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

by Ananthaswamy, Anil

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  Even though some, like Hiley, may disagree with Steinberg’s experiment, the average trajectories measured by Steinberg’s team brought out one aspect rather clearly: the paths of the photons did not cross the midline of the double-slit apparatus. The photons going through the left slit ended up on the left half of the far screen or camera, and those going through the right slit arrived at the right half of the detector. The paths would converge near the middle, but never cross.

  While the trajectories were in line with what’s expected from Bohmian mechanics, there was one nagging concern yet to be addressed. In 1992, Marlan Scully and his colleagues (dubbed ESSW, after the initials of the four team members), argued that Bohmian mechanics predicted something rather strange. If you could put a detector near the slits that could somehow tell which slit the particle went through without destroying the particle, ESSW showed that in some cases the detector near the left slit would fire, but the particle would end up at the right half of the far screen. According to Bohmian mechanics, a particle that hit the right half of the screen could have originated only in the right slit, because the trajectory cannot cross the midline. So, then, why was the math showing that sometimes, even though the particle hit the right half of the screen, the left slit detector fired? ESSW caustically called this out. “ Tersely: Bohm trajectories are not realistic, they are surrealistic,” they wrote.

  “To them, this was a kind of reductio ad absurdum for the Bohm interpretation,” Steinberg said. Over the years, many researchers (including Hiley) pointed out various problems with the ESSW analysis. Bohmian mechanics itself kept being tweaked, with physicists developing different versions of it, but the question of surreal trajectories never quite went away. “In essence, with any of these versions of the Bohm interpretation, you can find situations where one detector fires, but the Bohm model has the trajectories going through the other [slit],” said Steinberg. Surreal trajectories were a knock against the correctness of Bohm’s ideas.

  Steinberg’s team stepped up their game, bringing more sophisticated experimental techniques to the optical bench. They wanted to know: could surreal trajectories destroy Bohm’s ideas?

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  As an experimentalist, Steinberg is agnostic about theoretical interpretations of quantum mechanics. Even so, given the ESSW take on surreal trajectories, Steinberg was concerned about the validity of Bohmian mechanics. This despite the fact that the theory came with certain advantages. First, it restores determinism. “To a lot of people, the standard interpretation of quantum mechanics, which is very mathematical and abstract, gives up determinism, and they don’t understand why you would give it up if you don’t have to,” said Steinberg. “They say that it’s such an important philosophical assumption that if you showed me that it was in contradiction to reality, I’d give it up, but otherwise I’ll bend over backwards to keep it.” Bohmian mechanics keeps determinism intact.

  Second, it makes nonlocality more explicit. Tests of Bell’s inequality clearly show that the quantum world is nonlocal. “In the standard theory, the nonlocality looks mysterious, it looks like this spooky action at a distance, whereas in the Bohmian mechanics, it shows up exactly in the equations of motion,” said Steinberg. It’s clear how the motion of any given particle is instantly influenced by other particles. It’s built into the mathematics.

  Of course, Bohmian mechanics messes with the elegance of Schrödinger’s ideas, in which there is just the quantum state of the system in question (given by the wavefunction) that evolves according to the Schrödinger equation. “You can think of it as being a particle or a wave, but it is what it is,” said Steinberg. “In Bohmian mechanics, everything becomes two things. Everything is a particle and a wave. You have doubled the number of entities out there. That doesn’t really disturb me, but it’s an argument some people make.”

  What did disturb Steinberg, though, were surreal trajectories. “I also shared the ESSW intuition that these trajectories didn’t make any sense,” Steinberg told me. It “was one of the things that used to make me less enamored of the Bohmian picture.” After their tour de force 2011 paper on average trajectories of photons going through a double slit, it was time to test the ESSW claim about surreal trajectories.

  It required a small but significant tweak to their earlier experiment. Instead of a photon source that generated single photons, they began using a source that generated a pair of entangled photons. These photons are entangled in their polarization. The photons are polarized in the horizontal-vertical basis, so if one photon is measured and found to be polarized in the horizontal direction, then the other photon will be vertically polarized, and vice versa.

  Let’s call one of the entangled photons the system photon. This is sent through the same kind of setup that was used to measure average trajectories. The only difference being that instead of using a standard beam splitter, they used a polarizing beam splitter (PBS) to steer a vertically polarized photon into the left optical fiber and hence the left slit of the virtual double slit, and the horizontally polarized photon to the right slit. As we saw in earlier experiments, the polarization is converted into a path.

  The other photon is the “probe” photon: it contains the information needed to probe which way the system photon went, without disturbing the system photon.

  There are myriad things one can now do with this setup. For instance, if one simply measured the probe photon’s polarization in the horizontal-vertical basis and got either horizontal or vertical as an answer, it immediately reveals which path its partner system photon took through the double slit. So, for all those probe photons that are measured in the horizontal-vertical basis, the corresponding system photons that go through the double slit don’t show any interference, because we know which path they took and so they act like particles.

