Timescape

forces were there, mixing advanced and retarded tachyon solutions together with non-Euclidean sums. Markham blinked. In his cottony silence he sat very still, eyes racing, imagination leaping ahead to see where the equations would fold and part to yield up fresh effects.

The waves still stood, mutely confused. But there was no role left for the ship, for the classical observer. The old idea in conventional quantum mechanics had been to let the rest of the universe to be the observer, let it force the waves to collapse. In these new tensor terms, though, there was no way to regress, no way to let the universe as a whole be a stable spot from which all things were measured. No, the universe was coupled in firmly. The tachyon field wired each fragment of matter to every other. Hooking more particles into the network only worsened things. The old quantum theorists, from Heisenberg and Bohr on, had let in some metaphysics at this point, Markham remembered. The wave function collapsed and that was the irreducible fact. The probability of getting a certain solution was proportional to the amplitude of that solution inside the total wave, so in the end you got only a statistical weighting of what would come out of an experiment. But with tachyons that dab of metaphysics had to go. The Wickham terms—

Sudden motion caught his eye. A passenger in the next row was clutching at a steward, eyes glassy. His face was laced with pain. A stretched mouth, pale lips, brown teeth. Mottled pink splotched his cheeks. Markham pulled his earplugs. A brittle scream startled him. The steward got the man down on the floor in the middle of the aisle and pinned his frantically clawing hands. “I can’t—can’t—breathe!” A steward murmured something comforting. The man shook with a seizure, eyes rolling. Two stewards carried him past Markham. He noticed an acrid smell coming from the sick man and wrinkled his nose, forcing his glasses upward. The man panted in the enameled light. Markham replaced his plugs.

He settled again into the embalming quiet, conscious only of the reassuring hum of the engines. Without peaks and valleys of sound the world had a stuffed, spongy feel, as though Maxwell’s classical ether were a reality, could be sensed at the fingertips. Markham relaxed for a moment, reflecting on how much he loved this state. Concentration on an intricate problem could loft you into an insulated, fine-grained perspective. There were many things you could see only from a distance. Since childhood he had sought that feeling of slipping free, of being smoothly remote from the compromised churn of the world. He had used his oblique humor to distance people, yes, keep them safely away from the center of where he lived. Even Jan, sometimes. You had to form for yourself a lucid language for the world, to overcome the battering of experience, to replace everyday life’s pain and harshness and wretched dreariness with—no, not with certainty, but with an ignorance you could live with. Deep ignorance, but still a kind that knew its limits. The limits were crucial. Galileo’s blocks gliding across the marble Italian foyers, their slick slide obeying inertia’s steady hand—they were cartoons of the world, really. Aristotle had understood in his gut the awful fact that friction ruled, all things groaned to a stop. That was the world of man. Only the childlike game of infinite planes and smooth bodies, reality unwrinkled, cast a web of consoling order, infinite trajectories, harmonic life. From that cartoon world it was always necessary to slip back, cloaking exhilarating flights in a respectable, deductive style. But that did not mean, when the papers appeared in their disguise of abstracts and Germanic mannerisms, that you had not been to that other place, the place you seldom spoke of.

He paused in the impacted hush, and then went on.

He wondered distantly if his first guess was right: these new Wickham equations allowed no way out of the paradox, because the whole universe was swept into the experiment. The consequence of setting up the standing wave was to send tachyons forward and backward in time, yes, but also to spray them at superlight speeds throughout the entire universe. Within an instant, every piece of matter in the universe learned of the paradox. The whole structure of space-time became woven into one piece, instantly. That was the new element with tachyons; until their discovery, physics assumed that disturbances in the space-time metric had to propagate outward at light speed.

Markham realized he had been hunched forward, scribbling mathematical statements of these ideas. His back stabbed him with small, hot knives. His writing hand protested with a sweet ache. He leaned backward, reclining the seat. Below he saw the slate-gray plain of the sea like a giant blackboard for God’s idle equations. A freighter plowed a wake that curved with the currents, silver in the sun. They were descending toward Dulles International on a gentle long parabola.

Markham smiled with serene fatigue. The problems caught you up and carried you along, unminding currents. Was there any way to resolve the paradox? He knew intuitively that here lay the heart of the physics, the way of showing whether you could reach the past in a rigorous way. Peterson’s laconic bank vault note proved something had happened, but what?

Markham twisted uncomfortably, irked by the narrow, cramped seat. Air travel was getting to be a rich man’s route again, only this time without the perks. Then he fetched his mind back from these passing reminders of the relentlessly real world. The problem was not solved, and time remained.

But is the paradox decidable at all? he thought. The German mathematician Godel had shown that even simple systems of arithmetic contained things which were true, but unprovable. In fact, you couldn’t even show that arithmetic itself was consistent—that is, didn’t contain paradoxes. Godel had forced arithmetic into describing itself in its own language. He had trapped it into its own box, deprived it of ever proving itself by reference to things outside itself. And that was for arithmetic, the simplest logical system known! What of the universe itself, with tachyons launching through it, threading the cloth of space-time? How could all the squiggles on all the yellow pads in the world ever trap that vast weave into the old boxes of yes/no, true/false, past/future? Markham relaxed in his brimming warmth. The plane went clunk and tilted earthward.

The point that continued to puzzle him was whether Renfrew needed to send a message at all, to make a paradox. Tachyons were constantly being produced by natural collisions of high-energy particles—that’s how they had been discovered. Why didn’t those natural tachyons produce a paradox somehow? He frowned. The plane nosed further, giving the illusion of hanging over the lip of a pit, legs dangling. Natural tachyons… The answer had to be that it took some minimum impulse to trigger a paradox. Some critical volume of space-time had to be tweaked, and then the disturbance would propagate outward instantaneously, with enough amplitude to matter. You could change the past at will, yes, so long as you didn’t make paradoxes that had large amplitude. Once you exceeded the threshold, the tachyon wave would have a significant impact on the whole universe. But if so, how could you tell that had happened? What was the signature? How did the universe pick a way to resolve the paradox? They knew they had reached the past—Peterson proved that. But what more could happen?

Markham felt a sudden stab of perception. If the universe was a wholly linked system with no mythical classical observer to collapse the wave function, then the wave function did not have to collapse at all. It—

A wrenching thump. Markham looked out in surprise and saw the ground veer suddenly. Ahead were the patient green fields of Maryland. A clump of forest swarmed beneath the wings. In the cabin, a babble of voices. Shouts. A rasping buzz. The forest went whipping by. The trees were sharp, precise, with the clarity of good ideas. He watched them flick past as the airplane became light, airy, a gossamer webbing of metal that fell with him, mute matter tugged by gravity’s curved geometry. Skreeeeeee. The trees were pale rods in the slanting light, each with a ball of green exploding at the top. They rushed by faster and faster and Markham thought of a universe with one wave function, scattering into the new states of being as a paradox formed inside it like the kernel of an idea.—If the wave function did not collapse… Worlds lay ahead of him, and worlds lay behind. There was a sharp crack and he saw suddenly what should have been.

CHAPTER THIRTY TWO

PETERSON WOKE SLOWLY. HE KEPT HIS EYES CLOSED. His body told him not to move but he couldn’t remember why. There was a murmur of movement around him, subdued voices, somewhere in the distance a metallic clash. He opened his eyes briefly, saw white walls, a chrome rail. A whirling dizziness. He remembered where he was now. Gingerly he tested his body. A dull, cottony feel. Seeping, cold ache. The rail down the side of a