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


Chapter 5. The Frozen River


Time is among the most familiar yet least understood concepts that humanity has ever encountered. We say that it flies, we say that it’s money, we try to save it, we get annoyed when we waste it. But what is time? To paraphrase St. Augustine and Justice Potter Stewart, we know it when we see it, but surely, at the dawn of the third millennium our understanding of time must be deeper than that. In some ways, it is. In other ways, it’s not. Through centuries of puzzling and pondering, we have gained insight into some of time’s mysteries, but many remain. Where does time come from? What would it mean to have a universe without time? Could there be more than one time dimension, just as there is more than one space dimension? Can we “travel” to the past? If we did, could we change the subsequent unfolding of events? Is there an absolute, smallest amount of time? Is time a truly fundamental ingredient in the makeup of the cosmos, or simply a useful construct to organize our perceptions, but one not found in the lexicon with which the most fundamental laws of the universe are written? Could time be a derivative notion, emerging from some more basic concept that has yet to be discovered?

Finding complete and fully convincing answers to these questions ranks among the most ambitious goals of modern science. Yet the big questions are by no means the only ones. Even the everyday experience of time taps into some of the universe’s thorniest conundrums.

Time and Experience

Special and general relativity shattered the universality, the oneness, of time. These theories showed that we each pick up a shard of Newton’s old universal time and carry it with us. It becomes our own personal clock, our own personal lead relentlessly pulling us from one moment to the next. We are shocked by the theories of relativity, by the universe that is, because while our personal clock seems to tick away uniformly, in concert with our intuitive sense of time, comparison with other clocks reveals differences. Time for you need not be the same as time for me.

Let’s accept that lesson as a given. But what is the true nature of time for me? What is the full character of time as experienced and conceived by the individual, without primary focus on comparisons with the experiences of others? Do these experiences accurately reflect the true nature of time? And what do they tell us about the nature of reality?

Our experiences teach us, overwhelmingly so, that the past is different from the future. The future seems to present a wealth of possibilities, while the past is bound to one thing, the fact of what actually happened. We feel able to influence, to affect, and to mold the future to one degree or another, while the past seems immutable. And in between past and future is the slippery concept of now, a temporal holding point that rein-vents itself moment to moment, like the frames in a movie film as they sweep past the projector’s intense light beam and become the momentary present. Time seems to march to an endless, perfectly uniform rhythm, reaching the fleeting destination of now with every beat of the drummer’s stick.

Our experiences also teach us that there is an apparent lopsidedness to how things unfold in time. There is no use crying over spilled milk, because once spilled it can never be unspilled: we never see splattered milk gather itself together, rise off the floor, and coalesce in a glass that sets itself upright on a kitchen counter. Our world seems to adhere perfectly to a one-way temporal arrow, never deviating from the fixed stipulation that things can start like thisand end like that, but they can never start like that and end like this.

Our experiences, therefore, teach us two overarching things about time. First, time seems to flow. It’s as if we stand on the riverbank of time as the mighty current rushes by, sweeping the future toward us, becoming now at the moment it reaches us, and rushing onward as it recedes downstream into the past. Or, if that is too passive for your taste, invert the metaphor: we ride the river of time as it relentlessly rushes forward, sweeping us from one now to the next, as the past recedes with the passing scenery and the future forever awaits us downstream. (Our experiences have also taught us that time can inspire some of the mushiest metaphors.) Second, time seems to have an arrow.The flow of time seems to go one way and only one way, in the sense that things happen in one and only one temporal sequence. If someone hands you a box containing a short film of a glass of milk being spilled, but the film has been cut up into its individual frames, by examining the pile of images you can reassemble the frames in the right order without any help or instruction from the filmmaker. Time seems to have an intrinsic direction, pointing from what we call the past toward what we call the future, and things appear to change—milk spills, eggs break, candles burn, people age—in universal alignment with this direction.

These easily sensed features of time generate some of its most tantalizing puzzles. Does time really flow? If it does, what actually is flowing? And how fast does this time-stuff flow? Does time really have an arrow? Space, for example, does not appear to have an inherent arrow—to an astronaut in the dark recesses of the cosmos, left and right, back and forth, and up and down, would all be on equal footing—so where would an arrow of time come from? If there is an arrow of time, is it absolute? Or are there things that can evolve in a direction opposite to the way time’s arrow seems to point?

