by Brian Greene
This is the stunning connection we've been leading up to for the entire chapter. A splattering egg tells us something deep about the big bang. It tells us that the big bang gave rise to an extraordinarily ordered nascent cosmos.
The same idea applies to all other examples. The reason why tossing the newly unbound pages of War and Peace into the air results in a state of higher entropy is that they began in such a highly ordered, low entropy form. Their initial ordered form made them ripe for entropy increase. By contrast, if the pages initially were totally out of numerical order, tossing them in the air would hardly make a difference, as far as entropy goes. So the question, once again, is: how did they become so ordered? Well, Tolstoy wrote them to be presented in that order and the printer and binder followed his instructions. And the highly ordered bodies and minds of Tolstoy and the book producers, which allowed them, in turn, to create a volume of such high order, can be explained by following the same chain of reasoning we just followed for an egg, once again leading us back to the big bang. How about the partially melted ice cubes you saw at 10:30 p.m.? Now that we are trusting memories and records, you remember that just before 10 p.m. the bartender put fully formed ice cubes in your glass. He got the ice cubes from a freezer, which was designed by a clever engineer and fabricated by talented machinists, all of whom are capable of creating something of such high order because they themselves are highly ordered life forms. And again, we can sequentially trace their order back to the highly ordered origin of the universe.
The Critical Input
The revelation we've come to is that we can trust our memories of a past with lower, not higher, entropy only if the big bang—the process, event, or happening that brought the universe into existence—started off the universe in an extraordinarily special, highly ordered state of low entropy. Without that critical input, our earlier realization that entropy should increase toward both the future and the past from any given moment would lead us to conclude that all the order we see arose from a chance fluctuation from an ordinary disordered state of high entropy, a conclusion, as we've seen, that undermines the very reasoning on which it's based. But by including the unlikely, low-entropy starting point of the universe in our analysis, we now see that the correct conclusion is that entropy increases toward the future, since probabilistic reasoning operates fully and without constraint in that direction; but entropy does not increase toward the past, since that use of probability would run afoul of our new proviso that the universe began in a state of low, not high, entropy. 17 Thus, conditions at the birth of the universe are critical to directing time's arrow. The future is indeed the direction of increasing entropy. The arrow of time—the fact that things start like this and end like that but never start like that and end like this —began its flight in the highly ordered, low-entropy state of the universe at its inception. 18
The Remaining Puzzle
That the early universe set the direction of time's arrow is a wonderful and satisfying conclusion, but we are not done. A huge puzzle remains. How is it that the universe began in such a highly ordered configuration, setting things up so that for billions of years to follow everything could slowly evolve through steadily less ordered configurations toward higher and higher entropy? Don't lose sight of how remarkable this is. As we emphasized, from the standpoint of probability it is much more likely that the partially melted ice cubes you saw at 10:30 p.m. got there because a statistical fluke acted itself out in a glass of liquid water, than that they originated in the even less likely state of fully formed ice cubes. And what's true for ice cubes is true a gazillion times over for the whole universe. Probabilistically speaking, it is mind-bogglingly more likely that everything we now see in the universe arose from a rare but every-so-often-expectable statistical aberration away from total disorder, rather than having slowly evolved from the even more unlikely, the incredibly more ordered, the astoundingly low-entropy starting point required by the big bang. 19
Yet, when we went with the odds and imagined that everything popped into existence by a statistical fluke, we found ourselves in a quagmire: that route called into question the laws of physics themselves. And so we are inclined to buck the bookies and go with a low-entropy big bang as the explanation for the arrow of time. The puzzle then is to explain how the universe began in such an unlikely, highly ordered configuration. That is the question to which the arrow of time points. It all comes down to cosmology. 20
We will take up a detailed discussion of cosmology in Chapters 8 through 11, but notice first that our discussion of time suffers from a serious shortcoming: everything we've said has been based purely on classical physics. Let's now consider how quantum mechanics affects our understanding of time and our pursuit of its arrow.
7 - Time and the Quantum
INSIGHTS INTO TIME'S NATURE FROM THE QUANTUM REALM
When we think about something like time, something we are within, something that is fully integrated into our day-to-day existence, something that is so pervasive, it is impossible to excise—even momentarily—from common language, our reasoning is shaped by the preponderance of our experiences. These day-to-day experiences are classical experiences; with a high degree of accuracy, they conform to the laws of physics set down by Newton more than three centuries ago. But of all the discoveries in physics during the last hundred years, quantum mechanics is far and away the most startling, since it undermines the whole conceptual schema of classical physics.
So it is worthwhile to expand upon our classical experiences by considering some experiments that reveal eyebrow-raising features of how quantum processes unfold in time. In this broadened context, we will then continue the discussion of the last chapter and ask whether there is a temporal arrow in the quantum mechanical description of nature. We will come to an answer, but one that is still controversial, even among physicists. And once again it will take us back to the origin of the universe.
