The Fabric of the Cosmos: Space, Time, and the Texture of Reality - Brian Greene (2004)


Chapter 4. Entangling Space


To accept special and general relativity is to abandon Newtonian absolute space and absolute time. While it’s not easy, you can train your mind to do this. Whenever you move around, imagine your now shifting away from the nows experienced by all others not moving with you. While you are driving along a highway, imagine your watch ticking away at a different rate compared with timepieces in the homes you are speeding past. While you are gazing out from a mountaintop, imagine that because of the warping of spacetime, time passes more quickly for you than for those subject to stronger gravity on the ground far below. I say “imagine” because in ordinary circumstances such as these, the effects of relativity are so tiny that they go completely unnoticed. Everyday experience thus fails to reveal how the universe really works, and that’s why a hundred years after Einstein, almost no one, not even professional physicists, feels relativity in their bones. This isn’t surprising; one is hard pressed to find the survival advantage offered by a solid grasp of relativity. Newton’s flawed conceptions of absolute space and absolute time work wonderfully well at the slow speeds and moderate gravity we encounter in daily life, so our senses are under no evolutionary pressure to develop relativistic acumen. Deep awareness and true understanding therefore require that we diligently use our intellect to fill in the gaps left by our senses.

While relativity represented a monumental break with traditional ideas about the universe, between 1900 and 1930 another revolution was also turning physics upside down. It started at the turn of the twentieth century with a couple of papers on properties of radiation, one by Max Planck and the other by Einstein; these, after three decades of intense research, led to the formulation of quantum mechanics. As with relativity, whose effects become significant under extremes of speed or gravity, the new physics of quantum mechanics reveals itself abundantly only in another extreme situation: the realm of the extremely tiny. But there is a sharp distinction between the upheavals of relativity and those of quantum mechanics. The weirdness of relativity arises because our personal experience of space and time differs from the experience of others. It is a weirdness born of comparison. We are forced to concede that our view of reality is but one among many—an infinite number, in fact—which all fit together within the seamless whole of spacetime.

Quantum mechanics is different. Its weirdness is evident without comparison. It is harder to train your mind to have quantum mechanical intuition, because quantum mechanics shatters our own personal, individual conception of reality.

The World According to the Quantum

Every age develops its stories or metaphors for how the universe was conceived and structured. According to an ancient Indian creation myth, the universe was created when the gods dismembered the primordial giant Purusa, whose head became the sky, whose feet became the earth, and whose breath became the wind. To Aristotle, the universe was a collection of fifty-five concentric crystalline spheres, the outermost being heaven, surrounding those of the planets, earth and its elements, and finally the seven circles of hell.1 With Newton and his precise, deterministic mathematical formulation of motion, the description changed again. The universe was likened to an enormous, grand clockwork: after being wound and set into its initial state, the clockwork universe ticks from one moment to the next with complete regularity and predictability.

Special and general relativity pointed out important subtleties of the clockwork metaphor: there is no single, preferred, universal clock; there is no consensus on what constitutes a moment, what constitutes a now. Even so, you can still tell a clockworklike story about the evolving universe. The clock is your clock. The story is your story. But the universe unfolds with the same regularity and predictability as in the Newtonian framework. If by some means you know the state of the universe right now—if you know where every particle is and how fast and in what direction each is moving—then, Newton and Einstein agree, you can, in principle, use the laws of physics to predict everything about the universe arbitrarily far into the future or to figure out what it was like arbitrarily far into the past.2

Quantum mechanics breaks with this tradition. We can’t ever know the exact location and exact velocity of even a single particle. We can’t predict with total certainty the outcome of even the simplest of experiments, let alone the evolution of the entire cosmos. Quantum mechanics shows that the best we can ever do is predict the probability that an experiment will turn out this way or that. And as quantum mechanics has been verified through decades of fantastically accurate experiments, the Newtonian cosmic clock, even with its Einsteinian updating, is an untenable metaphor; it is demonstrably not how the world works.

But the break with the past is yet more complete. Even though Newton’s and Einstein’s theories differ sharply on the nature of space and time, they do agree on certain basic facts, certain truths that appear to be self-evident. If there is space between two objects—if there are two birds in the sky and one is way off to your right and the other is way off to your left—we can and do consider the two objects to be independent. We regard them as separate and distinct entities. Space, whatever it is fundamentally, provides the medium that separates and distinguishes one object from another. That is what space does. Things occupying different locations in space are different things. Moreover, in order for one object to influence another, it must in some way negotiate the space that separates them. One bird can fly to the other, traversing the space between them, and then peck or nudge its companion. One person can influence another by shooting a slingshot, causing a pebble to traverse the space between them, or by yelling, causing a domino effect of bouncing air molecules, one jostling the next until some bang into the recipient’s eardrum. Being yet more sophisticated, one can exert influence on another by firing a laser, causing an electromagnetic wave—a beam of light—to traverse the intervening space; or, being more ambitious (like the extraterrestrial pranksters of last chapter) one can shake or move a massive body (like the moon) sending a gravitational disturbance speeding from one location to another. To be sure, if we are over here we can influence someone over there, but no matter how we do it, the procedure always involves someone or something traveling from here to there, and only when the someone or something gets there can the influence be exerted.

Physicists call this feature of the universe locality, emphasizing the point that you can directly affect only things that are next to you, that are local. Voodoo contravenes locality, since it involves doing something over here and affecting something over there without the need for anything to travel from here to there, but common experience leads us to think that verifiable, repeatable experiments would confirm locality.3 And most do.

But a class of experiments performed during the last couple of decades has shown that something we do over here (such as measuring certain properties of a particle) can be subtly entwined with something that happens over there (such as the outcome of measuring certain properties of another distant particle), without anything being sent from here to there. While intuitively baffling, this phenomenon fully conforms to the laws of quantum mechanics, and was predicted using quantum mechanics long before the technology existed to do the experiment and observe, remarkably, that the prediction is correct. This sounds like voodoo; Einstein, who was among the first physicists to recognize—and sharply criticize—this possible feature of quantum mechanics, called it “spooky.” But as we shall see, the long-distance links these experiments confirm are extremely delicate and are, in a precise sense, fundamentally beyond our ability to control.

Nevertheless, these results, coming from both theoretical and experimental considerations, strongly support the conclusion that the universe admits interconnections that are not local.4 Something that happens over here can be entwined with something that happens over there even if nothing travels from here to there—and even if there isn’t enough time for anything, even light, to travel between the events. This means that space cannot be thought of as it once was: intervening space, regardless of how much there is, does not ensure that two objects are separate, since quantum mechanics allows an entanglement, a kind of connection, to exist between them. A particle, like one of the countless number that make up you or me, can run but it can’t hide. According to quantum theory and the many experiments that bear out its predictions, the quantum connection between two particles can persist even if they are on opposite sides of the universe. From the standpoint of their entanglement, notwithstanding the many trillions of miles of space between them, it’s as if they are right on top of each other.

Numerous assaults on our conception of reality are emerging from modern physics; we will encounter many in the following chapters. But of those that have been experimentally verified, I find none more mind-boggling than the recent realization that our universe is not local.

The Red and the Blue

To get a feel for the kind of nonlocality emerging from quantum mechanics, imagine that Agent Scully, long overdue for a vacation, retreats to her family’s estate in Provence. Before she’s had time to unpack, the phone rings. It’s Agent Mulder calling from America.

“Did you get the box—the one wrapped in red and blue paper?”

Scully, who has dumped all her mail in a pile by the door, looks over and sees the package. “Mulder, please, I didn’t come all the way to Aix just to deal with another stack of files.”

“No, no, the package is not from me. I got one too, and inside there are these little lightproof titanium boxes, numbered from 1 to 1,000, and a letter saying that you would be receiving an identical package.”

“Yes, so?” Scully slowly responds, beginning to fear that the titanium boxes may somehow wind up cutting her vacation short.

“Well,” Mulder continues, “the letter says that each titanium box contains an alien sphere that will flash red or blue the moment the little door on its side is opened.”

“Mulder, am I supposed to be impressed?”

“Well, not yet, but listen. The letter says that before any given box is opened, the sphere has the capacity to flash either red or blue, and it randomlydecides between the two colors at the moment the door is opened. But here’s the strange part. The letter says that although your boxes work exactly the same way as mine—even though the spheres inside each one of our boxes randomly choose between flashing red or blue—our boxes somehow work in tandem. The letter claims that there is a mysterious connection, so that if there is a blue flash when I open my box 1, you will also find a blue flash when you open your box 1; if I see a red flash when I open box 2, you will also see a red flash in your box 2, and so on.”

“Mulder, I’m really exhausted; let’s let the parlor tricks wait till I get back.”

“Scully, please. I know you’re on vacation, but we can’t just let this go. We’ll only need a few minutes to see if it’s true.”

Reluctantly, Scully realizes that resistance is futile, so she goes along and opens her little boxes. And on comparing the colors that flash inside each box, Scully and Mulder do indeed find the agreement predicted in the letter. Sometimes the sphere in a box flashes red, sometimes blue, but on opening boxes with the same number, Scully and Mulder always see the same color flash. Mulder grows increasingly excited and agitated by the alien spheres but Scully is thoroughly unimpressed.

“Mulder,” Scully sternly says into the phone, “ you really need a vacation. This is silly. Obviously, the sphere inside each of our boxes has been programmed to flash red or it has been programmed to flash blue when the door to its box is opened. And whoever sent us this nonsense programmed our boxes identically so that you and I find the same color flash in boxes with the same number.”

“But no, Scully, the letter says each alien sphere randomly chooses between flashing blue and red when the door is opened, not that the sphere has been preprogrammed to choose one color or the other.”

“Mulder,” Scully sighs, “my explanation makes perfect sense and it fits all the data. What more do you want? And look here, at the bottom of the letter. Here’s the biggest laugh of all. The ‘alien’ small print informs us that not only will opening the door to a box cause the sphere inside to flash, but any other tampering with the box to figure out how it works— for example, if we try to examine the sphere’s color composition or chemical makeup before the door is opened—will also cause it to flash. In other words, we can’t analyze the supposed random selection of red or blue because any such attempt will contaminate the very experiment we are trying to carry out. It’s as if I told you I’m really a blonde, but I become a redhead whenever you or anyone or anything looks at my hair or analyzes it in any way. How could you ever prove me wrong? Your tiny green men are pretty clever—they’ve set things up so their ruse can’t be unmasked. Now, go and play with your little boxes while I enjoy a little peace and quiet.”

