by Brian Greene
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 y
ears, 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 huma
n 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.