Let’s build up to our current understanding by first thinking about these questions in the context of classical physics. So, for the remainder of this and the next chapter (in which we’ll discuss the flow of time and the arrow of time, respectively) we will ignore quantum probability and quantum uncertainty. A good deal of what we’ll learn, nevertheless, translates directly to the quantum domain, and in Chapter 7 we will take up the quantum perspective.

Does Time Flow?

From the perspective of sentient beings, the answer seems obvious. As I type these words, I clearly feel time flowing. With every keystroke, each now gives way to the next. As you read these words, you no doubt feel time flowing, too, as your eyes scan from word to word across the page. Yet, as hard as physicists have tried, no one has found any convincing evidence within the laws of physics that supports this intuitive sense that time flows. In fact, a reframing of some of Einstein’s insights from special relativity provides evidence that time does not flow.

To understand this, let’s return to the loaf-of-bread depiction of spacetime introduced in Chapter 3. Recall that the slices making up the loaf are the nows of a given observer; each slice represents space at one moment of time from his or her perspective. The union obtained by placing slice next to slice, in the order in which the observer experiences them, fills out a region of spacetime. If we take this perspective to a logical extreme and imagine that each slice depicts all of space at a given moment of time according to one observer’s viewpoint, and if we include every possible slice, from the ancient past to the distant future, the loaf will encompass all of the universe throughout all time—the whole of spacetime. Every occurrence, regardless of when or where, is represented by some point in the loaf.

This is schematically illustrated in Figure 5.1, but the perspective should make you scratch your head. The “outside” perspective of the figure, in which we’re looking at the whole universe, all of space at every moment of time, is a fictitious vantage point, one that none of us will ever have. We are all within spacetime. Every experience you or I ever have occurs at some location in space at some moment of time. And since Figure 5.1 is meant to depict all of spacetime, it encompasses the totality of such experiences—yours, mine, and those of everyone and everything. If you could zoom in and closely examine all the comings and goings on planet earth, you’d be able to see Alexander the Great having a lesson with Aristotle, Leonardo da Vinci laying the final brushstroke on the Mona Lisa, and George Washington crossing the Delaware; as you continued scanning the image from left to right, you’d be able to see your grandmother playing as a little girl, your father celebrating his tenth birthday, and your own first day at school; looking yet farther to the right in the image, you could see yourself reading this book, the birth of your great-great-granddaughter, and, a little farther on, her inauguration as President. Given the coarse resolution of Figure 5.1, you can’t actually see these moments, but you can see the (schematic) history of the sun and planet earth, from their birth out of a coalescing gas cloud to the earth’s demise when the sun swells into a red giant. It’s all there.


Figure 5.1 A schematic depiction of all space throughout all time (depicting, of course, only part of space through part of time) showing the formation of some early galaxies, the formation of the sun and the earth, and the earth’s ultimate demise when the sun swells into a red giant, in what we now consider our distant future.

Unquestionably, Figure 5.1 is an imaginary perspective. It stands outside of space and time. It is the view from nowhere and nowhen. Even so—even though we can’t actually step beyond the confines of spacetime and take in the full sweep of the universe—the schematic depiction of Figure 5.1 provides a powerful means of analyzing and clarifying basic properties of space and time. As a prime example, the intuitive sense of time’s flow can be vividly portrayed in this framework by a variation on the movie-projector metaphor. We can envision a light that illuminates one time slice after another, momentarily making the slice come alive in the present—making it the momentary now—only to let it go instantly dark again as the light moves on to the next slice. Right now, in this intuitive way of thinking about time, the light is illuminating the slice in which you, sitting on planet earth, are reading this word, and now it is illuminating the slice in which you are reading this word. But, again, while this image seems to match experience, scientists have been unable to find anything in the laws of physics that embodies such a moving light. They have found no physical mechanism that singles out moment after moment to be momentarily real—to be the momentary now—as the mechanism flows ever onward toward the future.

