Monday, November 15, 1982
IF IT WASN’T for time, I could live forever. Does that make sense? If it wasn’t for space, I could be everywhere. Is there a difference? I want to go back to my happy college days. I want to be a newlywed again. I want to be three feet tall and sit on my mother’s lap. I don’t want to die. I want to see the future. Time won’t let me. Let’s kill time. Let’s get past time. Let’s reach through time and grab hold of eternity. Now there’s no time. There’s no time now.
Fig. 132. Let’s kill time.
Later. Do you hate time? Alarm clocks, sure. Changing the clocks for daylight-saving time is the worst. How can they just take an hour away like that? Remember in 1973 when Nixon took away two hours for the oil companies?
“The older I get, the faster time goes” my mother told me. “The years just fly by. Every time I turn around, it’s Christmas or Thanksgiving.” Party time speeds up and slows down like an out-of-control movie. Ten minutes lasts for two hours, but the next time you look at your watch, it’s three in the morning. Airport time. Sex time. Street time. Fast or slow, it all passes.
Fig. 133. Fast and slow.
That was my big realization twenty years ago. It all passes. Here I am at the bathroom door, and how can I ever get to the sink? How can high school ever end, how can I ever finish college, how can I ever be married? But then I’m at the sink, I’m back out the door, I have a Ph.D., I’m married with three kids, and twenty years have passed. Here I am alive, and how can I ever die? But I will, I know I will, I know it in my soul.
Death. It’s like the basic puzzle issued to each of us at birth. Hi, you’re alive now, isn’t it nice? Someday you’ll die and it’ll be over. What are you going to do about it? It’s awful, it’s terrifying, it’s enough to make a person commit suicide!
Fig. 134. It all passes.
Philosophia perennis — the phrase was coined by Leibniz; but the thing — the metaphysic that recognizes a divine Reality substantial to the world of things and lives and minds, the psychology that finds in the soul something similar to, or even identical with, divine Reality, the ethic that places man’s final end in the knowledge of the imminent and transcendent Ground of all being — the thing is immemorial and universal.
The Perennial Philosophy, 1944
If time didn’t pass, I’d always be here now, writing this chapter. I’m scared of dying. I’d like to think that time doesn’t really pass. What I’m going to do in this chapter is to present some scientific justifications for the belief that the passage of time is an illusion.
People ordinarily think of the world as being a three-dimensional space that changes with the passage of time. The past is gone, the future doesn’t exist yet, and only the present is real. But there is another way of looking at the world: we can regard the world as a block universe. When we think of the world as a block universe, we put all of space and time together to make a single huge object. The block universe is made up of spacetime. Spacetime is four-dimensional: three space dimensions plus one time dimension. To look at spacetime from the outside is to stand outside of history and view things sub specie aeternitatis.
“Spacetime” may sound like something technical and far removed from ordinary life. But I would argue that it is really a more natural concept than “space that changes with time.”
Suppose you work in an office miles away from your house. At 7:00 you see your bedroom; at 10:00 you see your desk. One day at 10:00 you sit in your office and wonder what is real. If you believe the world consists of a space that changes with time, then you are more or less committed to the view that the past is gone. So you will feel that your 10:00 bedroom exists, but your 7:00 bedroom does not exist. Yet your 10:00 bedroom is not something you can see, sitting there in your office. Wouldn’t it be more reasonable to believe that the 7:00 bedroom (which you saw and can well remember) is real, and that it is the 10:00 bedroom whose existence is doubtful?
Fig. 135. What’s real!
My world is, in the last analysis, the sum total of my sensations. These sensations can be most naturally arranged as a pattern in four-dimensional spacetime. My life is a sort of four-dimensional worm embedded in a block universe. To complain that my lifeworm is only (let us say) seventy-two years long is perhaps as foolish as it would be to complain that my body is only six feet long. Eternity is right outside of spacetime. Eternity is right now.
This is not a new idea by any means. The teaching that all history is an eternal Now is central to the classic mystic tradition. In one of his sermons, the fourteenth-century priest Meister Eckhart expressed the basic idea as vividly as anyone before or since:
A day, whether six or seven ago, or more than six thousand years ago, is just as near to the present as yesterday. Why? Because all time is contained in the present Now-moment.
To talk about the world as being made by God tomorrow, or yesterday, would be talking nonsense. God makes the world and all things in this present now. Time gone a thousand years ago is now as present and as near to God as this very instant.
Whether or not we share Eckhart’s beliefs about God, the image of spacetime being created all at once is a powerful one. Whenever I read his words I get an image of a big old man with a white beard flinging a bucket of paint at a barn wall. Splat: there’s all of spacetime, created all at once, created right now.
Fig. 136. “God makes the world and all the things in this present now.”
