The Fabric of the Cosmos: Space, Time, and the Texture of Reality (15 page)

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.
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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.

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.

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.
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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.
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