  But if you measure the probe photon’s polarization in the +45-degree direction, things change. The measurement involves sending the probe photon through a +45-degree polarizer: either it comes out (in which case, it’s polarized at a +45-degree angle) or it doesn’t. Crucially, the information about whether it was originally horizontally or vertically polarized is now erased. The math says that now it’s equally likely to be horizontally or vertically polarized. Consequently, the corresponding system photon is also equally likely to be horizontally or vertically polarized, and so ends up in a superposition of going through the left and right slits. Taken together, such system photons show an interference pattern on the CCD camera.

  This is essentially Marlan Scully’s quantum eraser experiment.

  Steinberg’s team had lots more to do besides erase the which-way information. For starters, they began measuring the average trajectories of the system photons through the double slit. But for each weak measurement they made on a system photon, courtesy of the calcite crystal, they also measured the probe photon, to see if it was polarized at some given angle. What effect did this polarization measurement have on the system photon traveling through the double slit?

  The team found that their choice of polarization angle for the measurement of the probe photon had an immediate effect on the system photon: its trajectory was altered (as determined via measurements over many, many particles). “So we directly see that this is a nonlocal theory,” said Steinberg. “We can’t really predict what these trajectories are without paying attention to the [probe] photon.”

  It was now finally time to ask the big question: were some trajectories surreal? To answer the question, they began studying the trajectories of the system photons, and for each trajectory, they looked at the polarization of the probe photon at various points in the trajectory of the system photon. Did the polarization change with the trajectory?

  The answer was a clear yes. Say a system photon’s trajectory started off at the left slit. The probe photon’s polarization would be vertical. But as the system photon moved through the apparatus, the probe photon’s polarization kept changing: another demonstration of the nonlocal interactio
n between the two photons. And there were situations when the system photon that began its journey at the left slit would reach the left half of the CCD camera screen, but the probe photon would end in a 50-50 mix of being horizontally and vertically polarized: its polarization was equally likely to be horizontal or vertical. More to the point, since the polarization of the probe photon is an indication of which slit the system photon took, the probe photon would sometimes indicate that the system photon took the left slit and at other times indicate it took the right slit, even though the Bohmian trajectory clearly showed that the system photon started at the left slit and remained in the left half of the apparatus, never crossing the midline.

  This was the surreal trajectory ESSW had theoretically identified. Except, to them, it had made no sense, because the Bohmian trajectories were at odds with the information in the which-way detector. But Steinberg’s experiment shows that the system photon, as it’s moving from the slit to the screen, is nonlocally influencing the polarization state of the probe photon: it’s nonlocally influencing the which-way detector. So, sometimes, at the end of the system photon’s trajectory, the probe photon’s polarization may have changed, say, from horizontal to vertical, leading one to erroneously interpret that the system photon went through the right slit, not the left one. If you didn’t know of the nonlocal interaction between the photons, you would see the results as a knock against Bohmian mechanics, as ESSW did. Steinberg’s team is arguing that Bohmian mechanics is consistent and defensible, and can’t be ruled out based on the ESSW argument.

  The probe photon shows the correct polarization value when the system photon is near the slits, but sometimes, at the moment the system photon hits the CCD camera, the probe photon’s polarization itself has changed, due to nonlocality. So the trajectory is surreal or untenable only if you think the which-way detector’s final value was always its value. That’s clearly not the case.

  While the findings remain controversial (partly because there are a few different versions of Bohm’s theory and partly because of the debate over the meaning of weak measurements), for some, including Steinberg, the fact that surreal trajectories have a perfectly sensible explanation makes it possible to think of Bohmian mechanics as a viable alternative to the Copenhagen interpretation. The experiment shows that it cannot be ruled out, yet.

  Of course, the same experimental results can be predicted using standard quantum theory. “It certainly doesn’t come down on one side or the other,” said Steinberg. “The best thing experiments like this can do is to remind people that the [Bohmian] interpretation exists—people who had either forgotten or never knew about it—and show them that although it might sound mysterious when you first hear it described, these hidden trajectories are related in a very straightforward way to things you can easily imagine going into a lab and measuring.”

  It took years for Bohm to get out of exile from Brazil and reach the UK, but it’s taken even more time for his ideas to start being treated as valid and worthy of such experimentation. “It’s an interpretation that hasn’t gotten enough attention, people aren’t aware of it, and we want . . . to bring it back to its rightful place among all other interpretations,” Steinberg said.

  Philosopher David Albert thinks the cold shoulder Bohm’s ideas received was in no small measure due to the politics of the time. “A large part of the story of the reception of Bohm’s theory has to do with the fact that when he was in the middle of proposing this he refused to testify before the Un-American Activities Committee and was hounded out of the country. A lot of the reception of Bohm’s theory is tied up with that,” said Albert. “Science is a very human endeavor, and the history of foundations of quantum mechanics are a particularly vivid example of this.”

  Even the rise of the Copenhagen interpretation, Albert argued, could be seen in the light of the “crisis of representation” that engulfed literature in the late 1800s and early 1900s. Could language capture objective reality? Modernist literature said no: it played with perspective, highlighting uncertainties and ambiguities inherent in any one view of the world. It was “ inspired by the modern realization of the observer’s role in both creating and curtailing the world of perception” and led to, at its extreme, “the view that there is no true world, since everything is but ‘a perspectival appearance whose origin lies in us.’”

