"What Wheeler and Feynmann showed was that the rest of the universe, when it's. .h.i.t by an advanced wave, acts like a whole lot of rocks dropped into that pond. The advanced wave goes back in time, makes all these other waves. They interfere with each other and the result is zero. Nothing."

"Ah. In the end the advanced wave cancels itself OUt."

Suddenly music blared over the Whim's stereo: "An' de Devil, he do de dance whump whump with Joan de Arc--"

Peterson shouted, "Turn that down, will you?"

The music faded. He leaned forward. '/ery well.

You've shown me why the advanced wave doesn't work. Time communication is impossible."

Markham gr'mned. "Every theory has a hidden a.s.sumption.

The trouble with the Wheeler and Feyn-mann model was that all those jiggling electrons in the universe in the past might not send back just the right waves. For radio signals, they do. For tachyons they don't. Wheeler and Feynmann didn't know about tachyons; they weren't even thought of until the middle '60s. Tachyons aren't absorbed the Right way. They don't interact with matter the way radio waves do."

"Why not?"

'qaey're different kinds of particles. Some guys named Feinberg and Sudarshan imagined tachyons decades ago, but n.o.body could find them. Seemed o ?

too unlikely. They have imaginary ma.s.s, for one thing." '- "Imaginary ma.s.s?"

"Yes, but don't take it too seriously."

"Seems a serious difficulty."

"Not really. The ma.s.s of these particles isn't what we'd call an observable. That means we can't bring a tachyon to rest, since it must always travel faster than light. So, if we can't bring it to a stop in our lab, we can't measure its ma.s.s at rest. The only definition of ma.s.s is what you can put on the scales and weigh--which you can't do, if it's moving. With tachyons, all you can measure is momentum--that is, impact.- "You have a complaint about the food, sir? I am the manager"

Peterson looked up to find a tall man in a conservative gray suit standing over their table, hands clasped behind him military style. ''Yes, I did. Mostly I preferred not to eat it, in view of what it did to that lady a short while ago."

"I do not know what the lady was eating, sir, but I should think your--"

"Well, I do, you see. It was certainly close enough to what my friend here ordered to make him uncomfortable."

The manager bridled slightly at Peterson's manner.

He was sweating slightly and had a harried look.

"I fail to see why a similar type of food should---"

"I can see it quite plainly. A pity you can't."

"I am afraid we shall have to charge you for-"

"Have you read the recent Home Office directives on imported meats? I had a hand in writing them."

Peterson gave the manager the full benefit of his a.s.sessing gaze. "I would say you probably get much of your imported meat from a local supplier, correct?"

"Well, of course, but---"

"Then you presumably know that there is a severe restriction on how long it can be kept before use?".

"Yes, I'm sure ..." the manager began, but then s 8 hesitated when he saw the look on Peterson's face.

"Well, ac ,t,ally I haven't read much of those lately because"I think I would take more care in future.""I am not sure 'the lady actually ate any imported meat whatever--""I would look into it, if I were you."Abruptly the man lost some of his military bearing.

Peterson looked at him with a.s.surance.''Well, I think we can forget the misunderstanding, sir, in light of--""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 a.s.sured that the ideas made any sense.Markham grimaced. "It's not easy to explain. The key was suspected decades ago, but n.o.body worked it out into a concrete physical theor3a 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."'he 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 yourgrandfather 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 o o hospital in time, he can meet your grandmother. Itdepends on-your aim.""I don't see ""Think about sending messages, instead of shotgunning grandfathers. Everybody a.s.sumes 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 thatswitch 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. Sa 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 informationm ! O0 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 forwardinto 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 fluttersaround 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.

! o !

It does avoid the paradoxes, tiaough. 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 p.r.o.ne 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 19637""Look, the point here is that our distinctions between cause and effect are an illusion. This little experiment we've been discuss'mg is a causal loopno 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 pa.s.sage 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 coor- ! o 2 dinate system in physics from which we can measure time pa.s.sing. 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."''es 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 backto 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 gla.s.s darkwith the thick stout. The manager placed Petersoh'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, thenfield trips to representative restaurants. You have toget the wrist action just right."Markham saluted with the stout. After this silent toast he said, "Oh yes, Renfrew. What Wheeler and Feynmann didn't notice was that if you send a message back which has nothing to do with shutting off the transmitter, there's no problem. Say I want to place a bet on a horse race. I've resolved that I'll send the results of the race back in time to a friend. I do.

