And by then- By then, more than a decade would have slipped by, and Heather would be into the high-risk age for pregnancy.
Choices.
Turning points.
It could go one way or the other.
At last they"d opted to have the child; countless student couples had done the same over the years. It would be difficult-a stretch financially, an additional demand on their already overtaxed time.
But it would be worth it. Surely it would be worth it.
Kyle remembered vividly the cla.s.s he"d been in the day Heather had told him she was pregnant. It had seemed so appropriate, somehow.
"Suppose," Professor Papineau had said to the dozen students in the seminar that had seemed to start out a long way from computer science, "that you live just north of Queen"s Park and you work just south of it. Further suppose that you walk to work each day. You"re faced with a choice every morning. You can"t walk down the center line, since the Parliament Buildings get in the way. Of course, I"m sure there"ve been times when many of us have wanted to plow through the Legislature in a tank . . . but I digress."
Laughter from the students. Papineau had been a wonderful prof; Kyle had gone to his retirement dinner fifteen years later, but hadn"t seen him since.
"No," said Papineau, once the chuckling had stopped, "you have to go around around the buildings-either to the east, or to the west. Each way is pretty much the same distance; you leave home at the same time and you arrive at work at the same time regardless of which route you choose. So, which route the buildings-either to the east, or to the west. Each way is pretty much the same distance; you leave home at the same time and you arrive at work at the same time regardless of which route you choose. So, which route do do you choose? You, there-Kyle. Which way would you go?" you choose? You, there-Kyle. Which way would you go?"
Kyle had his beard even back then. As today, it was red, even though his hair was black. But in those days he"d kept it scruffy, unkempt-never tr.i.m.m.i.n.g it, never shaving his neck beneath. He cringed now to think about it. "Down the west," he said, shrugging to convey that it was a purely arbitrary selection.
"A fine choice," said Papineau. "But it"s not the only choice. And in the many-worlds interpretation of quantum mechanics, we believe that any time a choice can be made one way, the alternative choice is also made-but in a parallel universe. If Kyle did indeed come down the west side in this universe, there would also exist a parallel universe in which he came down the east side."
"But surely that"s just a metaphor," said Glenda, a student Kyle sometimes thought he might have pursued had he not already met Heather. "Surely there"s really only one universe, no?"
"Or," said D"Annunzio, a biker type who always seemed out of place in cla.s.s, "even if another universe does exist, there"s no way to prove it, so it"s not a falsifiable hypothesis, and therefore not real science."
Papineau grinned broadly. "You know," he said, "if this were a nightclub performance, people would accuse me of having planted the two of you in the audience. Let"s look at that question: is there any direct evidence that multiple universes might exist? Roopshand, will you get the lights, please?"
A student in the back stood up and turned off the lights. Papineau moved next to a slide projector sitting on a metal cart; he turned it on. A diagram appeared on the screen.
"This picture shows some experimental apparatus," said Papineau. "At the top, we have a lightbulb. In the middle there"s a bar representing a horizontal wall as seen from above. You see those two breaks in the bar? Those are two vertical slits that go right through the wall-one on the left and one on the right." He used a small telescoping pointer to indicate these. "And at the bottom we have a horizontal line representing a sheet of photographic film seen edge-on from above. The wall in the middle is like Queen"s Park, and the two slits are like the two possible paths around the Parliament Buildings-one on the east and one on the west." He paused while the students digested this. "Now, what happens when we turn on the light-bulb?"
He pushed a key; the carousel clicked around and a new slide came on. The photographic film at the bottom showed a zebra pattern of light and dark lines.
"You all know what that is from high-school physics, right? It"s an interference pattern. Light from the bulb, traveling like a wave, pa.s.ses through the two slits-which behave now like two separate light sources, each with waves of light emanating from it. Well, when the two sets of waves crash against the photographic plate, some of the waves cancel out, leaving dark areas, and others reinforce each other, making the bright bands."
Some students nodded.
"But you also know from high-school physics that light doesn"t always behave like a wave-sometimes it behaves like a particle, too. And, of course, we call particles of light "photons." Now, what happens if we turn down the power going to the lightbulb? What happens when the power is turned down so low that photons are coming out of the lightbulb one at a time? Anyone?"
A redheaded woman held up a hand.
