The Wave Theory of Angels

by Alison Macleod

  It was a clear, cold day. Not a breath of a wind off the river. Below them, the fabled towers of the city exhaled long sighs of steam. Their coup de grâce flourishes – gilded minarets, neoclassical cupolas, bright arrows of glass – flashed in the late-morning light. Carver pointed out Michigan, Indiana, Wisconsin. You could see forty, maybe even fifty, miles. ‘Like infinity at your windshield,’ said Witten, and, for a few minutes, each was lost to the view.

  Then Witten said he was hungry. Could they pass on the slide show? He never bothered with breakfast, despite his wife’s blandishments, and now he was peckish. They ordered sandwiches from the deli on the restaurant level. Witten grabbed a souvenir ballpoint and a wedge of napkins.

  They talked noncompact global symmetries and massless spin −1 fields. Witten reached for his glasses and passed Carver the pen. Carver said, ‘Okay. Here goes,’ and started to sketch the latest solitonic solutions to various supergravity theories. ‘I don’t know what you’ve heard, but it’s not pie in the sky.’

  In fact, he said, he and others in the field had already shown that if one of the eleven dimensions was a circle its two edges could conceivably come together to form a kind of tube. ‘Or, in other words’ – he grinned – ‘something that could be mistaken for a string if you happened to be working in your – with respect – more meagre ten-dimensional continuum. And, even though we were ignored by just about everyone at the time, there’s no denying that certain of the supergravity symmetries do carry over to string theory. With gravity in tow.’

  Carver picked up the pen again, and his hand flew over napkin after napkin. The mathematics of the eleventh dimension was at his fingertips, literally.

  He pieced the fragments into a panoramic vision, hauling over the neighbouring table so it wouldn’t be interrupted. Then he sat back, and even he had to draw breath. The old equations still looked astonishingly elegant.

  ‘But you didn’t come here,’ he said, ‘to get reports from the outback.’

  Witten hesitated. ‘I’ve got a hunch.’

  Carver looked at the table, smiled. ‘And I’ve got a hunch you’ve got more than a hunch.’

  Witten started talking. Sometimes he’d consider the food on his plate: pick up a half of sandwich and put it down again, forgetting to eat. Finally he said, ‘It’s like this. What if the five competing string theories are just part of one bigger theory? It sounds crazy, I know.’

  ‘Word has it that I’m used to crazy.’

  ‘What if I’ve got another theory – it’s not strings or supergravity. Call it whatever you like. Pick a letter.’

  ‘What?’

  ‘Any letter.’

  ‘M.’

  ‘Okay, like I say, this theory, this M-theory, is not super-gravity, and it’s not strings either. But it has your eleven-dimensional supergravity, and all five string theories are among its possible low-energy manifestations.’

  Carver whistled low.

  ‘But of course there’s a catch, and the catch is strong coupling. You need to start with the Type IIA string and increase its coupling constant from a value much less than one to a value much greater than one. As the constant gets larger, your eleventh dimension becomes visible. And as the value increases, the dimension grows and things, for lack of a better phrase, ‘‘take life’’.’

  ‘Take life how exactly?’

  ‘Well, what we know as simple strings, they stretch and . . . and combine and sweep . . . A one-dimensional string stretches into something that looks like a ribbon which stretches into a cylinder of sorts which in turn stretches into a membrane. When the Type IIA description, or any one of the five theories, breaks down because a coupling parameter becomes too large, another description takes over.’

  Carver rubbed his temple.

  ‘And the math works. It all works. With electromagnetism, with the strong and weak nuclears, and with gravity.’

  ‘So you’re saying all five are merely different manifestations of . . .’

  ‘Of one underlying and, frankly, still mysterious theory. I think we’re looking at one dynamic structure of the physical world. A matrix. Maybe some kind of vast membrane after all. A membrane to which our world is tied.’

  ‘Paul Dirac. 1962.’

