The universe tends inexorably toward disorder. Energy is indestructible, but it dissipates. This is not a microscopic law. Is it a “fundamental” law, like F = ma? Some argue that it is not. From one point of view, laws governing individual constituents of the world—single particles, or a very few—are primary, and laws about multitudes must be derived from them. But to Eddington this second law of thermodynamics was the fundamental law: the one that holds “the supreme position among the laws of Nature”; the one that gives us time.
In Minkowski’s world past and future lie revealed before us like east and west. There are no one-way signs. So Eddington added one: “I shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space.” He noted three points of philosophical import:
1. It is vividly recognized by consciousness.
2. It is equally insisted upon by our reasoning faculty.
3. It makes no appearance in physical science except…
Except when we start to consider order and chaos, organization and randomness. The second law applies not to individual entities but to ensembles. The molecules in a box of gas comprise an ensemble. Entropy is a measure of their disorder. If you put a billion atoms of helium into one side of a box and a billion atoms of argon into the other side and allow them to bounce around for a while, they will not remain neatly separated but will eventually become a uniform—random—mixture. The probability that the next atom you find at a given place will be helium, rather than argon, will be 50 percent. The process of diffusion is not instantaneous and it runs in one direction. As you watch the distribution of the two elements, past and future are easily distinguishable. “A random element,” said Eddington, “brings the irrevocable into the world.” Without randomness, the clocks could run backward.
“The accidents of life” is the way Feynman liked to put it: “Well, you see that all there is to it is that the irreversibility is caused by the general accidents of life.” If you throw a cup of water into the sea, let time pass, and dip your cup back in, can you get the same water back? Well, you could—the probability is not zero. It’s just awfully small. Fifteen billiard balls could smash around a table and finally come to a stop in a perfect triangle—but when you see that happen, you know that the film has been reversed. The second law is a probabilistic law.
Mixing is one of those processes that follow the arrow of time. Unmixing takes work. “You cannot stir things apart,” says Stoppard’s Thomasina—entropy explained in five words. (Her tutor, Septimus, replies, “No more you can, time must needs run backward, and since it will not, we must stir our way onward mixing as we go, disorder out of disorder into disorder until pink is complete, unchanging and unchangeable, and we are done with it for ever.”) Maxwell himself wrote:
Moral. The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again.
But Maxwell predated Einstein. For him, time required no particular justification. He already “knew” that the past is past and the future still to come. Now matters are not so simple. In 1949, in a essay titled “Life, Thermodynamics, and Cybernetics,” Léon Brillouin said:
Time flows on, never comes back. When the physicist is confronted with this fact he is greatly disturbed.
To the physicist, it feels that a troublesome gap lies between the microscopic laws, where time has no preferred direction, because the laws are reversible, and the macroscopic world, where the arrow of time points from past to future. Some are content to say that fundamental processes are reversible and macro-scale processes are mere statistics. This gap is a disconnect—a lapse in explanation. How do you get from one place to the other? The gap even has a name: the arrow of time dilemma, or Loschmidt’s paradox.
Einstein admitted that the problem disturbed him at his moment of greatest understanding, in the creation of the general theory of relativity—“without my having succeeded in clarifying it.” In a diagram of the four-dimensional space-time continuum, let’s say that P is a “world-point” lying between two other world-points, A and B. “We draw a ‘time-like’ world-line through P,” suggested Einstein; “does it make any sense to provide the world-line with an arrow, and to assert that B is before P, A after P?” Only when thermodynamics enters the picture, he concluded—but he also said that any transfer of information involves thermodynamics. Communication and memory are entropic processes. “If it is possible to send (to telegraph) a signal from B to A, but not from A to B, then the one-sided (asymmetrical) character of time is secured, i.e. there exists no free choice for the direction of the arrow. What is essential in this is the fact that the sending of a signal is, in the sense of thermodynamics, an irreversible process, a process which is connected with the growth of entropy.”
In the beginning, therefore, the universe must have had low entropy. Very low entropy. It must have been in a highly ordered state, which is also an extremely improbable state. This is a cosmic mystery. Ever since, entropy has grown. “That is the way toward the future,” said Feynman, years later, when he was a famous man assembling his knowledge of physics into textbook form.
That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future.
And in the end?
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THE UNIVERSE TENDS toward maximum entropy, the condition of ultimate disorder from which there is no return. The eggs will all have scrambled, the sand castles blown down, the sun and stars faded to uniformity. H. G. Wells already knew about entropy and heat death. This is the destiny the Time Traveller nears, when he abandons Weena, departs the year 802,701, leaves behind the troglodytic Eloi and bovine Morlocks, the ruined Palace of Green Porcelain, its Gallery of Palaeontology long deserted, its library a wilderness of rotting paper, and drives his machine onward, swaying and vibrating through millions of years of grayness into a final twilight brooding over the earth. If you read The Time Machine when you are young, I think this is what lodges in your memory or your dreams, this final tableau where nothing happens. In one draft Wells called it “The Further Vision.” If Eden is alpha, here is omega. Eschatology for the enlightened. No hell, no apocalypse. Not with a bang but a whimper.
