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

by Ananthaswamy, Anil

  First, his team had to ensure that there was only one photon passing through their experiment. They began by using carefully calibrated lasers to excite atoms of calcium to a higher energy level. Such an excited atom falls back down to its previous state by emitting two photons, the first one a green photon at a wavelength of 551.3 nanometers (one nanometer equals 10-9 meters), followed almost immediately by a blue photon at 422.7 nanometers. So there’s a green-blue pair, followed by nothing, then another green-blue pair, then nothing, and so on. The pairs are well separated in time. “Good, I’m going to use this separation in time,” Aspect recalled thinking.

  The green photon heralds the arrival of the blue photon. So the team used the green photon to get their detectors ready for the arrival of the blue photon, which would come within nanoseconds. The crucial thing here is that there will be one and only one blue photon in the apparatus at that point in time. “The probability of having a second blue photon during that time was peanuts,” said Aspect. The initial test was to send the blue photon through the first beam splitter, without the second beam splitter in place. So the photon goes to either D1 or D2. Quantum theory says that only one of D1 or D2 should click for a given photon. This part of the experiment was successful. The blue photon always arrives at one or the other detector—and it’s clear which path it took. The two detectors never click together. The photon always travels as an undivided whole; it behaves like a particle.

  It was time to test the photon’s wave nature. The team added the second beam splitter. Now the two paths become indistinguishable. And so, just as Thomas Young observed interference with his split sunbeam, Aspect and Grangier saw it too.

  But what’s the meaning of interference in a Mach-Zehnder setup for a single photon? For a beam of light, we know that constructive interference results in a bright fringe, and destructive interference results in a dark fringe (no light). It turns out that in the interferometer, when the two paths are of equal length and you send in photons one by one, they all go to D1, and none go to D2. So D1 represents constructive interference and D2 represents destructive interference. Our earlier naive analysis of the 10,000 photons—that half should reach D1 and the other half should reach D2—is wrong. All 10,000 photons reach D1 and none arrive at D2.

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  The only way to explain the result is to think of light as a wave. When the wave encounters a beam splitter, the wave splits; half goes into one arm of the interferometer, and half into the other arm. Zooming into the structure of the beam splitter (which has a finite thickness), one can see that when a wave is reflected, it travels differently through the glass compared to a wave that’s transmitted.

  When the wavelength of the light and thickness of the beam splitter are chosen correctly, this can cause the reflected wave to lag behind the transmitted wave by a quarter of a wavelength.

  Add in one more reflection at the second beam splitter, and the wave that’s reflected twice, rr, now lags behind the wave that’s transmitted twice, tt, by half a wavelength. Both rr and tt reach D2. So the crest of one wave arrives at D2 at the same time as the trough of the other. That’s destructive interference. You get darkness at D2.

  The same analysis shows that the rt and tr paths arrive at D1 with their waves in sync, the crests of both waves reaching at the same time. The waves are said to be in phase. That’s constructive interference. All the light reaches D1.

  That’s a perfectly fine explanation for light composed of lots of photons and acting like an electromagnetic wave: it’s easy to conceptualize half the wave going one way and the other half the other way and then recombining to produce the interference effects. But exactly the same thing happens when you send in single photons. We seem to be getting constructive interference at D1 (all 10,000 photons, hence all the light, reaching D1), and destructive interference at D2 (no photons, hence no light, getting to D2).

  This is all very strange. For interference to happen, a wave has to split into two and then recombine. Can that happen to a single photon? When we add the second beam splitter, each photon seems to be splitting, going through both arms of the interferometer and recombining. But—and it’s worth pondering this to the point of pain—we know that a photon cannot split into two, for it’s an indivisible unit of light. What then is going through both arms of the interferometer (or through both slits of a double-slit setup)? Digging further reveals exactly why the quantum world is so confounding.

