Donald C. Williams, a realist from California, picked up that thread at midcentury with a paper on “The Sea Fight Tomorrow.” His brand of realism was four-dimensional—fully modern, in other words. He asserted “the view of the world, or the manner of speaking about it” (a nice distinction, so easily forgotten),
which treats the totality of being, of facts, or of events as spread out eternally in the dimension of time as well as the dimension of space. Future events and past events are by no means present events, but in a clear and important sense they do exist, now and forever, as rounded and definite articles of the world’s furniture.
In the 1960s, the sea battle of tomorrow got a new life in the journals of philosophy. An argument raged over the logic of fatalism, and a milestone in the debate was the essay “Fatalism” by Richard Taylor, a metaphysician and beekeeper at Brown University. “A fatalist,” he wrote, “thinks of the future in the manner in which we all think of the past.” Fatalists take both past and future as given, and equally so. They may get this view from religion or, lately, from science:
Without bringing God into the picture, one might suppose that everything happens in accordance with invariable laws, that whatever happens in the world at any future time is the only thing that can then happen, given that certain other things were happening just before, and that these, in turn, are the only things that can happen at that time, given the total state of the world just before then, and so on, so that again, there is nothing left for us to do about it.
Taylor proposed to prove fatalism entirely by philosophical reasoning, “without recourse to any theology or physics.” He used symbolic logic, representing the various statements about the sea battle in terms of P and P′ and Q and Q′. All he needed were “certain presuppositions made almost universally in contemporary philosophy.” Something had to give: either fatalism or the rules of logic. A philosophy battle ensued. One of Taylor’s presuppositions was not as evident to everyone else: “that time is not by itself ‘efficacious’; that is, that the mere passage of time does not augment or diminish the capacities of anything.” In other words, time itself is not an agent of change; more of an innocent bystander. Time doesn’t do anything. (“What is a mere passage of time” retorted one of his critics. “Could time possibly pass without something, somewhere, changing—without the tick of a clock, the movement of a planet, the twitch of a muscle, or the sight of a flash?”)
Two decades later, at Amherst College, an undergraduate philosophy student named David Foster Wallace, himself the son of a professional philosopher, grew obsessed with this nettlesome debate, “the famous and infamous Taylor argument.” He wrote to a friend, “If you read the Taylor literature, it’s really ulcer-city.” He plunged in nonetheless. His obsession became his honors thesis, which might have taken its title from the imaginary Bob Wilson’s “An Investigation into Certain Mathematical Aspects of a Rigor of Metaphysics.” He drew diagrams to sort out “world-situations” and their possible “daughters” and “mothers.” Yet as much as the formal, axiomatic side of philosophy appealed to Wallace—gave him continual pleasure and satisfaction—he never accepted it without reservation. The limits of logic and the limits of language remained live issues for him.
Words represent things but the words are not the things. We know that but we can forget. Fatalism is a philosophy built out of words, and ultimately its conclusions apply to words—not necessarily to reality. When Taylor leaves work, he summons the elevator just like the rest of us, by pressing the button. He does not think to himself, Don’t worry, the elevator will follow its destiny. He may think, When I press the elevator button, it is not a free choice—it was fated. But he still goes to the trouble of doing it. He doesn’t just stand there and wait.
Of course, Taylor himself knew this full well. He can’t be refuted so easily.
A fatalist—if there is any such—thinks he cannot do anything about the future. He thinks it is not up to him what is going to happen next year, tomorrow, or the very next moment. He thinks that even his own behavior is not in the least within his power, any more than the motions of the heavenly bodies, the events of remote history, or the political developments in China. It would, accordingly, be pointless for him to deliberate about what he is going to do, for a man deliberates only about such things as he believes are within his power to do.
He added, “And we are not, in fact, ever tempted to deliberate about what we have done and left undone.”
I wonder whether Taylor had read much time-travel fiction or even, for that matter, whether he lived in the world I live in, where regret is not unknown and people do sometimes speculate about what might have been. Everywhere we look, people are pressing elevator buttons, turning doorknobs, hailing taxicabs, lifting sustenance to their lips, and begging their lovers’ favor. We act as though the future is, if not in our control, not yet settled. Nonetheless, Taylor dismissed our “subjective feelings.” We would suffer illusions of free will, because, by happenstance, we tend to know less about the future than about the past.
Many philosophers, in the years that followed, had tried to refute Taylor, but his logic proved amazingly robust. Wallace wanted to defend the common intuition “that persons as agents are capable of influencing the course of events in their world.” He plunged into the depths of symbolic logic. “Since obviously under any analysis I have to do either O or O′ (since O′ is not-O), that is, since (O ∨ O′); and since by (I-4) it is either not possible that I do O or not possible that I do O′, (∼◊O ∨ ∼◊O′), which is equivalent to (∼◊∼∼O ∨ ∼◊∼O), which is equivalent to (∼O ∨ O), we are left with (O ∨ ∼O); so that it is necessary that whatever I do, O or O′, I do necessarily, and cannot do otherwise” is a sample sentence. (“Obviously”!) In the end he defeated Taylor’s fatalism by stepping back and viewing not only the chains of symbols but also the levels of symbolic representation—viewing them, as it were, from above. Wallace distinguished between the realm of semantics and the realm of metaphysics. Considered strictly as words, he argued, Taylor’s logic may be internally valid, but it’s cheating to leap from semantic premises and arguments to a metaphysical conclusion.
“Taylor’s claim was never really that fatalism was actually ‘true,’ only that it was forced upon us by proof from certain basic logical and semantic principles,” he concluded. “If Taylor and the fatalists want to force upon us a metaphysical conclusion, they must do metaphysics, not semantics.” In metaphysics we find the doctrine of determinism—we’ve seen this before, given its perfect expression by Laplace. Determinism is this (per Wallace):
the idea that, given a precise and total state of affairs at one instant, and the physical laws that govern the causal relations between states of affairs, there is one and only one possible state of affairs that could obtain at the next instant.
Taylor takes this for granted. If X, then Y means one thing in logic. In the physical world, it means something trickier and always (we should know by now) subject to doubt. In logic, it is rigid. In physics, there is slippage. Chance has a part to play. Accidents can happen. Uncertainty is a principle. The world is more complex than any model.
Taylor was begging the question. To prove fatalism he was assuming determinism. Many physicists do that, too, even now. “Physicists like to think that all you have to do is say, ‘These are the conditions, now what happens next,’ ” said Richard Feynman. Determinism is built into so many of their formalisms, just as it is for logicians. But formalisms are just that. The physical laws are a construct, a convenience. They are not coextensive with the universe.
Was that only possible which came to pass? Having spent years in these dark waters, Wallace had done enough philosophy for a while. He had an alternative future in mind, and he chose it. “I left there,” he said later, “and I didn’t go back.”
* * *
*1 When he writes of Bob Wilson, “His was a mixed nature, half hustler, half philosopher,” Heinlein is proudly describing himsel
f.
*2 “There is some sense, easier to feel than to state, in which time is an unimportant and superficial characteristic of reality.”
SIX
* * *
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 absorpti
on 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.”