Tuesday, November 16, 1982
Space is made up of locations; spacetime is made up of events. An “event” is just what it sounds like: a given place at a given time. Each of your sense impressions is a little event. The events you experience fall into a natural four-dimensional order: north/south, east/west, up/down, sooner/later. When you look back at your life, you are really looking at a four-dimensional spacetime pattern. So there is nothing very strange or confusing about spacetime, as long as we are looking at it from the “inside.”
Looking at spacetime from the “outside” is a little harder: four-dimensional things are always difficult to visualize. Let us, once again, think about Flatland. Imagine that A Square is resting alone in an empty field, and that shortly after noon his father, A Triangle, slides up to him and then slides off. If we take time to be a third dimension perpendicular to the plane of Flatland, then we can illustrate these events by a spacetime diagram as shown in figure 137. Here A Square and A Triangle are wormlike patterns in spacetime. Their brief encounter at 12:05 is represented as a bending together of their lifeworms. Nothing really moves here; this is just an eternal pattern in spacetime. At 12:05 A Triangle is next to A Square; this is an eternal fact, a fact that can never change.
Try to imagine a picture like figure 137 that encompasses the entire space and time of Flatland. This vast tangle of worms and threads would make up what we call the Flat-land block universe. You could think of making a model of the Flatland block universe by standing above Flatland and filming the action as the polygons move around. If you then cut apart the film’s frames and stacked them up in temporal order, you’d have a good model of part of the Flatland block universe.
Fig. 137. A region of Flatland’s spacetime.
Fig. 138. Flatland’s spacetime is like a stack of film frames.
Before going any further, I should stop to answer a question that some of you may be asking. If we’re going to think of time as a fourth dimension, does that mean that all the things we’ve said about the fourth dimension are really about time? The answer is no. Just as there is no one fixed direction in space that we always call “width,” there need be no one fixed higher dimension that is always called “time.” All our talk about the fourth dimension has enabled us to think of a variety of higher dimensions: a direction in which one can jump out of space, a direction in which space is curved, a direction in which one moves to reach alternate universes. We can, if we like, insist that the past/future axis of time is the fourth dimension. And then we pretty well have to say that the ana/kata axis out of space is the fifth dimension, and the sixth dimension is the direction to other curved spacetimes. But there’s no point being so rigid about it. Nobody goes around saying width is the second dimension and height is the third dimension. Instead we just say that height and width are space dimensions. Rather than saying time is the fourth dimension, it is more natural to say that time is just one of the higher dimensions.
Fig. 139. Space + Time + Hyperspace, for Lineland.
If we think of Lineland as being a one-dimensional (east/west) world whose space bulges into hyperspace (ana/kata) wherever matter is present, and whose space is different at different times (past/future), then we get a 3-D space-hyperspace-time diagram as drawn in figure 139. Of course, if 1-D Lineland were beefed up to a full 3-D space, the diagram would have to be 5-D. Staying with figure 139 for just another second, note that what is shown is two segments merging to make one large segment, and an extra-large segment giving birth to a smaller segment. This picture makes up part of what we might call the Lineland block universe.
O.K. So now I’ve made the point that although time is one of the higher dimensions, there are many other possible dimensions as well. By the end of this book I’ll be raving, and out-of-it, and saying space is infinite-dimensional, no doubt. But there’s still a lot more to say about spacetime and the concept of the block universe.
Many philosophers argue that it is wrong to say our reality is a block universe. They do not want to represent our past-present-future universe as a static 4-D spacetime pattern.
They feel that this eternal, unchanging image leaves out something important: the passage of time.
Of course, the whole reason for introducing the block universe was to get rid of the passage of time. But how can I say that so universally experienced a phenomenon is nonexistent?
Wednesday, November 17, 1982
Another day has passed, and here I am trying to claim that the passage of time is an illusion. What could be more ridiculous? I remember, about five years ago, visiting my father in the hospital. He was having heart trouble, and felt depressed. I tried to cheer him up by explaining the block universe to him, and by pointing out that one’s life is a permanent unchanging pattern in spacetime. “Rudy,” he said wearily, “all I know about time is that you get old and then you die.”
It certainly feels like time is passing; I’d be foolish to argue otherwise. But I want to show you that this feeling is a sort of illusion. Change is unreal. Nothing is happening. The feeling that time is passing is just that: a feeling that goes with being a certain sort of spacetime pattern.
Let me illustrate my thoughts with another excerpt from that imaginary classic, The Further Adventures of A Square.
That afternoon my Father came to advise me of my impending Arrest. Una’s husband had sworn out a Warrant of Complaint. Exhausted from my morning’s pleasure, I scoffed at the old Triangle’s warnings and sent him on his way. What need had I to fear the vengeance of flat Polygons? Who of them could harm me — friend and follower of A Cube? Filled by the delicious lassitude of passion spent, I fell into a slumber.
In Dream I saw the Sphere again, floating with me in some Higher Space. His surface glowed with a solemn Luster, and I was seized with shame at my Vice. Seeking to dissemble, I called out a confident greeting.