  Let’s go back to the full Mach-Zehnder setup and make one small change: block one of the arms to prevent any photons from going through. Let’s start with blocking arm R. What can we expect?

  Two things happen. First, the number of photons that make it to the second beam splitter is halved. By blocking one arm, we are preventing half the photons from getting through to the detectors.

  But something else happens that’s far more puzzling. Without the block in place, we know that all photons leaving the second beam splitter go to D1. However, with the block in place, while the number of photons reaching the second beam splitter is reduced to half, half of the ones that do get past the second beam splitter go to D1 and the other half to D2. Repeat the experiment by blocking arm T, and you will get the same results. The block, whether it’s in arm R or T, is like a detector: we know with certainty that the photons that reach the second beam splitter are traveling through the unblocked arm of the interferometer. There is no indistinguishability anymore, the photons act like particles, and there is no interference, leading to the 50-50 split at D1 and D2.

  With the second beam splitter in place and nothing blocking the photon’s path, each photon is doing something that is impossible to intuitively understand. It’s in a state of quantum superposition . As philosopher David Albert of Columbia University writes in his book Quantum Mechanics and Experience , the term superposition is “ just a name for something we don’t understand.” (And the above analysis is inspired by a similar analysis of a slightly different system in Albert’s book.)

  The photon is in a superposition of two states, one state in which it goes through one path, and another state in which it goes through another path. But this is not the same as saying it went through both paths, or that it went through only one or the other path, or that it went through neither path.

  “The double-slit experiment is usually used to establish that there can be situations in which it makes no sense to ask, say, which slit the particle went through,” Albert told me when we met at his home in New York City. “There fails to be a fact of the matter about which slit the particle went through. Asking which slit the particle went through is [like] asking about the marital status of the number five or the weight in grams of Catholicism. This is something philosophers call a category mistake.”

  Nonetheless, there’s interference. What is it that interferes? Interference has to do with quantum superposition, and the story of how quantum objects end up in, and fall out of, superposition is “ the most unsettling story perhaps, to have emerged from any of the physical sciences since the seventeenth century,” writes Albert.

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  Erwin Schrödinger was particularly unsettled by quantum superposition, and so was Einstein, and they came up with some morbid thought experiments to make their point that taking quantum mechanics as it is could result in untenable macroscopic realities. In doing so, they were taking direct aim at some of the key tenets of the Copenhagen interpretation.

  Take the Mach-Zehnder interferometer. According to the formalism, before one of the detectors clicks, signaling the arrival of a photon, the photon is in a superposition of two states, of taking one path and the other path. The wavefunction of the photon is said to be in a superposition of two states, where one state represents its progress along one path, and the other state its progress along the other path. Using this wavefunction, we can calculate the probability that it’ll be found at D1 or at D2, which, incidentally, turns out to be 1 and 0, respectively, when the length of the paths to D1 and D2 are exactly the same. C
reating small differences in the lengths of the paths can change these probabilities. According to the standard view, the photon has no definite position—the wavefunction is spread out—until there’s a measurement. The measurement at D1 or D2 causes the wavefunction to collapse to one definite value: the photon shows up at one of the detectors.

  The onus of collapsing the wavefunction falls on the measurement device, which is assumed to be some macroscopic, classical apparatus. But the Copenhagen interpretation does not really define the exact meaning of a measurement. How big does the measurement device have to be to count as classical? Where’s the boundary between the quantum and the classical? Such questions lead to the so-called measurement problem.

  To appreciate just how deep this problem runs, let’s assume the measuring devices are also something quantum mechanical—say they are themselves particles that interact with the photon and somehow change state to record the arrival of the photon. If one were to simply follow the mathematics, something weird happens. The wavefunction of the photon evolves until it is in a superposition of having gone through both paths, which recombine at the second beam splitter. Then it interacts with the measurement device, which is itself a quantum mechanical particle. The whole system then ends up in a superposition, mathematically speaking, of a state in which the photon has reached the measuring particle D1 and D1 has changed state and the photon has reached the measuring particle D2 and D2 has changed state. To collapse the wavefunction of the entire system so that we can figure out exactly where the photon went, we’ll have to do yet another measurement, with some ostensibly classical apparatus, to determine the state of D1 and D2.

