From Eternity to Here: The Quest for the Ultimate Theory of Time

by Sean M. Carroll

  To this day, scientists haven’t yet determined to anyone’s satisfaction whether the universe will continue to evolve forever, or whether it will eventually settle into a placid state of equilibrium.

  WHY CAN’T WE REMEMBER THE FUTURE?

  So the arrow of time isn’t just about simple mechanical processes; it’s a necessary property of the existence of life itself. But it’s also responsible for a deep feature of what it means to be a conscious person: the fact that we remember the past but not the future. According to the fundamental laws of physics, the past and future are treated on an equal footing, but when it comes to how we perceive the world, they couldn’t be more different. We carry in our heads representations of the past in the form of memories. Concerning the future, we can make predictions, but those predictions have nowhere near the reliability of our memories of the past.

  Ultimately, the reason why we can form a reliable memory of the past is because the entropy was lower then. In a complicated system like the universe, there are many ways for the underlying constituents to arrange themselves into the form of “you, with a certain memory of the past, plus the rest of the universe.” If that’s all you know—that you exist right now, with a memory of going to the beach that summer between sixth and seventh grade—you simply don’t have enough information to reliably conclude that you really did go to the beach that summer. It turns out to be overwhelmingly more likely that your memory is just a random fluctuation, like the air in a room spontaneously congregating over on one side. To make sense of your memories, you need to assume as well that the universe was ordered in a certain way—that the entropy was lower in the past.

  Imagine that you are walking down the street, and on the sidewalk you notice a broken egg that appears as though it hasn’t been sitting outside for very long. Our presumption of a low-entropy past allows us to say with an extremely high degree of certainty that not long ago there must have been an unbroken egg, which someone dropped. Since, as far as the future is concerned, we have no reason to suspect that entropy will decrease, there’s not much we can say about the future of the egg—too many possibilities are open. Maybe it will stay there and grow moldy, maybe someone will clean it up, maybe a dog will come by and eat it. (It’s unlikely that it will spontaneously reassemble itself into an unbroken egg, but strictly speaking that’s among the possibilities.) That egg on the sidewalk is like a memory in your brain—it’s a record of a prior event, but only if we assume a low-entropy boundary condition in the past.

  We also distinguish past from future through the relationship between cause and effect. Namely, the causes come first (earlier in time), and then come the effects. That’s why the White Queen seems so preposterous to us—how could she be yelping in pain before pricking her finger? Again, entropy is to blame. Think of the diver splashing into the pool—the splash always comes after the dive. According to the microscopic laws of physics, however, it is possible to arrange all of the molecules in the water (and the air around the pool, through which the sound of the splash travels) to precisely “unsplash” and eject the diver from the pool. To do this would require an unimaginably delicate choice of the position and velocity of every single one of those atoms—if you pick a random splashy configuration, there is almost no chance that the microscopic forces at work will correctly conspire to spit out the diver.

  In other words, part of the distinction we draw between “effects” and “causes” is that “effects” generally involve an increase in entropy. If two billiard balls collide and go their separate ways, the entropy remains constant, and neither ball deserves to be singled out as the cause of the interaction. But if you hit the cue ball into a stationary collection of racked balls on the break (provoking a noticeable increase in entropy), you and I would say “the cue ball caused the break”—even though the laws of physics treat all of the balls perfectly equally.

  THE ART OF THE POSSIBLE

  In the last chapter we contrasted the block time view—the entire four-dimensional history of the world, past, present, and future, is equally real—with the presentist view—only the current moment is truly real. There is yet another perspective, sometimes called possibilism: The current moment exists, and the past exists, but the future does not (yet) exist.

  The idea that the past exists in a way the future does not accords well with our informal notion of how time works. The past has already happened, while the future is still up for grabs in some sense—we can sketch out alternative possibilities, but we don’t know which one is real. More particularly, when it comes to the past we have recourse to memories and records of what happened. Our records may have varying degrees of reliability, but they fix the actuality of the past in a way that isn’t available when we contemplate the future.

  Think of it this way: A loved one says, “I think we should change our vacation plans for next year. Instead of going to Cancún, let’s be adventurous and go to Rio.” You may or may not go along with the plan, but the strategy should you choose to implement it isn’t that hard to work out: You change plane reservations, book a new hotel, and so forth. But if your loved one says, “I think we should change our vacation plans for last year. Instead of having gone to Paris, let’s have been adventurous and have gone to Istanbul,” your strategy would be very different—you’d think about taking your loved one to the doctor, not rearranging your past travel plans. The past is gone, it’s in the books, there’s no way we can set about changing it. So it makes perfect sense to us to treat the past and future on completely different footings. Philosophers speak of the distinction between Being—existence in the world—and Becoming—a dynamical process of change, bringing reality into existence.

  That distinction between the fixedness of the past and the malleability of the future is nowhere to be found in the known laws of physics. The deep-down microscopic rules of nature run equally well forward or backward in time from any given situation. If you know the exact state of the universe, and all of the laws of physics, the future as well as the past is rigidly determined beyond John Calvin’s wildest dreams of predestination.

