Chapter 2

“And so,” the lecturer concluded, “we have this emergent set of terms.”

In the silence that followed this, Carl heard a quiet gasp to his right. He looked, and saw Tom was staring with his eyes and mouth open. Frowning, Carl looked at the current display—trying to see what it was that his friend had discerned.

“Okay,” the lecturer commented, his voice amused. “I see that one of you has it now.” He paused for a full minute. “Let me do the final three steps over again, to make it a little clearer.” He did this, and even turned several of the terms in two equations bright green to draw the class’s attention to them.

It clicked, and Carl too gasped.

The revelation in his mind felt like a galvanic shock. He turned and exchanged a grin with Tom, while it felt like bubbles were filling his veins. This was it, everything, all laid out! The underlying force equations associated with the construction of artificial space-time bubbles.

Looking around, however, Carl decided that no one else in the class had yet gotten it, though, judging by some of the expressions, several were close.

The newly-derived formula at the bottom of the screen was now outlined in red and the instructor looked up at the class. “As you can see,” he said, “the third term of this solution can have a positive or a negative value.” An arrow pointed to the term he was referring to. “Which means that the stable eigenstate of the negative solution is imaginary—it involves the square root of minus one.” The instructor paused meaningfully. “And thatmeans that stable, localized space-time realities canbe generated.” He pointed to the second-last term, “They are spherical in shape.” He pointed to the final term, “And they are actually manifestations of what was initially termed anti-space.”

The instructor looked up at the class again, smiling, his face full of quiet exultation. Carl looked around at his classmates. Another two had gotten it, but most were still puzzled, though some looked like they had an inkling of the importance of this. Tom, meanwhile, had much the same expression as the lecturer.

Carl looked back at the screen, and felt another thrill of excitement. So, thiswas it. The mathematical basis of the spherical anti-space bubbles—more generally known as the fabled pirate crèches.

One of the cadets put up his hand. Carl looked over and saw that it was Ben, possibly the slowest person in math in the class—though everyone who entered the cadet training had to be gifted in both intelligence and math ability specifically. Ben was a known hard worker, andhe had the nerve to ask questions that most wouldn’t say out loud, being afraid of looking stupid. The instructor nodded at him.

The cadet rose to his feet. “But Sir,” he said, “doesn’t the exponent of the first term of the left-hand side of the equation mean that the energy required to sustain such a bubble is prohibitively large?”

Carl looked back at the display. It was a good question. During the first topic of study this year, when they had been presented with the cubic energy requirement of the Time Field and told that this limited a purely terrestrial time portal to roughly five hundred years, Ben had asked whether developments in energy production might extend this range. Carl could still remember the hostile expression that question had produced on Tom’s face. Tom had always seemed to harbor a dislike of Ben, something that Carl had never understood. At the time, the lecturer had replied that the cohesiveness of matter itself limited how much energy could be used, irrespective of what kind of generators we might develop. So, it had been a good question too. Carl had asked Tom about this limit at the time, and Tom had said laconically that it involved the short-range Strong force. It had seemed to make sense: involving the nuclear forces complicated things unimaginably, but Carl was puzzled by Tom’s reserve on the topic.

Anyway, now the instructor smiled at Ben’s question. “Does anyone have an answer for Mr. Dohaney?”

No one responded immediately. It was considered bad form to appear eager to show up other cadets. After a sufficient pause, however, and to no one’s surprise, Tom raised his hand.

“Mr. Remy.”

Tom stood up. “If you please, Sir,” he said. “The sign in the square of the penultimate equation means that the energy required would be negative.”

“Yes, it does,” agreed the lecturer. “But how is that important?”

“If you please, Sir, the energy generating the anti-space sphere would feed back onto itself. Its action would produceenergy. The field would be self-sustaining, and would even require a means for dissipating energy.”

The idea of a self-sustaining field made Carl’s head spin slightly, but looking at the display he saw that that was in fact what the math said—and, as Tom reminded him from time to time, math is always right.