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

by Ananthaswamy, Anil

  Such sensitivity could be undone by one of nature’s most majestic events: Saharan sandstorms. Massive storms of fine dust blowing off the Sahara Desert can engulf the Canary Islands, obscuring even normal visibility, let alone the kind needed to do single-photon experiments in the dead of night.

  But when the air is clear, then, under the cover of darkness, the telescope at Tenerife receives the photon. It’s time now to either retain the which-way information or erase it. The decision to erase or not to erase is based on the output of a quantum random number generator.

  If it outputs a “0,” the environment photon’s polarization is left untouched and the photon preserves the which-way information about its corresponding system photon at La Palma. The photon then passes through a polarizing beam splitter and ends up at D3 if horizontally polarized, and D4 if vertically polarized. Because of entanglement, we know that the corresponding system photon would have been oppositely polarized and thus we know which path it took at La Palma.

  But if the random number generator outputs a “1,” the environment photon’s polarization is scrambled, and the which-way information encoded in the environment photon is erased. It has now a 50 percent chance of going to D3 and a 50 percent chance of going to D4. There’s no way to tell whether the environment photon was horizontally or vertically polarized and so there’s no way to tell which path the corresponding system photon took at La Palma.

  The utterly confounding aspect of this experiment is that the measurements at Tenerife—erasing the which-way information or otherwise—are done some 0.5 milliseconds (an eternity for light) after the system photon has gone through the Mach-Zehnder interferometer and hit either detector D1 or D2 at La Palma. The events at Tenerife and La Palma, according to special relativity, should have no causal influence on each other. Quantum mechanics begs to differ—if one is relying on traditional notions of space and time.

  We are now coming to the heart of this experiment. This intricate version of the double-slit experiment combines all the mysterious aspects of quantum mechanics: randomness, wave-particle duality, and even entanglement.

  For those environment photons that were left untouched, if you look now at the clicks made at D1 or D2 by the corresponding subset of system photons at La Palma, you’ll find that there was no interference; they acted like particles: half of them would have gone to D1 and half to D2 when the two arms of the interferometer were of equal length (the experimenters changed the length of one of the paths in small increments continuously, leading to different photon counts at D1 and D2, but that’s a detail we can put aside).

  But for those environment photons whose which-way information was erased once the environment photons were detected at Tenerife, the corresponding system photons at La Palma showed wavelike behavior: all those photons ended up at D1 and none at D2 when the path lengths were equal.

  This is worth reiterating. The measurement on each system photon at La Palma is done 0.5 milliseconds before anything is done to the partner environment photon at Tenerife. The data on the system photon is already in the bag, so to say. Only later do we find that a subset of these photons ends up acting like particles, going through one or the other arm of the interferometer, and another subset acts like waves, with each photon ending up in a superposition of taking both paths. And because the determination of which subset does what is up to the quantum random number generator at Tenerife, if you did multiple runs of this experiment, each time a different subset of photons would show interference.

  For those disturbed by the implications of the standard way of thinking about quantum mechanics, this experiment raises the stakes. First, complementarity cannot be overcome. Second, entangled or spooky action at a distance, hence nonlocality, seems to be a real phenomenon. And as tests of Bell’s inequality had already showed, if quantum mechanics is complete, this seems to imply superluminal or faster-than-light signaling. Otherwise, what’s being done in Tenerife to the environment photon cannot have an effect on the outcome at La Palma.

  However, there is a deeper principle at stake here. Quantum mechanics is not only asking us to give up notions of locality in 3-D space but our notions of time too. The events at Tenerife, in our usual way of thinking, happen later in time, yet still influence the outcome of measurements at La Palma, even though each measurement at La Palma is done and dusted well before the partner environment photon reaches Tenerife.

  Language fails us at this point. Here and there, past and future don’t quite work.

  I asked Ursin if this made him think about interpretations of quantum mechanics—the various attempts to understand what may be happening at the most basic level of reality that go beyond the Copenhagen interpretation. Ursin, however, is interested in harnessing the weirdness of quantum mechanics for technological uses. Interpretations are for old fogies. “I am the young generation, the next generation of quantum physicists,” he said. “This is only a question which is interesting for gray-haired people, but I don’t have so many gray hairs.”

  This is hardly a modern-day response. Even during the times of Niels Bohr, when Bohr was persistent in his explorations about the nature of reality, the younger physicists around him, with the exception of course of Heisenberg and Pauli, were more nonchalant. The Danish physicist Christian Møller, who was Niels Bohr’s assistant at one time, said: “ Although we listened to hundreds and hundreds of talks about these things, and we were interested in it, I don’t think . . . that any of us were spending so much time with this thing . . . When you are young it is more interesting to attack definite problems. I mean this was so general, nearly philosophical.”