It would seem that Scully has this one soundly wrapped up on the side of science. Yet, here’s the thing. Quantum mechanicians—scientists, not aliens—have for nearly eighty years been making claims about how the universe works that closely parallel those described in the letter. And the rub is that there is now strong scientific evidence that a viewpoint along the lines of Mulder’s—not Scully’s—is supported by the data. For instance, according to quantum mechanics, a particle can hang in a state of limbo between having one or another particular property—like an “alien” sphere hovering between flashing red and flashing blue before the door to its box is opened—and only when the particle is looked at (measured) does it randomly commit to one definite property or another. As if this weren’t strange enough, quantum mechanics also predicts that there can be connections between particles, similar to those claimed to exist between the alien spheres. Two particles can be so entwined by quantum effects that their random selection of one property or another is correlated: just as each of the alien spheres chooses randomly between red and blue and yet, somehow, the colors chosen by spheres in boxes with the same number are correlated (both flashing red or both flashing blue), the properties chosen randomly by two particles, even if they are far apart in space, can similarly be aligned perfectly. Roughly speaking, even though the two particles are widely separated, quantum mechanics shows that whatever one particle does, the other will do too.

As a concrete example, if you are wearing a pair of sunglasses, quantum mechanics shows that there is a 50–50 chance that a particular photon—like one that is reflected toward you from the surface of a lake or from an asphalt roadway—will make it through your glare-reducing polarized lenses: when the photon hits the glass, it randomly “chooses” between reflecting back and passing through. The astounding thing is that such a photon can have a partner photon that has sped miles away in the opposite direction and yet, when confronted with the same 50–50 probability of passing through another polarized sunglass lens, will somehow do whatever the initial photon does. Even though each outcome is determined randomly and even though the photons are far apart in space, if one photon passes through, so will the other. This is the kind of nonlocality predicted by quantum mechanics.

Einstein, who was never a great fan of quantum mechanics, was loath to accept that the universe operated according to such bizarre rules. He championed more conventional explanations that did away with the notion that particles randomly select attributes and outcomes when measured. Instead, Einstein argued that if two widely separated particles are observed to share certain attributes, this is not evidence of some mysterious quantum connection instantaneously correlating their properties. Rather, just as Scully argued that the spheres do not randomly choose between red and blue, but instead are programmed to flash one particular color when observed, Einstein claimed that particles do not randomly choose between having one feature or another but, instead, are similarly “programmed” to have one particular, definite feature when suitably measured. The correlation between the behavior of widely separated photons is evidence, Einstein claimed, that the photons were endowed with identical properties when emitted, not that they are subject to some bizarre long-distance quantum entanglement.

For close to five decades, the issue of who was right—Einstein or the supporters of quantum mechanics—was left unresolved because, as we shall see, the debate became much like that between Scully and Mulder: any attempt to disprove the proposed strange quantum mechanical connections and leave intact Einstein’s more conventional view ran afoul of the claim that the experiments themselves would necessarily contaminate the very features they were trying to study. All this changed in the 1960s. With a stunning insight, the Irish physicist John Bell showed that the issue could be settled experimentally, and by the 1980s it was. The most straightforward reading of the data is that Einstein was wrong and there can be strange, weird, and “spooky” quantum connections between things over here and things over there.5

The reasoning behind this conclusion is so subtle that it took physicists more than three decades to appreciate fully. But after covering the essential features of quantum mechanics we will see that the core of the argument reduces to nothing more complex than a Click and Clack puzzler.

Casting a Wave

If you shine a laser pointer on a little piece of black, overexposed 35mm film from which you have scratched away the emulsion in two extremely close and narrow lines, you will see direct evidence that light is a wave. If you’ve never done this, it’s worth a try (you can use many things in place of the film, such as the wire mesh in a fancy coffee plunger). The image you will see when the laser light passes through the slits on the film and hits a screen consists of light and dark bands, as in Figure 4.1, and the explanation for this pattern relies on a basic feature of waves. Water waves are easiest to visualize, so let’s first explain the essential point with waves on a large, placid lake, and then apply our understanding to light.

A water wave disturbs the flat surface of a lake by creating regions where the water level is higher than usual and regions where it is lower than usual. The highest part of a wave is called its peak and the lowest part is called its trough. A typical wave involves a periodic succession: peak followed by trough followed by peak, and so forth. If two waves head toward each other—if, for example, you and I each drop a pebble into the lake at nearby locations, producing outward-moving waves that run into each other—when they cross there results an important effect known as interference, illustrated in Figure 4.2a. When a peak of one wave and a peak of the other cross, the height of the water is even greater, being the sum of the two peak heights. Similarly, when a trough of one wave and a trough of the other cross, the depression in the water is even deeper, being the sum of the two depressions. And here is the most important combination: when a peak of one wave crosses the trough of another, they tend to cancel each other out, as the peak tries to make the water go up while the trough tries to drag it down. If the height of one wave’s peak equals the depth of the other’s trough, there will be perfect cancellation when they cross, so the water at that location will not move at all.


Figure 4.1 Laser light passing through two slits etched on a piece of black film yields an interference pattern on a detector screen, showing that light is a wave.

The same principle explains the pattern that light forms when it passes through the two slits in Figure 4.1. Light is an electromagnetic wave; when it passes through the two slits, it splits into two waves that head toward the screen. Like the two water waves just discussed, the two light waves interfere with each other. When they hit various points on the screen, sometimes both waves are at their peaks, making the screen bright; sometimes both waves are at their troughs, also making it bright; but sometimes one wave is at its peak and the other is at its trough and they cancel, making that point on the screen dark. We illustrate this in Figure 4.2b.

When the wave motion is analyzed in mathematical detail, including the cases of partial cancellations between waves at various stages between peaks and troughs, one can show that the bright and dark spots fill out the bands seen in Figure 4.1. The bright and dark bands are therefore a telltale sign that light is a wave, an issue that had been hotly debated ever since Newton claimed that light is not a wave but instead is made up of a stream of particles (more on this in a moment). Moreover, this analysis applies equally well to any kind of wave (light wave, water wave, sound wave, you name it) and thus, interference patterns provide the metaphorical smoking gun: you know you are dealing with a wave if, when it is forced to pass through two slits of the right size (determined by the distance between the wave’s peaks and troughs), the resulting intensity pattern looks like that in Figure 4.1 (with bright regions representing high intensity and dark regions being low intensity).


Figure 4.2 (aOverlapping water waves produce an interference pattern. (bOverlapping light waves produce an interference pattern.

In 1927, Clinton Davisson and Lester Germer fired a beam of electrons—particulate entities without any apparent connection to waves—at a piece of nickel crystal; the details need not concern us, but what does matter is that this experiment is equivalent to firing a beam of electrons at a barrier with two slits. When the experimenters allowed the electrons that passed through the slits to travel onward to a phosphor screen where their impact location was recorded by a tiny flash (the same kind of flashes responsible for the picture on your television screen), the results were astonishing. Thinking of the electrons as little pellets or bullets, you’d naturally expect their impact positions to line up with the two slits, as in Figure 4.3a. But that’s not what Davisson and Germer found. Their experiment produced data schematically illustrated in Figure 4.3b: the electron impact positions filled out an interference pattern characteristic of waves. Davisson and Germer had found the smoking gun. They had shown that the beam of particulate electrons must, unexpectedly, be some kind of wave.


Figure 4.3 (aClassical physics predicts that electrons fired at a barrier with two slits will produce two bright stripes on a detector. (bQuantum physics predicts, and experiments confirm, that electrons will produce an interference pattern, showing that they embody wavelike features.

Now, you might not think this is particularly surprising. Water is made of H2O molecules, and a water wave arises when many molecules move in a coordinated pattern. One group of H2O molecules goes up in one location, while another group goes down in a nearby location. Perhaps the data illustrated in Figure 4.3 show that electrons, like H2O molecules, sometimes move in concert, creating a wavelike pattern in their overall, macroscopic motion. While at first blush this might seem to be a reasonable suggestion, the actual story is far more unexpected.

We initially imagined that a flood of electrons was fired continuously from the electron gun in Figure 4.3. But we can tune the gun so that it fires fewer and fewer electrons every second; in fact, we can tune it all the way down so that it fires, say, only one electron every ten seconds. With enough patience, we can run this experiment over a long period of time and record the impact position of each individual electron that passes through the slits. Figures 4.4a–4.4c show the resulting cumulative data after an hour, half a day, and a full day. In the 1920s, images like these rocked the foundations of physics. We see that even individual, particulate electrons, moving to the screen independently, separately, one by one, build up the interference pattern characteristic of waves.

This is as if an individual H2O molecule could still embody something akin to a water wave. But how in the world could that be? Wave motion seems to be a collective property that has no meaning when applied to separate, particulate ingredients. If every few minutes individual spectators in the bleachers get up and sit down separately, independently, they are not doing the wave. More than that, wave interference seems to require a wave from here to cross a wave from there. So how can interference be at all relevant to single, individual, particulate ingredients? But somehow, as attested by the interference data in Figure 4.4, even though individual electrons are tiny particles of matter, each and every one also embodies a wavelike character.


Figure 4.4 Electrons fired one by one toward slits build up an interference pattern dot by dot. In (a)–(cwe illustrate the pattern forming over time.

Probability and the Laws of Physics

If an individual electron is also a wave, what is it that is waving? Erwin Schrödinger weighed in with the first guess: maybe the stuff of which electrons are made can be smeared out in space and it’s this smeared electron essence that does the waving. An electron particle, from this point of view, would be a sharp spike in an electron mist. It was quickly realized, though, that this suggestion couldn’t be correct because even a sharply spiked wave shape—such as a giant tidal wave—ultimately spreads out. And if the spiked electron wave were to spread we would expect to find part of a single electron’s electric charge over here or part of its mass over there. But we never do. When we locate an electron, we always find all of its mass and all of its charge concentrated in one tiny, pointlike region. In 1927, Max Born put forward a different suggestion, one that turned out to be the decisive step that forced physics to enter a radically new realm. The wave, he claimed, is not a smeared-out electron, nor is it anything ever previously encountered in science. The wave, Born proposed, is a probability wave.

To understand what this means, picture a snapshot of a water wave that shows regions of high intensity (near the peaks and troughs) and regions of low intensity (near the flatter transition regions between peaks and troughs). The higher the intensity, the greater the potential the water wave has for exerting force on nearby ships or on coastline structures. The probability waves envisioned by Born also have regions of high and low intensity, but the meaning he ascribed to these wave shapes was unexpected: the size of a wave at a given point in space is proportional to the probability that the electron is located at that point in space. Places where the probability wave is large are locations where the electron is most likely to be found. Places where the probability wave is small are locations where the electron is unlikely to be found. And places where the probability wave is zero are locations where the electron will not be found.