  What if every piece of apparatus we choose obeys the laws of quantum mechanics, such that the entire setup always remains in superposition, and its total wavefunction never collapses? Will it eventually require a conscious human to cause a collapse, to see where the photon went?

  The Copenhagen interpretation, while it does not invoke the need for human consciousness, nonetheless demands a classical measurement. The corollary is that the quantum state of a system is adequately and indeed completely captured by the wavefunction, and since the wavefunction lets you calculate only the probability of finding the system in some state, and does not correspond to, say, where the photon actually is, reality does not exist in any meaningful sense independent of measurement with a classical apparatus.

  Einstein and Schrödinger were both deeply disturbed by such anti-realist ideas. Einstein pointed out his concerns in a letter to Schrödinger. In a thought experiment, Einstein imagined some gunpowder that can spontaneously combust because of quantum mechanical goings-on and has a certain probability of exploding within a year, and a certain probability of not exploding. The system starts off with a well-defined wavefunction, meaning it is in a definite state. But because it’s a quantum system, the wavefunction evolves according to the Schrödinger equation, into something that eventually puts the gunpowder in a quantum superposition of having exploded and not having exploded. Of course, macroscopically, in our understanding of the world at large, this is absurd. The gunpowder should either explode or not, whether we look at it or not. Einstein wrote to Schrödinger, saying, “ Through no art of interpretation can this ψ-function [wavefunction] be turned into an adequate description of a real state of affairs; [for] in reality there is just no intermediary between exploded and not-exploded.”

  Schrödinger ended up refining this thought experiment, making the seeming absurdity starker. He wrote to Einstein, saying, “ I am long past the stage where I thought that one can consider the ψ-function as somehow a direct description of reality. In a lengthy essay that I have just written I give an example that is very similar to your exploding powder keg.” He then went on to describe the experiment, an elaborate version of which appeared in his published paper.

  “ A cat is shut up in a steel chamber, together with the following diabolical apparatus (which one must keep out of the direct clutches of the cat): in a Geiger tube there is a tiny mass of radioactive substance, so little that in the course of an hour perhaps one atom of it disintegrates, but also with equal probability not even one; if it does happen, the [Geiger] counter responds and through a relay activates a hammer that shatters a little flask of prussic acid. If one has left this entire system to itself for an hour, then one will say to himself that the cat is still living, if in that time no atom has disintegrated. The first atomic disintegration would have poisoned it. The ψ-function of the entire system would express this situation by having the living and the dead cat mixed or smeared out (pardon the expression) in equal parts.”

  But surely the cat is either alive or dead, not in some weird mixture of both? At least that’s our classical intuition. Not so says the standard view of quantum mechanics. The paradox arises because in the Copenhagen interpretation, the wavefunction of the total system remains in a superposition of cat-dead and cat-alive states, until something classical interacts with the system. Say someone opens the steel chamber and takes a look, at which point the wavefunction of the entire system collapses to one or the other. The cat will be found either dead or alive.

  Quantum mechanics asks us to suspend disbelief and hold on to some counterintuitive notions of reality for long enough to be able to appreciate the bizarreness of the subatomic world. For example, even if Schrödinger’s thought experiment with the cat-in-a-steel-box stretches credulity, as it should (it was after all an exercise in trying to demonstrate the possible incompleteness of quantum mechanics), it is also a reminder of something that’s true of the quantum world: superposition exists, at least in the standard view.

