From ``Timescape'', by Gregory Benford.

They had both more drinks when Peterson said, ``Look, it's Sir Martin who's really the technical type on the British delegation. I'm a nonspecialist, as they call it. What I want to know is, how in hell do you get around this grandfather paradox bit? That fellow Davies explained about the discovery of tachyons right enough, and I accept that they can travel into our past, but I still can't see how one can logically change the past.''

Markham sighed, ``Until tachyons were discovered, everybody thought communication with the past was impossible. The incredible thing is that the physics of time communication had been worked out earlier, almost by accident, as far back as the 1940s. Two physicists named John Wheeler and Richard Feynmann worked out the correct description of light itself, and showed that there were two waves launched whenever you tried to make a radio wave, say.''

``Two?''

``Right. One of them we receive on our radio sets. The other travels backward in time -- the `advanced wave,' as Wheeler and Feynmann called it.''

``But we don't receive any message before it's sent.''

Markham nodded. ``True -- but the advanced wave is there, in the mathematics. There's no way around it. The equations of physics are all time-symmetric. That's one of the riddles of modern physics. How is it that we perceive time passing, and yet all the equations of physics say that time can run either way, forward or backward?''

``The equations are wrong, then?''

``No, they're not. They can predict anything we can measure -- but only as long as we use the `retarded wave,' as Wheeler and Feynmann called it. That's the one that you hear through your radio set.''

``Well, look, surely there's a way to change the equation round until you get only the retarded part.''

``No, there isn't. If you do that to the equations, there's no way to keep the retarded wave the same. You must have the advanced wave.''

``All right, where are those backward-in-time radio shows? How come I can't tune into the news from the next century?''

``Wheeler and Feyrunann showed that it can't get here.''

``Can't get into this year? I mean, into our present time?''

``Right. See, the advanced wave can interact with the whole universe -- it's moving back, into our past, so it eventually hits all the matter that's ever been. Thing is, the advanced wave strikes all that matter before the signal was sent.''

``Yes, surely." Peterson reflected on the fact that he was now, for the sake of argument, accepting the ``advanced wave'' he would have rejected only a few moments before.

``So the wave hits all that matter, and the electrons inside it jiggle around in anticipation of what the radio station will send.''

``Effect preceding a cause?''

``Exactly. Seerns contrary to experience, doesn't it?''

``Definitely.''

``But the vibration of those electrons in the whole rest of the universe has to be taken into account. They in turn send out both advanced and retarded waves. It's like dropping two rocks into a pond. They both send out waves. But the two waves don't just add up in a simple way.''

``They don't? Why not?''

``They interfere with each other. They make a criss-cross network of local peaks and troughs. Where the peaks and troughs from the separate patterns coincide, they reinforce each other. But where the peaks of the first stone meet the troughs of the second, they cancel. The water doesn't move.''

``Oh. All right, then.''

``What Wheeler and Feynmann showed was that the rest of the universe, when it's hit 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. ``Very well. You've shown me why the advanced wave doesn't work. Time communication is impossible.''

Markham grinned. ``Every theory has a hidden assumption. The trouble with the Wheeler and Feynmann 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 '6os. Tachyons aren't absorbed the right way. They don't interact with matter the way radio waves do.''

``Why not?''

``They're different kinds of particles. Some guys named Feinberg and Sudarshan imagined tachyons decades ago, but nobody could find them. Seemed too unlikely. They have imaginary mass, for one thing.''

``Imaginary mass?''

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

``Seems a serious difficulty.''

``Not really. The mass 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 fight. So, if we can't bring it to a stop in our lab, we can't measure its mass at rest. The only definition of mass 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 assessing 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 hesitated when he saw the look on Peterson's face. ``Well, actually 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 assurance.

``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 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 smded 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 rnake 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 bearn 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 systern 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.''

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 do with shutting off the transmitter, there's no problem. Say you want to place a bet on a horse race. I've resolved that I'll send results of the race back in time to a friend. I do. In the past, 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 the information -- in fact, I can easily arrange it so I only 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 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, ``Nobody knows. Nobody'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 of information, 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 utterly.''

``But what'll 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.''