  The way to reconcile these beliefs—the past is once-and-for-all fixed, while the future can be changed, but the fundamental laws of physics are reversible— ultimately comes down to entropy. If we knew the precise state of every particle in the universe, we could deduce the future as well as the past. But we don’t; we know something about the universe’s macroscopic characteristics, plus a few details here and there. With that information, we can predict certain broad-scale phenomena (the Sun will rise tomorrow), but our knowledge is compatible with a wide spectrum of specific future occurrences. When it comes to the past, however, we have at our disposal both our knowledge of the current macroscopic state of the universe, plus the fact that the early universe began in a low-entropy state. That one extra bit of information, known simply as the “Past Hypothesis,” gives us enormous leverage when it comes to reconstructing the past from the present.

  The punch line is that our notion of free will, the ability to change the future by making choices in a way that is not available to us as far as the past is concerned, is only possible because the past has a low entropy and the future has a high entropy. The future seems open to us, while the past seems closed, even though the laws of physics treat them on an equal footing.

  Because we live in a universe with a pronounced arrow of time, we treat the past and future not just as different from a practical perspective, but as deeply and fundamentally different things. The past is in the books, but the future can be influenced by our actions. Of more direct importance for cosmology, we tend to conflate “explaining the history of the universe” with “explaining the state of the early universe”—leaving the state of the late universe to work itself out. Our unequal treatment of past and future is a form of temporal chauvinism, which can be hard to eradicate from our mind-set. But that chauvinism, like so many others, has no ultimate justification in the laws of nature. When thinking about important fe
atures of the universe, whether deciding what is “real” or why the early universe had a low entropy, it is a mistake to prejudice our explanations by placing the past and future on unequal footings. The explanations we seek should ultimately be timeless.

  The major lesson of this overview of entropy and the arrow of time should be clear: The existence of the arrow of time is both a profound feature of the physical universe and a pervasive ingredient of our everyday lives. It’s a bit embarrassing, frankly, that with all of the progress made by modern physics and cosmology, we still don’t have a final answer for why the universe exhibits such a profound asymmetry in time. I’m embarrassed, at any rate, but every crisis is an opportunity, and by thinking about entropy we might learn something important about the universe.

  3

  THE BEGINNING AND END OF TIME

  What has the universe got to do with it? You’re here in Brooklyn! Brooklyn is not expanding!

  —Alvy Singer’s mom, Annie Hall

  Imagine that you are wandering around in the textbook section of your local university bookstore. Approaching the physics books, you decide to leaf through some volumes on thermodynamics and statistical mechanics, wondering what they have to say about entropy and the arrow of time. To your surprise (having been indoctrinated by the book you’re currently reading, or at least the first two chapters and the jacket copy), there is nothing there about cosmology. Nothing about the Big Bang, nothing about how the ultimate explanation for the arrow of time is to be found in the low-entropy boundary condition at the beginning of our observable universe.

  There is no real contradiction, nor is there a nefarious conspiracy on the part of textbook writers to keep the central role of cosmology hidden from students of statistical mechanics. For the most part, people interested in statistical mechanics care about experimental situations in laboratories or kitchens here on Earth. In an experiment, we can control the conditions before us; in particular, we can arrange systems so that the entropy is much lower than it could be, and watch what happens. You don’t need to know anything about cosmology and the wider universe to understand how that works.

  But our aims are more grandiose. The arrow of time is much more than a feature of some particular laboratory experiments; it’s a feature of the entire world around us. Conventional statistical mechanics can account for why it’s easy to turn an egg into an omelet but hard to turn an omelet into an egg. What it can’t account for is why, when we open our refrigerator, we are able to find an egg in the first place. Why are we surrounded by exquisitely ordered objects such as eggs and pianos and science books, rather than by featureless chaos?

  Part of the answer is straightforward: The objects that populate our everyday experience are not closed systems. Of course an egg is not a randomly chosen configuration of atoms; it’s a carefully constructed system, the assembly of which required a certain set of resources and available energy, not to mention a chicken. But we could ask the same question about the Solar System, or about the Milky Way galaxy. In each case, we have systems that are for all practical purposes isolated, but nevertheless have a much lower entropy than they could.

  The answer, as we know, is that the Solar System hasn’t always been a closed system; it evolved out of a protostellar cloud that had an even lower entropy. And that cloud came from the earlier galaxy, which had an even lower entropy. And the galaxy was formed out of the primordial plasma, which had an even lower entropy. And that plasma originated in the very early universe, which had an even lower entropy still.

  And the early universe came out of the Big Bang. The truth is, we don’t know much about why the early universe was in the configuration it was; that’s one of the questions motivating us in this book. The ultimate explanation for the arrow of time as it manifests itself in our kitchens and laboratories and memories relies crucially on the very low entropy of the early universe.