I: Hail, lordly Sphere. Long have I sought you, long have you lingered beyond my ken.
SPHERE: The Cube would teach you on his own. Space he has taught you, but now that your Death draws near, I return to teach you Time.
I: Why speak of Death? I have not sinned!
SPHERE: Ah Square, so small is your knowing, so great is your baseness. Wouldst lie to me, who sees All? I see your past, I see your future, and your future is fraught with Peril.
I: What must I do to escape?
SPHERE: Ask the villain Cube, when next you see him. Mayhap he knows some ruse to extend your Span. But it is all foolishness, your race is Mortal. The teaching I bring to this Vision is beyond your squalid struggle for more Time. My Teaching is that Time is Unreal, and Eternity is Now.
I: What kind of Death do you foresee?
SPHERE: Silence, fool. Behold!
And there before us I seemed to see a strange and intricate Form of three dimensions. It was like a Cube, but transparent and patterned all within. Tubes and Worms and Threads ran from this strange Cube’s bottom to its top; some of the Tubes were round in cross section, others were Triangular or Square. The uppermost surface of the Cube looked familiar to me, and suddenly I realized it was my World.
Fig. 140. A tangled tale.
There slumbered my Square form, there was my Father’s familiar Triangle, and in the distance cowered a chastened Una. A Hexagon and an Isosceles were near my sleeping form, evidently bent on Violence. Only my loyal Father’s intercession was keeping them at bay.
All this I saw atop the Cube. Moving my attention downward I could trace out the whole tangled history of Love and Hate.
The Isosceles’s Point attracted my notice above all else, and I begged the Sphere for aid.
I: You will save me, will you not, most noble Sphere?
SPHERE: Your salvation is not mine to grant. What is this object that we gaze upon?
I: An ingenious model of some part of Flatland. There on the top is my sleeping Form, my Father, and …
SPHERE: What of the Cube’s interior, Square?
I: You have stacked up many models of my world, O Teacher. Each plane cross section of the Cube displays a different instant of my recent (and regretted) Career. It is indeed a clever Construct, an inspired use of Higher Space.
SPHERE: Suppose I were to tell you this is no Construct? What you see is a higher level of Reality. What you see is your Space and Time. This is your World.
I: My Liege is pleased to be merry. This dead, unmoving Construct is to replace the passionate bustle of Flatland life? One could as well say that a painting breathes, or that a statue weeps!
SPHERE: The Teaching is strange, but it is no Jest. The block you see is a region of Flatland’s Spacetime.
I: Spacetime, my Lord?
SPHERE: Space plus Time, thou Dullard. Hear the words of a great Spaceland thinker: Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. Space is a shadow, Time’s passing is an illusion; only Spacetime is real.
Fig. 141. The moving “Now.”
I: Again I must protest, O Round One. Life consists of change and Motion. Where in this Construct of Flatland’s Spacetime is there Motion?
SPHERE: You may imagine the Motion as follows. Suppose that a plane were to move up through the Cube of Spacetime. Think of the plane as a moving “Now.” Fix your attention upon it, and you will see your Form dancing its sorry Jig.
I: You are saying, then, that my conscious Mind lights up a cross section of Spacetime, and that the passage of Time is the upward motion of my Mind?
SPHERE: I say no such thing. There is no motion in spacetime. Your Mind, such as it is, extends the length of your Span. More truly spoken, the Mind is everywhere, and you have no Mind at all.
I: I do not understand you, my Lord.
SPHERE: Nor do I understand myself.
Fig. 142. Time as the motion of the mind’s eye.
Thursday, November 18, 1982
The purpose of the last dialogue was to present what the physicist David Park has called “the fallacy of the animated Minkowski diagram.” A spacetime diagram such as figure 140 is called a Minkowski diagram in honor of Russian mathematician Hermann Minkowski (1864-1909), who was the first to think of drawing such pictures. A Square says that such a diagram is lacking something: the passage of time. We do not experience childhood, adolescence, and maturity all at once. We live through one stage, then the next, then the next, and so on. A Square feels that figure 140 is just a model, but that the reality would be best represented by moving an illuminated plane up through the spacetime solid. First one cross section would be lit up, then the next, then the next, and so on. In this manner the static Minkowski diagram could be animated, or brought to life. If we think of the spacetime diagram as being like a movie, it is as if A Square is saying that the movie needs to be taken out of the can and projected. If we think of the diagram as being like a novel, it is as if A Square is saying that the novel needs a reader who goes through it page by page.
But there are a lot of problems with the notion of an animated Minkowski diagram. One difficulty is that if we think of a static spacetime, and then imagine an external Mind, which sort of moves a searchlight up along it, we have introduced a second level of time: the time that lapses as the Mind moves its attention through spacetime. Now, if spacetime is to be everything, then it seems awkward and wrong to have a second kind of time lapsing external to it. With something like a novel, this poses no problem: the book incorporates its own time pattern, and the time it takes me to read the book is something else entirely. But we do not stand outside the universe like a reader outside a book; we are in our spacetime.