Quite the contrary. While the perspective of Figure 5.1 is certainly imaginary, there is convincing evidence that the spacetime loaf—the totality of spacetime, not slice by single slice—is real. A less than widely appreciated implication of Einstein’s work is that special relativistic reality treats all times equally. Although the notion of now plays a central role in our worldview, relativity subverts our intuition once again and declares ours an egalitarian universe in which every moment is as real as any other. We brushed up against this idea in Chapter 3 while thinking about the spinning bucket in the context of special relativity. There, through indirect reasoning analogous to Newton’s, we concluded that spacetime is at least enough of a something to provide the benchmark for accelerated motion. Here we take up the issue from another viewpoint and go further. We argue that every part of the spacetime loaf in Figure 5.1 exists on the same footing as every other, suggesting, as Einstein believed, that reality embraces past, present, and future equally and that the flow we envision bringing one section to light as another goes dark is illusory.

The Persistent Illusion of Past, Present, and Future

To understand Einstein’s perspective, we need a working definition of reality, an algorithm, if you will, for determining what things exist at a given moment. Here’s one common approach. When I contemplate reality—what exists at this moment—I picture in my mind’s eye a kind of snapshot, a mental freeze-frame image of the entire universe right now. As I type these words, my sense of what exists right now, my sense of reality, amounts to a list of all those things—the tick of midnight on my kitchen clock; my cat stretched out in flight between floor and windowsill; the first ray of morning sunshine illuminating Dublin; the hubbub on the floor of the Tokyo stock exchange; the fusion of two particular hydrogen atoms in the sun; the emission of a photon from the Orion nebula; the last moment of a dying star before it collapses into a black hole—that are, at this moment, in my freeze-frame mental image. These are the things happening right now, so they are the things that I declare exist right now. Does Charlemagne exist right now? No. Does Nero exist right now? No. Does Lincoln exist right now? No. Does Elvis exist right now? No. None of them are on my current now-list. Does anyone born in the year 2300 or 3500 or 57000 exist now? No. Again, none of them are in my mind’s-eye freeze-frame image, none of them are on my current time slice, and so, none of them are on my current now-list. Therefore, I say without hesitation that they do not currently exist. That is how I define reality at any given moment; it’s an intuitive approach that most of us use, often implicitly, when thinking about existence.

I will make use of this conception below, but be aware of one tricky point. A now-list—reality in this way of thinking—is a funny thing. Nothing you see right now belongs on your now-list, because it takes time for light to reach your eyes. Anything you see right now has already happened. You are not seeing the words on this page as they are now; instead, if you are holding the book a foot from your face, you are seeing them as they were a billionth of a second ago. If you look out across an average room, you are seeing things as they were some 10 billionths to 20 billionths of a second ago; if you look across the Grand Canyon, you are seeing the other side as it was about one ten-thousandth of a second ago; if you look at the moon, you are seeing it as it was a second and a half ago; for the sun, you see it as it was about eight minutes ago; for stars visible to the naked eye, you see them as they were from roughly a few years ago to 10,000 years ago. Curiously, then, although a mental freeze-frame image captures our sense of reality, our intuitive sense of “what’s out there,” it consists of events that we can’t experience, or affect, or even record right now. Instead, an actual now-list can be compiled only after the fact. If you know how far away something is, you can determine when it emitted the light you see now and so you can determine on which of your time slices it belongs—on which already past now-list it should be recorded. Nevertheless, and this is the main point, as we use this information to compile the now-list for any given moment, continually updating it as we receive light from ever more distant sources, the things that are listed are the things that we intuitively believe existed at that moment.

Remarkably, this seemingly straightforward way of thinking leads to an unexpectedly expansive conception of reality. You see, according to Newton’s absolute space and absolute time, everyone’s freeze-frame picture of the universe at a given moment contains exactly the same events; everyone’s now is the same now, and so everyone’s now-list for a given moment is identical. If someone or something is on your now-list for a given moment, then it is necessarily also on my now-list for that moment. Most people’s intuition is still bound up with this way of thinking, but special relativity tells a very different story. Look again at Figure 3.4. Two observers in relative motion have nows—single moments in time, from each one’s perspective—that are different: their nows slice through spacetime at different angles. And different nows mean different now-lists. Observers moving relative to each other have different conceptions of what exists at a given moment, and hence they have different conceptions of reality.

At everyday speeds, the angle between two observers’ now-slices is minuscule; that’s why in day-to-day life we never notice a discrepancy between our definition of now and anybody else’s. For this reason, most discussions of special relativity focus on what would happen if we traveled at enormous speeds—speeds near that of light—since such motion would tremendously magnify the effects. But there is another way to magnify the distinction between two observers’ conceptions of now, and I find that it provides a particularly enlightening approach to the question of reality. It is based on the following simple fact: if you and I slice up an ordinary loaf at slightly different angles, it will have hardly any effect on the resulting pieces of bread. But if the loaf is huge, the conclusion is different. Just as a tiny opening between the blades of an enormously long pair of scissors translates into a large separation between the blade tips, cutting an enormous loaf of bread at slightly different angles yields slices that deviate by a huge amount at distances far from where the slices cross. You can see this in Figure 5.2.

