Fundamental to Einstein and company’s reasoning was that quantum objects carried with them—on their backs, as it were—complete sets of definite properties at all times. Think again of that trusty billiard ball: it has a definite value of position and a definite value of momentum at any given moment, even if we choose to measure only one of those properties at a time. Einstein assumed the same must be true of electrons, photons, and the rest of the furniture of the microworld. Bohr, in a hurried response to the EPR paper, argued that it was wrong to assume that particle B had a real value for position all along, prior to any effort to measure it. Quantum objects, in his view, simply did not possess sharp values for all properties at all times. Such values emerged during the act of measurement, and even Einstein had agreed that no device could directly measure a particle’s position and momentum at the same time. Most physicists seemed content with Bohr’s riposte—or, more likely, they were simply relieved that someone else had responded to Einstein’s deep challenge.8
Bohr’s response never satisfied Einstein, however; nor did it satisfy John Bell. Bell realized that the intuition behind Einstein’s famous thought experiment—the reason Einstein considered it so damning for quantum mechanics—concerned “locality.” To Einstein, it was axiomatic that something that happens in one region of space and time should not be able to affect something happening in a distant region—more distant, say, than light could have traveled in the intervening time. As the EPR authors put it, “since at the time of measurement the two systems [particles A and B] no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system.” Yet Bohr’s response suggested something else entirely: the decision to conduct a measurement on particle A (either position or momentum) would instantaneously change the properties ascribed to the faraway particle B. Measure particle A’s position, for example, and—bam!—particle B would be in a state of well-defined position. Or measure particle A’s momentum, and—zap!—particle B would be in a state of well-defined momentum. Late in life, Bohr’s line still rankled Einstein. “My instinct for physics bristles at this,” Einstein wrote to a friend in March 1948. “Spooky actions at a distance,” he huffed.9
Fresh from his wrangles with Jauch, Bell returned to EPR’s thought experiment. He wondered whether such “spooky actions at a distance” were endemic to quantum mechanics, or just one possible interpretation among many. Might some kind of hidden variable approach reproduce all the quantitative predictions of quantum theory, while still satisfying Einstein’s (and Bell’s) intuition about locality? He focused on a variation of EPR’s setup, introduced by David Bohm in his 1951 textbook on quantum mechanics. Bohm had suggested swapping the values of the particles’ spins along the x- and y-axes for position and momentum.10
“Spin” is a curious property that many quantum particles possess; its discovery in the mid-1920s added a cornerstone to the emerging edifice of quantum mechanics. Quantum spin is a discrete amount of angular momentum—that is, the tendency to rotate around a given direction in space. Of course many large-scale objects possess angular momentum, too: think of the planet Earth spinning around its axis to change night into day. Spin in the microworld, however, has a few quirks. For one thing, whereas large objects like the Earth can spin, in principle, at any rate whatsoever, quantum particles possess fixed amounts of it: either no spin at all, or one-half unit, or one whole unit, or three-halves units, and so on. The units are determined by a universal constant of nature known as Planck’s constant, ubiquitous throughout the quantum realm. The particles that make up ordinary matter, such as electrons, protons, and neutrons, each possess one-half unit of spin; photons, or quanta of light, possess one whole unit of spin.11
In a further break from ordinary angular momentum, quantum spin can only be oriented in certain ways. A spin one-half particle, for example, can exist in only one of two states: either spin “up” or spin “down” with respect to a given direction in space. The two states become manifest when a stream of particles passes through a magnetic field: spin-up particles will be deflected upward, away from their previous direction of flight, while spin-down particles will be deflected downward. Choose some direction along which to align the magnets—say, the z-axis—and the spin of any electron will only ever be found to be up or down; no electron will ever be measured as three-quarters “up” along that direction. Now rotate the magnets, so that the magnetic field is pointing along some different direction. Send a new batch of electrons through; once again you will only find spin up or spin down along that new direction. For spin one-half particles like electrons, the spin along a given direction is always either +1 (up) or –1 (down), nothing in between.12 (Fig. 2.1.)
FIGURE 2.1. Device for measuring quantum particles’ spin. Spin one-half particles, such as electrons, emerge from the source on the left and travel through the magnetic field, which points up from the north pole, N, of the magnet toward the south pole, S. Particles with spin up will be deflected upward from the original direction of flight and collect in one region of the collecting screen (or photographic plate); particles with spin down will be deflected downward. (Illustration by Alex Wellerstein.)
No matter which way the magnets are aligned, moreover, one-half of the incoming electrons will be deflected upward and one-half downward. In fact, you could replace the collecting screen (such as a photographic plate) downstream of the magnets with two Geiger counters, positioned where the spin-up and spin-down particles get deflected. Then tune down the intensity of the source so that only one particle gets shot out at a time. For any given run, only one Geiger counter will click: either the upper one (indicating passage of a spin-up particle) or the lower one (indicating spin down). Each particle has a fifty-fifty chance of being measured as spin up or spin down; the sequence of clicks would be a random series of +1s (upper counter) and –1s (lower counter), averaging out over many runs to an equal number of clicks from each detector. Neither quantum theory nor any other scheme has yet produced a successful means of predicting in advance whether a given particle will be measured as spin up or spin down; only the probabilities for a large number of runs can be computed.