Figure 4.5 gives a “snapshot” of a probability wave with the labels emphasizing Born’s probabilistic interpretation. Unlike a photograph of water waves, though, this image could not actually have been made with a camera. No one has ever directly seen a probability wave, and conventional quantum mechanical reasoning says that no one ever will. Instead, we use mathematical equations (developed by Schrödinger, Niels Bohr, Werner Heisenberg, Paul Dirac, and others) to figure out what the probability wave should look like in a given situation. We then test such theoretical calculations by comparing them with experimental results in the following way. After calculating the purported probability wave for the electron in a given experimental setup, we carry out identical versions of the experiment over and over again from scratch, each time recording the measured position of the electron. In contrast to what Newton would have expected, identical experiments and starting conditions do not necessarily lead to identical measurements. Instead, our measurements yield a variety of measured locations. Sometimes we find the electron here, sometimes there, and every so often we find it way over there. If quantum mechanics is right, the number of times we find the electron at a given point should be proportional to the size (actually, the square of the size), at that point, of the probability wave that we calculated. Eight decades of experiments have shown that the predictions of quantum mechanics are confirmed to spectacular precision.


Figure 4.5 The probability wave of a particle, such as an electron, tells us the likelihood of finding the particle at one location or another.

Only a portion of an electron’s probability wave is shown in Figure 4.5: according to quantum mechanics, every probability wave extends throughout all of space, throughout the entire universe.6 In many circumstances, though, a particle’s probability wave quickly drops very close to zero outside some small region, indicating the overwhelming likelihood that the particle is in that region. In such cases, the part of the probability wave left out of Figure 4.5 (the part extending throughout the rest of the universe) looks very much like the part near the edges of the figure: quite flat and near the value zero. Nevertheless, so long as the probability wave somewhere in the Andromeda galaxy has a nonzero value, no matter how small, there is a tiny but genuine—nonzero—chance that the electron could be found there.

Thus, the success of quantum mechanics forces us to accept that the electron, a constituent of matter that we normally envision as occupying a tiny, pointlike region of space, also has a description involving a wave that, to the contrary, is spread through the entire universe. Moreover, according to quantum mechanics this particle-wave fusion holds for all of nature’s constituents, not just electrons: protons are both particlelike and wavelike; neutrons are both particlelike and wavelike, and experiments in the early 1900s even established that light—which demonstrably behaves like a wave, as in Figure 4.1—can also be described in terms of particulate ingredients, the little “bundles of light” called photons mentioned earlier.7 The familiar electromagnetic waves emitted by a hundred-watt bulb, for example, can equally well be described in terms of the bulb’s emitting about a hundred billion billion photons each second. In the quantum world, we’ve learned that everything has both particlelike and wavelike attributes.

Over the last eight decades, the ubiquity and utility of quantum mechanical probability waves to predict and explain experimental results has been established beyond any doubt. Yet there is still no universally agreed-upon way to envision what quantum mechanical probability waves actually are. Whether we should say that an electron’s probability wave is the electron, or that it’s associated with the electron, or that it’s a mathematical device for describing the electron’s motion, or that it’s the embodiment of what we can know about the electron is still debated. What is clear, though, is that through these waves, quantum mechanics injects probability into the laws of physics in a manner that no one had anticipated. Meteorologists use probability to predict the likelihood of rain. Casinos use probability to predict the likelihood you’ll throw snake eyes. But probability plays a role in these examples because we haven’t all of the information necessary to make definitive predictions. According to Newton, if we knew in complete detail the state of the environment (the positions and velocities of every one of its particulate ingredients), we would be able to predict (given sufficient calculational prowess) with certainty whether it will rain at 4:07 p.m. tomorrow; if we knew all the physical details of relevance to a craps game (the precise shape and composition of the dice, their speed and orientation as they left your hand, the composition of the table and its surface, and so on), we would be able to predict with certainty how the dice will land. Since, in practice, we can’t gather all this information (and, even if we could, we do not yet have sufficiently powerful computers to perform the calculations required to make such predictions), we set our sights lower and predict only the probability of a given outcome in the weather or at the casino, making reasonable guesses about the data we don’t have.

The probability introduced by quantum mechanics is of a different, more fundamental character. Regardless of improvements in data collection or in computer power, the best we can ever do, according to quantum mechanics, is predict the probability of this or that outcome. The best we can ever do is predict the probability that an electron, or a proton, or a neutron, or any other of nature’s constituents, will be found here or there. Probability reigns supreme in the microcosmos.

As an example, the explanation quantum mechanics gives for individual electrons, one by one, over time, building up the pattern of light and dark bands in Figure 4.4, is now clear. Each individual electron is described by its probability wave. When an electron is fired, its probability wave flows through both slits. And just as with light waves and water waves, the probability waves emanating from the two slits interfere with each other. At some points on the detector screen the two probability waves reinforce and the resulting intensity is large. At other points the waves partially cancel and the intensity is small. At still other points the peaks and troughs of the probability waves completely cancel and the resulting wave intensity is exactly zero. That is, there are points on the screen where it is very likely an electron will land, points where it is far less likely that it will land, and places where there is no chance at all that an electron will land. Over time, the electrons’ landing positions are distributed according to this probability profile, and hence we get some bright, some dimmer, and some completely dark regions on the screen. Detailed analysis shows that these light and dark regions will look exactly as they do in Figure 4.4.

Einstein and Quantum Mechanics

Because of its inherently probabilistic nature, quantum mechanics differs sharply from any previous fundamental description of the universe, qualitative or quantitative. Since its inception last century, physicists have struggled to mesh this strange and unexpected framework with the common worldview; the struggle is still very much under way. The problem lies in reconciling the macroscopic experience of day-to-day life with the microscopic reality revealed by quantum mechanics. We are used to living in a world that, while admittedly subject to the vagaries of economic or political happenstance, appears stable and reliable at least as far as its physical properties are concerned. You do not worry that the atomic constituents of the air you are now breathing will suddenly disband, leaving you gasping for breath as they manifest their quantum wavelike character by rematerializing, willy-nilly, on the dark side of the moon. And you are right not to fret about this outcome, because according to quantum mechanics the probability of its happening, while not zero, is absurdly small. But what makes the probability so small?

There are two main reasons. First, on a scale set by atoms, the moon is enormously far away. And, as mentioned, in many circumstances (although by no means all), the quantum equations show that a probability wave typically has an appreciable value in some small region of space and quickly drops nearly to zero as you move away from this region (as in Figure 4.5). So the likelihood that even a single electron that you expect to be in the same room as you—such as one of those that you just exhaled—will be found in a moment or two on the dark side of the moon, while not zero, is extremely small. So small, that it makes the probability that you will marry Nicole Kidman or Antonio Banderas seem enormous by comparison. Second, there are a lot of electrons, as well as protons and neutrons, making up the air in your room. The likelihood that all of these particles will do what is extremely unlikely even for one is so small that it’s hardly worth a moment’s thought. It would be like not only marrying your movie-star heartthrob but then also winning every state lottery every week for, well, a length of time that would make the current age of the universe seem a mere cosmic flicker.

This gives some sense of why we do not directly encounter the probabilistic aspects of quantum mechanics in day-to-day life. Nevertheless, because experiments confirm that quantum mechanics does describe fundamental physics, it presents a frontal assault on our basic beliefs as to what constitutes reality. Einstein, in particular, was deeply troubled by the probabilistic character of quantum theory. Physics, he would emphasize again and again, is in the business of determining with certainty what has happened, what is happening, and what will happen in the world around us. Physicists are not bookies, and physics is not the business of calculating odds. But Einstein could not deny that quantum mechanics was enormously successful in explaining and predicting, albeit in a statistical framework, experimental observations of the microworld. And so rather than attempting to show that quantum mechanics was wrong, a task that still looks like a fool’s errand in light of its unparalleled successes, Einstein expended much effort on trying to show that quantum mechanics was not the final word on how the universe works. Even though he could not say what it was, Einstein wanted to convince everyone that there was a deeper and less bizarre description of the universe yet to be found.

Over the course of many years, Einstein mounted a series of ever more sophisticated challenges aimed at revealing gaps in the structure of quantum mechanics. One such challenge, raised in 1927 at the Fifth Physical Conference of the Solvay Institute,8 concerns the fact that even though an electron’s probability wave might look like that in Figure 4.5, whenever we measure the electron’s whereabouts we always find it at one definite position or another. So, Einstein asked, doesn’t that mean that the probability wave is merely a temporary stand-in for a more precise description—one yet to be discovered—that would predict the electron’s position with certainty? After all, if the electron is found at X, doesn’t that mean, in reality, it was at or very near X a moment before the measurement was carried out? And if so, Einstein prodded, doesn’t quantum mechanics’ reliance on the probability wave—a wave that, in this example, says the electron had some probability to have been far from X— reflect the theory’s inadequacy to describe the true underlying reality?

Einstein’s viewpoint is simple and compelling. What could be more natural than to expect a particle to be located at, or, at the very least, near where it’s found a moment later? If that’s the case, a deeper understanding of physics should provide that information and dispense with the coarser framework of probabilities. But the Danish physicist Niels Bohr and his entourage of quantum mechanics defenders disagreed. Such reasoning, they argued, is rooted in conventional thinking, according to which each electron follows a single, definite path as it wanders to and fro. And this thinking is strongly challenged by Figure 4.4, since if each electron did follow one definite path—like the classical image of a bullet fired from a gun—it would be extremely hard to explain the observed interference pattern: what would be interfering with what? Ordinary bullets fired one by one from a single gun certainly can’t interfere with each other, so if electrons did travel like bullets, how would we explain the pattern in Figure 4.4?

Instead, according to Bohr and the Copenhagen interpretation of quantum mechanics he forcefully championed, before one measures the electron’s position there is no sense in even asking where it is. It does not have a definite position. The probability wave encodes the likelihood that the electron, when examined suitably, will be found here or there, and that truly is all that can be said about its position. Period. The electron has a definite position in the usual intuitive sense only at the moment we “look” at it—at the moment when we measure its position—identifying its location with certainty. But before (and after) we do that, all it has are potential positions described by a probability wave that, like any wave, is subject to interference effects. It’s not that the electron has a position and that we don’t know the position before we do our measurement. Rather, contrary to what you’d expect, the electron simply does not have a definite position before the measurement is taken.