In the past, my friend places a bet and makes money.

That doesn't change the outcome of the race. Afterward, my friend gives me some of the winnings. His handing over the money won't stop me from sending ! o the information--in fact, I can easily arrange it so Ionly get the-money after I've sent the message."

"No paradox.""Right. So you can change the past, but only if you don't try to make a paradox. If you try, the experiment hangs up in that stuck-in-between state."Peterson frowned. "But what's it like? I mean, what does the world seem like if you can change it round?"Markham said lightly, "n.o.body knows..n.o.body's ever tried it before.""There were no tachyon transmitters until now."

"And no reason to try to reach the past, either."

"Let me get this straight. How's Renfrew going to avoid creating a paradox? If he gives. them a lot otin-formation, they'll solve the problem and there'll be no reason for him to send the message.""That's the trick. Avoid the paradox, or you'll get a stuck switch. So Renfrew will send a piece of the vital information enough to get research started, but not enough to solve the problem utterl"But what 11 it be like for us? The world will change round us?"Markham chewed at his lower lip. "I think so.

We'll be in a different state. The problem will be reduced, the oceans not so badly off.""But what is this state? I mean, us sitting here? We know the oceans are in trouble.""Do we? How do we know this isn't the result of the experiment we're about to do? That is, if Renfrew hadn't existed and thought of this idea, maybe we'd-be worse off. The problem with causal loops is that our notion of time doesn't accept them. But think of that stuck switch again."Peterson shook his head as though to clear it. "It's hard to think about.""Like tying time in knots," Markham conceded.

"What I've given you is an interpretation of the mathematics. We know tachyons are real; what we don't know is what they imply."

! oa Peterson looked around at the Whim, now mostly deserted. "Strange, to think of this as being an outcome of what we haven't done yet. All looped together, like a hooked rug." He blinked, thinking of the past, when he had eaten here. "That coal stove how long have they had that?""Years, I suppose. Seems like a sort of trademark.

Keeps the place warm in winter, and it's cheaper than gas or electricity. Besides, they can cook at any time of day, not just the power hours. And it gives the customers something to watch while they're waiting for their orders."''Yes, coal's the long-term fuel for old England,"

Peterson murmured, apparently more to himself than Markham. "Bulky though'."'Vhen were you a student here?""In the '70s. I haven't been back very' often."

"Have things changed much?"Peterson smiled reminiscently. "I dare say my rooms haven't changed much. Picturesque view of the river and all my clothes get moldy from the damp ..." He shook off his mood. "I'll have to be getting back to London soon."They elbowed through the students to the door and out into the street. The June sunshine was dazzling after the pub's dark interior. They Stood for a moment, blinking, on the narrow sidewalk. Pedestrians stepped off into the street to walk past them and cyclists swerved around the pedestrians with a trilling of bells. They turned left and strolled back towards King's Parade. On the corner opposite the church, they paused to look 'in the windows of Bowes & Bowes bookstore."Do you mind if I go in for a minute?" Peterson asked. ''here's something I want to look for.""Sure. I'll come ini too. I'm a bookstore freak; never pa.s.s one by."Bowes & Bowes was almost as crowded as the Whim had been earlier, but the voices here were subdued.

They edged cautiously between the knots of i o $ students in black gowns and pyramids of books on display. Peterson pointed out one on a less conspicuous table towards the back of the store.

"Have you seen this?" he asked, picking up a copy and handing it to Markham.

"Holdren's book? No, I haven't read it yet, though I talked to him about it. Is it good?" Markham looked at the t.i.tle, stamped in red on a black coverraThe Geography of Calamity: Geopolitics of Human Dieback by John Holdren. In the bottom right corner was a small reproduction of a medieval engraving of a grinning skeleton with a scythe. He thumbed through it, paused, began to read. "Look at this," he said, holding the book out to Peterson. Peterson ran his eyes over the chart and nodded.Attributable Deaths (estimated)1984-96.

Java 8,750,000.1986.

Malawi 2,300,000.1987.

Philippines 1,600,000.1987-present Congo 3,700,000.1989-present India 68,000,000.1990-present Colombia, Ecuador, 1,600,000.Honduras1991-present Dominican Republic 750,000.1991-present Egypt, Pakistan 3,800,000.1993-present General Southeast Asia 11,3,500,000Markham whistled softly. "Is it accurate?"

"Oh, yes. Underestimated, if anything."

