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

by Ananthaswamy, Anil

  The problem they needed to solve, to do the experiment on an optical bench on Earth, was essentially the one that Penrose solved by going up into space: how to keep the photon in a superposition for a sufficiently long time to witness any potential collapse of the movable mirror’s superposition. On Earth, they needed to store a photon awhile before letting it come back into the interferometer and head toward the beam splitter. One option was to store the photon in an optical cavity, which is essentially made of two extremely high quality concave mirrors aligned such that the photon, once it enters the cavity, keeps bouncing back and forth between the mirrors and then, at some random time, leaks out again. It’s a way of storing the photon for a certain length of time.

  So the photon’s journey to satellites B and C is replaced by two optical cavities, each holding on to the photon for a while, as if it were traveling 10,000 miles and back. The optical cavity that replaces the part of the photon path with the movable mirror is somewhat unique. In this cavity, one of the mirrors is tiny and suspended on a cantilever arm. Bouwmeester decided to use optical and infrared photons—it’s easier to make high-quality mirrors for them than it is for X-ray photons, which Penrose had used in his original thought experiment. The photons bounce between the two mirrors inside the optical cavity. This creates a “radiation pressure” that is strong enough to displace the movable mirror. This phenomenon is itself quite curious. Quantum mechanically speaking, the photon is not localized. It’s all over the place inside the cavity, and over time, its delocalized presence creates the necessary pressure to push at the mirror.

  Now, just as the photon is in a superposition of being in two arms of the interferometer, the movable mirror ends up in a superposition of being displaced and not-displaced.

  At some random moment, the photon leaks out of the cavity and heads back toward the beam splitter. What happens next depends on whether the photon, and indeed the entire system (including the movable mirror), is still in a coherent state of superposition or has collapsed to one or the other state.

  If the entire system is still in superposition, the photon’s two states will interfere. Since one of the path lengths is fixed, the interference pattern will depend on the position of the movable mirror at the exact time the photon leaks out—it dictates the distance traveled by the photon in the arm of the interferometer with the movable mirror. The interference pattern created over many runs of this experiment—detected as the number of clicks at detectors D1 and D2—will have a signature that’s tied to the movable mirror’s oscillations.

  But if the mirror’s superposition has collapsed, the photon will act like a particle and has an equal chance of heading toward D1 or D2. As with Penrose’s space-based experiment, monitoring the statistics of the detections at D1 and D2 can tell us whether the tiny mirror has remained in superposition or not.

  The fundamental task at hand in such an experiment is to put a macroscopic object into superposition and keep it there long enough to do an experiment. When they wrote their paper in 2002, Bouwmeester and Penrose claimed that a tiny mirror could be put into a superposition of being at two locations if one could combine the state-of-the-art technologies for each piece of the puzzle. “That’s still true, but it is extremely hard to combine state-of-the-art low temperature physics with state-of-the-art optics with state-of-the-art mechanical fabrication and so forth,” Bouwmeester said. “That’s basically what we have been working on ever since.”

  It turns out that none of these issues is trivial. Far from it. First they had to learn how to fabricate mirrors several orders of magnitude smaller than a grain of sand. One technique involved using a focused beam of ions to cut out a mirror and then glue it to a tip of a cantilever, to make it movable; the mirror was so small and so hard to control that oftentimes it’d flip during the fabrication process and get glued upside down. Even if it was right side up, such a mirror was still too large. The team figured out how to make smaller mirrors cantilevered at the tip of slivers of silicon nitride. They also had to make these mirrors unbelievably cold. Otherwise the thermal jiggling of the molecules of the mirror would be such that the impact of a single photon would have no discernible effect. So the mirrors had to be cooled down to bring them to their quantum ground state—which meant achieving temperatures below 1 millikelvin. “That’s ridiculously low for a cryogenics experiment,” said Bouwmeester. But getting things so cold means using dilution refrigerators, pumps circulating helium, and the like—all sources of vibration that could render the whole exercise futile. And, therefore, they had to develop multiple systems to dampen vibrations. Of course, all of this has to be done inside a vacuum chamber. “In the end this apparatus costs several millions,” said Bouwmeester. All for a tiny mirror that stays so cold and quiet that it can be pushed around by a photon and end up in a superposition of two positions, one position that’s barely a few hundred atomic widths away from the other.