  “Literary modernism was supposed to be a response to the crisis of representation in literature. Physics wanted to have its crisis of representation too,” said Albert. And it got one, when quantum physics claimed that “there isn’t any such thing as telling the flat-footed, objective, true story of what’s happening to the particle in between this measurement and that measurement.”

  Bohm’s ideas certainly challenge this view. Goldstein is more than aware that the rumblings about Bohm’s ideas are growing. “After decades and decades, people are taking Bohmian mechanics a little bit more seriously,” he told me. “There was a time when you couldn’t even talk about it, because it was heretical, it wasn’t Copenhagen. There was a kind of political correctness about physics. It probably still is the kiss of death for a physics career to be actually working on Bohm, but maybe that’s changing.”

  But as much as Bohm’s realist, nonlocal theory appeals to some, there are others for whom it holds less sway. Even Steinberg, whose experiments are responsible for shining a favorable light on Bohmian mechanics, remains quietly skeptical of Bohm’s ideas. One problem for Steinberg is that Bohmian mechanics privileges position over other properties of a particle: it’s only position that gets the honor of being associated with a hidden variable. But what about a particle’s spin or its polarization? The theory treats these differently, and doesn’t accord them the same kind of hidden variable as it does position. “I must admit I always found that distasteful,” said Steinberg. “Because by the time I was raised in quantum mechanics, I didn’t see anything that special about position. There should be one consistent treatment of all kinds of measurements. If your measuring device uses polarization, there should be a different hidden variable that corresponds to polarization.”

  Goldstein thinks otherwise about according position the pride of place as a hidden variable. “I regard it as very much a virtue that one does not need to have additional reified observables in order to fully understand what is going on in any quantum measurement,” he said. “Position suffices. People have indeed proposed adding Bohmian versions of the other observables. The result is ugly and the effort rather pointless.”

  While Goldstein strongly favors Bohmian mechanics, Steinberg’s holding out for something more than either orthodox quantum mechanics or Bohmian mechanics. “I’m most attracted to the possibility of us discovering something beyond quantum mechanics that resolves these problems by saying that this wasn’t the complete theory to begin with,” he told me. “I’m waiting.”

  Roger Penrose, a theoretical physicist at Oxford University in the UK, shares Steinberg’s view that quantum mechanics may be incomplete. “Quantum mechanics is a provisional theory,” he told me when I met him at his home. Sitting in his bucolic backyard on the outskirts of Oxford, Penrose proceeded to explain why gravity (which we have ignored thus far in our attempts at understanding the quantum world) may have something to do with fixing quantum mechanics (at least in the minds of those who think it needs fixing). And as always, it began with a discussion of the double slit. This time, however, instead of a particle going through two slits, Penrose talked of a cat walking through two doors at once.

  7

  GRAVITY KILLS THE QUANTUM CAT?

  The Case for Adding Spacetime into the Mix

  A university student attending lectures on general relativity in the morning and . . . on quantum mechanics in the afternoon, might be forgiven for concluding that his professors are fools, or they haven’t talked to each other for at least a century.

  —Carlo Rovelli

  T he day I’m supposed to meet Roger Penrose at Oxford University, he has to stay hom
e. So I receive instructions to get to his house—a map that he drew by hand almost two decades ago for guests coming to his housewarming party, and which he has been updating ever since, as the neighborhood changes around him. The high-level map of where he lives near Oxford is at a different scale, but is informative enough, and there’s even a detailed, zoomed-in drawing of the roads and houses within a few hundred meters of his home (from macroscale to microscale, I think to myself). It contains warnings: “Fancy blocked entrance (not us!),” “Imposing old house, NOT us,” “Smart blocked entrance. NOT US.” And an arrow pointing to his house, saying, “Our broken down entrance.”

  Penrose’s penchant for drawing by hand is obvious when he gives talks. Eschewing sophisticated presentations with graphics and animations, he still relies on an overhead projector, oftentimes using multiple hand-drawn transparencies to project a single image, each transparency meticulously drawn and annotated in different colors. He then carefully fiddles around with them, stacking them, sliding them around, until a complex story emerges—like a cat in a superposition of being alive and dead at the same time.

  A mathematical physicist, Penrose is best known for his work on general relativity and cosmology, particularly on singularities that occur inside black holes or at the big bang, the places in the cosmos where our known laws of physics break down. Such breakdowns happen partly because the physics of intense gravitational fields has to coexist with the physics of the microscale. General relativity, which is a theory of gravity on large scales, has to confront quantum mechanics. But so far, gravity has stubbornly resisted succumbing to quantization, unlike the other three fundamental forces of nature (the quantum of the electromagnetic force is the photon, but there is no observed quantum of the gravitational force). There’s a consensus view, however, among those striving for a theory of quantum gravity that it’s general relativity that has to make way in this tussle for supremacy, and that quantum mechanics can continue untouched for the most part.