  ‘Only he couldn’t get the equations to pan out. Do you know Townsend’s stuff? At Cambridge. He went back to Dirac. I’ve seen the work. They’ve got it this time. They’ve discovered the membrane mathematically. On paper, it’s stunning. And I’ve got an idea for demonstrating how the extra dimension, that all-important eleventh, could shrink into a segment of a line. So you get two ten-dimensional universes, like this’ – he started drawing – ‘each at an end of the line of the eleventh dimension. But they’re not discrete. The two universes ‘‘communicate’’ with each other by . . . Are you ready?’

  ‘Gravity,’ breathed Carver.

  ‘Exactly.’

  ‘God.’

  ‘Thanks,’ he murmured, wiping his glasses, ‘but my wife still says, if only I could put up a shelf.’ He looked up, smiled, looked down again.

  ‘What kind of Planck energy do you think we’re talking about?’

  ‘Far less than that at which gravity has been expected to become strong.’ Witten passed him his jottings on the napkin. Circled a figure.

  Carver leaned back in his chair. Wiped his mouth with the back of his hand. ‘Get the road map, honey. We could be gone for a while.’

  ‘At least.’

  ‘So what are we looking at? What are you seeing?’

  ‘A kind of multiverse of universes, I suppose. Coexistent worlds. Worlds strung on a thread.’

  Carver nodded slowly, meeting Witten’s eye. Then, ‘There’s just one problem.’

  ‘Go on.’

  ‘The M of M-theory.’

  Witten smiled.

  ‘What does it stand for?’

  ‘Membrane?’ Witten mused, as if trying out a new book title.

  ‘Not too catchy.’

  ‘Matrix . . .’ Witten tried again.

  ‘What about Multiverse?’ Carver picked a gherkin off his plate and snapped it in two between his teeth. ‘Better yet . . . Mystery.’

  Witten laughed. ‘Wait. It’s coming . . .’ He smiled, waggling his considerable eyebrows like a quack conjuror. ‘Magic. M is for Magic.’

  Carver grabbed the salt and pepper shakers and reached for a neighbouring pair. He cast one, two, three, then four into the air, juggling them in a trickling cascade until the manager of the deli emerged and confiscated all four.

  They tried to clink cardboard cups, cold coffee sloshing over the rims. The waitress stared. They could only have looked ridiculous. Yet there was the sense of something unfolding, there, against the skyline of a crystalline winter’s day. And for a moment, no more, each went quiet, lost in his own thoughts; suspended in the space-time dream of the 103rd storey.

  That couldn’t have been long before Witten’s now famous M-theory paper at the University of Southern California in ’95. Carver had seen the abstract. ‘The richer theory, which has as limiting cases the five string theories studied in the last generation, has come to be called M-theory, where M stands for magic, mystery, membrane or matrix, according to taste.’ He’d laughed. And had silently toasted Ed Witten with the stale coffee on his desk.

  That day in ’94, Witten had seemed to him as open-minded as a kid. Carver’s enfant terrible reputation hadn’t fazed him. Not at all. In fact, they’d made a damned good double act. And the exchanges had continued, by letter, by email.

  The conference in Cambridge last month was huge. Already it was spawning a generation of M-theory zealots. So was that who was behind the phone calls? Some fervent postgrad looking for a father figure?

  No. Too easy.

  Something was going on.

  After all, his association with Witten had armed him with clout, hadn’t it? Who didn’t want a piece of M-theory these days? The Web was a good measure of just how far it had travelled. There was n
ew madness every day. Travel in eleven dimensions just steps away. Japanese teleport large objects across miles. M-theory’s living cosmos: the new Neoplatonism.

  Then there was The West Wing furore. In a ratings-winner of an episode some TV character up and reports the discovery of the Grand Unified Theory at Fermilab. The so-called Theory of Everything. It’s H. G. Wells and The War of the Worlds, twenty-first-century-style.

  The switchboard at Fermilab is jammed the next day. Reporters line the steps of Wilson Hall. Not because they’ve confused a TV show with the real thing, but because there’s allegedly been a Fermilab leak at the highest level. The particular West Wing episode is a double bluff, they claim. A carefully negotiated bit of spin to ensure the Everything story, by its nature uncontainable, is dismissed as TV sophistry.

  More media turned up for the West Wing story than for the discovery of the top quark in ’95.