This is a radically strange reality. In this view, when we measure the electron’s position we are not measuring an objective, preexisting feature of reality. Rather, the act of measurement is deeply enmeshed in creating the very reality it is measuring. Scaling this up from electrons to everyday life, Einstein quipped, “Do you really believe that the moon is not there unless we are looking at it?” The adherents of quantum mechanics responded with a version of the old saw about a tree falling in a forest: if no one is looking at the moon—if no one is “measuring its location by seeing it”—then there is no way for us to know whether it’s there, so there is no point in asking the question. Einstein found this deeply unsatisfying. It was wildly at odds with his conception of reality; he firmly believed that the moon is there, whether or not anyone is looking. But the quantum stalwarts were unconvinced.

Einstein’s second challenge, raised at the Solvay conference in 1930, followed closely on the first. He described a hypothetical device, which (through a clever combination of a scale, a clock, and a cameralike shutter) seemed to establish that a particle like an electron must have definite features—before it is measured or examined—that quantum mechanics said it couldn’t. The details are not essential but the resolution is particularly ironic. When Bohr learned of Einstein’s challenge, he was knocked back on his heels—at first, he couldn’t see a flaw in Einstein’s argument. Yet, within days, he bounced back and fully refuted Einstein’s claim. And the surprising thing is that the key to Bohr’s response was general relativity! Bohr realized that Einstein had failed to take account of his own discovery that gravity warps time—that a clock ticks at a rate dependent on the gravitational field it experiences. When this complication was included, Einstein was forced to admit that his conclusions fell right in line with orthodox quantum theory.

Even though his objections were shot down, Einstein remained deeply uncomfortable with quantum mechanics. In the following years he kept Bohr and his colleagues on their toes, leveling one new challenge after another. His most potent and far-reaching attack focused on something known as the uncertainty principle, a direct consequence of quantum mechanics, enunciated in 1927 by Werner Heisenberg.

Heisenberg and Uncertainty

The uncertainty principle provides a sharp, quantitative measure of how tightly probability is woven into the fabric of a quantum universe. To understand it, think of the prix-fixe menus in certain Chinese restaurants. Dishes are arranged in two columns, A and B, and if, for example, you order the first dish in column A, you are not allowed to order the first dish in column B; if you order the second dish in column A, you are not allowed to order the second dish in column B, and so forth. In this way, the restaurant has set up a dietary dualism, a culinary complementarity (one, in particular, that is designed to prevent you from piling up the most expensive dishes). On the prix-fixe menu you can have Peking Duck or Lobster Cantonese, but not both.

Heisenberg’s uncertainty principle is similar. It says, roughly speaking, that the physical features of the microscopic realm (particle positions, velocities, energies, angular momenta, and so on) can be divided into two lists, A and B. And as Heisenberg discovered, knowledge of the first feature from list A fundamentally compromises your ability to have knowledge about the first feature from list B; knowledge of the second feature from list A fundamentally compromises your ability to have knowledge of the second feature from list B; and so on. Moreover, like being allowed a dish containing some Peking Duck and some Lobster Cantonese, but only in proportions that add up to the same total price, the more precise your knowledge of a feature from one list, the less precise your knowledge can possibly be about the corresponding feature from the second list. The fundamental inability to determine simultaneously all features from both lists—to determine with certainty all of these features of the microscopic realm—is the uncertainty revealed by Heisenberg’s principle.

As an example, the more precisely you know where a particle is, the less precisely you can possibly know its speed. Similarly, the more precisely you know how fast a particle is moving, the less you can possibly know about where it is. Quantum theory thereby sets up its own duality: you can determine with precision certain physical features of the microscopic realm, but in so doing you eliminate the possibility of precisely determining certain other, complementary features.

To understand why, let’s follow a rough description developed by Heisenberg himself, which, while incomplete in particular ways that we will discuss, does give a useful intuitive picture. When we measure the position of any object, we generally interact with it in some manner. If we search for the light switch in a dark room, we know we have located it when we touch it. If a bat is searching for a field mouse, it bounces sonar off its target and interprets the reflected wave. The most common instance of all is locating something by seeing it—by receiving light that has reflected off the object and entered our eyes. The key point is that these interactions not only affect us but also affect the object whose position is being determined. Even light, when bouncing off an object, gives it a tiny push. Now, for day-to-day objects such as the book in your hand or a clock on the wall, the wispy little push of bouncing light has no noticeable effect. But when it strikes a tiny particle like an electron it can have a big effect: as the light bounces off the electron, it changes the electron’s speed, much as your own speed is affected by a strong, gusty wind that whips around a street corner. In fact, the more precisely you want to identify the electron’s position, the more sharply defined and energetic the light beam must be, yielding an even larger effect on the electron’s motion.

This means that if you measure an electron’s position with high accuracy, you necessarily contaminate your own experiment: the act of precision position measurement disrupts the electron’s velocity. You can therefore know precisely where the electron is, but you cannot also know precisely how fast, at that moment, it was moving. Conversely, you can measure precisely how fast an electron is moving, but in so doing you will contaminate your ability to determine with precision its position. Nature has a built-in limit on the precision with which such complementary features can be determined. And although we are focusing on electrons, the uncertainty principle is completely general: it applies to everything.

In day-to-day life we routinely speak about things like a car passing a particular stop sign (position) while traveling at 90 miles per hour (velocity), blithely specifying these two physical features. In reality, quantum mechanics says that such a statement has no precise meaning since you can’t ever simultaneously measure a definite position and a definite speed. The reason we get away with such incorrect descriptions of the physical world is that on everyday scales the amount of uncertainty involved is tiny and generally goes unnoticed. You see, Heisenberg’s principle does not just declare uncertainty, it also specifies—with complete certainty—the minimum amount of uncertainty in any situation. If we apply his formula to your car’s velocity just as it passes a stop sign whose position is known to within a centimeter, then the uncertainty in speed turns out to be just shy of a billionth of a billionth of a billionth of a billionth of a mile per hour. A state trooper would be fully complying with the laws of quantum physics if he asserted that your speed was between 89.99999999999999999999999999999999999 and 90.00000000000000000000000000000000001 miles per hour as you blew past the stop sign; so much for a possible uncertainty-principle defense. But if we were to replace your massive car with a delicate electron whose position we knew to within a billionth of a meter, then the uncertainty in its speed would be a whopping 100,000 miles per hour. Uncertainty is always present, but it becomes significant only on microscopic scales.

The explanation of uncertainty as arising through the unavoidable disturbance caused by the measurement process has provided physicists with a useful intuitive guide as well as a powerful explanatory framework in certain specific situations. However, it can also be misleading. It may give the impression that uncertainty arises only when we lumbering experimenters meddle with things. This is not true. Uncertainty is built into the wave structure of quantum mechanics and exists whether or not we carry out some clumsy measurement. As an example, take a look at a particularly simple probability wave for a particle, the analog of a gently rolling ocean wave, shown in Figure 4.6. Since the peaks are all uniformly moving to the right, you might guess that this wave describes a particle moving with the velocity of the wave peaks; experiments confirm that supposition. But where is the particle? Since the wave is uniformly spread throughout space, there is no way for us to say the electron is here or there. When measured, it literally could be found anywhere. So, while we know precisely how fast the particle is moving, there is huge uncertainty about its position. And as you see, this conclusion does not depend on our disturbing the particle. We never touched it. Instead, it relies on a basic feature of waves: they can be spread out.

Although the details get more involved, similar reasoning applies to all other wave shapes, so the general lesson is clear. In quantum mechanics, uncertainty just is.


Figure 4.6 A probability wave with a uniform succession of peaks and troughs represents a particle with a definite velocity. But since the peaks and troughs are uniformly spread in space, the particle’s position is completely undetermined. It has an equal likelihood of being anywhere.

Einstein, Uncertainty, and a Question of Reality

An important question, and one that may have occurred to you, is whether the uncertainty principle is a statement about what we can know about reality or whether it is a statement about reality itself. Do objects making up the universe really have a position and a velocity, like our usual classical image of just about everything—a soaring baseball, a jogger on the boardwalk, a sunflower slowly tracking the sun’s flight across the sky—although quantum uncertainty tells us these features of reality are forever beyond our ability to know simultaneously, even in principle? Or does quantum uncertainty break the classical mold completely, telling us that the list of attributes our classical intuition ascribes to reality, a list headed by the positions and velocities of the ingredients making up the world, is misguided? Does quantum uncertainty tell us that, at any given moment, particles simply do not possess a definite position and a definite velocity?

To Bohr, this issue was on par with a Zen koan. Physics addresses only things we can measure. From the standpoint of physics, that is reality. Trying to use physics to analyze a “deeper” reality, one beyond what we can know through measurement, is like asking physics to analyze the sound of one hand clapping. But in 1935, Einstein together with two colleagues, Boris Podolsky and Nathan Rosen, raised this issue in such a forceful and clever way that what had begun as one hand clapping reverberated over fifty years into a thunderclap that heralded a far greater assault on our understanding of reality than even Einstein ever envisioned.

The intent of the Einstein-Podolsky-Rosen paper was to show that quantum mechanics, while undeniably successful at making predictions and explaining data, could not be the final word regarding the physics of the microcosmos. Their strategy was simple, and was based on the issues just raised: they wanted to show that every particle does possess a definite position and a definite velocity at any given instant of time, and thus they wanted to conclude that the uncertainty principle reveals a fundamental limitation of the quantum mechanical approach. If every particle has a position and a velocity, but quantum mechanics cannot deal with these features of reality, then quantum mechanics provides only a partial description of the universe. Quantum mechanics, they intended to show, was therefore an incomplete theory of physical reality and, perhaps, merely a stepping-stone toward a deeper framework waiting to be discovered. In actuality, as we will see, they laid the groundwork for demonstrating something even more dramatic: the nonlocality of the quantum world.

Einstein, Podolsky, and Rosen (EPR) were partly inspired by Heisenberg’s rough explanation of the uncertainty principle: when you measure where something is you necessarily disturb it, thereby contaminating any attempt to simultaneously ascertain its velocity. Although, as we have seen, quantum uncertainty is more general than the “disturbance” explanation indicates, Einstein, Podolsky, and Rosen invented what appeared to be a convincing and clever end run around any source of uncertainty. What if, they suggested, you could perform an indirect measurement of both the position and the velocity of a particle in a manner that never brings you into contact with the particle itself? For instance, using a classical analogy, imagine that Rod and Todd Flanders decide to do some lone wandering in Springfield’s newly formed Nuclear Desert. They start back to back in the desert’s center and agree to walk straight ahead, in opposite directions, at exactly the same prearranged speed. Imagine further that, nine hours later, their father, Ned, returning from his trek up Mount Springfield, catches sight of Rod, runs to him, and desperately asks about Todd’s whereabouts. Well, by that point, Todd is far away, but by questioning and observing Rod, Ned can nevertheless learn much about Todd. If Rod is exactly 45 miles due east of the starting location, Todd must be exactly 45 miles due west of the starting location. If Rod is walking at exactly 5 miles per hour due east, Todd must be walking at exactly 5 miles per hour due west. So even though Todd is some 90 miles away, Ned can determine his position and speed, albeit indirectly.