Bell realized that Bohm’s variation of the EPR thought experiment, involving particles’ spins, offered two main advantages over EPR’s original version. First, the measurements always boiled down to either a +1 or a –1; no fuzzy continuum of values to worry about, as there would be when measuring position or momentum. Second, physicists had accumulated decades of experience building real machines that could manipulate and measure particles’ spin; as far as thought experiments went, this one could be grounded on some well-earned confidence. And so Bell began to analyze the spin-based EPR arrangement. Because the particles emerged in a special way—spat out from a source that had zero spin before and after they were disgorged—the total spin of the two particles together likewise had to be zero. When measured along the same direction, therefore, their spins should always show perfect correlation: if A’s spin were up then B’s must be down, and vice versa. Back in the early days of quantum mechanics, Erwin Schrödinger had termed such perfect correlations “entanglement.”13
Bell demonstrated that a hidden-variables model that satisfied locality—in which the properties of A remained unaffected by what measurements were conducted on B—could easily reproduce the perfect correlation when A’s and B’s spins were measured along the same direction. At root, this meant imagining that each particle carried with it a definite value of spin along any given direction, even if most of those values remained hidden from view. The spin values were considered to be properties of the particles themselves; they existed independent of and prior to any effort to measure them, just as Einstein would have wished.
Next Bell considered other possible arrangements. One could choose to measure a particle’s spin along any direction: the z-axis, the y-axis, or any angle in between. All one had to do was rotate the magnets between which the particle passed. W
hat if one measured A’s spin along the z-axis and B’s spin along some other direction? (Fig. 2.2.) Bell homed in on the expected correlations of spin measurements when shooting pairs of particles through the device, while the detectors on either side were oriented at various angles. He considered detectors that had two settings, or directions along which spin could be measured. To keep track of all the possible combinations, he labeled the settings on the left-hand detector—which would measure the spin of particle A—as a and a': a for when the left-hand detector was oriented along the z-axis, and a' for when that detector was oriented along its other direction. Same for the right-hand detector, toward which particle B careened: b when the right-hand detector was oriented along the z-axis, and b' when it was oriented along its other direction. (Bell took the settings a' and b' to lie in the same direction: when the detectors were set to a' and b', every pair of particles would be measured as having opposite spin; same for when both detectors were set to a and b.)
FIGURE 2.2. Bell’s updated thought experiment, based on Bohm’s version of the EPR setup. A source shoots out pairs of particles, A and B. Each detector has two directions along which it can measure a particle’s spin, corresponding to the orientation of the magnets used to separate particles with spin up from those with spin down. As shown here, the apparatus is set to measure the spin of particle A along one direction (setting a) and the spin of particle B along a different direction (setting b' ). (Illustration by Alex Wellerstein.)
Bell labeled the outcomes of each of these measurements. He denoted the measured outcome of the spin of particle A when the left-hand detector was in setting a as A, and the outcome when the left-hand detector was set to a' as A'; similarly for B and B' for the measurements on particle B. All of these measurement outcomes—A, A', B, and B'—were just plain numbers. In fact, they were particularly simple ones: because every spin measurement, along any direction, could only ever result in spin up or spin down, A, A', B, and B' could only ever equal +1 or –1. Bell could then consider various combinations of measurements, such as AB, the product of outcomes when the left-hand detector was set to a and the right-hand detector to b; or AB', which arose when the left-hand detector was set to a and the right-hand detector to b'. Since each measurement outcome (A, A', B, B') could only equal +1 or –1, the pairs—AB or AB', and so on—would likewise just equal +1 or –1. One could then consider a particular combination, S, built from all the various correlations that could arise:
S = AB – A'B+AB'+A'B'=(A–A' )B+(A+A' ) B'
One of the terms in parentheses would always vanish, and the other would always equal +2 or –2. Perhaps in one instance A = +1 and A' = +1; then (A – A' ) = 0, and (A + A' ) = 2. Or it could be that A = –1 and A' = +1, so that (A – A' ) = –2 and (A + A' ) = 0. Since B and B' always equal +1 or –1, the combination, S, must always equal +2 or –2; no other value could ever arise. Bell imagined emitting a large number of particle pairs from the source, one pair at a time, and recording the measured outcomes at each detector (noting carefully the settings at each detector for each particular run). After many pairs of particles had been measured, one would expect to find the average value for S, Saverage, to fall within the range –2 ≤ Saverage ≤ +2: sometimes S would equal +2 and other times –2, so that the average of large numbers of runs should give some value in between.14
So far, so good. But Bell wasn’t finished yet. As he demonstrated next, quantum mechanics made unambiguous predictions for the probabilities of various correlations between the spins of particles A and B as one varied the direction along which they were measured. For various choices of the angle between detector settings a and b' (or, equivalently, between settings a' and b), quantum mechanics predicted clear violations of the innocuous-looking inequality, –2 ≤ S ≤ +2. In fact, for judicious choices of angle, the quantum predictions exceeded this bound by a sizable amount—more than 40 percent. In effect, quantum mechanics predicted that particles A and B should be more strongly correlated than the bound on S would allow. (Fig. 2.3.)