"Yes, Tina?" said Papineau.
"Well, if only one photon is going through, then it should make one little spot of light on the photographic film-a.s.suming it finds its way through one of the slits."
Papineau smiled. "That"s what you"d expect, yes. But even when photons are released one at a time, you still still get the light and dark bands. You still get interference patterns." get the light and dark bands. You still get interference patterns."
"But how can you get interference if there"s only one particle pa.s.sing through at a time?" asked Kyle. "I mean, what"s the particle interfering with?" with?"
Papineau raised his index finger. "That is is the question! And there are two possible answers. The one that"s simply weird is that in transit between the lightbulb and the film, the single photon breaks up into a series of waves, some of which go through one slit and some through the other, forming the interference pattern. the question! And there are two possible answers. The one that"s simply weird is that in transit between the lightbulb and the film, the single photon breaks up into a series of waves, some of which go through one slit and some through the other, forming the interference pattern.
"But the other answer-the really interesting answer-is that the photon never breaks up, but rather remains a discrete particle, and as such, it has no choice but to go through only one of the two possible slits-in this universe. But just as you, Kyle, could have taken either route around Queen"s Park, so the photon could have taken the path through either slit- But just as you, Kyle, could have taken either route around Queen"s Park, so the photon could have taken the path through either slit-and in a parallel universe, it took the other path." in a parallel universe, it took the other path."
"But how come we see the interference pattern?" asked D"Annunzio, chewing gum as he spoke. "I mean, if we stood south of the Parliament Buildings, we"d never see two versions of Graves, one coming around the east side and one around the west."
"Excellent question!" crowed Papineau. "The answer is that the two-slit experiment is a very special example of parallel universes. The original single universe splits into two universes once the photon encounters the slits, but the two universes exist separately only so long as the photon is traveling. Since it makes no difference now or ever or ever which path the photon actually took, the universes collapse back together into a single universe. The only evidence that the two universes ever existed is the interference pattern left behind on the film." which path the photon actually took, the universes collapse back together into a single universe. The only evidence that the two universes ever existed is the interference pattern left behind on the film."
"But what if it does does make a difference which slit was chosen?" asked Roopshand from the back. make a difference which slit was chosen?" asked Roopshand from the back.
"In any experiment you can devise in which the choice of slit actually matters-indeed, in any experiment in which you can detect which slit the photon went through-you don"t get the interference pattern. If it matters at all, the universes never st.i.tch back together into one; they continue on as two separate universes.
It had been a heady cla.s.s-as all of Papineau"s were. And it had also been a metaphor that Kyle carried with him throughout his life: choices, branching paths.
Back then, back in 1996, even though he and Heather were still students, he knew which choice he wanted. He wanted to live in the universe in which they did did have a baby. have a baby.
And so that November, their first child, Mary Lorraine Graves, was born.
5.
Kyle was walking along Willc.o.c.ks Street, heading from New College back toward Mullin Hall, but he was accosted before he could cross St. George.
"Sir-excuse me. Sir, pardon me! Yes, you. Dale Wong, City-TV. We"d like to ask you a question."
"A streeter?" said Kyle, the word coming to him from somewhere.
The young man with the camcorder was amused. "Exactly, sir. A streeter. Here"s our question. Today is the tenth anniversary of the receipt of the first radio message from Alpha Centauri."
"Is it really?"
"Yes, sir. How has it affected you this past decade, knowing that there"s intelligent life elsewhere in the universe?"
Kyle frowned, thinking. "Well, that"s a good question. It"s certainly interesting-my wife actually works on trying to decode the alien radio messages."
"But how has it changed you-changed your outlook?"
"Well, I suppose it gives me a little perspective on things. You know-all our problems don"t amount to much, compared to the limitless universe." The words rang false as they came out. Kyle paused-long enough, he knew, that the man wouldn"t be able to use the video clip without editing. "No, no, that"s not it. You want the truth? It hasn"t changed a d.a.m.n thing. No matter how big the universe gets, we"re always looking inside."
"Thank you, sir. Thank-Ma"am! Ma"am! A moment of your time, please!"
Kyle continued to walk. He hadn"t really thought about it before, but his current research project clearly had had its genesis back in the spring of 1996, the same day he"d learned that Heather was pregnant.