Einstein and his colleagues applied a similar strategy to the quantum domain. There are well-known physical processes whereby two particles emerge from a common location with properties that are related in somewhat the same way as the motion of Rod and Todd. For example, if an initial single particle should disintegrate into two particles of equal mass that fly off “back-to-back” (like an explosive shooting off two chunks in opposite directions), something that is common in the realm of subatomic particle physics, the velocities of the two constituents will be equal and opposite. Moreover, the positions of the two constituent particles will also be closely related, and for simplicity the particles can be thought of as always being equidistant from their common origin.

An important distinction between the classical example involving Rod and Todd, and the quantum description of the two particles, is that although we can say with certainty that there is a definite relationship between the speeds of the two particles—if one were measured and found to be moving to the left at a given speed, then the other would necessarily be moving to the right at the same speed—we cannot predict the actual numerical value of the speed with which the particles move. Instead, the best we can do is use the laws of quantum physics to predict the probability that any particular speed is the one attained. Similarly, while we can say with certainty that there is a definite relationship between the positions of the particles—if one is measured at a given moment and found to be at some location, the other necessarily is located the same distance from the starting point but in the opposite direction—we cannot predict with certainty the actual location of either particle. Instead, the best we can do is predict the probability that one of the particles is at any chosen location. Thus, while quantum mechanics does not give definitive answers regarding particle speeds or positions, it does, in certain situations, give definitive statements regarding the relationships between the particle speeds and positions.

Einstein, Podolsky, and Rosen sought to exploit these relationships to show that each of the particles actually has a definite position and a definite velocity at every given instant of time. Here’s how: imagine you measure the position of the right-moving particle and in this way learn, indirectly, the position of the left-moving particle. EPR argued that since you have done nothing, absolutely nothing, to the left-moving particle, it must have had this position, and all you have done is determine it, albeit indirectly. They then cleverly pointed out that you could have chosen instead to measure the right-moving particle’s velocity. In that case you would have, indirectly, determined the velocity of the left-moving particle without at all disturbing it. Again, EPR argued that since you would have done nothing, absolutely nothing, to the left-moving particle, it must have had this velocity, and all you would have done is determine it. Putting both together—the measurement that you did and the measurement that you could have done—EPR concluded that the left-moving particle has a definite position and a definite velocity at any given moment.

As this is subtle and crucial, let me say it again. EPR reasoned that nothing in your act of measuring the right-moving particle could possibly have any effect on the left-moving particle, because they are separate and distant entities. The left-moving particle is totally oblivious to what you have done or could have done to the right-moving particle. The particles might be meters, kilometers, or light-years apart when you do your measurement on the right-moving particle, so, in short, the left-moving particle couldn’t care less what you do. Thus, any feature that you actually learn or could in principle learn about the left-moving particle from studying its right-moving counterpart must be a definite, existing feature of the left-moving particle, totally independent of your measurement. And since if you had measured the position of the right particle you would have learned the position of the left particle, and if you had measured the velocity of the right particle you would have learned the velocity of the left particle, it must be that the left-moving particle actually has both a definite position and velocity. Of course, this whole discussion could be carried out interchanging the roles of left-moving and right-moving particles (and, in fact, before doing any measurement we can’t even say which particle is moving left and which is moving right); this leads to the conclusion that both particles have definite positions and speeds.

Thus, EPR concluded that quantum mechanics is an incomplete description of reality. Particles have definite positions and speeds, but the quantum mechanical uncertainty principle shows that these features of reality are beyond the bounds of what the theory can handle. If, in agreement with these and most other physicists, you believe that a full theory of nature should describe every attribute of reality, the failure of quantum mechanics to describe both the positions and the velocities of particles means that it misses some attributes and is therefore not a complete theory; it is not the final word. That is what Einstein, Podolsky, and Rosen vigorously argued.

The Quantum Response

While EPR concluded that each particle has a definite position and velocity at any given moment, notice that if you follow their procedure you will fall short of actually determining these attributes. I said, above, that you could have chosen to measure the right-moving particle’s velocity. Had you done so, you would have disturbed its position; on the other hand, had you chosen to measure its position you would have disturbed its velocity. If you don’t have both of these attributes of the right-moving particle in hand, you don’t have them for the left-moving particle either. Thus, there is no conflict with the uncertainty principle: Einstein and his collaborators fully recognized that they could not identify both the location and the velocity of any given particle. But, and this is key, even without determining both the position and velocity of either particle, EPR’s reasoning shows that each has a definite position and velocity. To them, it was a question of reality. To them, a theory could not claim to be complete if there were elements of reality that it could not describe.

After a bit of intellectual scurrying in response to this unexpected observation, the defenders of quantum mechanics settled down to their usual, pragmatic approach, summarized well by the eminent physicist Wolfgang Pauli: “One should no more rack one’s brain about the problem of whether something one cannot know anything about exists all the same, than about the ancient question of how many angels are able to sit on the point of a needle.”9Physics in general, and quantum mechanics in particular, can deal only with the measurable properties of the universe. Anything else is simply not in the domain of physics. If you can’t measure both the position and the velocity of a particle, then there is no sense in talking about whether it has both a position and a velocity.

EPR disagreed. Reality, they maintained, was more than the readings on detectors; it was more than the sum total of all observations at a given moment. When no one, absolutely no one, no device, no equipment, no anything at all is “looking” at the moon, they believed, the moon was still there. They believed that it was still part of reality.

In a way, this standoff echoes the debate between Newton and Leibniz about the reality of space. Can something be considered real if we can’t actually touch it or see it or in some way measure it? In Chapter 2, I described how Newton’s bucket changed the character of the space debate, suddenly suggesting that an influence of space could be observed directly, in the curved surface of spinning water. In 1964, in a single stunning stroke that one commentator has called “the most profound discovery of science,”10 the Irish physicist John Bell did the same for the quantum reality debate.

In the following four sections, we will describe Bell’s discovery, judiciously steering clear of all but a minimum of technicalities. All the same, even though the discussion uses reasoning less sophisticated than working out the odds in a craps game, it does involve a couple of steps that we must describe and then link together. Depending on your particular taste for detail, there may come a point when you just want the punch line. If this happens, feel free to jump to this page, where you’ll find a summary and a discussion of conclusions stemming from Bell’s discovery.

Bell and Spin

John Bell transformed the central idea of the Einstein-Podolsky-Rosen paper from philosophical speculation into a question that could be answered by concrete experimental measurement. Surprisingly, all he needed to accomplish this was to consider a situation in which there were not just two features—for instance, position and velocity—that quantum uncertainty prevents us from simultaneously determining. He showed that if there are three or more features that simultaneously come under the umbrella of uncertainty—three or more features with the property that in measuring one, you contaminate the others and hence can’t determine anything about them—then there is an experiment to address the reality question. The simplest such example involves something known as spin.

Since the 1920s, physicists have known that particles spin—they execute rotational motion akin to a soccer ball’s spinning around as it heads toward the goal. Quantum particle spin, however, differs from this classical image in a number of essential ways, and foremost for us are the following two points. First, particles—for example, electrons and photons— can spin only clockwise or counterclockwise at one never-changing rate about any particular axis; a particle’s spin axis can change directions but its rate of spin cannot slow down or speed up. Second, quantum uncertainty applied to spin shows that just as you can’t simultaneously determine the position and the velocity of a particle, so also you can’t simultaneously determine the spin of a particle about more than one axis. For example, if a soccer ball is spinning about a northeast-pointing axis, its spin is shared between a northward- and an eastward-pointing axis—and by a suitable measurement, you could determine the fraction of spin about each. But if you measure an electron’s spin about any randomly chosen axis, you never find a fractional amount of spin. Ever. It’s as if the measurement itself forces the electron to gather together all its spinning motion and direct it to be either clockwise or counterclockwise about the axis you happened to have focused on. Moreover, because of your measurement’s influence on the electron’s spin, you lose the ability to determine how it was spinning about a horizontal axis, about a back-and-forth axis, or about any other axis, prior to your measurement. These features of quantum mechanical spin are hard to picture fully, and the difficulty highlights the limits of classical images in revealing the true nature of the quantum world. Nevertheless, the mathematics of quantum theory, and decades of experiment, assure us that these characteristics of quantum spin are beyond doubt.

The reason for introducing spin here is not to delve into the intricacies of particle physics. Rather, the example of particle spin will, in just a moment, provide a simple laboratory for extracting wonderfully unexpected answers to the reality question. That is, does a particle simultaneously have a definite amount of spin about each and every axis, although we can never know it for more than one axis at a time because of quantum uncertainty? Or does the uncertainty principle tell us something else? Does it tell us, contrary to any classical notion of reality, that a particle simply does not and cannot possess such features simultaneously? Does it tell us that a particle resides in a state of quantum limbo, having no definite spin about any given axis, until someone or something measures it, causing it to snap to attention and attain—with a probability determined by quantum theory—one particular spin value or another (clockwise or counterclockwise) about the selected axis? By studying this question, essentially the same one we asked in the case of particle positions and velocities, we can use spin to probe the nature of quantum reality (and to extract answers that greatly transcend the specific example of spin). Let’s see this.

