The EPR paper triumphantly concluded that “the wavefunction does not provide a complete description of physical reality.” They did not address what a complete theory would look like but said, “We believe, however, that such a theory is possible.”
Any such theory that augments the wavefunction with additional variables came to be called a hidden variable theory. The irony of the EPR paper was that a few years earlier, in 1932, John von Neumann had ostensibly proved that any theory that could replicate the experimental successes of quantum theory could not have hidden variables. Those who swore by the Copenhagen take on the quantum world were only too happy to accept von Neumann’s proof.
So much so that one philosopher’s protestations were lost to the world. Grete Hermann was a German philosopher, and “ the first and only female doctoral student” of Emmy Noether, a formidable mathematician whose work underpins much of modern physics. Hermann straddled the worlds of philosophy and mathematics with ease. In 1935, she published a paper in a German journal in which she showed that von Neumann’s proof was incorrect. “ A thorough examination of the proof of von Neumann reveals . . . that in his argumentation he makes an assumption which is equivalent to the statement he wants to prove,” she wrote. “Therefore, the proof is circular.”
Even Einstein, around 1938, is reported to have said of the assumption Hermann identified: “ Why should we believe in that?” Einstein, of course, was increasingly being thought of as a curmudgeonly old man who was holding on to his precious ideas of realism, locality, and at times even determinism. Though, to be fair to Einstein, the lack of determinism did not overly bother him. The overused quote of his in popular culture, that “God does not play dice with the world,” misrepresents his stand on the issue. He certainly did, during the early 1920s, express concerns about the indeterminate nature of the quantum world, saying that he found the idea “intolerable,” and if it were true, he “ would rather be a cobbler, or even an employee of a gaming house, than a physicist.” But as quantum mechanics matured, Einstein backed off from his disavowal of indeterminism. It was an aspect of reality he was willing to accept. Not so with anti-realism and nonlocality. In any case, it was easy for the younger crowd to be dismissive of Einstein’s views as he grew older.
The reasons why Hermann’s work never gained widespread attention are less clear. Publishing in an obscure German philosophy journal didn’t help. But that’s not the entire explanation, since Heisenberg and his colleagues were aware of her work. Maybe, swayed by their own ideas, they overlooked the implications of Hermann’s claims. Political affiliations supposedly played a part. Or maybe it was the sexism of the time, argues philosopher Patricia Shipley, but adds, “ If that had something to do with it, I don’t think it was the primary reason, it could have been a secondary reason.”
It was David Bohm who, in 1952, a year after he reworked Einstein’s EPR argument into a simpler thought experiment, implicitly undermined von Neumann’s proof by constructing a hidden variable theory. Decades later, John Bell would say, “ In 1952, I saw the impossible done,” referring to Bohm’s formulation that went against von Neumann’s impossibility proof.
In an interview with Omni magazine in 1988, Bell was scathing: “ The von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It’s not just flawed, it’s silly. If you look at the assumptions made, it does not hold up for a moment. It’s the work of a mathematician, and he makes assumptions that have a mathematical symmetry to them. When you translate them into terms of physical disposition, they’re nonsense . . . The proof of von Neumann is not merely false but foolish. ”
Unimpressed by von Neumann’s proof, but inspired by Bohm and Einstein, Bell saw a way to turn the EPR argument into a test of quantum mechanics. The result was his 1964 paper, with his eponymous theorem.
Here’s one description of an experiment based on Bell’s theorem. It’s a slight variation of Bohm’s EPR thought experiment but is closer in spirit to what experimentalists like Aspect actually do. It involves photons of light and a property called polarization.
We saw earlier that light is an electromagnetic wave, so it’s got an oscillating electric field and an oscillating magnetic field. Polarization has to do with the plane in which the electric field is vibrating relative to the direction in which the light is traveling. For example, if light is moving along the X direction (again, left to right on the page), then the electric field could be oscillating in the X-Y plane (up-down). If so, the light is said to be vertically polarized. If the electric field is vibrating in the X-Z plane (in-out), the light is horizontally polarized. But those are not the only allowed values: the electric field can vibrate in any plane that’s at an arbitrary angle to the vertical—this is the so-called angle of polarization. Also, the angle of polarization can hold steady as the light travels, or it can keep changing. Individual photons of light, which are pulses of electromagnetic waves, are also polarized.
Imagine now a source that spits out two photons entangled in their polarization that start moving away from each other toward two observers, Alice and Bob. Alice does one of two measurements on the photon: she checks to see whether the photon is polarized either in the A direction or in the B direction. Quantum mechanics tells us that for each type of measurement, she’ll get either a YES or a NO for an answer. Similarly, Bob checks to see if his photon is polarized in one of two directions of his choosing, say, C or D. They repeat this for many, many pairs of photons that come from the source.
Crucially, for each photon pair, Alice and Bob make their measurements independently of each other: neither knows the direction the other is choosing for the measurement.
Now, if the photons that leave the source are not entangled, the outcomes of measurements done by Alice will have no correlation with the outcomes of measurements done by Bob, beyond what’s expected by random chance.