  “You first have to prove that you can create a quantum superposition of a macroscopic object before you can investigate its decoherence,” said Bouwmeester. “In the end, we are still quite far away from it. [But] the developments have been enormous.”

  Decoherence specifically refers to the loss of coherent superposition of a quantum mechanical system due to its interaction with the environment, such that it ends up in some classical state. Penrose’s ideas and GRW-like collapse theories are not theories about decoherence: they explicitly advocate collapse, which leads to decoherence.

  As we talked, Bouwmeester admitted that despite being inspired by Penrose’s ideas to carry out such difficult experiments, he thinks the experiments will most likely not see any collapse of quantum superpositions of more and more massive objects, as long as the objects are well-enough isolated from their environments to prevent decoherence. In which case, Bouwmeester says that he’d be forced to take seriously the idea that there is no quantum-classical boundary, that wavefunctions evolve and there is no collapse. Different parts of the wavefunction continue evolving, and as they interact with their environment, they behave as if decoherence has set in, making it difficult if not impossible to get the separately evolving wavefunctions to interact. “They become independent and there is no interference anymore,” said Bouwmeester. “But this is rather strange, because then you are really back to Schrödinger’s cat.”

  Yes, back to the poor cat, but in a subtly different way. Instead of being a demonstration of the absurdity of quantum mechanics, it becomes an unflinching exploration of its implications. In this way of thinking, Bouwmeester is hinting at the argument that both the dead cat and the live cat exist, and so does someone who has seen a dead cat and someone who has seen a live cat. They are two distinct minds, and there are possibly two different worlds that these two minds inhabit, which don’t interact anymore. “That’s not a ridiculous way of looking at things,” he said. “You just have to go through quantum mechanics for a little while to understand how elegant and simple it actually is.”

  Some physicists take the simplicity and elegance of quantum mechanics to heart, such as the straightforward evolution of the wavefunction according to Schrödinger’s equation and the attendant superpositions, and refuse to add anything to its formalism, even the notion of collapse due to measurement, which is a modification of the Schrödinger evolution. And they end up with a startling conclusion: superpositions of systems that cannot interfere with each other anymore now each exist in their own right. The idea leads us to a notion of “many worlds,” where every possibility exists somewhere. For Bouwmeester, if experiments like his never see collapse, even as the macroscopic objects in superposition keep getting bigger and bigger, that’s a sign. “In that case I am really going to take the many worlds interpretation seriously,” he said.

  Bouwmeester first realized just how earnestly some physicists regard the many worlds interpretation when he met Lev Vaidman (of Elitzur-Vaidman bomb puzzle fame) on a bus in China, on their way to a conference. Vaidman has famously written in one of his
papers, “ The collapse [of the wavefunction] . . . is such an ugly scar on quantum theory, that I, along with many others, am ready to . . . deny its existence. The price is the many-worlds interpretation (MWI), i.e., the existence of numerous parallel worlds.”

  “ He was rather upset when I met him,” Bouwmeester said, speaking at the Institute for Quantum Computing in Waterloo, Canada. Vaidman, it seems, had been trying to get a patent approved for a watch that would help him make a difficult “yes or no” life decision. The watch would have a single photon source. The photon would go through a beam splitter and be detected by one of two single-photon detectors inside the watch. If one of them clicks, the watch says “YES,” do it; if the other clicks, the watch says “NO,” don’t. Vaidman’s point being that no matter what decision you make, you can rest easy because you know that in another branch of the wavefunction, you have done the opposite.

  One person who likely would have been unfazed by Vaidman’s watch is Hugh Everett III, a mathematician and quantum theorist who first advocated, in his PhD thesis in 1957, taking the collapse-free evolution of the wavefunction seriously, as a way of solving the measurement problem. His thesis led to possibly the most unsettling solution to the paradox of the double-slit experiment yet entertained—the many worlds interpretation.