As explicitly shown by the physicist David Bohm,11 the reasoning of Einstein, Podolsky, and Rosen can easily be extended to the question of whether particles have definite spins about any and all chosen axes. Here’s how it goes. Set up two detectors capable of measuring the spin of an incoming electron, one on the left side of the laboratory and the other on the right side. Arrange for two electrons to emanate back-to-back from a source midway between the two detectors, such that their spins—rather than their positions and velocities as in our earlier example—are correlated. The details of how this is done are not important; what is important is that it can be done and, in fact, can be done easily. The correlation can be arranged so that if the left and right detectors are set to measure the spins along axes pointing in the same direction, they will get the same result: if the detectors are set to measure the spin of their respective incoming electrons about a vertical axis and the left detector finds that the spin is clockwise, so will the right detector; if the detectors are set to measure spin along an axis 60 degrees clockwise from the vertical and the left detector measures a counterclockwise spin, so will the right detector; and so on. Again, in quantum mechanics the best we can do is predict the probability that the detectors will find clockwise or counterclockwise spin, but we can predict with 100 percent certainty that whatever one detector finds the other will find, too.7

Bohm’s refinement of the EPR argument is now, for all intents and purposes, the same as it was in the original version that focused on position and velocity. The correlation between the particles’ spins allows us to measure indirectly the spin of the left-moving particle about some axis by measuring that of its right-moving companion about that axis. Since this measurement is done far on the right side of the laboratory, it can’t possibly influence the left-moving particle in any way. Hence, the latter must all along have had the spin value just determined; all we did was measure it, albeit indirectly. Moreover, since we could have chosen to perform this measurement about anyaxis, the same conclusion must hold for any axis: the left-moving electron must have a definite spin about each and every axis, even though we can explicitly determine it only about one axis at a time. Of course, the roles of left and right can be reversed, leading to the conclusion that each particle has a definite spin about any axis.12

At this stage, seeing no obvious difference from the position/velocity example, you might take Pauli’s lead and be tempted to respond that there is no point in thinking about such issues. If you can’t actually measure the spin about different axes, what is the point in wondering whether the particle nevertheless has a definite spin—clockwise versus counterclockwise—about each? Quantum mechanics, and physics more generally, is obliged only to account for features of the world that can be measured. And neither Bohm, Einstein, Podolsky, nor Rosen would have argued that the measurements can be done. Instead, they argued that the particles possess features forbidden by the uncertainty principle even though we can never explicitly know their particular values. Such features have come to be known as hidden features, or, more commonly, hidden variables.

Here is where John Bell changed everything. He discovered that even if you can’t actually determine the spin of a particle about more than one axis, still, if in fact it has a definite spin about all axes, then there are testable, observable consequences of that spin.

Reality Testing

To grasp the gist of Bell’s insight, let’s return to Mulder and Scully and imagine that they’ve each received another package, also containing titanium boxes, but with an important new feature. Instead of having one door, each titanium box has three: one on top, one on the side, and one on the front.13 The accompanying letter informs them that the sphere inside each box now randomly chooses between flashing red and flashing blue when any one of the box’s three doors is opened. If a different door (top versus side versus front) on a given box were opened, the color randomly selected by the sphere might be different, but once one door is opened and the sphere has flashed, there is no way to determine what would have happened had another door been chosen. (In the physics application, this feature captures quantum uncertainty: once you measure one feature you can’t determine anything about the others.) Finally, the letter tells them that there is again a mysterious connection, a strange entanglement, between the two sets of titanium boxes: Even though all the spheres randomly choose what color to flash when one of their box’s three doors is opened, if both Mulder and Scully happen to open the same door on a box with the same number, the letter predicts that they will see the same color flash. If Mulder opens the top door on his box 1 and sees blue, then the letter predicts that Scully will also see blue if she opens the top door on her box 1; if Mulder opens the side door on his box 2 and sees red, then the letter predicts that Scully will also see red if she opens the side door on her box 2, and so forth. Indeed, when Scully and Mulder open the first few dozen boxes—agreeing by phone which door to open on each—they verify the letter’s predictions.

Although Mulder and Scully are being presented with a somewhat more complicated situation than previously, at first blush it seems that the same reasoning Scully used earlier applies equally well here.

“Mulder,” says Scully, “this is as silly as yesterday’s package. Once again, there is no mystery. The sphere inside each box must simply be programmed. Don’t you see?”

“But now there are three doors,” cautions Mulder, “so the sphere can’t possibly ‘know’ which door we’ll choose to open, right?”

“It doesn’t need to,” explains Scully. “That’s part of the programming. Look, here’s an example. Grab hold of the next unopened box, box 37, and I’ll do the same. Now, imagine, for argument’s sake, that the sphere in my box 37 is programmed, say, to flash red if the top door is opened, to flash blue if the side door is opened, and to flash red if the front door is opened. I’ll call this program red, blue, red. Clearly, then, if whoever is sending us this stuff has input this same program into your box 37, and if we both open the same door, we will see the same color flash. This explains the ‘mysterious connection’: if the boxes in our respective collections with the same number have been programmed with the same instructions, then we will see the same color if we open the same door. There is no mystery!”

But Mulder does not believe that the spheres are programmed. He believes the letter. He believes that the spheres are randomly choosing between red and blue when one of their box’s doors is opened and hence he believes, fervently, that his and Scully’s boxes do have some mysterious long-range connection.

Who is right? Since there is no way to examine the spheres before or during the supposed random selection of color (remember, any such tampering will cause the sphere instantly to choose randomly between red or blue, confounding any attempt to investigate how it really works), it seems impossible to prove definitively whether Scully or Mulder is right.

Yet, remarkably, after a little thought, Mulder realizes that there is an experiment that will settle the question completely. Mulder’s reasoning is straightforward, but it does require a touch more explicit mathematical reasoning than most things we cover. It’s definitely worth trying to follow the details—there aren’t that many—but don’t worry if some of it slips by; we’ll shortly summarize the key conclusion.

Mulder realizes that he and Scully have so far only considered what happens if they each open the same door on a box with a given number. And, as he excitedly tells Scully after calling her back, there is much to be learned if they do not always choose the same door and, instead, randomly and independently choose which door to open on each of their boxes.

“Mulder, please. Just let me enjoy my vacation. What can we possibly learn by doing that?”

“Well, Scully, we can determine whether your explanation is right or wrong.”

“Okay, I’ve got to hear this.”

“It’s simple,” Mulder continues. “If you’re right, then here’s what I realized: if you and I separately and randomly choose which door to open on a given box and record the color we see flash, then, after doing this for many boxes we must find that we saw the same color flash more than 50 percent of the time. But if that isn’t the case, if we find that we don’t agree on the color for more than 50 percent of the boxes, then you can’t be right.”

“Really, how is that?” Scully is getting a bit more interested.

“Well,” Mulder continues, “here’s an example. Assume you’re right, and each sphere operates according to a program. Just to be concrete, imagine the program for the sphere in a particular box happens to be blue, blue, red. Now since we both choose from among three doors, there are a total of nine possible door combinations that we might select to open for this box. For example, I might choose the top door on my box while you might choose the side door on your box; or I might choose the front door and you might choose the top door; and so on.”

“Yes, of course,” Scully jumps in. “If we call the top door 1, the side door 2, and the front door 3, then the nine possible door combinations are just (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3).”

“Yes, that’s right,” Mulder continues. “Now here is the point: Of these nine possibilities notice that five door combinations—(1,1), (2,2), (3,3), (1,2), (2,1)—will result in us seeing the spheres in our boxes flash the same color. The first three door combinations are the ones in which we happen to choose the same door, and as we know, that always results in our seeing the same color. The other two door combinations, (1,2) and (2,1), result in the same color because the program dictates that the spheres will flash the same color—blue—if either door 1 or door 2 is opened. Now, since 5 is more than half of 9, this means that for more than half—more than 50 percent—of the possible combination of doors that we might select to open, the spheres will flash the same color.”

“But wait,” Scully protests. “That’s just one example of a particular program: blue, blue, red. In my explanation, I proposed that differently numbered boxes can and generally will have different programs.”

“Actually, that doesn’t matter. The conclusion holds for all of the possible programs. You see, my reasoning with the blue, blue, red program only relied on the fact that two of the colors in the program are the same, and so an identical conclusion follows for any program: red, red, blue, or red, blue, red, and so on. Any program has to have at least two colors the same; the only programs that are really different are those in which all three colors are the same—red, red, red and blue, blue, blue. But for boxes with either of these programs, we’ll get the same color to flash regardless of which doors we happen to open, and so the overall fraction on which we should agree will only increase. So, if your explanation is right and the boxes operate according to programs—even with programs that vary from one numbered box to another—we must agree on the color we see more than 50 percent of the time.”

That’s the argument. The hard part is now over. The bottom line is that there is a test to determine whether Scully is correct and each sphere operates according to a program that determines definitively which color to flash depending on which door is opened. If she and Mulder independently and randomly choose which of the three doors on each of their boxes to open, and then compare the colors they see—box by numbered box—they must find agreement for more than 50 percent of the boxes.

When cast in the language of physics, as it will be in the next section, Mulder’s realization is nothing but John Bell’s breakthrough.

Counting Angels with Angles

The translation of this result into physics is straightforward. Imagine we have two detectors, one on the left side of the laboratory and another on the right side, that measure the spin of an incoming particle like an electron, as in the experiment discussed in the section before last. The detectors require you to choose the axis (vertical, horizontal, back-forth, or one of the innumerable axes that lie in between) along which the spin is to be measured; for simplicity’s sake, imagine that we have bargain-basement detectors that offer only three choices for the axes. In any given run of the experiment, you will find that the incoming electron is either spinning clockwise or counterclockwise about the axis you selected.

According to Einstein, Podolsky, and Rosen, each incoming electron provides the detector it enters with what amounts to a program: Even though it’s hidden, even though you can’t measure it, EPR claimed that each electron has a definite amount of spin—either clockwise or counterclockwise—about each and every axis. Hence, when an electron enters a detector, the electron definitively determines whether you will measure its spin to be clockwise or counterclockwise about whichever axis you happen to choose. For example, an electron that is spinning clockwise about each of the three axes provides the program clockwise, clockwise, clockwise; an electron that is spinning clockwise about the first two axes and counterclockwise about the third provides the program clockwise, clockwise, counterclockwise, and so forth. In order to explain the correlation between the left-moving and right-moving electrons, Einstein, Podolsky, and Rosen simply claim that such electrons have identical spins and thus provide the detectors they enter with identical programs. Thus, if the same axes are chosen for the left and right detectors, the spin detectors will find identical results.

Notice that these spin detectors exactly reproduce everything encountered by Scully and Mulder, though with simple substitutions: instead of choosing a door on a titanium box, we are choosing an axis; instead of seeing a red or blue flash, we record a clockwise or counterclockwise spin. So, just as opening the same doors on a pair of identically numbered titanium boxes results in the same color flashing, choosing the same axes on the two detectors results in the same spin direction being measured. Also, just as opening one particular door on a titanium box prevents us from ever knowing what color would have flashed had we chosen another door, measuring the electron spin about one particular axis prevents us, via quantum uncertainty, from ever knowing which spin direction we would have found had we chosen a different axis.

All of the foregoing means that Mulder’s analysis of how to learn who’s right applies in exactly the same way to this situation as it does to the case of the alien spheres. If EPR are correct and each electron actually has a definite spin value about all three axes—if each electron provides a “program” that definitively determines the result of any of the three possible spin measurements—then we can make the following prediction. Scrutiny of data gathered from many runs of the experiment—runs in which the axis for each detector is randomly and independently selected—will show that more than half the time, the two electron spins agree, being both clockwise or both counterclockwise. If the electron spins do not agree more than half the time, then Einstein, Podolsky, and Rosen are wrong.