That’s just my opinion, of course. I have, in fact, met people who do hold to the belief that spacetime is something like a novel being “read” by their soul, the “soul” being some kind of eye or observer that stands outside spacetime, slowly moving its gaze up along the time axis. I find this unsatisfying.
Fig. 143. Three animations of the same life.
If your life is like a novel that your soul is “reading,” then the past is not so real after all. Even worse, death is just as real as ever: death is when the soul runs out of spacetime pattern to “read.”
Another confusing point the animated Minkowski diagram raises is this: what if the diagram is animated more than once? What if, in other words, there is a second “reader of the novel,” or a third, or a fourth, or infinitely many? What if a whole series of souls moves through your spacetime, living your life over and over? What if a whole infinite continuum of souls is moving up through your life, one at each instant at all times? But then your whole life is “lit up,” so why say any thing’s moving at all?
The very starting point of special relativity theory consists in the discovery of a new and very astonishing property of time, namely the relativity of simultaneity, which to a large extent implies that of succession. The assertion that the events A and B are simultaneous loses its objective meaning, in so far as another observer, with the same claim to correctness, can assert that A and B are not simultaneous.
Following up the consequences of this strange state of affairs one is led to conclusions about the nature of time which are very far-reaching indeed. In short, it seems that one obtains an unequivocal proof for the view of those philosophers who, like Parmenides, Kant, and the modern idealists, deny the objectivity of change and consider change as an illusion or an appearance due to our special mode of perception. The argument runs as follows: Change becomes possible only through the lapse of time. The existence of an objective lapse of time, however, means that reality consists of an infinity of layers of ’now’ which come into existence successively. But, if simultaneity is something relative in the sense just explained, reality cannot be split up into such layers in an objectively determined way. Each observer has his own set of ’nows,’ and none of these various systems of layers can claim the prerogative of representing the objective lapse of time.
“A Remark on the Relationship Between Relativity Theory and Idealistic Philosophy,” 1959
Friday, November 19, 1982
What I want to say is that each of us is a certain spacetime pattern in the block universe. Today, or the day of my birth, or the day of my death — all are equally real, all are different pieces of the block universe. I will never stop living this instant. This instant will never cease to exist; this instant has always existed.
About ten years ago I had a chance to meet the great logician Kurt Gödel. I used to phone him up and ask him questions about philosophy. In my book Infinity and the Mind I have a section that describes a conversation I had with Gödel about the passage of time:
We talked a little set theory, and then I asked him my last question: “What causes the illusion of the passage of time?”
Gödel spoke not directly to this question, but to the question of what my question meant — that is, why anyone would even believe that there is a perceived passage of time at all.
He went on to relate the getting rid of belief in the passage of time to the struggle to experience the One Mind of mysticism. Finally he said this: “The illusion of the passage of time arises from confusing the given with the real. Passage of time arises because we think of occupying different realities. In fact, we occupy only different givens. There is only one reality.”
By a “given,” Gödel means a person’s sensations at some particular time. At any moment the world “gives” us a collection of sights, sounds, smells, and so on. By a more or less unconscious process, we organize these sensations into a stable framework. This background framework, which everyone agrees on, is reality: a continuum of three space dimensions and one time dimension. When I am in my office, I do not doubt the existence of my home. By the same token, when it is 10:00, I do not doubt the existence of 7:00. I do not think of a person as an object adrift in space; a person is a certain kind of pattern in spacetime.
A human body changes most of its atoms every few years. Daily one eats and inhales billions of new atoms, daily one excretes, sheds, and breathes out billions of old ones. Physically, my present body has almost nothing in common with the body I had twenty years ago. Since I feel that I am still the same person, it must be that “I” am something other than the collection of atoms making up my body. “I” am not so much my atoms as I am the pattern in which my atoms are arranged. Some of the atom patterns in my brain code up certain memories; it is the continuity of these memories that gives me my sense of personal identity.
Fig. 144. People are spacetime braids of atom threads.
In figure 144 we have drawn a picture to represent the fact that people are persistent spacetime patterns. To simplify things we represent a person as a braid of three atom threads (where an “atom thread” is the spacetime trail of an individual atom). Note that in neither of the two braid-people in the picture’s center do we have any single atom thread going the whole length. Note also that an atom can leave one person’s braid and become part of someone else’s.
What I find most striking about figure 144 is that the gray boxes enclosing individual lives are purely imaginary. The simple processes of eating and breathing weave all of us together into a vast four-dimensional tapestry. No matter how isolated you may sometimes feel, no matter how lonely, you are never really cut off from the whole.
I find this insight a great comfort. Instead of thinking of myself as a decaying bag of meat, I can think of myself as a part of eternal spacetime. This is a way to cheat death. Instead of identifying myself with my specific body pattern, I identify myself with the block universe as a whole. I am, as it were, an eye that the cosmos uses to look at itself. The Mind is not mine alone; the Mind is everywhere. If I do not exist, then how can I die?