This twilight beach recurs again and again in science fiction. We come to land’s end—J. G. Ballard’s “derelict landscape,” the terminal beach, where the last man says farewell: “Such a leave-taking required him to fix his signature on every one of the particles in the universe.” In Wells’s unforgettable final pages, the Time Traveller sits shivering in his saddle and watching “the life of the old earth ebb away.” Nothing stirs. All he sees is stained red, pinkish, bloody, in the dim light of the dying sun. He imagines some black thing flopping about, but it is only a rock.
I stared aghast at the blackness that was creeping over the day….A cold wind began to blow….Silent? It would be hard to convey the stillness of it….The darkness thickened….All else was rayless obscurity….A horror of this great darkness came on me. The cold, that smote my marrow.
This is the way the world ends.
* * *
* A retronym is a lexical time machine. It calls up entities past and present and juxtaposes them in the mind’s eye.
SEVEN
* * *
A River, a Path, a Maze
Time is a river that sweeps me along, but I am the river; it is a tiger that mangles me, but I am the tiger; it is a fire that consumes me, but I am the fire.
—Jorge Luis Borges (1946)
TIME IS a river. Does the truism require elaboration?
It did in 1850. Case in point: an American novel titled The Mistake of a Life-Time; or, The Robber of the Rhin
e Valley. A Story of the Mysteries of the Shore, and the Vicissitudes of the Sea. The author, Waldo Howard, promises “a truthful panorama of the events of a stirring and romantic period.” Let us jump to chapter 13, “Lady Gustine and the Jew.”
Lady Gustine is a dignified and high-toned beauty of eighteen years (“summers”), while her companion for the evening (not the Jew, obviously) is an equally dignified and beautiful twenty-year-old. They have been dancing. She is fatigued. “I fear you are fatigued,” says the gentleman. “ ‘Oh, no,’ said the lady, panting to regain the breath she had expended in the waltz.”
Conveniently, their balcony overlooks a river. They gaze upon it awhile. Presently dialogue occurs:
“Are you dreaming?”
“O, no, lady. I—I was thinking how truly the passage of yonder tiny craft resembles that of our own life bark on the tide of time.”
“And how?”
“See you not how quietly its hull is borne along with the current?…[etc., etc.]
“Well.” [He’s boring her.]
“Thus we are moving now, lady, rapidly, with silent, but steady, and never ceasing motion, down the swift river of time, that sets through the valley of life; all unconsciously we glide on, nodding like this same helmsman, indifferently, as we hold the rudder that guides our own fate—while we swiftly approach the ocean of eternity.”
And more like that. Pretty soon he “dwells upon the beauties of her native valley” but we needn’t follow him there. The first metaphor is bad enough.
Time = river. Self = boat. Eternity = ocean.
When time is a river, then time travel becomes plausible. You might get out and run up or down the banks.
People have been comparing time to a river at least since Plato began a long tradition of misquoting Heraclitus: “You can’t step into the same river twice.” Or “We step and do not step into the same rivers.” Or “We both step and do not step, are and are not in the same rivers.”*1 No one knows exactly what Heraclitus said, because he lived in a time and place that lacked writing (his work is published under the title The Complete Fragments, no irony intended), but according to Plato:
Heraclitus, I believe, says that all things pass and nothing stays, and comparing existing things to the flow of a river, he says you could not step twice into the same river.
Heraclitus was saying something important: namely, that things change. The world is in flux. That may seem self-evident, but his approximate contemporary Parmenides took a different view: change is an illusion of our senses; beneath the transitory world of appearances lies the true reality—stable, timeless, eternal. This was the view that appealed to Plato.
Notice that no one so far is saying that time is like a river. The universe is like a river. It flows. (Or it doesn’t, if you’re Plato.)
Alfred Jarry, constructing his time machine in 1899, said it had already become “a banal poetic figure to compare Time to a flowing stream.”*2 Banality didn’t stop anyone. “Time, that impalpable and fatal river,” the Parisian astronomer Charles Nordmann said in 1924, “strewn with dead leaves, our wistful hours carried down stream.” Where are we in this picture—we, the conscious observer? We are merely a bump in the viscosity, said the absurdist Jarry. The Christian hymn says, “Time, like an ever rolling stream / Bears all its sons away.” The river carries us toward eternity, which is to say past death. Miguel de Unamuno wrote, “Nocturno el río de las horas fluye…”—though he imagined it flowing from the future, “el mañana eterno.” Marcus Aurelius, Stoic philosopher and emperor, said that time is a river because everything rushes by, while we watch. “No sooner has anything appeared than it is past, and now another thing is passing, and that yonder will presently be here.”
If time is a river, can we ask how fast it flows? That seems a natural question to ask about a river, but it’s not a good question to ask about time itself. How fast does time flow? Measured how? We have plunged into a tautology. It’s no better to ask, How fast are we advancing through time?