The Past According to the Quantum
Probability played a central role in the last chapter, but as I stressed there a couple of times, it arose only because of its practical convenience and the utility of the information it provides. Following the exact motion of the 10 24 H 2 O molecules in a glass of water is well beyond our computational capacity, and even if it were possible, what would we do with the resulting mountain of data? To determine from a list of 10 24 positions and velocities whether there were ice cubes in the glass would be a Herculean task. So we turned instead to probabilistic reasoning, which is computationally tractable and, moreover, deals with the macroscopic properties— order versus disorder; for example, ice versus water—we are generally interested in. But keep in mind that probability is by no means fundamentally stitched into the fabric of classical physics. In principle, if we knew precisely how things were now—knew the positions and velocities of every single particle making up the universe—classical physics says we could use that information to predict how things would be at any given moment in the future or how they were at any given moment in the past. Whether or not you actually follow its moment-to-moment development, according to classical physics you can talk about the past and the future, in principle, with a confidence that is controlled by the detail and the accuracy of your observations of the present. 1
Probability will also play a central role in this chapter. But because probability is an inescapable element of quantum mechanics, it fundamentally alters our conceptualization of past and future. We've already seen that quantum uncertainty prevents simultaneous knowledge of exact positions and exact velocities. Correspondingly, we've also seen that quantum physics predicts only the probability that one or another future will be realized. We have confidence in these probabilities, to be sure, but since they are probabilities we learn that there is an unavoidable element of chance when it comes to predicting the future.
When it comes to describing the past, there is also a critical difference between classical and quantum physics. In classical physics, in keeping with its egalitarian t
reatment of all moments in time, the events leading up to something we observe are described using exactly the same language, employing exactly the same attributes, we use to describe the observation itself. If we see a fiery meteor in the night sky, we talk of its position and its velocity; if we reconstruct how it got there, we also talk of a unique succession of positions and velocities as the meteor hurtled through space toward earth. In quantum physics, though, once we observe something we enter the rarefied realm in which we know something with 100 percent certainty (ignoring issues associated with the accuracy of our equipment, and the like). But the past—by which we specifically mean the "unobserved" past, the time before we, or anyone, or anything has carried out a given observation—remains in the usual realm of quantum uncertainty, of probabilities. Even though we measure an electron's position as right here right now, a moment ago all it had were probabilities of being here, or there, or way over there.
And as we've seen, it is not that the electron (or any particle for that matter) really was located at only one of these possible positions, but we simply don't know which. 2 Rather, there is a sense in which the electron was at all of the locations, because each of the possibilities—each of the possible histories—contributes to what we now observe. Remember, we saw evidence of this in the experiment, described in Chapter 4, in which electrons were forced to pass through two slits. Classical physics, which relies on the commonly held belief that happenings have unique, conventional histories, would say that any electron that makes it to the detector screen went through either the left slit or the right slit. But this view of the past would lead us astray: it would predict the results illustrated in Figure 4.3a, which do not agree with what actually happens, as illustrated in Figure 4.3b. The observed interference pattern can be explained only by invoking an overlap between something that passes through both slits.
Quantum physics provides just such an explanation, but in doing so it drastically changes our stories of the past—our descriptions of how the particular things we observe came to be. According to quantum mechanics, each electron's probability wave does pass through both slits, and because the parts of the wave emerging from each slit commingle, the resulting probability profile manifests an interference pattern, and hence the electron landing positions do, too.
Compared with everyday experience, this description of the electron's past in terms of criss-crossing waves of probability is thoroughly unfamiliar. But, throwing caution to the wind, you might suggest taking this quantum mechanical description one step further, leading to a yet more bizarre-sounding possibility. Maybe each individual electron itself actually travels through both slits on its way to the screen, and the data result from an interference between these two classes of histories. That is, it's tempting to think of the waves emerging from the two slits as representing two possible histories for an individual electron—going through the left slit or going through the right slit—and since both waves contribute to what we observe on the screen, perhaps quantum mechanics is telling us that both potential histories of the electron contribute as well.
Surprisingly, this strange and wonderful idea—the brainchild of the Nobel laureate Richard Feynman, one of the twentieth century's most creative physicists—provides a perfectly viable way of thinking about quantum mechanics. According to Feynman, if there are alternative ways in which a given outcome can be achieved—for instance, an electron hits a point on the detector screen by traveling through the left slit, or hits the same point on the screen but by traveling through the right slit—then there is a sense in which the alternative histories all happen, and happen simultaneously. Feynman showed that each such history would contribute to the probability that their common outcome would be realized, and if these contributions were correctly added together, the result would agree with the total probability predicted by quantum mechanics.
