Eifelheim (23 page)

“I assumed it was measurement imprecision.”

“So did I, at first. Look at the spread in the Michelson-Morley data! But precision is random, not a secular trend. The use of different methods …”

Tom nodded vigorously.
“A measurement is defined by the operations performed to produce it
. So different methods give different numbers. It’s even worse in cliology—”

“Right.” She stopped him before he could hijack the celebration. “Partly, the trend was due to physicists discovering more accurate methods. Galileo used shuttered lanterns in two towers a mile apart, and concluded that light speed was infinite. But clocks weren’t precise enough back then and his baseline was
way
too short. Using stellar aberration, the mean value was 299,882 kilometers per second. But the mean value using rotating mirrors—”

“Michaelson and Morley!”

“Among others. Light speed using rotating mirrors was 299,874; using geodimeters, 299,793; using lasers, 299,792 kiss. But method changes took place sequentially; so how much was due to the method, and how much to the thing being measured?”

Tom said, “Ummm …” which was all he really could hope to say at that point.

“From 1923 to 1928, the five published determinations alternated between the stellar aberration method and polygonal
mirrors, with averages of 299,840 and 299,800, respectively.”

Tom was deep into MEGO by then. My Eyes Glaze Over. Normally, he was fascinated by matters statistic, but look up “fascination” someday. His “ummm” had turned into “unh-huh.”

“But there are little hints,” Sharon bubbled on. “Van Flandern—Naval Observatory—saw a deviation between the moon’s orbital period and atomic clocks, and claimed atomic phenomena were slowing down. But he was called a crank, and no one took him seriously. Maybe the moon was speeding up. Even allowing for all that, there seems to be a monotonically decreasing series whose asymptote is the Einsteinian constant.” She beamed in triumph, even thought she had discovered only a curiosity and not an explanation.

Tom had finished imitating a fish. “Umm. Correct me if I’m wrong, but aren’t there good reasons why light speed is
supposed
to be constant? That Einstein guy? I mean, I don’t know much about it, but I grew up believing in motherhood, apple pie, and the constancy of c.”

“Question of scale,” Sharon explained, waving an impaled cucumber at him. “Duhem wrote that a law satisfactory to one generation of physicists may become unsatisfactory to the next, as precision improves. The slope falls within the band of measurement error, so c
is
constant ‘for all practical purposes.’ Hell, for most
practical
purposes, we can still use Newton … But if we go back to the Big Clap and arm wrestle with flatness, or the horizon problem … You know,” she said, making a sudden conversational right turn, “Dirac almost found the same thing, but from a different direction.”

“Wouldn’t that be a different Diraction?”

Sharon really was a somber sort of creature and Tom’s bent to spontaneous low humor could rub her the way cat fur rubbed amber. “Be serious, would you,” she said. “Dirac found that the ratio of the electric force to the gravitational
force of an electron-proton pair is roughly equal to the ratio of the age of the universe to the time it takes light to traverse an atom.”

Tom laughed. “I’ll take your word on that one.” He filled both their wineglasses again. “Okay, but the age of the universe isn’t a constant. It’s increasing….”

“At the rate of one second per second. Who says time travel’s impossible? It’s the speed and direction that’s a problem.” Sharon did have a sense of humor. It was more deadpan than Tom’s. The Marx Brothers were more deadpan than Tom. The wine was warming her quite nicely. If Tom was a bumbler, still he meant well, and there were too many who did not to remain angry at one who did. “Have some more fish,” she said. “It’s brain food.”

“Two helpings, then …”

They had not laughed together in several weeks, and the release was palpable. Problems could be obsessive, but worse, they could be solitary. It was good to connect again.

“So, there’s only one point in time when Dirac’s ratios could be equal,” he prompted.

She nodded. “Coincidence is the usual explanation. The Anthropic Principle says that the age of the universe is what it is because that’s how long it takes the universe to assemble physicists capable of estimating it. But think … If space and time can contort for the sole purpose of maintaining a constant ratio—velocity of light—why can’t the rest of the universe be as cooperative?”

“Uh …?” he prompted. Not the most incisive question, but questions weren’t in it. Sharon was on a roll. Nothing like wine for lubricating the words so they tumble out faster.

“Dirac set his two ratios equal and solved for G, the gravitational constant; but his theory of slowly evaporating gravity was eventually ruled out by experiment.”

“So … you solved his equation for c,” Tom guessed.

She nodded. “And c is a function of the inverse cube root of time, which …”

“Which gives a decreasing speed of light,” he finished.
“But the asymptote is zero, not Einstein’s constant,
n’estce pas?”

Sharon wiggled her hand. “Haven’t worked it all out yet, but the
coefficient
involves the rest masses of the electron and proton.”

“Which means?”

“The coefficient isn’t constant, either. Lorentz-Fitzgerald contraction. If c is decreasing, what happens to mass?”

“Beats me.”

“Come on, this is grade school stuff. As velocity increases toward c, mass increases. Everyone knows that. So, switch frames. What’s the difference if c decreases toward velocity?”

“Hunh, none, I suppose.”

“Right, so the universe is becoming more massive.”

Tom patted his stomach. “I thought it was your cooking.”

Sharon gave him The Look, but he grinned until finally she had to grin, too. “Okay, I’ll connect your dots.” She pushed her dinner plate to one side and leaned forward with her arms on the table. “Velocity is distance over time, right? High school physics.”

“They taught it just after the Lorentz-Fitzgerald stuff.”

“Don’t be cute.”

“Can’t help it.”

“Well, the universe is expanding.”

He almost patted his stomach again, but caught himself in time. “Big Bang. The universe started as a little ball and exploded, right? And it’s been expanding ever since.”