  Hearing Ursin talk also brought to mind something John Wheeler wrote in one of his papers. He quoted Gertrude Stein on modern art (possibly erroneously): “ It looks strange and it looks strange and it looks very strange, and then it suddenly doesn’t look strange at all and you can’t understand what made it look strange in the first place.” For a younger generation raised on the mysteries of quantum mechanics, the strangeness may be passé.

  Xiao-Song Ma, however, who is of the same generation as Ursin, has philosophical concerns. While he doesn’t dismiss the Copenhagen interpretation, he hopes experiments can lead us to better ones. “I hope there will be some more intuitive interpretations of quantum physics [that are] more involved than Copenhagen,” he told me. He’s back in China creating ever more sophisticated experiments to further expose the apparent strangeness of the quantum world.

  For him and others of his ilk, Wheeler’s own words are a salve: “ The final story of the relation between the quantum and the universe is unfinished business. We can well believe that we will first understand how simple the universe is when we will recognize how strange it is.”

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  One of the key tenets of the Copenhagen interpretation is the idea of the collapse of the wavefunction, which ostensibly happens when we perform a measurement using classical instruments. These measurements are considered irreversible and they imply a boundary between the quantum and the classical. The quantum eraser experiment pushes us to reexamine our notions of what constitutes a measurement (and hence collapse) and the existence of a quantum-classical boundary.

  Take the environment photon in the Canary Islands experiment. It contains information about which path the system photon took through the interferometer. Measuring the environment photon in Tenerife involved a silicon avalanche photodiode, which detects a photon by turning it into an electrical signal involving billions of electrons. The wavefunction of the system-environment photon pair is said to have collapsed at that point.

  But given that there has never been an experiment that has found any physical evidence of this process of collapse, it’s unclear what collapse actually means. Experimentally, what one is doing is making measurements and predicting the likely outcomes, and if those statistics are borne out over a number of identical experiments, quantum mechanics claims collapse happened in each run of the experiment. But did it?


  Quantum mechanics doesn’t claim collapse when the environment photon is in flight. But theoretically, one could argue for collapse, because as long as the environment photon contains which-way information that can be extracted, the system photon is going to behave like a particle. The only difference here is that the collapse can be reversed, because the environment photon is itself quantum mechanical. One can erase the which-way information, thus undoing what could have been thought of as a collapse of the wavefunction.

  It’s the interaction of the environment photon with the photodiode that creates a situation where the information is now entangled with billions of electrons. It’s impossible to reverse the quantum states of all those electrons. This does have the whiff of an actual collapse.

  Consider, however, a scenario in which the environment photon interacts with a single atom and deposits its information in the energy state of the atom. Such an atom, if held in isolation, is a quantum mechanical object, and its state can be reversed in principle and the information erased, and any earlier collapse undone. Why can’t we treat the interaction with the environment photon and the atom as the boundary at which the wavefunction collapses? Well, because this particular measurement, using an atom, is reversible.

  “If I replace the macroscopic detector with a microscopic [detector] that physically I do know how to reverse the evolution of, then you can show, ‘Oh, look, collapse never happened,’” said Aephraim Steinberg when I met him at the University of Toronto. Steinberg is a highly regarded experimentalist who is equally at ease with the theoretical and philosophical aspects of quantum mechanics. “That’s the motivation of the quantum eraser.” If the information in the environment photon had actually caused a collapse of the system photon’s wavefunction, then nothing could bring back the interference. But the quantum eraser allows you to do so.

  The only way to test whether an actual collapse happens, thus making it impossible to reverse the state of the system, is to do an experiment where quantum mechanics claims there is a collapse—such as when a photon hits a photodiode and causes an avalanche of electrons—and then reverse the process, and somehow erase the which-way information encoded in all those electrons, and then check to see if the interference fringes come back.

  If the interference doesn’t come back, then one could rightfully say that the wavefunction did collapse. But such an experiment has never been done, and is likely never going to be done, because it involves the near-impossible task of reversing the evolution of macroscopic systems and then looking for interference. It’d be like trying to unscramble an egg.

  So, either one has to say that collapse sometimes happens, but our technologies are unable to test if the collapse permanently destroys interference, or one has to say that the wavefunction continues to evolve according to the Schrödinger equation (the wavefunction now involves not just the system-environment photon pair but the states of the billions of electrons they engendered as well)—and that there is no real collapse.

  These are the key stumbling blocks of the Copenhagen interpretation and indeed of the standard formulation of quantum mechanics. What constitutes a measurement? Where is the boundary between the classical and the quantum? What does it mean to say that the wavefunction collapses? There’s an even more basic question staring at us from within the formalism: Is the wavefunction real? Does it have—as philosophers like to say—“ontological” reality?

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  Lev Vaidman can still recall his 1991 meeting with Avshalom Elitzur. Vaidman was working in what was for him a five-year “dead-end” program at Tel Aviv University, which involved doing research and teaching high school students. Elitzur, like Vaidman, was in his thirties. But Elitzur never finished high school and instead started teaching himself quantum physics, among other subjects (in his résumé today, there are only two entries under the heading “Education,” one of which is “Autodidact”). It was while he was still a student studying philosophy of science with no high school diploma or undergraduate or graduate degree to his name that Elitzur came to Vaidman and posed a serious question: can quantum mechanics be used to find objects without interacting with them?