Peterson moved towards the back of the store. A girl was perched on a high stool adding a column of figures into an auto-accountant. Her fair hair hung forward, hiding her face. Peterson studied her covertly while leating through some of the books in front of him. Nice legs. Fashionably dressed in some frilly peasant style he disliked. A blue Liberty scarf ! o artfully arranged at her neck. Slim now, but not for many more years, probably. She looked about nineteen.

As though aware of his gaze, she looked up straight at him. He continued to stare at her. Yes, nineteen and very pretty and very aware of it, too.

She slid from her stool and, clutching papers defen-sively to her chest, came over to him.'qVlay I help you?""I don't know," he said with a slight smile.

"Maybe. I'll let you know if you can."She took this as a flirtatious overture and responded with a routine which probably, he reflected, was a knock-out with the local boys. She turned away from him and looked back over her shoulder, saying huskily, "Let me know then." She gave him a long look from under her lashes, then grinned cheek-ily and flaunted her ways towards the front of the store. He was amused. At first, he had really thoughtthat she intended her coquettish routine seriously,* which would have been ludicrous if she hadn't been so pretty. Her grin showed that she was playacting.

Peterson felt suddenly in very good spirits and almost immediately noticed the book he had been looking for.He picked it up and went to look for Markham.

The girl was with two others, her back to him. Her companions were laughing and staring. They obviously told her he was watching them, because she tttrned to look at him. She really was exceptionally rretty. He made a sudden decision. Markham wasowsing through the science fiction selection."I have a couple of errands," Peterson said. "Why don't you go on ahead and tell Renfrew I'll be there in half an hour?""Okay, fine," Markham said. Peterson watched him as he strode out the door, moving athletically, and disappeared into the alley behind the building known as Schools.Peterson looked for the girl again. She was serving someone else, a student. He watched as she went ! o ?through another routine, leaning forward more than was necessars, to write a receipt, quite enough to enable the student to look down the front of her blouse.

Then she straightened up and looked quite offhand as she gave him his book in a white paper bag. The student went out, with. a disconcerted look on his face. Peterson caught her eye and lifted the book in his hand. She slammed the cash register shut and came over to him."Yes?" she asked. "Have you made 'up your mind?""I think so. I'll take this book. And maybe you could help me with something else. You live in Cambridge, do you?""Yes. You don't?". "No, I'm from London. I'm on the Couficil." He despised himself immediately. Like shooting a rabbit with a cannon. No artistry at all. Anyway, he had all her attention now, so he might as well take advantage of it. "I wondered if you could recommend any good restaurants around here to me?""Well, there's the Blue Boar. And there's a French one in Grantchester that's supposed to be good, LeMarquis. And a new Italian one, I1 Pavone."

"Have you eaten at any of them?"''Well, no ..." She blushed slightly and he knew she regretted appearing at a disadvantage. He was well aware that she had named the three most expensive restaurants. His own favorite had not been mentioned; it was less showy and less expensive, but the food was excellent."If you could choose, which one would you go to?""Oh, Le Marquis. It looks a lovely place.""The next time I'm up from London, if you're not doing anything, I would count it as a great favor if you would have dinner there with me." He smiled intimately at her. "It gets pretty dull, traveling alone, eating alone.""Really?" she gasped. "Oh, I mean ..." She strug- I o $ Gregory Ben fordgled furiously to repress her triumphant excitement.

"Yes, I'd like that very much.""Fine. If I could have your telephone number ..."

She hesitated and Peterson guessed she had no telephone.

"Or if you'd rather, I can simply stop by this shop early on.""Oh yes, that would be best," she said, seizing on this graceful out."I'll look forward to it."They walked forward to the front desk, where he paid for his book. When he left Bowes & Bowes, he turned the corner towards Market Square. Through the side windows of the bookstore he could see her in consultation with her two friends. Well, that was easy, he thought. Good G.o.d, I don't even know her name.He crossed the square and walked through Pefy Cury with its bustling throng of shoppers, coming out opposite Christ's. Through its open gate the green lawn in its quad was visible and behind that, the vivid colors of a herbaceous border against the gray wall of the Master's Lodge. In the gateway he porter sat reading a paper. A knot of students stood studying some lists on the bulletin board. Peterson kept on going and turned into Hobson's Alley. He finally found the place he was looking for: Foster and Jagg, coal merchants.

CHAPTER TEN.

JOHN RENFREW SPENT SAt.u.r.dAY MORNING PUTTING.up new shelving on the long wall in their kitchen.