Monday, November 22, 1982
“How can I die?” Well, I could have fallen off that broken viaduct I was drunkenly standing at the edge of, Saturday night, just to show off. Ow. Why, at my age, do I still do things like that? To prove that I have free will.
Every so often, one likes to do something foolish or unexpected. Much of life is quite predictable, but it is the crazy zigzags that give human life its peculiar savor. It’s not really necessary to do something stupid and dangerous … Taking your wife out for dinner on a Wednesday night can be unusual enough.
If we are indeed spacetime patterns in a block universe, then the future already exists. Does this conflict with the notion that we have free will?
Not really. When I say the future is already there, I am not saying that the future can be predicted. When you are halfway through a detective novel, the ending is already there, printed on the last pages. But this does not mean that you can always guess what the ending will be. I feel that my entire life exists as a timeless whole. But this does not mean that I can predict with certainty what I’ll write tomorrow, or where I’ll live next year.
Sometimes when I try to explain the spacetime viewpoint to people they say, “If you’re just a pattern in spacetime and the future’s already fixed, then why don’t you kill yourself and get it over with? I mean, you’re going to die anyway, right? Why not shoot yourself?” The answer is simple: “Because I don’t want to.” I may enjoy dramatizing the choice between life and death by standing at the edge of a hundred-meter drop — but I’m damn careful not to fall off.
Fig. 145. I don’t want to die.
It is a plant’s nature to grow toward the sun, to bloom, and to bear fruit. It is a person’s nature to live and love and work. In all likelihood, there is no big “Answer,” and life has no significance outside itself. But that’s enough. As Don Juan puts it in Carlos Castaneda’s A Separate Reality:
I choose to live, and to laugh, not because it matters, but because that choice is the bent of my nature … A man of knowledge chooses a path with heart and follows it … Nothing being more important than anything else, a man of knowledge chooses any act, and acts it out as if it matters to him.
The idea here is that your life is a whole, and the overall pattern is what counts. The unexpected kinks in the pattern correspond to places where you feel yourself to be making a free will decision.
Some people object very much to this view. So strong is their belief in the importance of their own free will, that they feel the future does not exist at all. They may grant that the past exists, but they feel that the block universe is something that is growing upward as time goes on. In figure 146 we illustrate this viewpoint, along with the block universe viewpoint, and the viewpoint that gives reality only to the present instant.
Fig. 146. Differing world views.
The great advantage the block universe has over the other viewpoints is that in the block universe there is no objectively existing “Now.” Nothing is moving in the block universe, and there is no need to try to find some absolute and objective meaning for the horizontal space sheet that the other two models depend on.
As it turns out, it is actually impossible to find any objective and universally acceptable definition of “all of space, taken at this instant.” This follows, as we shall see, from Einstein’s special theory of relativity. The idea of the block universe is, thus, more than an attractive metaphysical theory. It is a well-established scientific fact.
Tuesday, November 23, 1982
Today I want to draw a lot of Minkowski diagrams: pictures of spacetime. To make things easier, we’ll think of space as a one-dimensional line, and we’ll think of objects as points moving back and forth on this line. The spacetime trail of a dot is called the dot’s world line. In figure 147 we see five different sorts of world lines. A represents a motionless point, and B represents a point that moves steadily to the right. C is a dot that starts out motionless but then begins moving faster and faster to the right. D makes an excursion to the right and then comes back to his starting point. E is in a steady state of right-left oscillation.
If we say that the fourth dimension is time, then it is possible to construct a hypersphere in space and time. How?
Fig. 147. Various kinds of motion.
It is really a bit misleading to say that A is motionless, and B is moving to the right. If A and B are actual people, say astronauts floating in empty space, then all they can really be sure of is that they are moving apart from each other.
Fig. 148. Three descriptions of the same state of affairs.
Since it is impossible to make marks on the fabric of space, there really is no such thing as absolute motion. The only kind of motion one can hope to observe is the motion of one object relative to some other object. This is the content of Einstein’s principle of relativity: “The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.” In formulating his theory of space and time, Einstein makes one other assumption, the principle of the constancy of the speed of light: Whenever someone measures the speed of light, he or she will always come up with the same value c (= 29,979,245,620 centimeters per second ≈ one billion miles per hour). These two assumptions have strong empirical support. Taken together, they lead to a number of surprising consequences.
Usually, in drawing Minkowski diagrams, one adopts a system of units so that the path of a light ray is represented by a 45° line. Light moves at about one billion miles per hour, so the idea is to mark off the space axis in units of billions of miles and mark off the time axis in units of one hour. In figure 149 we have marked the axes in this way, and we have drawn in the world line of a pulse of light. At time 1, A sends a light flash off to the right. One billion miles away stands M, patiently holding a mirror. After an hour’s travel time, the light hits M’s mirror and bounces back to the left. A gets out of the light’s way, and it continues traveling to the left indefinitely.
