Time Travel: A History (2016)
Arrow of Time
The great thing about time is that it goes on. But this is an aspect of it which the physicist sometimes seems inclined to neglect.
—Arthur Eddington (1927)
WE ARE FREE to leap about in time—all this hard-won expertise must be good for something—but let’s just set the clock to 1941 again. Two young Princeton physicists make an appointment to call at the white clapboard house at 112 Mercer Street, where they are led into Professor Einstein’s study. The great man is wearing a sweater but no shirt, shoes but no socks. He listens politely as they describe a theory they are cooking up to describe particle interactions. Their theory is unconventional—full of paradoxes. It seems that particles must exert their influence on other particles not only forward in time but also backward.
John Archibald (“Johnny”) Wheeler, thirty years old, had arrived at Princeton in 1938 after working with Niels Bohr in Copenhagen, at the citadel of the new quantum mechanics. Bohr had now sailed westward and Wheeler was working with him again, this time on the possibilities of nuclear fission in the uranium atom. Richard (“Dick”) Feynman, age twenty-two, was Wheeler’s favorite graduate student, a brash and whip-smart New Yorker. Johnny and Dick were nervous, and Einstein offered them sympathetic encouragement. He didn’t mind the occasional paradox. He had considered something along these lines himself, back in 1909, as he recalled.
Physics is made of mathematics and words, always words and mathematics. Whether the words represent “real” entities is not always a productive question. In fact, physicists do well to ignore it. Are light waves “real”? Is the gravitational field? The space-time continuum? Leave it to theologians. One day the idea of fields is indispensable—you can practically feel them in your bones; anyway you can see the iron filings arranging themselves around the magnet—and the next day you wonder whether you can toss out fields and start over. That’s what Wheeler and Feynman were doing. The magnetic field, also the electric field, but really just the electromagnetic field, was barely a century old, the invention (or discovery) of Faraday and Maxwell. Fields fill the universe: gravitational fields, boson fields, Yang-Mills fields. A field is a quantity that varies in space and time. It expresses variations in force. The earth feels the gravitational field of the sun, spreading outward through space. The apple dangling from the tree manifests the earth’s gravitational field. Without fields, you have to believe in what looks like magic: action at a distance, through a vacuum, with no levers or strings.
Maxwell’s equations for electromagnetic fields worked so beautifully, but by the 1930s and 1940s physicists were having problems in the quantum realm. They understood very well the equations connecting the energy of the electron with its radius. So they could compute the size of the electron quite precisely. Only, in quantum mechanics, it looks as though the electron has no radius at all: it is a point particle, zero-dimensional, taking up no space. Unfortunately for the mathematics, this picture led to infinities—the result of dividing by zero. To Feynman it seemed that many of these infinities came from a circular effect of the electron upon itself, its “self-energy.” To eliminate these nasty infinities, he had the idea of simply not allowing electrons to act upon themselves. This meant eliminating the field. Particles would be allowed only to interact with other particles, directly. Not instantaneously: relativity had to be obeyed. The interactions occurred at the speed of light. That’s what light is: interaction between electrons.
Feynman explained later, in Stockholm, upon receiving the Nobel Prize:
It was just that when you shook one charge, another would shake later. There was a direct interaction between charges, albeit with a delay. The law of force connecting the motion of one charge with another would just involve a delay. Shake this one, that one shakes later. The sun atom shakes; my eye electron shakes eight minutes later, because of a direct interaction across.
The problem—if it was a problem—was that the rules for interaction worked backward in time as well as forward. They were symmetrical. This is the kind of thing that happens in Minkowski’s world, where past and future are geometrically identical. Even before relativity, it was well known that Maxwell’s equations for electromagnetism and, before that, Newton’s for mechanics were symmetrical with respect to time. Wheeler had toyed with the idea that the positron—antiparticle of the electron—was an electron moving backward in time. So Johnny and Dick plunged ahead with a theory in which electrons appeared to be shining both forward into the future and back into the past. “I was enough of a physicist at that time,” Feynman continued, “not to say, ‘Oh, no, how could that be?’ For today all physicists know from studying Einstein and Bohr that sometimes an idea which looks completely paradoxical at first, if analyzed to completion in all detail and in experimental situations, may, in fact, not be paradoxical.”
