Timescape

“Indeed.” Peterson nodded, dismissing him. He turned back to Markham. “You still haven’t got round the grandfather thing. If tachyons can carry a message back to the past, how do you avoid paradoxes?” Peterson did not mention that he had gone through a discussion with Paul Davies at King’s about this, but understood none of it. He was by no means assured that the ideas made any sense.

Markham grimaced. “It’s not easy to explain. The key was suspected decades ago, but nobody worked it out into a concrete physical theory. There’s even a sentence in the original Wheeler-Feynmann paper—’It is only required that the description should be logically self-consistent.’ By that they meant that our sense of the’ flow of time, always going in one direction, is a bias. The equations of physics don’t share our prejudice—they’re time- symmetric. The only standard we can impose on an experiment is whether it’s logically consistent.”

“But it’s certainly illogical that you can be alive even after you’ve knocked off your own grandfather. Killed him before he produced your father, I mean.”

“The problem is, we’re used to thinking of these things as though there was some sort of switch involved, that only had two settings. I mean, that your grandfather is either dead or he isn’t.”

“Well, that’s certainly true.”

Markham shook his head. “Not really. What if he’s wounded, but recovers? Then if he gets out of the hospital in time, he can meet your grandmother. It depends on your aim.”

“I don’t see—”

“Think about sending messages, instead of shotgunning grandfathers. Everybody assumes the receiver—back there in the past—can be attached to a switch, say. If a signal from the future comes in, the switch is programmed to turn off the transmitter—before the signal was sent. There’s the paradox.”

“Right.” Peterson leaned forward, finding himself engrossed despite his doubts. There was something he liked about the way scientists had of setting up problems as neat little thought experiments, making a clean and sure world. Social issues were always messier and less satisfying. Perhaps that was why they were seldom solved.

“Trouble is, there’s no switch that has two settings—on and off—with nothing in between.”

“Come now. What about the toggle I flip to turn on the lights?”

“Okay, so you flip it. There’s a time when that switch is hanging in between, neither off nor on.”

“I can make that a very short time.”

“Sure, but you can’t reduce it to zero. And also, there’s a certain impulse you have to give that switch to make it jump from off to on. In fact, it’s possible to hit the switch just hard enough to make it go halfway—try it. That must’ve happened to you sometime. The switch sticks, balanced halfway between.”

“All right, granted,” Peterson said impatiently. “But what’s the connection to tachyons? I mean, what’s new about all this?”

“What’s new is thinking of these events—sending and receiving—as related in a chain, a loop. Say, we send back an instruction saying, ‘Turn off the transmitter.’ Think of the switch moving over to ‘off.’ This event is like a wave moving from the past to the future. The transmitter is changing from ‘on’ to ‘off.’ Now, that—well, let’s call it a wave of information— moves forward in time. So the original signal doesn’t get sent”

“Right. Paradox.”

Markham smiled and held up a finger. He was enjoying this. “But wait! Think of all these times being in a kind of loop. Cause and effect mean nothing in this loop. There are only events. Now as the switch moves towards ‘off,’ information propagates forward into the future. Think of it as the transmitter getting weaker and weaker as that switch nears the ‘off’ position. Then the tachyon beam that transmitter is sending out gets weaker.”

“Ah!” Peterson suddenly saw it. “So the receiver in turn gets a weaker signal from the future. The switch isn’t hit so hard because the backward-in-time signal is weaker. So it doesn’t move so quickly toward the ‘off’ mark.”

“That’s it. The closer it gets to ‘off,’ the slower it goes. There’s an information wave traveling forward into the future, and—like a reflection—the tachyon beam comes back into the past.”

“What does the experiment do then?”

“Well., say the switch gets near ‘off,’ and then the tachyon beam gets weak. The switch doesn’t make it all the way to ‘off’ and—like that toggle controlling the lights—it starts to fall back toward ‘on.’ But the nearer it gets to ‘on,’ the stronger the transmitter gets in the future.”

“So the tachyon beam gets stronger,” Peterson finished for him. “That in turn drives the switch away from ‘on’ and back towards ‘off.’ The switch is hung up in the middle.”

Markham leaned back and drained his stout. His tan, weakened by the dim Cambridge winter, crinkled with the lines of his wry smile. “It flutters around there in the middle.”

“No paradox.”

“Well…” Markham shrugged imperceptibly. “No logical contradictions, yes. But we still don’t actually know what that intermediate, hung-up state means. It does avoid the paradoxes, though. There’s a lot of quantum-mechanical formalism you can apply to it, but I’m not sure what a genuine experiment will give.”

“Why not?”

Markham shrugged again. “No experiments. Renfrew hasn’t had the time to do them, or the money.”

Peterson ignored the implied criticism; or was that his imagination? It was obvious that work in these fields had been cut back for years now. Markham was simply stating a fact. He had to remember that a scientist might be more prone simply to state things as they were, without calculating a statement’s impact. To change the subject Peterson asked, “Won’t that stuck-in-the-middle effect prevent your sending information back to 1963?”

“Look, the point here is that our distinctions between cause and effect are an illusion. This little experiment we’ve been discussing is a causal loop—no beginning, no end. That’s what Wheeler and Feynmann meant by requiring only that our description be logically consistent. Logic rules in physics, not the myth of cause and effect. Imposing an order to events is our point of view. A quaintly human view, I suppose. The laws of physics don’t care. That’s the new concept of time we have now—as a set of completely interrelated events, linked self-consistently. We think we’re moving along in time, but that’s just a bias.”

“But we know things happen now, not in the past or future.”

“When is ‘now’? Saying that ‘now’ is ‘this instant’ is going around in circles. Every instant is ‘now’ when it ‘happens.’ The point is, how do you measure the rate of moving from one instant to the next? And the answer is, you can’t. What’s the rate of the passage of time?”

“Well, it’s—” Peterson stopped, thinking.

“How can time move? The rate is one second of movement per second! There’s no conceivable coordinate system in physics from which we can measure time passing. So there isn’t any. Time is frozen, as far as the universe is concerned.”

“Then…” Peterson raised a finger to cover his confusion, frowning. The manager appeared as though out of nowhere.

“Yes sir?” the man said with extreme politeness.

“Ah, another round.”

“Yes sir.” He hustled off to fill the order himself. Peterson took a small pleasure in this little play. To get such a response with a minimum display of power was an old game with him, but still satisfying.

“But you still believe,” Peterson said, turning back to Markham, “that Renfrew’s experiment makes sense? All this talk of loops and not being able to close switches…”

“Sure it’ll work.” Markham accepted a glass dark with the thick stout. The manager placed Peterson’s ale carefully before him and began, “Sir, I want to apol—”

Peterson waved him into silence, impatient to hear Markham. “Perfectly all right,” he said quickly.

Markham eyed the manager’s retreating back. “Very effective. Do they teach that in the best schools?”

Peterson smiled. “Of course. There’s lecture, then field trips to representative restaurants. You have to get the wrist action just right.”