  As if there could be a shred of experimental data. To find a string itself, and not just the ghostly trace of one, they’d need an accelerator the size of the Milky Way.

  Irrelevant, apparently. Doubletalk. Fermilab had reality’s number.

  Paranoia, after all, is only a surplus of logic – as Carver sometimes comforts himself.

  One cock-eyed journalist ran with the story: ‘Dark Matters: the Universe Rattling in Fermilab’s Closet’. His byline went coast to coast. Fermilab’s Office of Public Affairs could barely cope. It was fiction hurdling the real.

  In the days when Giles Carver could still tell which was which.

  5

  When he returns to the hospital, Christina’s feet are uncovered, and there are wedges of pink sponge between her toes.

  Maggie is at the foot of the bed. She has a bottle of nail polish in one hand and a brush in the other. The sight of her there, bending awkwardly over her sister, takes him aback. ‘What you up to, Maggiekins?’

  She turns, trying to look casual. ‘The nurse suggested it.’ She hadn’t wanted to. She couldn’t tell the nurse. She can’t say it now. She is afraid of her sister’s comatose body.

  He looks away. ‘Is there a vase somewhere in here?’

  ‘By the sink. Sssh, Dad. I’m concentrating.’ Summer Fire-weed. She found it in the drug store in the hospital lobby. Only it’s going everywhere now. She can’t make her fingers work.

  He runs the water, unwraps the large arum lily from its tissue paper and places it in the vase. She glances back over her shoulder. She doesn’t remind him that Tina never liked lilies. He places the vase on the bedside table, next to the snapshot of their mother. ‘Have you been talking to her, Maggiekins?’

  She blows on her sister’s toes, her face darkening. ‘No . . .’

  ‘Only I’m sure she’d – ’

  ‘No one’s sure, Dad.’ She looks up. ‘Not even you.’

  ‘She’s going to wake up, Maggie.’

  ‘I wish you wouldn’t say it like that.’

  ‘Like what?’

  ‘Like there’s no problem, really. Like Tina might not be gone already.’ Her eyes are filling.

  ‘For God’s sake, Maggie. What if she can hear you?’

  ‘I don’t think she can.’

  ‘The doctors said to keep – ’

  ‘She barely hears me when I try to wake her if she over-sleeps. So I can’t believe she’s going to hear me now.’

  He sinks into the chair by the bed and leans back, contemplating the blank of the ceiling. ‘Sweetheart, I could really use a coffee from the cafeteria. Maybe a Danish. You could get yourself something to eat while you’re at it.’

  She closes the bottle and turns to him. ‘What are you going to talk to her about?’

  ‘I’m allowed to talk to her, aren’t I?’

  She sighs, exasperated. ‘Don’t play hard done by, Dad. You always do that. I’m just saying I can’t pretend for you, okay?’

  ‘Pretend what?’ He passes her his wallet and winks. ‘Maggie?’

  She meets his eyes begrudgingly.

  ‘Either you’re with me . . .’

  She half smiles, in spite of herself.

  ‘. . . or you’re with me. Which is it?’

  She rolls her eyes. ‘I’m with you.’ She picks up the paperback she’s been reading. Jane Eyre. ‘When haven’t I been?’ She’s at the bit where Rochester calls ‘Jane! Jane! Jane!’ and, miraculously, Jane hears him across the miles. She’d rather let the story go now – she’s not in the mood any more – but she can never not finish one of her mother’s old books. In case she turns over a page and finds one of her scribbled messages. ‘Okay. One coffee, black, and one Danish.’

  In its original form, enchantment was magic by language – literally, conjuring with words.

  Take the standard medieval case of possession. Here, the priest needed a command of Latin, of course, some garbled Greek, and a secret lexicon that might, forgivably, be mistaken for gibberish: ‘Amara Tonta Tyra post hos firabis ficalir: Elypolis starras poly polyque lique linarras buccabor uel bartin vel Titram celi massis Metumbor o priczoni Jordan Ciriacus Valentinus.’