Riverine flow can be complicated. Can temporal flow? “There is a theory,” explains Spock in a classic episode of Star Trek. “There could be some logic to the belief that time is fluid, like a river, with currents, eddies, backwash.”
If time is a river, does it have tributaries? Whence does it spring? From the big bang, or are we now mixing metaphors? If time is a river, where are the banks that contain it? W. G. Sebald asked that question in his last novel, Austerlitz:
Where, seen in those terms, where are the banks of time? What would be this river’s qualities, qualities perhaps corresponding to those of water, which is fluid, rather heavy, and translucent?
Sebald also asked, “In what way do objects immersed in time differ from those left untouched by it?” This was a nice conceit: that some parts of our world, like dusty, shuttered rooms, may stand outside of time, may be cut off from time, immune to the flow.
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IN POINT OF FACT, time is not a river. We possess a great metaphorical tool kit with utensils for every occasion. We say that time passes, time goes by, and time flows, and all those are metaphors. “Time is a fluid medium for the culture of metaphors,” writes Nabokov metaphorically. We also think of time as a medium in which we exist. And as a quantity that we can possess, waste, or save. Time is like money, it is like a road, a path, a maze (Borges again, of course), a thread, a tide, a ladder, and an arrow. All at once.
“The idea that Time ‘flows’ as naturally as an apple thuds down on a garden table implies that it flows in and through something else,” says Nabokov, “and if we take that ‘something’ to be Space then we have only a metaphor flowing along a yardstick.”
Is it even possible to talk about time without using metaphors? Perhaps:
Time present and time past
Are both perhaps present in time future,
And time future contained in time past.
Although, if that isn’t metaphor, what trope is it? Pregnant words: “present in…”; “contained in…” In the same poem T. S. Eliot also had some words about words.
Words strain,
Crack and sometimes break, under the burden,
Under the tension, slip, slide, perish,
Decay with imprecision, will not stay in place,
Will not stay still.
Everything was so unsettled about time. Philosophers, physicists, poets, and pulp writers all struggled. They were using the same word bag. They drew their tiles and moved them around the playing board. (Slip, slide, perish, decay with imprecision.) Philosophers’ words alluded to the philosophers’ words that came before. Physicists’ words were special, more precisely defined, and anyway they were mostly numbers. Physicists don’t generally call time a river. They don’t generally depend on metaphor; at least, they don’t like to admit it. Even “arrow of time” is not so much a metaphor as a catchphrase.
In the twentieth century the physicists took the moral lead—they had the power—and the philosophers mainly reacted or resisted. After Einstein’s message sank in, metaphysicians began to say without blushing that time and space have the same “ontological standing,” that they exist “in the same way.” As for poets, they lived in the same world, pulled the same tiles from the bag, and knew better than to trust all the words. Proust searching for lost time. Woolf stretching and warping it. Joyce assimilating the news about time as it came from the frontier of science. “Temporal or spatial,” says Stephen in A Portrait of the Artist as a Young Man, “the esthetic image is first luminously apprehended as selfbounded and selfcontained upon the immeasurable background of space or time which is not it.” No, it is not. Later came Ulysses, the book of a single day, exodus and return. “An unsatisfactory equation between an exodus and return in time through reversible space and an exodus and return in space through irreversible time.” Leopold Bloom worries about magnetism and time, the sun and the stars, pulling and being pulled: “Very strange about my watch. Wristwatches are always going wrong.” Oh, the
re was unease.
Not everyone liked T. S. Eliot’s last long poem, Four Quartets, published from 1936 to 1942. Some accused it of self-parodic inscrutability. Not everyone thought it was a poem about time, but it is. Here the impossible union / Of spheres of existence is actual, / Here the past and future / Are conquered, and reconciled. Does all time exist together? Is the future already contained in the past? Didn’t Einstein say so?
Along with quite a few of his contemporaries, Eliot was influenced by a slightly crackpot book, An Experiment with Time, written by an Irish aeronautical pioneer named John William Dunne. Dunne was an acquaintance of Wells who at the turn of the century began building aircraft models, then gliders, then powered biplanes, all tailless (a design with stability problems). In the twenties, having left aeronautics behind, he noticed that his dreams sometimes predicted future events. They were “precognitive dreams,” he decided. Reverse memory. He had dreamed of a volcano killing four thousand on a French island and then, later (or so he recalled), read in the newspaper of the Pelée eruption on Martinique, killing forty thousand. He began keeping a notebook and pencil under his pillow; he interviewed his friends about their dreams; and he put two and two together. By 1927 he had a theory and a book.
Dunne proposed to replace the foundations of epistemology with his new system. “If prevision be a fact, it is a fact which destroys the entire basis of all our past opinions of the universe.” The past and the future coexist, in “the time dimension.” Incidentally, he wrote, he had stumbled upon “the first scientific argument for human immortality.” He put forward not a four-dimensional but a five-dimensional view of space and time. In explaining this, he adverted to Einstein and Minkowski and, as another authority, to Mr. H. G. Wells, who “through the mouth of one of his fictional characters, stated his case with a clearness and conciseness which has rarely, if ever, been surpassed.”