by Tom DeMarco
He didn’t seem to expect an answer. Loren waited for him to go on. After a pause of more than a minute, he did:
“I have always felt uncomfortable about the concept of time. It never seemed quite right to me. Other things I can feel. Students have trouble understanding how light can be both a particle and a wave, but I never had a problem with that. I could feel it. I would sit outside in the sunlight, and I could feel the little particles falling down onto me, the photons. I could almost hear them pattering on the leaves like a fine rain. And I could sense the waves too, the feeling that they could make the hair on my arms stand up a bit as it would in the presence of static electric charge. Only it wasn’t a charge, it was light.
“I can feel quantum movement of electrons, I can feel that the speed of light has to be a limit of all speed. I can feel each of the effects of Relativity. Just like Mr. Tompkins on his bicycle, I can feel the very small change in mass that comes from pedaling faster. I don’t need to go to another universe where the speed of light is slower. I can feel it in this universe.
“But time I can’t feel. Or what I feel is just not what it’s supposed to be like. I never understood it. The little t that I write to represent time in an equation, for me it is nothing but a fudge-factor that I put in to make the equation come out right. I always think of myself as a big fraud when I write down that t because I can’t feel what it is. What is time? Tell me Loren, what is it?”
“Time is like…a river,” Loren offered. He knew it was a weak answer.
“Ah, a river. That’s a big help. Time is like a river. The River t.” Homer looked tired. “We need to think about that river, Loren, to think about it and learn to feel what it’s like.”
Realization dawns without volition, without control; it simply comes. Loren could not have stopped it or retarded it or even turned away. His role was only to absorb. The absorbing proceeded at its own pace, over the course of nearly an hour. In that time he did not move, nor did Homer. The hour unfolded, realization dawned and nothing else happened at all. At the end he knew what he had not even considered before: The false constant was hiding inside our notion of time. It was masquerading as part of the little t. A part of the t could vary separately from time as we have understood it. It could vary, but it never had. Until the beam. Inside the beam, perhaps for the first time in history, time was slowed down almost infinitesimally. The fine red shaft of light created a local disturbance in the meaning of time.
“Time is different inside the beam, isn’t it, Homer?”
“Yes.”
“It’s slower.”
“Yes.”
“The flame is burning at the same rate inside as out, only it’s time itself that is not the same.”
“Yes.”
“You knew this already.”
“Yes.”
With a breakthrough is supposed to come a sense of elation. But Loren felt nothing. He supposed it would come later. For the present, there was only confusion. He felt like an archaeologist who has just found proof that the culture he was studying had been created in a stroke of the wand by a wizard. What had seemed sensible and bounded before now seemed crazy. It was a card game with all cards wild.
Homer pointed a long finger at him. “Now I have an assignment for you, my young friend. I want you to work it through all the way and write down for me what is happening inside the beam.”
“But you have already done this, I think.”
“Yes.” Homer looked positively smug. “But I want you to do it again. Work it all out and put it in a form that you can present to me and to the others. It’s a little homework assignment.”
Loren had never accepted an assignment from Homer with anything but enthusiasm. But there was something galling in this one. Why couldn’t Homer simply show him what he had discovered? Why put him through the exercise of working it out for himself? He wasn’t a first year student who needed to learn from guided discovery. He was supposed to be an esteemed co-worker. He tried to keep his annoyance from showing. But Homer had seen it already. He was grinning. Damn him.
Loren slammed the door behind him on the way out.
8
T-PRIME
It was a child’s exercise. Homer’s challenge to work out the relationships in one day had been given at 8 P.M. on Sunday. By 10 A.M. on Monday the work was done. If Homer had challenged him to do the work in four hours instead of a day, the result would not have been so very different. In four hours, he could have written the equations and sketched out a series of empirical tests to confirm their validity. Four hours would have been plenty.
It had been a matter of honor not to start working on his assignment right away. In fact, he hadn’t even begun to think about it until morning. The remaining hours of Sunday were devoted to indulging his irritation at the way Homer had treated him. When his snit died away, Loren carried a huge bundle of dirty clothes up to the all-night Laundromat on College Avenue. While his six machines went through their cycle, he browsed through the racks of the adjacent all-night book store. During the dry cycle, he shopped for groceries at the all-night market on the other side of the laundry. And then, back in his own kitchen, he washed all the dishes accumulated in the sink and set out two frying pans, a mixing bowl, a cutting board and large knife.