But we know that the photons are entangled and quantum mechanics says they are described by the same wavefunction (as far as their polarization is concerned). So, for a given entangled pair of photons, if Alice were to measure her photon’s polarization in some direction and get an answer of YES, then we can predict with certainty that if Bob measures his photon in the same direction, he’ll get an answer of NO, and vice versa.
Here’s where Bell’s theorem comes in. For measurements in which the polarization directions used by Alice and Bob are not the same, Bell calculated the amount of correlation that one can expect if Einstein was correct in his assertion that there must be a hidden variable theory that underpins quantum mechanics and also obeys the laws of locality. The correlation is a measure of how many times Alice and Bob would have got contradictory answers.
Bell showed that if Einstein is correct, the correlation has to be less than or equal to a certain amount (hence it’s called the Bell inequality test). More specifically, Bell showed that if quantum mechanics is correct and the measurement of a photon’s polarization by Alice does instantly influence the state of Bob’s photon (and vice versa), then the amount of correlation should exceed that threshold, thus violating the inequality. If so, the quantum world would be manifestly nonlocal.
Soon after Bell published his theorem, experimentalists started testing the inequality. These were not variations of the double-slit experiment, but their findings would have tremendous import for understanding the double slit’s essential mystery. Among the forerunners who did such Bell experiments were, most notably, Stuart Freedman and John Clauser at the University of California, Berkeley, Richard Holt and Francis Pipkin at Harvard University, and Edward Fry and Randall Thompson at Texas A&M University. By 1976, a total of seven such experiments had been done, and while two of these experiments disagreed with quantum mechanics (in that they did not violate the Bell inequality), the consensus was that quantum mechanics was correct. The world, at its most fundamental, seemed nonlocal.
It was then that a young Aspect came into the picture. He realized that the i
deal experiment as imagined by Bell had yet to be done using single pairs of entangled photons in such a way that the measurements on each pair of photons were space-like separated (so that there was no way that nature could, through some unknown mechanism, let Alice and Bob know of each other’s measurement settings any faster than the speed of light). This meant choosing the settings for the measurement devices—the direction in which to measure the polarization (A or B for Alice, C or D for Bob)—on the fly at either end. The settings, literally, had to be chosen while the photons were in flight from the source to the detectors.
The other challenge was “to build a source of entangled photons which would be able to deliver enough pairs of entangled photons per second,” Aspect told me. “At the end, any experiment boils down to the signal-to-noise ratio.”
As mentioned earlier, Aspect succeeded in building such a source (it was the technology he’d later use for the single photon double-slit experiment). “It took me five years. By 1980, I had a fantastic source of entangled photons. It was by far the best source of entangled photons in the world,” he said. “What Clauser would do in one day, what Fry would do in one hour, I could do in one minute.”
With the mass of statistics and the space-like separation between Alice’s and Bob’s measurements, Aspect was able to show—unequivocally—that the Bell inequality is violated by quantum mechanics. There remained subtle, nitpicky ways in which Alice’s measurements could influence Bob’s device and vice versa, but those were for the purists. For most physicists, Aspect’s experiment had sealed the deal. The experiment made Aspect a star of the lecture circuit (and brought him in touch with Feynman). “It allowed me to propagate the idea that Bell’s theorem was really something very important, and that yes, Bell’s inequalities are violated, so there is something in entanglement which goes beyond all our ideas of how the world works,” Aspect said.
That something is nonlocality. This was a setback for Einstein’s hope for a local, realistic hidden variable theory. He never lived to see the results of these experiments, and one can only wonder how he’d react to the growing realization among many followers of standard quantum mechanics that reality is nonlocal. He’d write to Max Born in a letter dated March 3, 1947, “ I cannot seriously believe in it [quantum theory] because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance .” Einstein died in 1955.
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Under the gaze of the tall Nyamwezi figures, in his apartment overlooking one of New York’s greenest squares, Tim Maudlin explained why entanglement and nonlocality make the double-slit experiment even more intriguing than mere wave-particle duality. With his hands he mimed the wavefunction splitting into two parts, one going through one slit and the other through the second slit. These two parts, as they spread out from each slit, evolve independently and eventually interfere. To calculate the probability of finding the particle at some location away from the two slits, you have to take into account a linear superposition of these two wavefunctions. Say the combined wavefunction hits a photographic plate. The particle appears somewhere on that plate: it gets localized. But at all the other locations on the photographic plate where the particle had a nonzero probability of existing, nothing happens. These are simultaneous events and nonlocal.
“How puzzling is that?” said Maudlin.
Do this for particle after particle, and an interference pattern emerges on the photographic plate. The standard analysis of the double-slit experiment usually highlights the appearance of this pattern as emblematic of the mystery of quantum mechanics. In one sense, it undoubtedly is. Each spot that the particle makes on a photographic plate is indicative of both something delocalized—the wavefunction?—going through both slits, and the nonlocal events that result in the particle seemingly appearing at one location on the photographic plate, and simultaneously disappearing from everywhere else.