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  HEALING AN UGLY SCAR

  The Many Worlds Medicine

  Actualities seem to float in a wider sea of possibilities from out of which they were chosen; and somewhere , indeterminism says, such possibilities exist, and form a part of the truth.

  —William James

  I f there is one place that could be said to have harbored a handful of quantum dissenters—those who found the Copenhagen interpretation problematic, if not distasteful—it’d have to be Princeton, New Jersey. Einstein, the original dissenter, came to the Institute for Advanced Study in 1933 and lived out the rest of his life there, and remained forever of the opinion that quantum mechanics wasn’t complete. David Bohm, who came to Princeton University in 1946, started thinking contrarian views there, before going into exile in Brazil in 1951, from where he published his hidden variable theory. Soon after Bohm left Princeton, a mathematically minded young man named Hugh Everett III, having just gotten a bachelor’s degree in chemical engineering, came to Princeton University in 1953 and by 1955 had begun working on his PhD in quantum physics. His supervisor was John Wheeler. Though Wheeler was a staunch supporter of Niels Bohr and the Copenhagen interpretation, Wheeler’s protégé would turn out to be one of the most imaginative of the nonconformists.

  Wheeler put a lot of stock in taking the equations of physics seriously and seeing where they led us. Soon after Einstein came up with his general theory of relativity, solutions of his equations were pointing physicists toward topological structures in spacetime that taxed common sense. In the 1960s, Wheeler would coin the terms black hole and wormhole for such structures. But even earlier, Wheeler’s attitude likely rubbed off on Everett—and he’d apply it to the mathematics of quantum physics.

  It started with taking seriously the wavefunction and its evolution, in all its simplicity and elegance. The essence of Everett’s thinking was that the wavefunction is all there is: a universal wavefunction for the entire universe, which describes the universe as being in a superposition of any number of classical states, and this wavefunction and the superpositions evolve continuously, deterministically, and forever.

  Everett’s intuition was informed by the need to do away with the measurement problem. By 1955, he had identified what he thought of as the key issue with the quantum formalism then in vogue. If the state of a quantum system at any instant is given by the wavefunction psi, ψ, then Everett pointed out that there are two processes that govern it. First, the wavefunction evolves in time according to Schrödinger’s equation, a completely deterministic process. But upon measurement, the wavefunction abruptly changes to a definite state with some probability that can be calculated—a so-called probabilistic jump. Everett found this untenable.

  He asked if these two processes were compatible with each other. More specifically, he asked, “ What actually does happen in the process of measurement?”

  Consider a photon that goes through a beam splitter. According to standard quantum mechanics, it goes into a superposition of being in two paths. The wavefunction of the photon at this point is a linear combination of two wavefunctions, one in which the photon takes the reflected path, and the other in which it takes the transmitted path. (As we saw earlier, if ψ = a.ψref + b.ψtr, where the coefficients “a” and “b” are complex numbers, then the square of the modulus of a, or |a|2 , is the probability of finding the photon in the reflected path, and |b|2 the probability of finding it in the transmitted path. If the beam splitter is built to reflect half the light and transmit half the light, then the probabilities are each equal to 0.5.)

  Now, if you have detectors D1 and D2, one at the end of each path, then for each photon that goes through the beam splitter, we’ll get a click at either D1 or D2. In the Copenhagen interpretation, because the detectors are somehow magically treated as classical objects, the measurement causes the collapse of the wavefunction, and the photon is localized at either D1 or D2. Recall that in the 1960s, Eugene Wigner too found this distinction between the quantum and the classical rather arbitrary, and argued that it’s the consciousness of an observer that causes the collapse.