The same is true for spacetime. At everyday speeds, the slices depicting now for two observers in relative motion will be oriented at only slightly different angles. If the two observers are nearby, this will have hardly any effect. But, just as in the loaf of bread, tiny angles generate large separations between slices when their impact is examined over large distances. And for slices of spacetime, a large deviation between slices means a significant disagreement on which events each observer considers to be happening now. This is illustrated in Figures 5.3 and 5.4, and it implies that individuals moving relative to each other, even at ordinary, everyday speeds, will have increasingly different conceptions of now if they are increasingly far apart in space.

To make this concrete, imagine that Chewie is on a planet in a galaxy far, far away—10 billion light-years from earth—idly sitting in his living room. Imagine further that you (sitting still, reading these words) and Chewie are not moving relative to each other (for simplicity, ignore the motion of the planets, the expansion of the universe, gravitational effects, and so on). Since you are at rest relative to each other, you and Chewie agree fully on issues of space and time: you would slice up spacetime in an identical manner, and so your now-lists would coincide exactly. After a little while, Chewie stands up and goes for a walk—a gentle, relaxing amble—in a direction that turns out to be directly away from you.


Figure 5.2 (a) In an ordinary loaf, slices cut at slightly different angles don’t separate significantly. (b) But the larger the loaf, for the same angle, the greater the separation.

This change in Chewie’s state of motion means that his conception of now, his slicing up of spacetime, will rotate slightly (see Figure 5.3). This tiny angular change has no noticeable effect in Chewie’s vicinity: the difference between his new now and that of anyone still sitting in his living room is minuscule. But over the enormous distance of 10 billion light years, this tiny shift in Chewie’s notion of now is amplified (as in the passage from Figure 5.3a to 5.3b, but with the protagonists now being a huge distance apart, significantly accentuating the shift in their nows). His now and your now, which were one and the same while he was sitting still, jump apart because of his modest motion.


Figure 5.3 (a) Two individuals at rest relative to each other have identical conceptions of now and hence identical time slices. If one observer moves away from the other their time slices—what each observer considers now—rotate relative to each other; as illustrated, the darkened now slice for the moving observer rotates into the past of the stationary observer. (b) A greater separation between the observers yields a greater deviation between slices—a greater deviation in their conception of now.

Figures 5.3 and 5.4 illustrate the key idea schematically, but by using the equations of special relativity we can calculate how different your nows become.1 If Chewie walks away from you at about 10 miles per hour (Chewie has quite a stride) the events on earth that belong on his new now-list are events that happened about 150 years ago, according to you! According to his conception of now—a conception that is every bit as valid as yours and that up until a moment ago agreed fully with yours— you have not yet been born. If he moved toward you at the same speed, the angular shift would be opposite, as schematically illustrated in Figure 5.4, so that his now would coincide with what you would call 150 years in the future! Now, according to his now, you may no longer be a part of this world. And if, instead of just walking, Chewie hopped into the MillenniumFalcon traveling at 1,000 miles per hour (less than the speed of a Concorde aircraft), his now would include events on earth that from your perspective took place 15,000 years ago or 15,000 years in the future, depending on whether he flew away or toward you. Given suitable choices of direction and speed of motion, Elvis or Nero or Charlemagne or Lincoln or someone born on earth way into what you call the future will belong on his new now-list.


Figure 5.4 (a) Same as figure 5.3a, except when one observer moves toward the other, her now slice rotates into the future, not the past, of the other observer. (b) Same as 5.3b—a greater separation yields a greater deviation in conceptions of now, for the same relative velocity— with the rotation being toward the future instead of the past.