Fig. 149. World line of a photon.
As far as we know, nothing travels faster than light. It is interesting to realize that you are never actually seeing the world right now. What you see is always slightly in the past, as it takes the light time to get to you; what you hear is even
Fig. 150. Sight is faster than smell.
A person has all sorts of lags built into him, Kesey is saying. One, the most basic, is the sensory lag, the lag between the time your senses receive something and you are able to react. One-thirtieth of a second is the time it takes, if you’re the most alert person alive, and most people are a lot slower than that … We are all of us doomed to spend our lives watching a movie of our lives — we are always acting on what has just finished happening. It happened at least 1/30 of a second ago. We think we’re in the present, but we aren’t. The present we know is only a movie of the past, and we will really never be able to control the present through ordinary means. That lag has to be overcome some other way, through some kind of total breakthrough.
The Electric Kool-Aid Acid
further in the past; and smells travel even slower than sounds. You see the sky rocket’s flash, you hear its explosion, you smell the smoke. Your sensations, at any given instant, are all signals from various events in the past. Even what you feel and taste is not happening quite exactly now,
Fig. 151. One’s sensations all come from the past.
Fig. 152. Bug Bites, UFO Zooms, Moon Booms.
as it takes some time for nerve impulses to travel from your skin to your brain.
To talk about “all of space, taken right now,” is really to speak very abstractly. You certainly don’t see all of space right now. The tree you see is really the tree of a ten-millionth of a second ago, the moon you see is the moon of two seconds ago, the light from the setting sun started out nine minutes ago, and the twinkling stars are scattered back hundreds and thousands of years in the past. In point of fact, you can’t see anything that’s happening right now. You have to wait for the light to get to you.
It is, of course, possible for us to piece together some kind of mental image of space right now. Suppose, for instance, that it is midnight, and you are sitting outside, looking at the moon. A mosquito bites you, and then two seconds later you see the flash of some huge explosion on the moon. Since you know that it takes light two seconds to travel from moon to earth, you can conclude that the “Now” that had you being bitten by the mosquito also included the explosion on the moon.
So far this does not seem to go against any of the viewpoints that hold that there really is a spacelike “Now” moving forward through time. But there is a problem with the way in which we construct our notion of “all space taken right now.” The problem is that if someone is moving relative to us, then he will construct his spacelike “Now” in a different way.
Suppose, to be specific, that a flying saucer had drifted past the Earth-moon system on that fateful night when the mosquito bit you and you saw a flash on the moon. If the aliens happen to be moving from Earth toward the moon, then they will actually reach the conclusion that the explosion happened first. If they are moving from the moon toward the Earth, they will, in their frame of reference, say that the explosion happened second. The reasoning behind these two claims is not obvious, and I won’t try to give it here.
The point is simply this: differently moving observers will differ on whether or not certain events happen at the same time. Nobody can really be at both the mosquito bite and the explosion. Whether these two events happen at the same time is really just a matter of opinion; nature stipulates no absolute answer to the question.
The phenomenon just alluded to is called the relativity of simultaneity. The important consequence of the relativity of simultaneity is that differently moving observers will find different ways of slicing spacetime up into a stack of “Nows.” The three observers drawn in figure 153 could be peacefully living in three different galaxies that are moving relative to one another. What reason could we possibly have to say that one of the three ways of slicing up spacetime is correct, and the other two are wrong?
Now and the future.
What kind of ideas about the past and future are embodied in this picture, where one thinks of the spacetime solid as being something like a block of ice that melts from the bottom up?
So relativity theory implies that there is no one preferred way in which to slice spacetime into a stack of “Nows.” Recall that relativity is based on the assumption that it is impossible to permanently mark a given space location. Another way of putting this is that “right here” has no real meaning over a period of time. We have seen that this assumption, oddly enough, implies that “right now” has no real meaning over a region of space. Since there is no one preferred way of defining “Now,” it must be that “Now” has no objective meaning. This means that there really is no moving present, and that the block universe viewpoint is the correct one. Spacetime is a single unified whole, and the passage of time is just an illusion.
Fig. 153. Three ways to slice spacetime.
Wednesday, November 24, 1982
The special theory of relativity is extremely well tested. It makes a number of definite predictions about the behavior of matter in motion. These predictions have been borne out thousands and thousands of times in experiments involving particle accelerators.
Yesterday I was discussing one of the very attractive implications of relativity: the implication that we are eternal spacetime patterns in an unchanging block universe. But relativity also has some less pleasant consequences. The worst thing about relativity is that it implies that we can never travel faster than the speed of light.
Some people get almost paranoid about this galling prediction. Without ever bothering to learn anything about relativity, they jump to the conclusion that Einstein was simply a dogmatic spoilsport not much different from the people who used to say that man will never fly. “Why shouldn’t we be able to go faster than a billion miles per hour? If you get a big enough rocket and run it long enough, you can go as fast as you like, right? What’s the matter with Einstein anyway? Wasn’t he a German or a Jew or something? Un-American for sure, and probably scared of progress!”