"So," Professor Papineau had said, "the interference patterns that result when a single photon pa.s.ses through two slits might be proof of the existence of multiple universes. But what, you may ask, does this have to do with computing?" He beamed at his seminar students.
"Well, remember our example of Kyle coming to work. In one universe, he walks around the east side of Queen"s Park; in the other, he walks around the west side. Now, Kyle, suppose your boss had asked you to solve two problems before you came into work, and-having never overcome your student ways-you"ve left them both to the last moment. There"s time to puzzle out the answer to just one of them in your head as you walk to work. Let"s say that if you went down the west side, you"d spend your time solving problem A, and if you went down the east side, you"d spend your time solving problem B. Is there any way without slowing down or taking the journey around the Parliament Buildings twice that by the time you got to work, you"d have the answers to both problems?"
Kyle was sure he"d had a blank expression.
"Anyone?" asked Papineau, bushy eyebrows raised.
"I"m surprised you think Graves would come up with even one answer," said D"Annunzio.
Snickers from several students. Papineau smiled.
"Well, there is is a way," said the professor. "You know the old saying, "Two heads are better than one"? Well, if our Kyle-the one from this universe who went down the west side and who solved problem A-could join back up with the other Kyle-the one from the parallel universe who went down the east side and solved problem B-then he"d have both answers." a way," said the professor. "You know the old saying, "Two heads are better than one"? Well, if our Kyle-the one from this universe who went down the west side and who solved problem A-could join back up with the other Kyle-the one from the parallel universe who went down the east side and solved problem B-then he"d have both answers."
A hand went up.
"Glenda?"
"But when talking about the photon and the slits, you said the only way the two universes could rejoin is if there was no way to tell which slit the photon had taken in each universe."
"Exactly. But if we could devise a method by which it made no difference whatsoever which way Kyle went in this universe-indeed, a method by which Kyle himself didn"t know which way he had gone, and no one saw him during his journey- then, at the end of it all, the two universes might st.i.tch back together. But in the rejoined universe, Kyle would know the answer to both problems, even though he"d really only had time to solve one of them."
Papineau grinned at the cla.s.s.
"Welcome," he said, "to the world of quantum computing." He paused. "Of course, there were really more than two possible universes for Kyle-he could have stayed home, he could have driven to work, he could have taken a cab. Likewise, it"s possible to envision the lightbulb experiment with dozens or even hundreds of slits. Well, suppose each of the photons coming off the lightbulb represented a single bit of information. Remember, all computing is done with glorified abacuses; we actually move things around in order to compute, whether it"s pebbles or atoms or electrons or photons. But if each of those things could simultaneously be in multiple places at once, across parallel universes, extraordinarily complex computing problems could be solved very, very quickly.
"Consider, for instance, the factoring of numbers. How do we do that? Essentially by trial and error, although there are a few tricks that help. If we want to determine the factors of eight, we start dividing numbers into it. We know that one goes evenly into eight-it goes evenly into every whole number. What about two? Yes, it"s a factor: it goes in four times. Three? No-it doesn"t go in evenly. Four? Yes, it goes in twice. That"s how we do it: by brute-force computing, testing every possible factor in turn. But as numbers get bigger, the number of factors they have get bigger. Earlier this year, a network of sixteen hundred computers succeeded in finding all the factors of a 129-digit number-the largest number ever factored. The process took eight eight months. months.
"But imagine a quantum computer-one that was in touch with all the possible alternative computers in parallel universes. And imagine a program that factors large numbers by working on all the possible solutions simultaneously. simultaneously. Peter Shor, a mathematician at AT&T Bell Laboratories, has worked out a program to do just that; it would try every possible factor of the big number simultaneously by testing just one possible factor in each of many parallel universes. The program outputs its results as interference patterns, sent to a piece of photographic film. Shor"s algorithm would cause those numbers that aren"t factors to cancel out in the interference pattern, leaving darkness. The patterns of light and dark would form a sort of barcode that could be read to indicate which numbers actually are factors of the big number you started with. And since the calculations are performed across parallel universes, in the time it takes for our universe to test any one number, all the other numbers are tested as well, and we have the result. So long as it makes no difference which number our own computer calculated, the result should be achieved almost instantaneously; what normal computers took eight months to do, quantum computers could do in a matter of seconds." Peter Shor, a mathematician at AT&T Bell Laboratories, has worked out a program to do just that; it would try every possible factor of the big number simultaneously by testing just one possible factor in each of many parallel universes. The program outputs its results as interference patterns, sent to a piece of photographic film. Shor"s algorithm would cause those numbers that aren"t factors to cancel out in the interference pattern, leaving darkness. The patterns of light and dark would form a sort of barcode that could be read to indicate which numbers actually are factors of the big number you started with. And since the calculations are performed across parallel universes, in the time it takes for our universe to test any one number, all the other numbers are tested as well, and we have the result. So long as it makes no difference which number our own computer calculated, the result should be achieved almost instantaneously; what normal computers took eight months to do, quantum computers could do in a matter of seconds."