  If it did not, you could not explain the interference pattern seen in a double-slit experiment done with single particles. In Aspect and Grangier’s Mach-Zehnder setup, until each photon was detected, it was in a superposition of having taken both paths. Mathematically, here’s what is happening in the Mach-Zehnder experiment. There is one wavefunction that describes the state of the photon going via one path, and another wavefunction for the state of the photon going via the other path. The final wavefunction is a linear combination of the two wavefunctions, which lets you calculate the probabilities of detection at D1 or D2 (ψtotal = a1.ψD1 + a2.ψD2 , where the probability of finding the photon at D1 is given by the modulus-squared of a1, and the probability of finding it at D2 is the modulus-squared of a2. The total probability has to add up to unity, so |a1|2 + |a2|2 = 1. The exact values for a1 and a2 depend on the path lengths of the interferometer, whether they are identical or slightly different).

  In the early days of quantum mechanics, it was often said that the interference pattern appears because a particle interferes with itself (to paraphrase Paul Dirac). But that turns out to be a somewhat limited view of what’s happening. The more profound realization is that what are really interfering are two different states of the system. In the case of an interferometer with two paths, the two states are the two possible paths for each photon. If there were multiple possible states or paths for the photon, say you had five slits instead of two, then the superposition would involve the photon going through all five slits, and a very different interference pattern would emerge on the far screen.

  Whether it’s the Mach-Zehnder interferometer with two well-defined possible paths, or an apparatus with five slits, the standard quantum formalism makes it impossible to visualize the path of an individual photon—there are no equations to calculate trajectories. The Copenhagen interpretation of this formalism insists that such trajectories don’t exist. In fact, the notion of the path has no meaning, just as the notion of an electron’s orbit around the nucleus has no meaning. If realism is the idea that the world objectively exists out there, with well-defined properties, even if we are not privy to them, then the Copenhagen view is anti-realist. In its telling, the only world we can talk of definitively is the one that reveals itself upon measurement; talking about anything else is meaningless.

  Aspect, for one, is holding out hope for pa
rt of Einstein’s dream. “I’m really sitting on the side of Einstein,” he told me. “I think there is a real world.” Meaning a reality independent of observers, experiments, and experimentalists. For now, Aspect is willing to accept quantum mechanics for what it’s saying about the world. “The world is not as simple as one could think. But physicists were smart enough to develop mathematical tools to render an account of what happens.”

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  The impossibility of talking about exactly what’s happening to a quantum system—say a photon working its way through a Mach-Zehnder interferometer—within the confines of the Copenhagen interpretation was highlighted by theoretical physicist John Wheeler in the late 1970s and early 1980s, most creatively by his use of the metaphor of the “ great smoky dragon.” Wheeler imagined, and got someone to sketch for him, a dragon whose head and tail are clearly visible. The tail represents the unambiguous quantum state of the photon that is about to enter an interferometer. The head represents the definite detection of the photon at either detector D1 or D2. But the dragon’s body is fuzzy, ambiguous, smoky, hence the name. “ What the dragon does or looks like in between [the head and the tail] we have no right to speak [of],” wrote Wheeler and his colleague Warner Miller. The dragon’s blurry body, of course, represents the state of the photon as it winds its way through the interferometer (if it does that at all).

  Wheeler, like Einstein, loved thought experiments. The one most associated with him bears his name: Wheeler’s delayed-choice experiment. It’s an experiment that’s easy to conceptualize, now that we know of Aspect and Grangier’s 1985 experiment done with single photons, using a Mach-Zehnder interferometer. Wheeler, of course, thought of it before anyone had done such experiments.

  The delayed-choice experiment brings into stark relief Bohr’s complementarity principle. Bohr argued that the wave nature and particle nature of a quantum system are mutually exclusive ways of looking at reality: what you observe depends on the experimental setup, and you cannot have both types of setups in the same experiment. And if you try to do both (as Einstein tried to with his thought experiment with the double slit), then Bohr’s claim was that the uncertainty principle ensures that you cannot see the interference pattern (the actual explanation, it’ll turn out, is more involved than Bohr understood).