Feynman called this the sum over histories approach to quantum mechanics; it shows that a probability wave embodies all possible pasts that could have preceded a given observation, and illustrates well that to succeed where classical physics failed, quantum mechanics had to substantially broaden the framework of history. 3
To Oz
There is a variation on the double-slit experiment in which the interference between alternative histories is made even more evident because the two routes to the detector screen are more fully separated. It is a little easier to describe the experiment using photons rather than electrons, so we begin with a photon source—a laser—and we fire it toward what is known as a beam splitter. This device is made from a half-silvered mirror, like the kind used for surveillance, which reflects half of the light that hits it while allowing the other half to pass through. The initial single light beam is thus split in two, the left beam and the right beam, similar to what happens to a light beam that impinges on the two slits in the double-slit setup. Using judiciously placed fully reflecting mirrors, as in Figure 7.1, the two beams are brought back together further downstream at the location of the detector. Treating the light as a wave, as in the description by Maxwell, we expect—and, indeed, we find—an interference pattern on the screen. The length of the journey to all but the center point on the screen is slightly different for the left and right routes and so while the left beam might be reaching a peak at a given point on the detector screen, the right beam might be reaching a peak, a trough, or something in between. The detector records the combined height of the two waves and hence has the characteristic interference pattern.
Figure 7.1 (a) In a beam-splitter experiment, laser light is split into two beams that travel two separate paths to the detector screen. (b) The laser can be turned down so that it fires individual photons; over time, the photon impact locations build up an interference pattern.
The classical/quantum distinction becomes apparent as we drastically lower the intensity of the laser so that it emits photons singly, say, one every few seconds. When a single photon hits the beam splitter, classical intuition says that it will either pass through or will be reflected. Classical reasoning doesn't even allow a hint of any kind of interference, since there is nothing to interfere: all we have are single, individual, particulate photons passing from source to detector, one by one, some going left, some going right. But when the experiment is done, the individual photons recorded over time, much as in Figure 4.4, do yield an interference pattern, as in Figure 7.1b. According to quantum physics, the reason is that each detected photon could have gotten to the detector by the left route or by going via the right route. Thus, we are obliged to combine these two possible histories in determining the probability that a photon will hit the screen at one particular point or another. When the left and right probability waves for each individual photon are merged in this way, they yield the undulating probability pattern of wave interference. And so, unlike Dorothy, who is perplexed when the Scarecrow points both left and right in giving her directions to Oz, the data can be explained perfectly by imagining that each photon takes both left and right routes toward the detector.
Prochoice
Although we have described the merging of possible histories in the context of only a couple of specific examples, this way of thinking about quantum mechanics is general. Whereas classical physics describes the present as having a unique past, the probability waves of quantum mechanics enlarge the arena of history: in Feynman's formulation, the observed present represents an amalgam—a particular kind of average— of all possible pasts compatible with what we now see.
In the case of the double-slit and beam-splitter experiments, there are two ways for an electron or photon to get from the source to the detector screen—going left or going right—and only by combining the possible histories do we get an explanation for what we observe. If the barrier had three slits, we'd have to take account of three kinds of histories; with 300 slits, we'd need to include the contributions of the whole slew of resulting possible histories. Taking this to the limit, if we imagine cutting an enormous number of slits—so many
, in fact, that the barrier effectively disappears—quantum physics says that each electron would then traverse every possible path on its way to a particular point on the screen, and only by combining the probabilities associated with each such history could we explain the resulting data. That may sound strange. (It is strange.) But this bizarre treatment of times past explains the data of Figure 4.4, Figure 7.1b, and every other experiment dealing with the microworld.
You might wonder how literally you should take the sum over histories description. Does an electron that strikes the detector screen really get there by traveling along all possible routes, or is Feynman's prescription merely a clever mathematical contrivance that gets the right answer? This is among the key questions for assessing the true nature of quantum reality, so I wish I could give you a definitive answer. But I can't. Physicists often find it extremely useful to envision a vast assemblage of combining histories; I use this picture in my own research so frequently that it certainly feels real. But that's not the same thing as saying that it is real. The point is that quantum calculations unambiguously tell us the probability that an electron will land at one or another point on the screen, and these predictions agree with the data, spot on. As far as the theory's verification and predictive utility are concerned, the story we tell of how the electron got to that point on the screen is of little relevance.
But surely, you'd continue to press, we can settle the issue of what really happens by changing the experimental setup so that we can also watch the supposed fuzzy mélange of possible pasts melding into the observed present. It's a good suggestion, but we already know that there has to be a hitch. In Chapter 4, we learned that probability waves are not directly observable; since Feynman's coalescing histories are nothing but a particular way of thinking about probability waves, they, too, must evade direct observation. And they do. Observations cannot tease apart individual histories; rather, observations reflect averages of all possible histories. So, if you change the setup to observe the electrons in flight, you will see each electron pass by your additional detector in one location or another; you will never see any fuzzy multiple histories. When you use quantum mechanics to explain why you saw the electron in one place or another, the answer will involve averaging over all possible histories that could have led to that intermediate observation. But the observation itself has access only to histories that have already merged. By looking at the electron in flight, you have merely pushed back the notion of what you mean by a history. Quantum mechanics is starkly efficient: it explains what you see but prevents you from seeing the explanation.