  You won’t usually find any discussion of this story in conventional textbooks on statistical mechanics. They assume that we are interested in systems that start with relatively low entropy, and take it from there. But we want more—why did our universe have such a small entropy at one end of time, thereby setting the stage for the subsequent arrow of time? It makes sense to start by considering what we do know about how the universe has evolved from its beginning up to today.

  THE VISIBLE UNIVERSE

  Our universe is expanding, filled with galaxies gradually moving apart from one another. We experience only a small part of the universe directly, and in trying to comprehend the bigger picture it’s tempting to reach for analogies. The universe, we are told, is like the surface of a balloon, on which small dots have been drawn to represent individual galaxies. Or the universe is like a loaf of raisin bread rising in the oven, with each galaxy represented by one of the raisins.

  These analogies are terrible. And not only because it seems demeaning to have something as majestic as a galaxy be represented by a tiny, wrinkled raisin. The real problem is that any such analogy brings along with it associations that do not apply to the actual universe. A balloon, for example, has an inside and an outside, as well as a larger space into which it is expanding; the universe has none of those things. Raisin bread has an edge, and is situated inside an oven, and smells yummy; there are no corresponding concepts in the case of the universe.

  So let’s take another tack. To understand the universe around us, let’s consider the real thing. Imagine standing outside on a clear, cloudless night, far away from the lights of the city. What do we see when we look into the sky? For the purposes of this thought experiment, we can grant ourselves perfect vision, infinitely sensitive to all the different forms of electromagnetic radiation.

  We see stars, of course. To the unaided eye they appear as points of light, but we have long since figured out that each star is a massive ball of plasma, glowing through the energy of internal nuclear reactions, and that our Sun is a star in its own right. One problem is that we don’t have a sense of depth—it’s hard to tell how far away any of those stars are. But astronomers have invented clever ways to determine the distances to nearby stars, and the answers are impressively large. The closest star, Proxima Centauri, is about 40 trillion kilometers away; traveling at the speed of light, it would take about four years to get there.

  Stars are not distributed uniformly in every direction. On our hypothetical clear night, we could not help but notice the Milky Way—a fuzzy band of white stretching across the sky, from one horizon to the other. What we’re seeing is actually a collection of many closely packed stars; the ancient Greeks suspected as much, and Galileo verified that idea when he turned his telescope on the heavens. In fact, the Milky Way is a giant spiral galaxy—a collection of hundreds of billions of stars, arranged in the shape of a disk with a bulge in the center, with our Solar System located as one of the distant suburbs on one edge of the disk.

  For a long time, astronomers thought that “the galaxy” and “the universe” were the same thing. One could easily imagine that the Milky Way constituted an isolated collection of stars in an otherwise empty void. But it was well known that, in addition to pointlike stars, the night sky featured fuzzy blobs known as “nebulae,” which some argued were giant collections of stars in their own right. After fierce debates between astronomers in the early years of the twentieth century,34 Edwin Hubble was eventually able to measure the distance to the nebula M33 (the thirty-third object in Charles Messier’s catalog of fuzzy celestial objects not to be confused by when one was searching for comets), and found that it is much farther away than any star. M33, the Triangulum Galaxy, is in fact a collection of stars comparable in size to the Milky Way.

  Upon further inspection, the universe turns out to be teeming with galaxies. Just as there are hundreds of billions of stars in the Milky Way, there are hundreds of billions of galaxies in the observable universe. Some galaxies (including ours) are members of groups or clusters, which in turn describe sheets and filaments of large-scale structure. On av
erage, however, galaxies are uniformly distributed through space. In every direction we look, and at every different distance from us, the number of galaxies is roughly equal. The observable universe looks pretty much the same everywhere.

  BIG AND GETTING BIGGER

  Hubble was undoubtedly one of the greatest astronomers of history, but he was also in the right place at the right time. He bounced around a bit after graduating from college, spending time variously as a Rhodes scholar, high school teacher, lawyer, soldier in World War I, and for a while as a basketball coach. But ultimately he earned a Ph.D. in astronomy from the University of Chicago in 1917 and moved to California to take up a position at the Mount Wilson Observatory outside Los Angeles. He arrived to find the brand-new Hooker telescope, featuring a mirror 100 inches across, at the time the world’s largest. It was at the 100-inch that Hubble made the observations of variable stars in other galaxies, establishing for the first time their great distance from the Milky Way.

  Meanwhile other astronomers, led by Vesto Slipher, had been measuring the velocity of spiral nebulae using the Doppler effect.35 If an object is moving with respect to you, any wave it emits (such as light or sound) will get compressed if it’s moving toward you, and stretched if it’s moving away. In the case of sound, we experience the Doppler effect as a raising of the pitch of objects that are coming toward us, and a lowering of the pitch as they move away. Similarly, we see the light from objects moving toward us shifted toward the blue (shorter wavelengths) than we would expect, and light from objects moving away is shifted toward the red (longer wavelengths). So an approaching object is blueshifted, while a receding object is redshifted.