’ll be either UP or DOWN. The same holds true if you were to measure the spin in the Y direction (the up-down direction on this page) or the Z direction (an axis going in and out of this page), or in any arbitrary direction.

  This is als
o the case if you were to measure only the spin of particle B in any arbitrarily chosen direction. There’s absolutely no way of predicting with certainty the result of the measurement.

  Now comes the part that bothered Einstein. A and B are entangled. So, if you were to measure A’s spin in the X direction, and find it to be UP, the quantum formalism tells you with absolute certainty that B will have a spin of DOWN in the X direction. You don’t have to measure B to know it to be so, but if you do the measurement, it will be so. If A is measured first, then the fate of B’s spin is sealed, and vice versa, as long as you measure the spins of both particles in the same direction, say along the X-axis. It’s as if what we did at the location of particle A instantly influenced particle B—a form of apparent nonlocality.

  The EPR argument explicitly assumed locality, making such influences impossible. With this assumption, EPR could make an argument for the existence of the reality of the spin of particle B: “ If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity ” [italics in original].

  That’s exactly what the measurement of particle A achieves. If the world is local, then what we do at the location of particle A cannot disturb particle B. Yet we can now instantly predict with certainty the value of the spin of particle B, no matter how far away B is from A. So particle B must have had that value before the measurement at A. And if a particle has a property whose value does not depend on a measurement, then it’s possible to have a variable in the theory that captures that property. You can see where this is going. All quantum mechanics has is a wavefunction that tells you the probability of outcomes of measurements; it does not have such hidden variables (say, for the position of a particle; the fact that a variable for the position of a particle would be called hidden was “ a piece of historical silliness,” wrote Bell).