While surprising, none of this generates any contradiction or paradox because, as we explained above, the farther away something is, the longer it takes to receive light it emits and hence to determine that it belongs on a particular now-list. For instance, even though John Wilkes Booth’s approaching the State Box at Ford’s Theatre will belong on Chewie’s new now-list if he gets up and walks away from earth at about 9.3 miles per hour,2 he can take no action to save President Lincoln. At such an enormous distance, it takes an enormous amount of time for messages to be received and exchanged, so only Chewie’s descendants, billions of years later, will actually receive the light from that fateful night in Washington. The point, though, is that when his descendants use this information to update the vast collection of past now-lists, they will find that the Lincoln assassination belongs on the same now-list that contains Chewie’s just getting up and walking away from earth. And yet, they will also find that a moment before Chewie got up, his now-list contained, among many other things, you, in earth’s twenty-first century, sitting still, reading these words.3

Similarly, there are things about our future, such as who will win the U.S. presidential election in the year 2100, that seem completely open: more than likely, the candidates for that election haven’t even been born, much less decided to run for office. But if Chewie gets up from his chair and walks toward earth at about 6.4 miles per hour, his now-slice—his conception of what exists, his conception of what has happened—will include the selection of the first president of the twenty-second century. Something that seems completely undecided to us is something that, for him, has already happened. Again, Chewie won’t know the outcome of the election for billions of years, since that’s how long it will take our television signals to reach him. But when word of the election results reaches Chewie’s descendants and they use it to update Chewie’s flip-card book of history, his collection of past now-lists, they will find that the election results belong on the same now-list in which Chewie got up and started walking toward earth—a now-list, Chewie’s descendants note, that occurs just a moment after one that contains you, in the early years of earth’s twenty-first century, finishing this paragraph.

This example highlights two important points. First, although we are used to the idea that relativistic effects become apparent at speeds near that of light, even at low velocities relativistic effects can be greatly amplified when considered over large distances in space. Second, the example gives insight into the issue of whether spacetime (the loaf) is really an entity or just an abstract concept, an abstract union of space right now together with its history and purported future.

You see, Chewie’s conception of reality, his freeze-frame mental image, his conception of what exists now, is every bit as real for him as our conception of reality is for us. So, in assessing what constitutes reality, it would be stunningly narrow-minded if we didn’t also include his perspective. For Newton, such an egalitarian approach wouldn’t make the slightest difference, because, in a universe with absolute space and absolute time, everyone’s now-slice coincides. But in a relativistic universe, our universe, it makes a big difference. Whereas our familiar conception of what exists right now amounts to a single now-slice—we usually view the past as gone and the future as yet to be—we must augment this image with Chewie’s now-slice, a now-slice that, as the discussion revealed, can differ substantially from our own. Furthermore, since Chewie’s initial location and the speed with which he moves are arbitrary, we should include the now-slices associated with all possibilities. These now-slices, as in our discussion above, would be centered on Chewie’s—or some other real or hypothetical observer’s—initial location in space and would be rotated at an angle that depends on the velocity chosen. (The only restriction comes from the speed limit set by light and, as explained in the notes, in the graphic depiction we are using this translates into a limit on the rotation angle of 45 degrees, either clockwise or counterclockwise.) As you can see, in Figure 5.5, the collection of all these now-slices fills out a substantial region of the spacetime loaf. In fact, if space is infinite—if now-slices extended infinitely far—then the rotated now-slices can be centered arbitrarily far away, and hence their union sweeps through every point in the spacetime loaf.9

So: if you buy the notion that reality consists of the things in your freeze-frame mental image right now, and if you agree that your now is no more valid than the now of someone located far away in space who can move freely, then reality encompasses all of the events in spacetime. The total loaf exists. Just as we envision all of space as really being out there, as really existing, we should also envision all of time as really being out there, as really existing, too. Past, present, and future certainly appear to be distinct entities. But, as Einstein once said, “For we convinced physicists, the distinction between past, present, and future is only an illusion, however persistent.”5 The only thing that’s real is the whole of spacetime.


Figure 5.5 A sample of now-slices for a variety of observers (real or hypothetical) situated at a variety of distances from earth, moving with a variety of velocities.

Experience and the Flow of Time

In this way of thinking, events, regardless of when they happen from any particular perspective, just are. They all exist. They eternally occupy their particular point in spacetime. There is no flow. If you were having a great time at the stroke of midnight on New Year’s Eve, 1999, you still are, since that is just one immutable location in spacetime. It is tough to accept this description, since our worldview so forcefully distinguishes between past, present, and future. But if we stare intently at this familiar temporal scheme and confront it with the cold hard facts of modern physics, its only place of refuge seems to lie within the human mind.