But to Maudlin, the mystery of the double slit is even more pronounced when one tries to detect which slit the particle goes through. The interference pattern goes away. But why? It’s because the system being used to detect the particle as it goes through the double slit becomes entangled with the particle. “Schrödinger said that what was really new about quantum mechanics was entanglement,” said Maudlin. “And so from that point of view, the really [surprising] quantum mechanical effect is the disappearance of the interference.”
The double-slit experiment doesn’t merely embody wave-particle duality, the “central mystery,” as Feynman said; it incorporates entanglement too. Once physicists began appreciating this, it made possible a new wave of double-slit experiments, each probing deeper into the mysteries of the quantum world. It made possible the delayed-choice quantum eraser experiment.
5
TO ERASE OR NOT TO ERASE
Mountaintop Experiments Take Us to the Edge
These experiments are a magnificent affront to our conventional notions of space and time. Something that takes place long after and far away from something else nevertheless is vital to our description of that something else. By any classical—commonsense—reckoning, that’s, well, crazy. Of course, that’s the point: classical reckoning is the wrong kind of reckoning to use in a quantum universe.
—Brian Greene
E xperimental quantum physicists prefer lab benches and tightly controlled environments. So it’s highly unusual that some of the most intriguing experiments in quantum mechanics have been done atop mountains in the Canary Islands, an archipelago just off the coast of northwestern Africa. On a clear day, from the summit of Roque de los Muchachos, the 2,400-meter-high mountain on the small island of La Palma, one can see straight across the blue waters of the Atlantic Ocean to the tops of the volcanic mountains on Tenerife, the archipelago’s biggest island, about 144 kilometers away. The experiments, however, have to be done after the sun has set and the moon is still below the horizon, with only the Milky Way spread across the night sky. The foreboding darkness is essential, for the experiments involve sending single photons toward Tenerife’s Mount Teide, in the shadow of which a telescope has its sights trained on the photon source at La Palma.
The driving force behind these experiments is the Austrian physicist Anton Zeilinger. He and Alain Aspect are compatriots. Both forged their reputations as clear-thinking experimentalists at about the same time (and were recognized for their efforts in 2010, when they won, along with John Clauser, the Wolf Prize in Physics). But Zeilinger and Aspect couldn’t be further apart when it comes to interpreting quantum physics. Aspect, as we saw in the previous chapter, leans toward being a realist in the mold of Einstein. Zeilinger takes after Bohr.
“All quantum mechanics gives us is probability distributions for possible measurement results,” he told me. Their tests of Bell’s inequality (Zeilinger’s team did more sophisticated versions of Aspect’s pioneering experiment) have shown that there is no local hidden reality that quantum mechanics is failing to capture. The probabilities one observes, in the Copenhagen view, don’t seem to be the outcome of lack of information the way probabilities of outcomes in classical physics of, say, a throw of dice are the result of incomplete information. The Copenhagen followers regard probabilities as intrinsic to quantum mechanics.
“And that is amazing,” said Zeilinger when I met him at his office on Boltzmanngasse in Vienna, Austria, a few days after I met Aspect in Paris. Zeilinger’s office is a short walk from the Donaukanal, a waterway of the river Danube. The region reeks of history. There are, of course, the street names: Boltzmanngasse for Ludwig Boltzmann, a stalwart of late-nineteenth-century physics and a key figure behind the development of the kinetic theory of gases and statistical mechanics, both of which leaned heavily on probability theory. A few doors away from Zeilinger’s building is the Erwin Schrödinger International Institute for Mathematics and Physics, which, before it moved to Boltzmanngasse in 1996, was housed in Schrödinger’s home a few hundred meters away on Pasteu
rgasse, a street named after Louis Pasteur. If the influence of science, especially physics and mathematics, is overwhelming, there are the Sigmund Freud and the Strauss museums, each about a ten-minute walk away.
And so it was that in a building on a street named after a man who put probabilities into classical physics, Zeilinger expressed wonderment at probability’s role in quantum physics. “How can that be? How can we just have probability distributions and nothing behind it?”
Then in the very next breath, he said, “The probabilities are the reality we have. There is nothing behind it. The probability is not about a hidden reality . . . full stop.” He added he’s probably a “non-realist” but said he hates labels. “They are silly categories,” he said.
But despite going against Einstein’s views, Zeilinger professed enormous respect for his impact on quantum physics. “Sometimes people belittle Einstein’s contribution, which is wrong,” said Zeilinger. Einstein, more often than not, is recalled as raising concerns about aspects of quantum mechanics that did not make, well, classical sense. But Einstein did more than that. “He pointed the finger at these things not because as some people say he did not understand quantum mechanics,” said Zeilinger, but because he understood it very well. Zeilinger mused about what Einstein would have made of their experiments. “I’d give a lot to hear his comments about this situation,” he said. With a light laugh, he said he’d ask Einstein, “You know our results, what do you say?”
Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality Page 9