Time Travel: A History (13 page)

“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 himself.

*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 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.