Undeniably, our conscious experience seems to sweep through the slices. It is as though our minds provide the projector light referred to earlier, so that moments of time come to life when they are illuminated by the power of consciousness. The flowing sensation from one moment to the next arises from our conscious recognition of change in our thoughts, feelings, and perceptions. And the sequence of change seems to have a continuous motion; it seems to unfold into a coherent story. But—without any pretense of psychological or neurobiological precision—we can envision how we might experience a flow of time even though, in actuality, there may be no such thing. To see what I mean, imagine playing Gone with the Wind through a faulty DVD player that randomly jumps forward and backward: one still frame flashes momentarily on the screen and is followed immediately by another from a completely different part of the film. When you watch this jumbled version, it will be hard for you to make sense of what’s going on. But Scarlett and Rhett have no problem. In each frame, they do what they’ve always done in that frame. Were you able to stop the DVD on some particular frame and ask them about their thoughts and memories, they’d respond with the same answers they would have given had you played the DVD in a properly functioning player. If you asked them whether it was confusing to romp through the Civil War out of order, they’d look at you quizzically and figure you’d tossed back one too many mint juleps. In any given frame, they’d have the thoughts and memories they’ve always had in that frame—and, in particular, those thoughts and memories would give them the sensation that time is smoothly and coherently flowing forward, as usual.

Similarly, each moment in spacetime—each time slice—is like one of the still frames in a film. It exists whether or not some light illuminates it. As for Scarlett and Rhett, to the you who is in any such moment, it is the now, it isthe moment you experience at that moment. And it always will be. Moreover, within each individual slice, your thoughts and memories are sufficiently rich to yield a sense that time has continuously flowed to that moment. This feeling, this sensation that time is flowing, doesn’t require previous moments—previous frames—to be “sequentially illuminated.”6

And if you think about it for one more moment, you’ll realize that’s a very good thing, because the notion of a projector light sequentially bringing moments to life is highly problematic for another, even more basic reason. If the projector light properly did its job and illuminated a given moment—say, the stroke of midnight, New Year’s Eve, 1999—what would it mean for that moment to then go dark? If the moment were lit, then being illuminated would be a feature of the moment, a feature as everlasting and unchanging as everything else happening at that moment. To experience illumination—to be “alive,” to be the present, to be the now—and to then experience darkness—to be “dormant,” to be the past, to be what was—is to experience change. But the concept of change has no meaning with respect to a single moment in time. The change would have to occur through time, the change would mark the passing of time, but what notion of time could that possibly be? By definition, moments don’t include the passing of time—at least, not the time we’re aware of— because moments just are, they are the raw material of time, they don’t change. A particular moment can no more change in time than a particular location can move in space: if the location were to move, it would be a different location in space; if a moment in time were to change, it would be a different moment in time. The intuitive image of a projector light that brings each new now to life just doesn’t hold up to careful examination. Instead, every moment is illuminated, and every moment remains illuminated. Every moment is. Under close scrutiny, the flowing river of time more closely resembles a giant block of ice with every moment forever frozen into place.7

This conception of time is significantly different from the one most of us have internalized. Even though it emerged from his own insights, Einstein was not hardened to the difficulty of fully absorbing such a profound change in perspective. Rudolf Carnap8 recounts a wonderful conversation he had with Einstein on this subject: “Einstein said that the problem of the now worried him seriously. He explained that the experience of the now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.”

This resignation leaves open a pivotal question: Is science unable to grasp a fundamental quality of time that the human mind embraces as readily as the lungs take in air, or does the human mind impose on time a quality of its own making, one that is artificial and that hence does not show up in the laws of physics? If you were to ask me this question during the working day, I’d side with the latter perspective, but by nightfall, when critical thought eases into the ordinary routines of life, it’s hard to maintain full resistance to the former viewpoint. Time is a subtle subject and we are far from understanding it fully. It is possible that some insightful person will one day devise a new way of looking at time and reveal a bona fide physical foundation for a time that flows. Then again, the discussion above, based on logic and relativity, may turn out to be the full story. Certainly, though, the feeling that time flows is deeply ingrained in our experience and thoroughly pervades our thinking and language. So much so, that we have lapsed, and will continue to lapse, into habitual, colloquial descriptions that refer to a flowing time. But don’t confuse language with reality. Human language is far better at capturing human experience than at expressing deep physical laws.