This is Bell’s discovery. It shows that even though you can’t actually measure the spin of an electron about more than one axis—even though you can’t explicitly “read” the program it is purported to supply to the detector it enters—this does not mean that trying to learn whether it nonetheless has a definite amount of spin about more than one axis is tantamount to counting angels on the head of a pin. Far from it. Bell found that there is a bona fide, testable consequence associated with a particle having definite spin values. By using axes at three angles, Bell provided a way to count Pauli’s angels.

No Smoke but Fire

In case you missed any of the details, let’s summarize where we’ve gotten. Through the Heisenberg uncertainty principle, quantum mechanics claims that there are features of the world—like the position and the velocity of a particle, or the spin of a particle about various axes—that cannot simultaneously have definite values. A particle, according to quantum theory, cannot have a definite position and a definite velocity; a particle cannot have a definite spin (clockwise or counterclockwise) about more than one axis; a particle cannot simultaneously have definite attributes for things that lie on opposite sides of the uncertainty divide. Instead, particles hover in quantum limbo, in a fuzzy, amorphous, probabilistic mixture of all possibilities; only when measured is one definite outcome selected from the many. Clearly, this is a drastically different picture of reality than that painted by classical physics.

Ever the skeptic about quantum mechanics, Einstein, together with his colleagues Podolsky and Rosen, tried to use this aspect of quantum mechanics as a weapon against the theory itself. EPR argued that even though quantum mechanics does not allow such features to be simultaneously determined, particles nevertheless do have definite values for position and velocity; particles do have definite spin values about all axes; particles do have definite values for all things forbidden by quantum uncertainty. EPR thus argued that quantum mechanics cannot handle all elements of physical reality—it cannot handle the position and velocity of a particle; it cannot handle the spin of a particle about more than one axis—and hence is an incomplete theory.

For a long time, the issue of whether EPR were correct seemed more a question of metaphysics than of physics. As Pauli said, if you can’t actually measure features forbidden by quantum uncertainty, what difference could it possibly make if they, nevertheless, exist in some hidden fold of reality? But, remarkably, John Bell found something that had escaped Einstein, Bohr, and all the other giants of twentieth-century theoretical physics: he found that the mere existence of certain things, even if they are beyond explicit measurement or determination, does make a difference—a difference that can be checked experimentally. Bell showed that if EPR were correct, the results found by two widely separated detectors measuring certain particle properties (spin about various randomly chosen axes, in the approach we have taken) would have to agree more than 50 percent of the time.

Bell had this insight in 1964, but at that time the technology did not exist to undertake the required experiments. By the early 1970s it did. Beginning with Stuart Freedman and John Clauser at Berkeley, followed by Edward Fry and Randall Thompson at Texas A&M, and culminating in the early 1980s with the work of Alain Aspect and collaborators working in France, ever more refined and impressive versions of these experiments were carried out. In the Aspect experiment, for example, the two detectors were placed 13 meters apart and a container of energetic calcium atoms was placed midway between them. Well-understood physics shows that each calcium atom, as it returns to its normal, less energetic state, will emit two photons, traveling back to back, whose spins are perfectly correlated, just as in the example of correlated electron spins we have been discussing. Indeed, in Aspect’s experiment, whenever the detector settings are the same, the two photons are measured to have spins that are perfectly aligned. If lights were hooked up to Aspect’s detectors to flash red in response to a clockwise spin and blue in response to a counterclockwise spin, the incoming photons would cause the detectors to flash the same color.

But, and this is the crucial point, when Aspect examined data from a large number of runs of the experiment—data in which the left and right detector settings were not always the same but, rather, were randomly and independently varied from run to run—he found that the detectors did not agree more than 50 percent of the time.

This is an earth-shattering result. This is the kind of result that should take your breath away. But just in case it hasn’t, let me explain further. Aspect’s results show that Einstein, Podolsky, and Rosen were proven by experiment—not by theory, not by pondering, but by nature—to be wrong. And that means there has to be something wrong with the reasoning EPR used to conclude that particles possess definite values for features—like spin values about distinct axes—for which definite values are forbidden by the uncertainty principle.

But where could they have gone wrong? Well, remember that the Einstein, Podolsky, and Rosen argument hangs on one central assumption: if at a given moment you can determine a feature of an object by an experiment done on another, spatially distant object, then the first object must have had this feature all along. Their rationale for this assumption was simple and thoroughly reasonable. Your measurement was done over here while the first object was way over there. The two objects were spatially separate, and hence your measurement could not possibly have had any effect on the first object. More precisely, since nothing goes faster than the speed of light, if your measurement on one object were somehow to cause a change in the other—for example, to cause the other to take on an identical spinning motion about a chosen axis—there would have to be a delay before this could happen, a delay at least as long as the time it would take light to traverse the distance between the two objects. But in both our abstract reasoning and in the actual experiments, the two particles are examined by the detectors at the same time. Therefore, whatever we learn about the first particle by measuring the second must be a feature that the first particle possessed, completely independent of whether we happened to undertake the measurement at all. In short, the core of the Einstein, Podolsky, Rosen argument is that an object over there does not care about what you do to another object over here.

But as we just saw, this reasoning leads to the prediction that the detectors should find the same result more than half the time, a prediction that is refuted by the experimental results. We are forced to conclude that the assumption made by Einstein, Podolsky, and Rosen, no matter how reasonable it seems, cannot be how our quantum universe works. Thus, through this indirect but carefully considered reasoning, the experiments lead us to conclude that an object over there does care about what you do to another object over here.

Even though quantum mechanics shows that particles randomly acquire this or that property when measured, we learn that the randomness can be linked across space. Pairs of appropriately prepared particles— they’re called entangled particles—don’t acquire their measured properties independently. They are like a pair of magical dice, one thrown in Atlantic City and the other in Las Vegas, each of which randomly comes up one number or another, yet the two of which somehow manage always to agree. Entangled particles act similarly, except they require no magic. Entangled particles, even though spatially separate, do not operate autonomously.

Einstein, Podolsky, and Rosen set out to show that quantum mechanics provides an incomplete description of the universe. Half a century later, theoretical insights and experimental results inspired by their work require us to turn their analysis on its head and conclude that the most basic, intuitively reasonable, classically sensible part of their reasoning is wrong: the universe is not local. The outcome of what you do at one place can be linked with what happens at another place, even if nothing travels between the two locations—even if there isn’t enough time for anything to complete the journey between the two locations. Einstein’s, Podolsky’s, and Rosen’s intuitively pleasing suggestion that such long-range correlations arise merely because particles have definite, preexisting, correlated properties is ruled out by the data. That’s what makes this all so shocking.14

In 1997, Nicolas Gisin and his team at the University of Geneva carried out a version of the Aspect experiment in which the two detectors were placed 11 kilometers apart. The results were unchanged. On the microscopic scale of the photon’s wavelengths, 11 kilometers is gargantuan. It might as well be 11 million kilometers—or 11 billion light-years, for that matter. There is every reason to believe that the correlation between the photons would persist no matter how far apart the detectors are placed.

This sounds totally bizarre. But there is now overwhelming evidence for this so-called quantum entanglement. If two photons are entangled, the successful measurement of either photon’s spin about one axis “forces” the other, distant photon to have the same spin about the same axis; the act of measuring one photon “compels” the other, possibly distant photon to snap out of the haze of probability and take on a definitive spin value—a value that precisely matches the spin of its distant companion. And that boggles the mind.8

Entanglement and Special Relativity: The Standard View

I have put the words “forces” and “compels” in quotes because while they convey the sentiment our classical intuition longs for, their precise meaning in this context is critical to whether or not we are in for even more of an upheaval. With their everyday definitions, these words conjure up an image of volitional causality: we choose to do something here so as to cause or force a particular something to happen over there. If that were the right description of how the two photons are interrelated, special relativity would be on the ropes. The experiments show that from the viewpoint of an experimenter in the laboratory, at the precise moment one photon’s spin is measured, the other photon immediately takes on the same spin property. If something were traveling from the left photon to the right photon, alerting the right photon that the left photon’s spin had been determined through a measurement, it would have to travel between the photons instantaneously, conflicting with the speed limit set by special relativity.

The consensus among physicists is that any such apparent conflict with special relativity is illusory. The intuitive reason is that even though the two photons are spatially separate, their common origin establishes a fundamental link between them. Although they speed away from each other and become spatially separate, their history entwines them; even when distant, they are still part of one physical system. And so, it’s really not that a measurement on one photon forces or compels another distant photon to take on identical properties. Rather, the two photons are so intimately bound up that it is justified to consider them—even though they are spatially separate—as parts of one physical entity. Then we can say that one measurement on this single entity—an entity containing two photons—affects the entity; that is, it affects both photons at once.

While this imagery may make the connection between the photons a little easier to swallow, as stated it’s vague—what does it really mean to say two spatially separate things are one? A more precise argument is the following. When special relativity says that nothing can travel faster than the speed of light, the “nothing” refers to familiar matter or energy. But the case at hand is subtler, because it doesn’t appear that any matter or energy is traveling between the two photons, and so there isn’t anything whose speed we are led to measure. Nevertheless, there is a way to learn whether we’ve run headlong into a conflict with special relativity. A feature common to matter and energy is that when traveling from place to place they can transmit information. Photons traveling from a broadcast station to your radio carry information. Electrons traveling through Internet cables to your computer carry information. So, in any situation where something—even something unidentified—is purported to have traveled faster than light speed, a litmus test is to ask whether it has, or at least could have, transmitted information. If the answer is no, the standard reasoning goes, then nothing has exceeded light speed, and special relativity remains unchallenged. In practice, this is the test that physicists often employ in determining whether some subtle process has violated the laws of special relativity. (None has ever survived this test.) Let’s apply it here.

Is there any way that, by measuring the spin of the left-moving and the right-moving photons about some given axis, we can send information from one to the other? The answer is no. Why? Well, the output found in either the left or the right detector is nothing but a random sequence of clockwise and counterclockwise results, since on any given run there is an equal probability of the particle to be found spinning one way or the other. In no way can we control or predict the outcome of any particular measurement. Thus, there is no message, there is no hidden code, there is no information whatsoever in either of these two random lists. The only interesting thing about the two lists is that they are identical—but that can’t be discerned until the two lists are brought together and compared by some conventional, slower-than-light means (fax, e-mail, phone call, etc.). The standard argument thus concludes that although measuring the spin of one photon appears instantaneously to affect the other, no information is transmitted from one to the other, and the speed limit of special relativity remains in force. Physicists say that the spin results are correlated—since the lists are identical—but do not stand in a traditional cause-and-effect relationship because nothing travels between the two distant locations.

