EQUIVALENCE PRINCIPLE
Robert Scherrer
If economics is the dismal science,
then surely metrology is the boring science, thought Edward Melton as he
crumpled his empty Cheetos bag and tossed it into the trashcan in the corner
of Professor Witherspoon’s laboratory. And
was a Ph.D. project really supposed to take ten years? A decade of tinkering with Witherspoon’s
atomic clock, working on a dissertation which always seemed just another year
away.
A knock at the door jolted Melton upright. Dewey Witherspoon stepped into the lab,
sporting plaid shorts and a red baseball cap, perched rakishly atop a shock of
blond hair. His blue eyes twinkled as he
swished the air with his tennis racket.
“Melton,” he said, “I’m off to the Faculty Club for a tennis date. Have you fixed the problem with the clock
yet?”
“I’m still working on it. I’ve been
doing some calculations -- maybe the clock isn’t broken --”
“Not broken? Gold atoms don’t just suddenly disappear, and
atomic clocks don’t run fast unless they’re malfunctioning. There’s clearly a problem, so please fix
it. I’ll be back later today.” Witherspoon stepped into the hall, then stuck
his head back through the doorway.
“Melton, you look like hell. You
need to get out more, like I do. Get
some exercise.” Witherspoon’s head
disappeared, and Melton could hear him humming “Happy Days are Here Again” as
he strolled down the hall.
Melton opened his notebook to recheck
his calculations. A steady diet of
partially hydrogenated soybean oil, washed down with vending-machine hot
chocolate, had transformed his body into something resembling a sphere, so he
had to sit back from the desk and lean forward to read his notes. He glanced sideways at the massive metal
cylinder in the center of the lab. The
microwave cavity of the atomic clock rested above a spaghetti bowl of cables
and circuit boards -- his constant companion for the past decade. Hell, he’d spent more time with the atomic
clock than he had with Professor Witherspoon.
“Well, Ingrid,” he said to the clock, leaning over to pat the side of
the cylinder, “let’s see if we can figure out what’s wrong with you.”
Witherspoon’s project had seemed
simple at the beginning. Most atomic clocks used the hyperfine transition in
cesium, but any element with only a single electron in the outer shell would do
just as well -- people built clocks that used hydrogen or rubidium. Witherspoon had come up with the bright idea
-- as far as Melton could tell, the only original idea he’d ever had -- of
using other elements, stripping off the electrons until only a single electron
remained in the outer shell, and then pumping the ionized atoms into the
microwave cavity of the clock.
The first few elements had worked
fine, but every time Melton wanted to write up his dissertation, Witherspoon
had insisted on trying “just one more element.”
Eventually, it seemed like he wanted to run through the entire damn
periodic table. Every month brought a
new element, a new set of data, a new roadblock between Melton and his Ph.D.
The only consolation was that they
would eventually run out of elements -- Melton had already purchased a lab
notebook and inscribed the cover with “Uranium.” He kept it in the linen closet of his
apartment, next to an unopened bottle of champagne.
But when they got to atomic number
79, gold, the experiment went haywire. The
clock ran twice as fast as it should have, and the gold atoms seemed to
disappear from the microwave cavity. But
what was special about gold? It was the
most ductile element, and an excellent conductor, but none of that seemed
relevant. Melton laced his fingers
behind his head and leaned back to think.
The boring science, the dismal science, the boring, dismal science. Suddenly his eyes widened, and he began
scribbling furiously in his notebook.
Melton
scurried down the hall and burst into Witherspoon’s office. “I’ve got it, Professor Witherspoon! I’ve solved the problem. We’ll be famous!”
Witherspoon
glanced up from his copy of Golf Digest. “What is it,
Melton? I’m quite busy.”
Melton sketched a wavy line on
Witherspoon’s blackboard, filling the air with a haze of chalk dust. “Physics over the last century,” he said,
“has been all about developing equivalencies between apparently disparate
physical quantities.” Melton coughed to
clear the chalk dust from his throat. “Quantum
mechanics gave us an equivalence between particles and waves. We know now that they’re simply two different
aspects of the same thing.”
Witherspoon’s
gaze wandered toward the door. Melton hurriedly
erased the board with his shirt-sleeve and scrawled a ragged line of equations. “And of course, Einstein was responsible for
two of the most important of these relations:
space and time are related through the speed of light, while energy and
mass are related by E = mc2. In
string theory, the Maldacena conjecture suggests an equivalence between space
and matter --”
“Get to the
point, man,” said Witherspoon. “I don’t
have all day. I’m meeting a colleague
for drinks in half an hour.”
“I think
what we’re seeing here is another fundamental equivalence, at least as
important as any of these.” Melton
stared briefly at his feet. “The gold
atoms are disappearing, and the clock is running fast. I think the gold atoms are being transformed
into time.”
“What?” Witherspoon rubbed his forehead for a
moment. He opened his mouth, then closed
it, then opened it again. “You can’t mean --”
“Exactly.” Melton grinned and tossed the chalk into the
air. “Energy is mass. Space is time. And time is money.”
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