  Or, more reasonably, perhaps: ‘In nomine Patris, et Filii, et Spiritus Sancti. By the power of the Lord, may the Cross + (here the priest crosses himself) and the passion of Christ + be a medicine for me. May the five wounds of the Lord be my medicine +. May the Virgin Mary aid and defend me from every malign demon and from every malign spirit, amen. + A + G + L + A + Tetragrammaton + alpha + O.’

  Meaning?

  Once upon a time, words did more than mean.

  Giles Carver takes his sleeping daughter’s hand in his. He bows his head, covers his face with one hand, and tries to pray to something he can’t believe in. ‘Please. Please let – ’ A food cart rattles past in the corridor. There is a quick knock at the door before it opens. ‘Coffee? Tea?’

  He shakes his head. The door closes again. Through the window’s open vents, he can hear people in the parking lot below. A new baby is crying – its first time in the open air.

  He strokes his daughter’s forehead. ‘Sssh,’ he says. ‘Sssh,’ as if she is upset. ‘Everything is going to be okay.’

  Promise? Her eight-year-old voice. Slightly nasal. She hasn’t yet had her adenoids removed.

  Promise.

  When are you going to take us to your work again and make the frog fly?

  We’ll see.

  Is Maggie already in bed?

  Not yet.

  Then why do I have to go to sleep? I’m older.

  You’re not feeling well, ladybug.

  But I can stay up longer than her when I get better.

  We’ll see.

  Tell me some secret words.

  You don’t listen to the ones I tell you.

  Is that why you tell Maggie?

  Maggie needs some too.

  But you don’t give her my ones?

  Would they be secret if I did?

  Tell me.

  I don’t know any more tonight.

  Yes you do.

  Okay, okay. Close your eyes. Closed? Right, now not a word.

  Not a word.

  That was three.

  Oops.

  That was one.

  . . .

  . . .

  . . .

  ‘I never . . . saw a moor,

  I never saw the sea;

  Yet know I how the heather looks,

  And what a wave must be.’

  I never saw . . .

  A moor. I never . . .

  Saw the sea.

  Yet know I how the . . .

  There’s a girl at school called Heather. She –

  How the heather looks. Your go.

  And what a wave must be.

  Very good, ladybug.

  I won’t remember. I never do in the morning.

  That’s because they’re secret words.

  What do they mean?

  You’ll know as soon as you’re asleep.

  Really?

  Really.

  Night, Daddy. />
  Night, my baby.

  Alone in the cafeteria, her midday breakfast still untouched, Maggie withdraws the bookmark from her book and turns it over. She copied the number in small, neat numbers before wiping all trace of it from the palm of her sister’s hand. When she discovered it that morning, painting Christina’s nails, the number was already faint.

  What is it? The number of a friend from school she met on the bus? The number of some take-out place, quickly scribbled? The number of one of the other forest preserve volunteers? Tina was out there just yesterday afternoon.

  Has it faded as a matter of course? Did Christina herself try to wash it away, last night before bed? Or was a nurse simply indiscriminate as she sponge-bathed her sister’s body late last night, before they moved her into the private room?

  Maggie opens her father’s wallet, fishes in the change pocket for a quarter, then walks to the payphone on the opposite side of the cafeteria. She picks up the receiver, punches the buttons and waits.

  No answering machine. No voicemail. No answer.

  6

  The payphone rings and rings. A few passersby glance that way, but no one stops. It’s Saturday lunchtime in the metropolis. Labor Day weekend. Everyone has somewhere they want to be. A trumpeter with a prosthetic arm is playing ‘Fly Me to the Moon’. He squeezes his eyes against the ringing of the phone but he doesn’t miss a beat.

  The shoeshine kid, on the other hand, is hardly aware. He’s sizing up his prey. Tourists today. The heat means too many are in sandals and sneakers, but he’s not giving up. Brits are good. They get off the plane at O’Hare and think they’ve walked into a movie. He’s not even halfway through the patter before they’re nodding. Cos they’re thinking: shoe brush in the jacket pocket or handgun? Shoe brush? Handgun? He likes Canadians the best. They know he’s ripping them off, but they’re too PC to turn down an inner-city kid on the make.