The lesson didn’t get any easier.
“After five years of intensive study, we do now have a handle on how a warp bubble might be created,” Liu Zheng was saying. He filled up his board with new kinds of diagrams, showing sheets and cylinders. “The expansion or contraction of spacetime locally reflects a change in Einstein’s cosmological constant omega, which, as you know, describes vacuum energy, which is like an antigravity field that permeates spacetime-the engine of universal expansion.
“Now, we believe that our universe has a small extension in higher dimensions-higher, that is, than the three of space and one of time we experience. But those extra dimensions are small. Our universe is like a hosepipe, rolled up around the extra dimensions. The cosmological constant is inversely proportional to the fourth power of the characteristic radius of that hosepipe. Inversely. So the smaller that hosepipe radius, the higher the constant and the greater the expansive effect. Therefore, if you can change that radius locally, you can adjust the cosmological constant, and thus control the expansion of spacetime as you desire. To make a spacetime bubble you pinch the hosepipe.
“But how to pinch that hosepipe? On face value that would seem to require reaching out of the local three- dimensional plane of the universe itself…”
Now he spun off again, into “string theory,” which described space as filled not with point particles like electrons and quarks and neutrinos, but with strings, tiny filaments whose characteristic vibrations determined the properties of the “particles” they defined, such as charge and mass. Holle had heard of these ideas. It was as if the whole universe was a symphony played on tiny violins.
But, Liu said, the strings could interact with those rolled-up extra dimensions of spacetime. In particular the strings could wrap around the extra dimensions, like spiderweb wisps around the hosepipe. That was how the dimensions stayed compact in the first place. And that meant-
“You can squeeze the hosepipe,” Holle burst out, her imagination racing away.
Liu turned to her. “And how would you do that, Ms. Groundwater?”
“With a particle acce-” She stumbled over the word.
“Accelerator?”
“Yes. With an accelerator you’re manipulating matter at its smallest levels. You can yank on the tiny strings.”
Everybody was staring at her. Don and Kelly looked around, Don with amusement, Kelly with something more like resentment.
“I’m sorry,” she said. “I was thinking out loud.”
“Don’t be sorry,” Liu said. “You got it about right; that is what we’re planning. We’re setting up a hadron collider outside the city, based on scavenged components from accelerators in the US and overseas. Though we’re still years away from even a ground test the energies required are ferocious…” He gestured at the board. “And can you see how that basic concept is expressed in my equations?”
“No,” she said frankly.
Kelly laughed. “That figures.”
But Liu was unperturbed. “That’s not important. Intuition is the thing. But though we have a conceptual design for the creation of the warp bubble, we have a fundamental problem. The energy requirement is literally astronomical. A warp bubble is an artifact of curved space-time analogous in some ways to a black hole. Now, suppose we built a bubble a hundred meters in radius. That should be big enough to house a respectably sized spacecraft, shouldn’t it? Give me an order of magnitude estimate of the mass-energy required.”
The students huddled over their computers. Kelly muttered, “The radius of a black hole is twice the mass times the gravitational constant divided by speed of light squared…”
“Ten to power twenty-nine kilograms,” Venus Jenning called out. She was a black girl whose family had come from Utah, fleeing the gathering Mormon uprising. As far as Holle could tell she’d figured that number out in her head. Even while she worked, she was reading a yellowing paperback book under her desk, a gaudy science fiction title.
“Give me that in English,” Liu snapped back. “What does that number mean?”
Kelly said, “One-tenth the mass of the sun. You’d have to convert one-tenth of all the sun’s mass to energy to be able to build a warp bubble of that size.”
“Not exactly practical,” Liu said. “And that remains our fundamental problem, after years of studying this concept. We just don’t have the energy resources to build a warp bubble of the size we need.” He drew a big red cross through the equations and diagrams on the board.
Again Holle found herself thinking out loud. “If the answer’s not the one you want, maybe you’re asking the wrong question.”
Liu turned to her again.
“I’m sorry,” she said. “It’s something my dad always says.”
“Then what is the right question?”
Zane said quietly, “Maybe, how big a warp bubble can we create?”
Liu thought that over. “OK. Let’s run with that. What’s the most energetic event humans can control?”
“Nuclear bombs,” Thomas Windrup called. “Thermonuclear actually.”
“Right,” Liu said. “And the biggest blast of all was?”
That sent them scrambling to their computers, and whispering into search engines.
It was Susan Frasier who came up with the answer. “30th October 1961. A Russian test. Fifty-seven megatons, detonated at Novaya Zemlya.” She smiled, always friendly, always eager to please.
“All right. And if that mass-energy was applied to creating a black hole?”
It took them a minute to find out how to convert energy measured in an equivalent tonnage of TNT into joules. This time Kelly made sure she was the first to come up with the final answer. “Its radius would be ten to minus twenty-seven meters.”
Liu said, “Give me that-”
“In English,” Don said. “Well, it’s eight orders of magnitude above the Planck length, the smallest possible. But it’s only one-thousandth of the radius of a one-mega-electron-volt neutrino! You couldn’t even fit a neutrino in there, let alone a spaceship!”
There was a ripple of laughter, and Zane blushed.
But Liu just stood in silence, his eyes working as if chasing an elusive thought. “Class dismissed.” Abruptly he walked out.
Grumbling, the students started packing away their stuff. Don said to Holle, “Now see what you’ve done. Liu’s like that when he gets an idea. You better hope it’s a good one or he’ll rip your head off for wasting his time. Come on. I’ll show you where to buy a soda.”
13
Holle was relieved to get home that night, to the apartment her father had rented in the same block as the Tattered Cover Book Store, a secondhand store that was still one of Denver’s most thriving businesses as nobody was printing new books any more. She dumped her bag in the hall, fetched a glass of water and made her way to the big living room, where the wall-mounted TV was showing updates on the Rocky Mountain News channel.
Patrick didn’t hear her come in. He was sitting on the floor, his back against the sofa, one arm over a cushion and the other hand cradling a glass of corn liquor. He had his shirt open at the neck, his shoes off, his black-socked feet crossed.
The news was uniformly awful, Holle saw as she glanced at the big multiscreen. In Denver the police were shaping up for another night of trouble from the itinerant agricultural workers in the City Park. Elsewhere diplomatic notes were being exchanged with Utah; Mormon leaders in Salt Lake City were now refusing to pay federal taxes. President Vasquez was going to make a statement about that. Seawater forcing its way up the Tennessee valley from Alabama was causing yet another evacuation crisis, producing yet more images of sodden, huddled people tramping along rain-spattered highways. The government was considering sending troops into the Friedmanburgs, the troubled new cities on the Great Plains, where residents were protesting against exploitation