Entanglement and Special Relativity: The Contrarian View

Is that it? Is the potential conflict between the nonlocality of quantum mechanics and special relativity fully resolved? Well, probably. On the basis of the above considerations, the majority of physicists sum it up by saying there is a harmonious coexistence between special relativity and Aspect’s results on entangled particles. In short, special relativity survives by the skin of its teeth. Many physicists find this convincing, but others have a nagging sense that there is more to the story.

At a gut level I’ve always shared the coexistence view, but there is no denying that the issue is delicate. At the end of the day, no matter what holistic words one uses or what lack of information one highlights, two widely separated particles, each of which is governed by the randomness of quantum mechanics, somehow stay sufficiently “in touch” so that whatever one does, the other instantly does too. And that seems to suggest that some kind of faster-than-light something is operating between them.

Where do we stand? There is no ironclad, universally accepted answer. Some physicists and philosophers have suggested that progress hinges on our recognizing that the focus of the discussion so far is somewhat misplaced: the real core of special relativity, they rightly point out, is not so much that light sets a speed limit, as that light’s speed is something that all observers, regardless of their own motion, agree upon.16 More generally, these researchers emphasize, the central principle of special relativity is that no observational vantage point is singled out over any other. Thus, they propose (and many agree) that if the egalitarian treatment of all constant-velocity observers could be squared with the experimental results on entangled particles, the tension with special relativity would be resolved.17 But achieving this goal is not a trivial task. To see this concretely, let’s think about how good old-fashioned textbook quantum mechanics explains the Aspect experiment.

According to standard quantum mechanics, when we perform a measurement and find a particle to be here, we cause its probability wave to change: the previous range of potential outcomes is reduced to the one actual result our measurement finds, as illustrated in Figure 4.7. Physicists say the measurement causes the probability wave to collapse and they envision that the larger the initial probability wave at some location, the larger the likelihood that the wave will collapse to that point—that is, the larger the likelihood that the particle will be found at that point. In the standard approach, the collapse happens instantaneously across the whole universe: once you find the particle here, the thinking goes, the probability of its being found anywhere else immediately drops to zero, and this is reflected in an immediate collapse of the probability wave.

In the Aspect experiment, when the left-moving photon’s spin is measured and is found, say, to be clockwise about some axis, this collapses its probability wave throughout all of space, instantaneously setting the counterclockwise part to zero. Since this collapse happens everywhere, it happens also at the location of the right-moving photon. And, it turns out, this affects the counterclockwise part of the right-moving photon’s probability wave, causing it to collapse to zero too. Thus, no matter how far away the right-moving photon is from the left-moving photon, its probability wave is instantaneously affected by the change in the left-moving photon’s probability wave, ensuring that it has the same spin as the left-moving photon along the chosen axis. In standard quantum mechanics, then, it is this instantaneous change in probability waves that is responsible for the faster-than-light influence.


Figure 4.7 When a particle is observed at some location, the probability of finding it at any other location drops to zero, while its probability surges to 100 percent at the location where it is observed.

The mathematics of quantum mechanics makes this qualitative discussion precise. And, indeed, the long-range influences arising from collapsing probability waves change the prediction of how often Aspect’s left and right detectors (when their axes are randomly and independently chosen) should find the same result. A mathematical calculation is required to get the exact answer (see notes section18 if you’re interested), but when the math is done, it predicts that the detectors should agree precisely50 percent of the time (rather than predicting agreement more than 50 percent of the time—the result, as we’ve seen, found using EPR’s hypothesis of a local universe). To impressive accuracy, this is just what Aspect found in his experiments, 50 percent agreement. Standard quantum mechanics matches the data impressively.

This is a spectacular success. Nevertheless, there is a hitch. After more than seven decades, no one understands how or even whether the collapse of a probability wave really happens. Over the years, the assumption that probability waves collapse has proven itself a powerful link between the probabilities that quantum theory predicts and the definite outcomes that experiments reveal. But it’s an assumption fraught with conundrums. For one thing, the collapse does not emerge from the mathematics of quantum theory; it has to be put in by hand, and there is no agreed-upon or experimentally justified way to do this. For another, how is it possible that by finding an electron in your detector in New York City, you cause the electron’s probability wave in the Andromeda galaxy to drop to zero instantaneously? To be sure, once you find the particle in New York City, it definitely won’t be found in Andromeda, but what unknown mechanism enforces this with such spectacular efficiency? How, in looser language, does the part of the probability wave in Andromeda, and everywhere else, “know” to drop to zero simultaneously?19

We will take up this quantum mechanical measurement problem in Chapter 7 (and as we’ll see, there are other proposals that avoid the idea of collapsing probability waves entirely), but suffice it here to note that, as we discussed in Chapter 3, something that is simultaneous from one perspective is not simultaneous from another moving perspective. (Remember Itchy and Scratchy setting their clocks on a moving train.) So if a probability wave were to undergo simultaneous collapse across space according to one observer, it will not undergo such simultaneous collapse according to another who is in motion. As a matter of fact, depending on their motion, some observers will report that the left photon was measured first, while other observers, equally trustworthy, will report that the right photon was measured first. Hence, even if the idea of collapsing probability waves were correct, there would fail to be an objective truth regarding which measurement—on the left or right photon—affected the other. Thus, the collapse of probability waves would seem to pick out one vantage point as special—the one according to which the collapse is simultaneous across space, the one according to which the left and right measurements occur at the same moment. But picking out a special perspective creates significant tension with the egalitarian core of special relativity. Proposals have been made to circumvent this problem, but debate continues regarding which, if any, are successful.20

Thus, although the majority view holds that there is a harmonious coexistence, some physicists and philosophers consider the exact relationship between quantum mechanics, entangled particles, and special relativity an open question. It’s certainly possible, and in my view likely, that the majority view will ultimately prevail in some more definitive form. But history shows that subtle, foundational problems sometimes sow the seeds of future revolutions. On this one, only time will tell.

What Are We to Make of All This?

Bell’s reasoning and Aspect’s experiments show that the kind of universe Einstein envisioned may exist in the mind, but not in reality. Einstein’s was a universe in which what you do right here has immediate relevance only for things that are also right here. Physics, in his view, was purely local. But we now see that the data rule out this kind of thinking; the data rule out this kind of universe.

Einstein’s was also a universe in which objects possess definite values of all possible physical attributes. Attributes do not hang in limbo, waiting for an experimenter’s measurement to bring them into existence. The majority of physicists would say that Einstein was wrong on this point, too. Particle properties, in this majority view, come into being when measurements force them to—an idea we will examine further in Chapter 7. When they are not being observed or interacting with the environment, particle properties have a nebulous, fuzzy existence characterized solely by a probability that one or another potentiality might be realized. The most extreme of those who hold this opinion would go as far as declaring that, indeed, when no one and no thing is “looking” at or interacting with the moon in any way, it is not there.

On this issue, the jury is still out. Einstein, Podolsky, and Rosen reasoned that the only sensible explanation for how measurements could reveal that widely separated particles had identical properties was that the particles possessed those definite properties all along (and, by virtue of their common past, their properties were correlated). Decades later, Bell’s analysis and Aspect’s data proved that this intuitively pleasing suggestion, based on the premise that particles always have definite properties, fails as an explanation of the experimentally observed nonlocal correlations. But the failure to explain away the mysteries of nonlocality does not mean that the notion of particles always possessing definite properties is itself ruled out. The data rule out a local universe, but they don’t rule out particles having such hidden properties.

In fact, in the 1950s Bohm constructed his own version of quantum mechanics that incorporates both nonlocality and hidden variables. Particles, in this approach, always have both a definite position and a definite velocity, even though we can never measure both simultaneously. Bohm’s approach made predictions that agreed fully with those of conventional quantum mechanics, but his formulation introduced an even more brazen element of nonlocality in which the forces acting on a particle at one location depend instantaneously on conditions at distant locations. In a sense, then, Bohm’s version suggested how one might go partway toward Einstein’s goal of restoring some of the intuitively sensible features of classical physics—particles having definite properties—that had been abandoned by the quantum revolution, but it also showed that doing so came at the price of accepting yet more blatant nonlocality. With this hefty cost, Einstein would have found little solace in this approach.

The need to abandon locality is the most astonishing lesson arising from the work of Einstein, Podolsky, Rosen, Bohm, Bell, and Aspect, as well as the many others who played important parts in this line of research. By virtue of their past, objects that at present are in vastly different regions of the universe can be part of a quantum mechanically entangled whole. Even though widely separated, such objects are committed to behaving in a random but coordinated manner.

We used to think that a basic property of space is that it separates and distinguishes one object from another. But we now see that quantum mechanics radically challenges this view. Two things can be separated by an enormous amount of space and yet not have a fully independent existence. A quantum connection can unite them, making the properties of each contingent on the properties of the other. Space does not distinguish such entangled objects. Space cannot overcome their interconnection. Space, even a huge amount of space, does not weaken their quantum mechanical interdependence.

Some people have interpreted this as telling us that “everything is connected to everything else” or that “quantum mechanics entangles us all in one universal whole.” After all, the reasoning goes, at the big bang everything emerged from one place since, we believe, all places we now think of as different were the same place way back in the beginning. And since, like the two photons emerging from the same calcium atom, everything emerged from the same something in the beginning, everything should be quantum mechanically entangled with everything else.

While I like the sentiment, such gushy talk is loose and overstated. The quantum connections between the two photons emerging from the calcium atom are there, certainly, but they are extremely delicate. When Aspect and others carry out their experiments, it is crucial that the photons be allowed to travel absolutely unimpeded from their source to the detectors. Should they be jostled by stray particles or bump into pieces of equipment before reaching one of the detectors, the quantum connection between the photons will become monumentally more difficult to identify. Rather than looking for correlations in the properties of two photons, one would now need to look for a complex pattern of correlations involving the photons and everything else they may have bumped into. And as all these particles go their ways, bumping and jostling yet other particles, the quantum entanglement would become so spread out through these interactions with the environment that it would become virtually impossible to detect. For all intents and purposes, the original entanglement between the photons would have been erased.

Nevertheless, it is truly amazing that these connections do exist, and that in carefully arranged laboratory conditions they can be directly observed over significant distances. They show us, fundamentally, that space is not what we once thought it was.

What about time?