The body awake, the mind in repose. Nothing more to do than watch idly the spectacle of his own hands cutting potatoes and onions into nearly perfect three millimeter slices. He stopped twice to sharpen the French knife against a rod. The vegetables went together with some olive oil into a heavy skillet over a low flame. While they cooked he washed the kitchen floor. Next he beat five eggs in a mixing bowl. He put them into some sizzling butter in the other skillet and quickly mixed in the onions and potatoes. He washed the first skillet, stopping occasionally to shake the one on the stove. When the tortilla de patata was finished on one side, he shook it a final time, then flipped it over in the air, just the way Asunción did, to cook the other side. He set the table for one. Then he sat down and ate most of the tortilla with half a loaf of French bread and a glass of wine. After that, he put the kitchen back in order, ran himself a bath and soaked in it. He cut and filed his nails. Stupid Homer. He dressed slowly in front of the mirror. The young man who stared morosely back at him was about to be part of an important happening in the world of physics, there was no doubt of that. What Homer had discovered was fundamental. It would alter the science forever after. And Loren was part of the team. He would get some of the credit for what he was about to commit to paper in the hours just ahead. He wondered idly how deBroglie had felt at such a moment, or Thomson. What was Newton’s mood just before sitting down to write the Principia? Surely they must have felt something. Loren felt nothing at all.
Back into the kitchen with a sigh. Again he seemed like a spectator, watching his hands at work. The hands cut open one of the brown grocery bags and smoothed it out on the table. The right hand began to write equations with a black pen. His intellect might not have been involved at all, or not very. The process was mechanical, just like slicing potatoes.
By mid-morning, six equations were staring up at him, the six equations that would redefine the science of quantum physics.
Homer, Sonia and Edward would be in by 6:30 or 7 that night. What would be expected of Loren then was a presentation. It would convey no new information at all to Homer, but Loren suspected that the effect on Sonia and Ed would be staggering. So it might as well be done competently. He went back to Clark Hall to work up some visuals to be projected on the plasma board during the presentation. As he arrived, Curly Burlingame was just on his way out to lunch.
“Oh, Loren. You’re here. Well, I’ve got a question.”
“Sure.”
“You think I’m just an administrator. But I’ve got some knowledge of physics too, you know. I mean, I can read. I read this, for example.” He thrust a newspaper clipping at Loren. It was from the Syracuse Herald American of the day before. Circled twice and underlined was th
e following item:
“Scientists can now measure very precisely that 99.97 percent of the mass of an atom is in its nucleus. They can also observe that 99.87 percent of the mass of the solar system lies in the sun.”
“What do you think of that?” Burlingame seemed excited.
“Interesting.”
“Oh very interesting. But do you think it’s just a coincidence?”
“Um. I do, sort of. I mean, what else would it be?”
“Order. There is phenomenal order in the universe.”
“There is. That’s true.”
“But not just order like you and I might be able to arrange on our desks, for example. I mean a really otherworldly order.”
“Uh huh. Why do you suppose there is a tenth of a percent difference?”
“I don’t know. That’s what I wanted to ask you.”
“Oh.” Loren stared back at him, unsure of what to say next.
“There is a significance to that difference,” Burlingame went on. “I just know there is. There is a significance to a lot of things if you can only dope it out. It’s so close to perfect, but not quite. There is a message in that fact. It’s like skywriting from the Creator.” He held up his hand as though pointing to writing in the sky. “Skywriting that says, THIS IS THE TRUTH… OR MAYBE NOT. See, it’s a puzzle, kind of a challenge. I don’t know. I was hoping you would have an explanation.” He looked hopefully at Loren.
There must be some best response, something to make the man happy. Keeping Burlingame happy was important to the project. Loren tried to think of how Senator Hopkins would handle the question, how he would like Loren to handle it. He drew a blank.
“My explanation would be coincidence, I guess. Or in this case, near coincidence.”
It wasn’t the answer Burlingame had been looking for. He looked irked. “Coincidence. Tell me, Doctor Martine, how many degrees are there between freezing and boiling?”
“One hundred.”
“I mean in America, damn it.”
“In Fahrenheit, one hundred and eighty degrees: two hundred twelve minus thirty two.”
“Right. And how many degrees are there between North and South?”
“One hundred and eighty degrees.”
“And I suppose you think that is coincidence too.” He turned on his heel and stormed out the door.
It took longer to work up the presentation than it had taken to discover the nature of the false constant lurking inside time. Loren keyed in a dozen visuals. After a little thought, he constructed a simple diagram to illustrate the concept. Finally he ran the easiest of the confirming experiments he had devised. It was measurement of the phase shift of a beam of white light as it approached the maser beam. He used the office digital camera to take pictures of the test apparatus and of the recorded results, and passed the digital images through for display on the plasma board by SHIELA during the presentation. When the others arrived, he was ready. Twenty minutes later they all knew as much as he did.
There was a long silence when he stopped talking. They were all reacting, but the words took a while to come.
Sonia’s reaction was almost purely emotional. “It’s beautiful, Loren. It’s the most beautiful thing I’ve ever seen.” She jumped up and hugged him. Then, very solemnly, she kissed him in front of the others. It was the first time she had ever kissed him with anyone else present.
He also got a kiss from Kelly. It seemed unlikely that she had really understood what he’d said, but she knew it was important. And she was as excited as any of them. “Loren,” she said. “We’re very proud of you.”
“It was brilliant,” said Sonia. “You are brilliant.”
“It was all Homer.” Loren wasn’t feeling bitter any more, only a little sad not to have had more to do with it.
“Homer had the hunch,” Sonia countered. “We all knew he was on to something about the nature of time. But you were the one who figured out what it meant.”