Marjorie had been after him for months to do it. Her bland asides about where the planes of wood should go "when you get around to it" had slowly accreted into a pressing weight, an agreed duty, unavoidable.

The markets were open only a few days each week--"to avoid fluctuations in supply" was the common explanation, rendered on the nightly news---and with the power cuts, refrigerating was impossible.

Marjorie had turned to putt'mg up vegetables and was ama.s.sing a throng of thick-lipped jars. They waited in cardboard boxes for the promised shelving.,Renfrew a.s.sembled his tools systematicall with as much care as he took in the laboratory. Their house was old and leaned slightly, as though blown by an unfelt wind. Renfrew found that his plumb line, nailed to the wainscotting, weaved a full three inches out from the scuffed molding. The floor sagged with an easy fatigue, like a well-used mat- I I 0 Gregory Ben fordtress. He stepped back from the tilting walls, squinted, and saw that the lines of his home were askew. You put down the money on a place, he reflected, and you get a maze of jambs and beams and cornices, all pushed slightly out of true by history. A bit of settling in that corner, a diagonal misaimed there. He had a sudden memory of when he had been a boy, looking up from a stone floor at his father, who squinted at the plaster ceiling as if to judge whether the roof would fall.As he studied the problem his own children caromed through the house. Their feet thumped on the margins of polished wood that framed the thin rugs.

They reached the front door and ricocheted outside in a game of tag. He realized that to them he probably had that same earnest wrenched look of his father, face skewed in concentration.He arrayed his tools and began to work. The piles of lumber on the back porch gradually dwindled as he cut them into a suitable lattice. To fit the thin planks at the roof he had to make oblique cuts with a rip saw. The wood splintered under his lunging thrusts, but kept to line. Johnny appeared, tired of tag with his older sister. Renfrew set him to work fetching tools as they were needed. Through the window a tinny radio announced that Argentina had joined the nuclear club. "What's a nuclear club, Daddy?" Johnny asked, eyes big. "People who can drop bombs." Johnny fingered a wood file, frowning at the fine lines that rubbed his thumb. "Can I join?"

Renfrew paused, licked his lips, peered into a sky of carbon blue. "Only fools get to join," he said, andset back to work.The radio detailed a Brazilian rejection of preferential trade agreements, which would have established a Greater American Zone with the US. There were reports that the Americans had tied the favor of cheaper imports to their aid on the southern Atlantic bloom problem. "A bloom, Daddy? How can the ocean do like a flower?" Renfrew said gruffly, "A dif- I ! !.

ferent kind of bloom." He hoisted boards under his arm and took them inside.

He was sanding down the ripped edges when Marjorie came in from the garden for inspection. She had mercifully taken the battery-operated radio into the garden with her. "Why's it jut out at the base?"

she asked by way of greeting. She put the radio on the kitchen table. It seemed to go with her everywhere these days, Renfrew noted, as though she could not bear to be alone with a bit of quiet.

"The shelves are straight. It's the walls that are tilted."

"They look odd. Are you sure ... ?"

* "Have a go." He handed her his carpenter's level.

She put it gingerly on a rough-cut board. The bubble bobbed precisely into the place between the two defining lines. "See? Dead level."

"Well, I suppose," Marjorie reluctantly conceded.

"Worry not, your jars aren't going to topple off."

He put several jars on a shelf. This ritual act completed the job. The boxy frame stood out, functional pine against aged oak paneling. Johnny stroked the sheets of wood tentatively, as though awed that he had had a hand in making this wood lattice.

"Think I'll be off to the lab for a bit," Renfrew said, collecting his rip saw and chisels.

"Steady on, there's more fathering needs do'rag.

You're to take Johnny on the mercury hunt."

"Oh h.e.l.l, I forgot. Look, I'd thought--"

"You'd put in an afternoon tinkering," Marjorie finished for him with mild reproof. "'Fraid not."

"Well look, I'll just go round to pick up some notes, then, on Markham's work."

"Best make it on the way with Johnny. Can't you leave off for a weekend, though? I thought you had settled things yesterday."

"We worked out a message with Peterson. Ocean stuff, for the most part. We're letting pa.s.s the lot on ma.s.s fermentation of sugar cane for fuel."

"What's wrong with that? Burning alcohol is ! 2 Gregory Ben fordcleaner than that wretched petrol they're sellingnow."Renfrew scrubbed his hands in the washbasin.