In the end, the paradoxical ideas turned out not to be necessary for the theory of quantum electrodynamics. As Feynman well understood, such theories are models: never complete, never perfect, not to be confused with reality, which remains out of reach.
It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling you can show the relationship….There is always another way to say the same thing that doesn’t look at all like the way you said it before….
Many different physical ideas can describe the same physical reality.
On the side another issue loomed. Thermodynamics, the science of heat, offered a different version of time. Sure, the microscopic laws of physics say nothing about time having a favored direction. (Some would say “fundamental laws,” rather than “microscopic laws,” but that is not quite the same thing.) The laws of Newton, Maxwell, and Einstein are invariant with respect to past and future. Changing the direction of time is as easy as changing a sign from plus to minus. The microscopic laws are reversible. If you make a movie of a few colliding billiard balls or interacting particles, you can run the film through the projector backward and it will look fine. But make a movie of a cue ball breaking the rack—fifteen balls, at rest in a perfect triangle, sent flying to every corner of the table. If you play that one backward, it looks comically unreal: the balls careering about and then assembling themselves as if by magic into regimental order.
In the macroscopic world, the world we inhabit, time has a definite direction. When the technology of cinema was still new, filmmakers discovered they could create amusing effects by reversing their strips of celluloid. The Lumière brothers reversed their short Charcuterie mécanique to show a sausage unmade and a pig unbutchered. In a backward movie an omelet could organize into white and yolk and return to the egg, with shell fragments neatly reassembling themselves. A rock flies out of a turbulent pond, a reverse fountain of droplets closing in to seal the hole. Smoke pours down a fireplace into the flames as coals grow into logs. Not to mention life itself: the quintessential irreversible process. William Thomson, Lord Kelvin, saw the problem in 1874—and saw that consciousness and memory were part of the problem: “Living creatures would grow backward, with conscious knowledge of the future, but no memory of the past, and would become again unborn.”
Every so often it is good to remind ourselves that most natural processes are not reversible. They work only one way, forward in time. For starters here is a little list from Lord Kelvin: “friction of solids; imperfect fluidity of fluids; imperfect elasticity of solids [all these imperfects]; inequalities of temperature, and consequent conduction of heat produced by stresses in solids and fluids; imperfect magnetic retentiveness; residual electric polarization of dielectrics; generation of heat by electric currents inducted by motion; diffusion of fluids, solutions of solids in fluids, and other chemical changes; and absorption of radiant heat and light.” That last is where Johnny and Dick came in.
At some point we have to talk about entropy.
THERE’S A CATCHPHRASE, the arrow of time, familiarly used by scientists and philosophers in many languages (la flèche du temps, Zeitpfeil, zamanın oku, ось времени) as shorthand for a complex fact that everyone knows: time has a direction. The phrase spread widely in the 1940s and 1950s. It came from the pen of Arthur Eddington, the British astrophysicist who first championed Einstein. In a series of lectures at the University of Edinburgh in the winter of 1927 Eddington was attempting to comprehend the great changes under way in the nature of scientific thought. The next year he published his lectures as a popular book, The Nature of the Physical World.
It struck him that all previous physics was now seen to be classical physics, another new expression. “I am not sure that the phrase ‘classical physics’ has ever been closely defined,” he told his listeners. No one called it classical until it broke down. (Now “classical physics” is a retronym, like acoustic guitar, dial telephone, and cloth diaper.)* Millennia had gone by without scientists needing special shorthand like “time’s arrow” to state the obvious—the great thing about time is that it goes on. Now, however, it was no longer obvious. Physicists were writing laws of nature in a way that made time directionless, a mere change of sign separating +t from -t. But one law of nature is different: the second law of thermodynamics. That’s the one about entropy.
“Newton’s equations go forwards and backwards, they do not care which way,” explains Thomasina, the teenage prodigy invented by Tom Stoppard in Arcadia. “But the heat equation cares very much, it goes only one way.”
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?
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.