  As Elitzur and Vaidman figured out, the answer is yes, and the principles behind it were first identified in 1960, by German physicist Mauritius Renninger.

  Consider a source of single photons aimed at a beam splitter. The photon will go toward either detector D1 or D2. But unlike the setup we saw earlier when building up to a Mach-Zehnder interferometer, the arm lengths in this setup are unequal, with D2 being much, much farther away than D1, so that it takes, say, 1 second to reach D1 but 5 seconds to reach D2. Quantum mechanics says that, until there’s a measurement at either D1 or D2, the wavefunction of the photon will be in a superposition of having taken both paths. If one second later the photon is detected at D1, the wavefunction collapses; the photon is now at D1 and not at D2. Now consider the case when the photon is detected at D2. The detector will click after 5 seconds. But here’s the intriguing aspect of this experiment: after 1 second, if D1 hasn’t clicked, we know that the photon has gone the other way and is headed to D2. The negative result (the nondetection at D1 after 1 second) is already giving us information that the photon will reach D2: the wavefunction has potentially already collapsed, even though the actual measurement at D2 is yet to occur. It’s the simplest example of an interaction-free measurement.

  Elitzur and Vaidman applied this principle to solve what’s now called the Elitzur-Vaidman bomb problem, which we encountered in the prologue. It’s time to revisit it. There’s a factory that’s making bombs with triggers so sensitive that even a single photon hitting the trigger can cause the bomb to explode. But the factory produces some duds with no triggers. The task at hand is to separate the duds from the good bombs. You are allowed to blow up some bombs in the process. Of course, looking at the bomb to see if it has a trigger is out of the question, because looking involves shining light, and that would result in a detonation. Turns out the double slit or its special case, the Mach-Zehnder interferometer, is tailor-made for the task.

  Imagine the bomb (dud or live) alongside one of the arms of the interferometer. The live bomb has a trigger, and it’s the trigger that lies in a photon’s path and obstructs the path. A dud has no trigger, and hence does not impede the path. For argument’s sake, let’s also assume that one can physically pick up and move these bombs around without exploding them: it’s just photons that can blow them up (maybe they are being handled by robots in a dark room).

  The duds are easy to find. The interferometer functions as if there’s no obstruction in any of the paths, so the photons will be in superposition of taking both paths and there will be interference. If you send a million photons, one by one, into the interferometer (with today’s technologies, that can be done in no time at all), all of them will end up at detector D1 and none will go to detector D2.

  Now, if there’s a live bomb in one of the paths, things change. The bomb acts like a which-way detector or a sensor for telling which path the photon takes through the interferometer. So the photons are going to act like particles: each photon is going to go through either path a or path b (which has the bomb). There are three possible outcomes:

  One is that the photon takes path b, encounters the trigger, and detonates the bomb. That’s that, then—the bomb is lost, and so is the interferometer; let’s assume that we can build one more in a jiffy and start all over again.

  Now say the photon takes path a and encounters the second beam splitter. Because the photon is now acting as a particle, it has a 50-50 chance of exiting through either arm of the second beam splitter. So half the time the photon will go to D1. This is the second outcome. Unfortunately, D1 also clicks in the case of a dud bomb, so the result is inconclusive. We repeat with more photons for a different result.

  The third outcome is the key. The photon takes path a, goes through the second beam splitter, and ends up at D2. This is a clear sign that there’s a live bomb obstructing o
ne of the interferometer paths. We know that if both paths are unobstructed, we get interference—which means all photons go to D1 and never to D2. But if D2 clicks, as in this third scenario, that’s because there is no interference. The photon is taking one path or the other, because something is acting like a which-way measurement—in this case the live bomb. We have essentially detected the presence of the live bomb without blowing it up.

  The probabilities of the outcomes with a live bomb in place are easy to compute. Half the time, a live bomb will cause the interferometer to blow up. One-quarter of the time, the photon will end up at D1—but the information is useless. One-quarter of the time, the photon ends up at D2: we know we have a live bomb in path b. Quantum mechanics has allowed us to do something that is impossible to do with classical physics: we have distinguished a live bomb from a dud without looking at it.

  Today the idea of interaction-free measurements has become relatively commonplace. In 1991, its importance was far from obvious. Elitzur and Vaidman began circulating preprints of their paper on the topic (with a section on “How to test a bomb without exploding it”), and also sent it to Physical Review Letters . They got back a referee report saying that while the paper was interesting, it wasn’t the kind of work that PRL usually published. Physics Letters A also rejected it (the then editor of the journal told Vaidman later that the unnamed, nay-saying referee “was a very big shot”).