"But there"s no such thing as a quantum computer," said Kyle.
Papineau nodded at him. "That"s right, at least not yet. But someday someone is going to build a quantum computer. And then we"ll know for sure."
6.
Kyle and Heather had dinner together every Monday night.
They"d been separated for a year now. It had never been intended to be permanent-and they"d never mentioned the D-word. They"d just needed some time, they both felt, to come to terms with Mary"s death. They"d both been on edge, sniping at each other, little things that shouldn"t have mattered at all escalating into huge fights, unable to console each other, unable to comprehend why it had happened.
They"d never missed a Monday dinner together, and although tensions were high since Becky"s visit four days ago, Kyle a.s.sumed that Heather would show up at their usual restaurant, a Swiss Chalet franchise a few blocks from their house.
Kyle stood outside, enjoying the warm evening breeze. He couldn"t bring himself to go in yet; Heather"s car wasn"t in the lot, and if she didn"t show, the embarra.s.sment would be too much.
At about 6:40-ten minutes late-Heather"s powder-blue skimmer floated into the lot.
Still, things were different. For an entire year now, they"d greeted each other on Monday nights with a quick kiss, but this time-this time they both hesitated. They entered the restaurant, Kyle holding the door for Heather.
The server tried to seat them beside another couple, even though there was no one else in the place. Kyle hated that at the best of times, and this evening he did protest. "We"ll sit over there," he said, pointing to a distant corner.
The server acquiesced, and they were escorted to a booth at the back. Kyle ordered red wine; Heather asked for a gla.s.s of the house white.
"I was beginning to think you weren"t coming," said Kyle.
Heather nodded, but her face was impa.s.sive. The lamp hanging above their table made her normally pleasant features look severe. "I"m sorry I was late."
There was silence for a time.
"I don"t know what we"re going to do about this," said Kyle.
Heather looked away. "Me neither."
"I swear to you-"
"Please," said Heather, cutting him off. "Please."
Kyle nodded slowly. He was quiet for a moment longer, then: "I went to see Zack on Sat.u.r.day."
Heather looked apprehensive. "And?"
"And nothing. I didn"t get into a fight with him, I mean. We talked a bit. I wanted him to agree to come to the forensics lab at the university. I was going to take a lie-detector test, prove that I didn"t do it."
"And?" said Heather again.
"He refused." Kyle lowered his eyes, looking at the paperite place mat with the current month"s chicken promotion ill.u.s.trated on it. He looked up again and sought Heather"s eyes. "I could do the same thing for you," he said. "I could prove my innocence."
Heather opened her mouth, but immediately closed it.
It was a turning point, a crux. Kyle knew it, and he was sure Heather knew it, too. The future depended on what would happen next.
She had to be thinking it all through . . .
If he was innocent- If he was innocent, she must know he"d never be able to forgive her for demanding proof, for her lack of faith. If he was innocent, then surely their marriage should should survive this crisis. They"d both thought they would get back together again, sooner or later. If not by the beginning of the coming school year, surely by its end. survive this crisis. They"d both thought they would get back together again, sooner or later. If not by the beginning of the coming school year, surely by its end.
If he was innocent, the marriage should survive, but if Heather had doubt, and admitted it, admitted the possibility, would he ever be able to hold her again, to love her again? When he"d needed her most, had she believed in him?
"No," she said, closing her eyes. "No, that won"t be necessary." She looked at him. "I know you didn"t do anything." Kyle kept his expression neutral; he knew she must be searching his face for any sign that he thought the words might be insincere.
"Thank you," he said softly.