There are, according to relativity theory, two problems with faster-than-light travel. The first problem is that the closer any object gets to the speed of light, the greater the object’s mass becomes. And the greater an object’s mass is, the harder it is to accelerate the object to a yet higher speed. It would require, in point of fact, an infinite amount of rocket fuel to accelerate a spaceship up to the speed of light.
Fig. 154. Past, Future, and Elsewhere.
If I can never travel faster than the speed of light, then only a limited region of spacetime is accessible to me. Those events that I can still reach without traveling faster than light are called my “future.” This is a use of the word that is peculiar to relativity theory. Normally I think of my future as being those events I will actually experience, but here I am using “future” to mean all the events that I could conceivably attend or influence, without using faster-than-light travel. In a similar vein, I can take my “past” to be all the spacetime locations from which it would have been possible to travel, in order to reach me here and now. The rest of spacetime is called “elsewhere,” a lovely word. It always relaxes me to think about events as being “elsewhere.” Whatever our leaders in Washington may be doing right this instant doesn’t really matter: it’s “elsewhere.” Unfortunately, these important people’s actions don’t stay elsewhere — my “past” is larger at points further along my world line.
Fig. 155. “Elsewhere” today, “Past” tomorrow.
The second problem with faster-than-light travel has to do with the relativity of simultaneity. Given any event at all in your “elsewhere,” there will be some observer to say it is happening at the same time as your “here and now.” The whole of “elsewhere” is a sort of smeared out “Now.” Usually we think of “Now” as a line between “past” and “future,” but in relativity theory, this “Now” smears out into the hourglass-shaped “elsewhere.” What this means is that one path into “elsewhere” is as good as any other. The trouble is that some kinds of paths into “elsewhere” seem too weird to be possible. In figure 156 I have drawn three paths into “elsewhere.” The top one is unproblematic; it simply corresponds to someone who travels two billion miles per hour, or twice the speed of light. The next path is horizontal and, relative to the initial frame of reference, seems to represent a person who travels billions of miles in no time at all. This corresponds to an infinite velocity. The bottom path is the worst. Here the traveler seems to go backward in time. If he were to return from such a trip along a horizontal path, he would be able to meet up with his own past self! In other words, faster-than-light travel can lead to time travel — and many scientists feel that time travel must be impossible. The trouble with time travel is that it leads to some really vicious paradoxes, paradoxes we’ll go into in the next chapter. For now, suffice it to say that so far as we know, no chains of cause and effect can proceed faster than light.
Fig. 156. Trips into Elsewhere.
Willy Lee says X happens simultaneously with B.
“The relativity of simultaneity” says that different moving observers will have different opinions about which events are simultaneous. In this problem we see how the relativity of simultaneity follows from the two basic assumptions: (1) that moving observers are free to think of themselves as being at rest, and (2) that light always travels at the same speed.
The situation is as follows. A rigid platform is moving to the right at about half the speed of light On the left end stands Mr. Willy Lee, and on the right end stands Mr. Rye. Mr. Lee sends a flash of light down the platform toward Mr. Rye. Mr. Rye holds a mirror that bounces the light flash back toward Mr. Lee. Mr. Lee receives the return signal. Call these events A, B, and C, respectively. Mr. Lee notes the times of events A and C on his world line. After a little thought he decides which event X on his world line is simultaneous with B. Where does he put X, and why? (Hint: We would place X horizontally across from B, but Mr. Lee will not. Simultaneity is relative!)
Well, that’s all I have time for. I have to go home early today, to help get ready for Thanksgiving. Seems like every time you turn around it’s Christmas or Thanksgiving.
“The number of all the atoms which make up the world is, although excessive, finite, and as such only capable of a finite (although also excessive) number of permutations. Given an infinite length of time, the number of possible permutations must be exhausted, and the universe must repeat itself. Once again you will be born of the womb, once again your skeleton will grow, once again this page will reach your same hands, once again you will live all the hours until the hour of your incredible death.” Such is the customary order of the argument, from its insipid prelude to the enormous threatening dénouement.
JORGE LUIS BORGES,
“The Doctrine of Cycles,” 1934
Tuesday, November 30, 1982
Another holiday over with. My mother came, and my brother Embry with his wife and two kids. It was nice to see the five little cousins enjoying it: the treats, the wheel of the seasons, the eternal return.
Borges has an interesting essay on the esoteric doctrine of “the eternal return.” This is the idea that everything repeats itself.