“No! That’s wrong! That’s newspaper science. The urblock ‘exploded!’ The ur-block ‘exploded!’ What did it explode
into
, for crying out loud? You’re thinking of stars and galaxies being flung out into space; but the ur-block
was
space. Galaxies are racing away
from each other
, not from a common center. They aren’t flying farther out
into
space; space is expanding
between
them. The cosmological fluid. Get it?” A part of her—that part able to stand outside herself—could see that she had maybe drunk too
much of the wine. She was babbling, and she wished she could stop, but she was goddam, freaking
happy
, and didn’t want to.

Tom shook his head. “Cosmological fluid …” He had a sudden, Aristotelian vision of the universe as a plenum, rather than empty space.

Sharon pressed him, eager that he should understand, for she wanted to share her joy. “Look, imagine galaxies as dots painted on the outside of a balloon—”

He slapped the table in triumph. “I knew we’d get to the balloon eventually!”

“Picture yourself as a little flat bug somewhere on the balloon.
That
should be easy. Now inflate the balloon. What happens to all the dots?”

Tom looked up at the lamp that hung over the dining table and tugged at his lip. “Can I see around the curve of the balloon?”

She nodded. “Yes. But it’s curved Flatland, and you can’t see up, or down into the balloon.”

Tom closed his eyes. “All the dots are racing away from me,” he decided.

“And the dots that are farthest away?”

He opened his eyes and looked at her with a grin. “They’re receding the fastest. Son of a bitch! So that’s why—”

“—Astronomers use red shift velocity to estimate distance. Now plunk yourself down somewhere else on the balloon. What do you see now?”

He shrugged.
“Simil atque
, obviously.”

She picked up the little peppermill from the table and set it between them. She pointed to it. “So how can the same galaxy be receding from point A …” She touched herself. “—
and
from point B?” She pointed to him.

Tom squinted at the surrogate galaxy. “We’re living on the surface of a balloon,
hein?
Space is expanding between us, so each of us sees the other as drifting farther away.” He was more right than he knew.

“The three-dimensional surface of a very weird balloon. I call it the ‘perceived universe’.”

“And your ‘polyverse’ includes the inside of the balloon.”

“Right. Quantum dimensions, they’re called. They’re literally
inside
the perceived universe. I’ve been studying their orthogonality under Janatpour’s hypothesis.”

“And the speed of light?”

“Right.” She set the saltcellar next to the peppermill. “Mark off a kilometer on the surface of the balloon. Light will take, oh, maybe a third of a microsecond to cross it. The kilometer fixed to the balloon’s surface and a kilometer stick
inside
the balloon are the same. Blow up the balloon and what happens?”

“Umh. The distance
on
the balloon gets longer but the distance inside doesn’t.”

“And if light speed is constant
in the polyverse
, how far does the light get in a third of a microsecond?”

“As far as the original kilometer … Which falls short of your kilometer mark.”

“Right. So a beam of light takes longer to cover the ‘same’ distance than it did before.”

Tom pulled on his lower lip and studied the lamp again. “Cute,” he said.

She leaned farther across the table. “It gets cuter.”

“How?”

“I can only account for half the estimated decrease in light speed.”

He looked at her and blinked. “Where’d the other half go?”

She grinned. “Distance over
time
, lover. What if seconds were getting shorter? A ‘constant’ beam of light would cover fewer kilometers in the ‘same’ number of seconds. All that stuff about ‘rods’ and ‘clocks’ … They’re not privileged, not outside the universe. When I couple the expansion of space with the contraction of time and extrapolate backward to the Big Bang—I mean, the Big
Clap—I get infinaly … I mean, infinitely long second—and in-fi-nite-ly fast light speed—at the decoupling; and tha’s … Well, it’s innersting, because of Milne’s kinematic theory of relativity. E-spare-men’ly … Ex-peri-men-t’ly, you can’t tell Milne from Einshtein. ‘Til now. Here’s t’me.” This time, she did toast herself, draining the last of her wine. When she upended the bottle over her glass to refill it, she found that it was empty.

Tom shook his head. “I always thought the years went faster as I got older.”

S
HARON WOKE
up with a headache and a warm, fuzzy feeling. She wanted to lie in bed. She liked the feel of Tom’s arm across her. It made her feel safe. But the headache won. She slipped out from under him—not that anything short of Krakatoa would wake him—and tiptoed to the bathroom, where she shook two aspirin into her palm.

“Newton,” she said to the tablets. She rattled them like dice, as she studied her reflection. “What are you smiling about?” She was a woman who put great store in her dignity, and she had behaved the night before in a decidedly undignified manner. “You know what you’re like when you drink too much,” she scolded her image.

Of course, you knew
, her image smirked.
That’s why you did it
.

“Nonsense. You’ve got the causal arrows backward. I wanted to celebrate my discovery. What happened afterward was spin-off.”

Yeah, right
. She swallowed the aspirin, washed them down. Then, because she was already up, she went to the living room and began gathering her clothes. The dishes in the dining alcove reproached her for the food hardened upon them. Now she remembered why she didn’t cook more often. She hated disorder. She’d spend all day cleaning now, instead of doing physics.

“Newton …” Now why on Earth was Sir Isaac on her mind? He was passé, the old clockwork physics. Einstein had made him a special case, just as she would make Einstein
a special case. But Newton had said that a change in velocity requires a force to explain it.

So, if time were accelerating …

She straightened abruptly, scattering all her clothes. “Why, what a very peculiar place this universe is!”

IX
OCTOBER
, 1348
The Freiburg Markets