FIGURE 2.3. Predicted values for the quantity S, made up of combinations of spin measurements on particles A and B along various directions. The horizontal axis shows the angle between detector settings a and b' (or, equivalently, between a' and b). As Bell demonstrated, the assumption that particles A and B carried definite values for spin along each direction prior to measurement—as Einstein and his collaborators had urged—limited S to lie between +2 and –2. Yet the quantum-mechanical prediction for the correlation violated that bound by more than 40 percent for certain choices of angle. (Illustration by Alex Wellerstein, based on Aspect [2002], 130.)
Using only a few lines of algebra, Bell thus proved that no local hidden-variables theory could ever reproduce the same degree of correlations as one varied the angles between detectors. The result has come to be known as “Bell’s theorem.” Simply assuming that each particle carried a full set of definite values on its own, prior to measurement—even if most of those values remained hidden from view—necessarily clashed with quantum theory. Nonlocality was indeed endemic to quantum mechanics, Bell had shown: somehow, the outcome of the measurement on particle B depended on the measured outcome on particle A, even if the two particles were separated by huge distances at the time those measurements were made. Any effort to treat the particles (or measurements made upon them) as independent, subject only to local influences, necessarily led to predictions different from those of quantum mechanics. Here was what Bell had been groping for, on and off since his student days: some quantitative means of distinguishing Bohr’s interpretation of quantum mechanics from other coherent, self-consistent possibilities. The problem—entanglement versus locality—was amenable to experimental test. In his bones he hoped locality would win.15
In the years since Bell formulated his theorem, many physicists (Bell included) have tried to articulate what the violation of his inequality would mean, at a deep level, about the structure of the microworld. Most prosaically, entanglement suggests that on the smallest scales of matter, the whole is more than the sum of its parts. Put another way: one could know everything there is to know about a quantum system (particles A + B), and yet know nothing definite about either piece separately. As one expert in the field has written, entangled quantum systems are not even “divisible by thought”: our natural inclination to analyze systems into subsystems, and to build up knowledge of the whole from careful study of its parts, grinds to a halt in the quantum domain.16
Physicists have gone to heroic lengths to translate quantum nonlocality into everyday terms. The literature is now full of stories about boxes that flash with red and green lights; disheveled physicists who stroll down the street with mismatched socks; clever Sherlock Holmes–inspired scenarios involving quantum robbers; even an elaborate tale of a baker, two long conveyor belts, and pairs of soufflés that may or may not rise.17 My favorite comes from a “quantum-mechanical engineer” at MIT, Seth Lloyd. Imagine twins, Lloyd instructs us, separated a great distance apart. One steps into a bar in Cambridge, Massachusetts, just as her brother steps into a bar in Cambridge, England. Imagine further (and this may be the most difficult part) that neither twin has a cell phone or any other device with which to communicate back and forth. No matter what each bartender asks them, they will give opposite answers. “Beer or whiskey?” The Massachusetts twin might respond either way, with equal likelihood; but no matter which choice she makes, her twin brother an ocean away will respond with the opposite choice. (It’s not that either twin has a decided preference; after many trips to their respective bars, they each wind up ordering beer and whiskey equally often.) The bartenders could equally well have asked, “Bottled beer or draft?” or “Red wine or white?” Ask any question—even a question that no one had decided to ask until long after the twins had traveled far, far away from each other—and you will always receive polar opposite responses. Somehow one twin always “knows” how to answer, even though no information could have traveled between them, in jus
t such a way as to ensure the long-distance correlation.18
From today’s vantage point, Bell’s theorem is of unparalleled significance. His proof that quantum mechanics necessarily implied nonlocality—that a measurement of particle A would instantaneously affect particle B, even if they were a galaxy apart—dramatized the philosophical stakes involved when trying to make sense of quantum reality. Bell’s short article has accumulated more than 3200 citations in the professional scientific literature, an astonishing level of interest rivaled by roughly 1 out of every 10,000 physics papers ever published. Today Bell’s theorem, and the entangled states at its core, is the centerpiece of everything from quantum computing, to quantum encryption, to quantum teleportation. (The special beams of light at the heart of the 2004 money transfer in Vienna consisted of entangled pairs of photons.) Without question, physicists, philosophers, and historians now see Bell’s theorem, entanglement, and nonlocality as among the most important developments in quantum theory. As authors of a recent textbook put it, Bell’s theorem and entanglement have become “a fundamentally new resource in the world that goes essentially beyond classical resources; iron to the classical world’s bronze age.”19 (Fig. 2.4.)
How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival Page 6