Many things in our ordinary experience do repeat themselves. Exhale/inhale, day/night, summer/winter, parent/child: these are cycles that repeat themselves endlessly. Obviously, my 1982 Thanksgiving is not identical with all the other Thanksgivings. Yet, on some level, they are all the same, at least as regards the broadest features, the turkey and gravy, loud children, drunkenness, quarreling, laughter, and prayer. At some point during a long holiday’s welcome ordeal, most of us will experience moments, or even quarter-hours, of transcendence, of timelessness, of that full acceptance of time’s fabric, which, paradoxically, sets one free from time entirely. The very repetitiousness of human rituals provides some kind of glimpse into eternity; the endless line is bent into a circle.
Fig. 157. The Eternal Return.
Despite all this, the eternal return is still a very unlikely notion. Can anyone really believe that at some future time the universe will be in exactly the same state as it is now? But this is what the doctrine of the eternal return asserts: there is some fixed length of time, some cosmic cycle, after which the entire history of the universe repeats itself. We might suppose a full cycle to last, say, twenty billion years.
Fig. 158. Endless, repeating time.
There are two different ways of looking at a cosmos that has the property of repeating itself. We can imagine that time extends to infinity in both directions, and that space-time is made up of infinitely many identical horizontal “stripes.” Alternatively, we can imagine that time is bent into a finite, yet endless, circle. If a person is strongly committed to the “moving Now” viewpoint, then the first alternative will seem more attractive. If, that is, you believe that only the present has real existence, then you will feel that even if the universe were to repeat itself, the next cycle would be somehow different. But for someone who holds to the “block universe” view of spacetime, the second way of illustrating the eternal return will seem more natural. If spacetime is indeed a solidly existing thing, then we have no real problem with bending it into a “cylinder.”
Fig. 159. Circular time.
See, I answer him that ask-eth, “What did God before He made heaven and earth? I answer not as one is said to have done merrily (eluding the pressure of the question), “He was preparing hell (saith he) for pryers into mysteries.” It is one thing to answer enquiries, another to make sport of enquirers.
Confessions, A.D. 400
The notion of “circular time” leads to some interesting paradoxes, which we’ll discuss in puzzle 10.5. But right now let’s go on and look at some of the other overall shapes that spacetime might have.
Keep in mind that in all of these pictures, we think of the horizontal axis as being space, and we think of the vertical axis as being time. The horizontal axis is, if you will, our concept of “now,” and the vertical axis is our concept of “here.” The event that we call “here and now” is, of course, the point where the two axes intersect. One often “reads” these spacetime diagrams by imagining the horizontal axis to move upward as time goes on. But, as I have repeatedly pointed out, it is not always necessary or desirable to animate our Minkowski diagrams in such fashion.
Figure 160 shows three kinds of spacetime. In each of them, space is infinite, stretching out endlessly in both directions; and in each of them, the future also is endless. The models differ in the way they depict the past. The picture in the middle shows a universe in which all of space springs into existence at once, and the left-hand picture shows a universe that has no beginning in time. The right-hand picture shows a much odder situation, a universe in which different parts of space come into existence at different times. In such a universe there might be, for instance, a big hole in space out between Neptune and Uranus, a hole that would eventually shrink and disappear. (In the picture I have labeled the event of such a hole’s disappearance with the letter D.)
Fig. 160. Three ways to start the universe.
Fig. 161. Circular space.
Another type of spacetime model arises if we assume that space is “hyperspherical,” as was proposed in chapter 8. In terms of Lineland, this would mean that space is a circle, leading to the kind of picture drawn in figure 161. Figure 162 shows an alternate way of viewing a universe in which traveling far enough in any direction always leads to a region apparently identical with your starting point. Instead of showing space as curving back on itself, figure 162 shows space as extending to infinity in both directions, and with spacetime divided into infinitely many identical vertical strips. A mysterious harmony would have to be invoked to explain the repetition. Figure 161 is, of course, much more natural, just as a “circular time” model was a more natural way of representing the eternal return.
Fig. 162. Endless, repeating space.
In figure 161, we drew a picture of a circular space that remains the same size as time goes on. A widely held present-day view of the universe is that our space is an expanding hypersphere, which started out as point-sized about twelve billion years ago. Can you draw a picture of spacetime that represents our space as an expanding circle?
Fig. 163. A pre-established harmony?
One reason that I’ve been dating the sections of this chapter as I write them is simply to make a little fun of my argument that time is unreal. A more serious reason is that I feel like an Arctic explorer, keeping a log of the trip as he pushes further and further into the unexplored waste. At night the barking of the dogs, the mad splendour of the Aurora Borealis. The goal of my quest is a certain vision, a vision of the cosmos as a pattern in infinite-dimensional space. I want a comprehensive and absolute model for the world around me, a system that includes the realities of ordinary human life as well as the cold truths of science.
Fig. 164. Onward!
Until today I’ve been unsure as to whether I can finish the journey. But this morning I caught sight of the goal. Reality is one, it is a thing that provides an answer to any of the infinitely many questions one might ask; it is, in other words, a coloring-in of infinite-dimensional space. Stick with me, we’ll get there yet!