The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

  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." 9 Physics 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 b
e 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 page 112, 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.