  Everett took a different tack. If you follow the math and treat the detectors quantum mechanically too, then the entire apparatus ends up in a superposition of D1 clicking and D2 clicking. Why just the detector? Why not also treat the observer quantum mechanically? If so, the observer ends up in a superposition of hearing D1 click and hearing D2 click. According to Everett, if you consider only a part of this wavefunction in which D1 clicks, you are left with a definite observer who hears the click. And examining another part of the wavefunction reveals a definite observer who hears D2 click. “ In other words, the observer himself has split into a number of observers, each of which sees a definite result of the measurement,” he wrote.

  What Everett was proposing is that there is no collapse of the wavefunction and hence no measurement problem. All possibilities exist (and we’ll soon come to what exist might mean, again). In the simple case of a beam splitter and two detectors, we end up with two observers, each of whom hears one of the detectors click.

  Now think of an observer in one of those branches. Having observed, say, D1 click, the observer sends another photon through the same beam splitter. Again, the observer splits, into one who hears D1 click and one who hears D2 click. There’s no collapse, no probabilistic jump, just the continuing evolution of the wavefunction. This process can be carried on ad infinitum—and we get a treelike structure of observers. If you follow any one branch of this tree, you will find an observer who hears the detectors click, for example, in the following sequence: D1, D1, D2, D1, D2, D1, D1, D2 . . . ; or D1, D1, D1, D2, D1, D2, D1, D1 . . . ; or a seemingly random combination of D1s and D2s.

  So, even though there is no probabilistic jump occurring in any one such sequence of detections—in the sense of the wavefunction collapsing randomly to one or other state—for each observer it seems as if D1 or D2 clicks randomly, and thus there is a perception of a collapse to one state or the other. Everett argued that “ for almost all of the ‘branches’ of his ‘life tree,’” an observer would hear D1 or D2 clicking at a frequency that would tally with the probabilities given by the initial superposition, provided of course one carried out this experiment enough times (it’d turn out to be not quite so simple).

  Everett was proposing a theory that was continuous (there were no real jumps, just apparent jumps) and causal, because everything evolved deterministically according to the rules of the Schrödinger equation. Yet, for any given observer, the theory is discontinuous because of the perceived jumps in states, and the jumps are seemingly random. The theory, Everett wrote, “ can lay claim to a certain completeness, s
ince it applies to all systems, of whatever size . . . The price, however, is the abandonment of the concept of the uniqueness of the observer, with its somewhat disconcerting philosophical implications.”

  He even came up with an analogy to drive home the point: “ One can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree. The question of the identity or non identity of two amoebas at a later time is somewhat vague. At any time we can consider two of them, and they will possess common memories up to a point (common parent) after which they will diverge according to their separate lives thereafter . . . The same is true if one accepts the hypothesis of the universal wavefunction. Each time an individual splits he is unaware of it, and any single individual is at all times unaware of his ‘other selves’ with which he has no interaction from the time of splitting.”

  Wheeler was impressed by Everett’s work, and yet he had serious reservations about these “disconcerting philosophical implications.” Everett was taking on the Copenhagen interpretation, and as such, Wheeler—who admired Niels Bohr—wanted to discuss Everett’s work with those in Copenhagen. But Wheeler had concerns about splitting observers and amoebas. “ I am frankly bashful about showing it to Bohr in its present form, valuable & important as I consider it to be, because of parts subject to mystical misinterpretations by too many unskilled readers,” Wheeler told Everett.

  Everett avoided some of these “mystical” overtones in his thesis, especially the bit about splitting amoebas, and then submitted it to Wheeler in 1956. While expounding his ideas in great detail and with mathematical rigor, he nonetheless took aim at Bohr and the Copenhagen interpretation, calling it conservative and overcautious (quite the irony, when you consider that the Copenhagen view, in its extreme, says that reality doesn’t exist until one observes it). “ We do not believe that the primary purpose of theoretical physics is to construct ‘safe’ theories at severe cost in the applicability of their concepts, which is a sterile occupation, but to make useful models which serve for a time and are replaced as they are outworn,” wrote Everett. He criticized the Copenhagen interpretation for relying on a form of “ objectionable” dualism, splitting the world into the classical and the quantum, and ascribing to the classical world a reality that it denied to the quantum.