“No. Homer had done that too. He just gave it to me as an exercise to duplicate his answer.”
They all looked at Homer, who was grinning. He looked like a kid who has just invented a whole new kind of mischief. “Nope. I never did. I tried to, but I couldn’t.”
“But you said you did. On Sunday.”
“This was a very small white lie. We have this special kind of lie in America, Loren, the white lie.”
“You lied!”
Homer didn’t look repentant at all. “Only a white lie. I had a hunch, like Sonia said. I thought that there might be something in the idea. But when it came time to work out what it was, I couldn’t get to first base…I mean, I couldn’t get anywhere. I could never have written down your first equation. That required a leap of understanding. The rest I could have done if I could ever have gotten the first one, but I couldn’t. What a dummy I was! Now that you showed me, I feel dumb. But I was smart in one way. I figured out that if I told you I had already been through to the end, then you might be able to make the leap. I couldn’t make it because I just didn’t believe. But you believed. Because you were hoodwinked.”
“What the hell is hoodwinked?”
“Bamboozled, flummoxed, faked out. I’m using the technical terms.”
“You old phoney.”
“An old phoney. Very old and very phoney. But not dead yet. Still kicking! Too old for heavy thinking, but not too old for hoodwinkery. And look at the nice result! Nice like Relativity was nice, like Quantum Mechanics was nice. This is…” he reached out to the board toward the first of the six equations. “This is terribly, terribly…nice.”
Edward still hadn’t said a word. He looked shaken. “Jesus, Loren, it’s scary. I feel like I’m at the edge of an abyss, looking over. I feel undressed. If I knew a thousand truths half an hour ago, I’m not sure of any of them now. Time was a known quantity. It was something you used to construct an understanding of everything else. When I was seven years old I learned that Rate times Time equals Distance. And now I’m thirty-one and all of a sudden, even that might not be so. What the hell does it mean that there are two variables, not just one? What does it mean that what we have referred to as time is really the cross product of t and what you call t-prime?”
“Well it doesn’t mean anything for the most part, as long as t-prime never changes. And it almost never does. Rate multiplied by Time is still equal to Distance. It almost always is.”
“‘Almost always,’” Ed repeated. “The difference between ‘always’ and ‘almost always’ is an abyss.”
Then he was on his feet, shaking Loren’s hand. “But it is beautiful, Loren, just as Sonia said. I never expected to be present at such a moment.” He threw an arm over Loren’s shoulder.
For a moment the excitement seemed to be dying down. It looked like they might even be about to get back to work, to examine some of the consequences of what they had just seen. Then it hit Homer all over again. He leaned way back in his chair and let out a loud “Hoooooo heeeee!” The chair went right over backward. Homer hopped up and began dancing like an Apache. It was hard not to join in. They were all dancing and pounding each other on the back. Homer stopped it as suddenly as he had begun it.
“Hey you people! What is this? Is this party time on the government payroll? The government is paying you all big bucks to do work and you are dancing around like crazy people. Really! Hugging and kissing on government time! I need to Curly Burlingame this project. Set you back on the straight and narrow. Now, no more of that!” He pointed an accusing finger at Sonia and Loren. “No more of that stuff. Everybody sit down. Down.”
They sat down grinning. Homer made himself be serious. There was a lot of work to do. They might be busy celebrating while Berkeley or Princeton was taking the next step. Who knows how far they had come. They might be ahead. They might be the first to publish. Future physics students might refer to t-prime as the Princeton factor or even the Armitage number. It was too awful to contemplate. Get these people back to work before their great
discovery was stolen from them by the competition.
“T-prime. What the hell is it? We know something. But it’s what we don’t know that I want to know. Why does t-prime change inside the beam? Why inside the maser beam, but not inside a laser beam? How can time be distorted in one place and flowing along perfectly happy two inches away? Why is the change in t-prime abrupt not gradual as you move outside the beam? Why does it change an inch outside the beam and not on its edge? Why does the flame burn a lot lower inside the beam when Andronescu pointed out that there was only a 0.04 percent difference in gas volume? The effect on the flame is much greater than that, enough to be visible. What can we do with the effect? What use is it? What would happen if you put a person in there? Could he live? How would it be different? That’s maybe eleven questions. I expect two and three quarters answers from each of you pronto. Who wants what?
Edward held his hand up. “I think I know why the flame burns the way it does. Let me work on that. I’ll have something to show you in an hour, if I’m right.”
“Ed’s got the flame. Sonia?”
“I want to think about what it means, Homer. We know there are two possible values for t-prime, the one that has always obtained and the one inside the beam. But there are three solutions to the last equation, not just two. So there is an additional stable state for t-prime above the norm. I want to think about what that second one might mean.”
“Dr. Duryea assigned to the second stable state. Loren?”
“I want to work on what induces the change.”
“Loren on inducement. Kelly, you and I are going to set up the other five confirmation experiments that Loren suggested and record the results. Everybody writes something in the daybook today. No coitus interruptus. Off you go.”
