Renegades from the Time War

Chapter 1: Temporal Equations

Chapter 1: Temporal Equations

The cadets were smartly dressed in their black uniforms, fresh-faced and eager for the class to begin. This was their first day back after the summer break, the start of second year. First year at the Academy had been background and introductory. Now they were ready for the real thing.

Seated behind the long, curving desks that rose in three tiers in the lecture hall, there were only fourteen cadets in all. This made the hall look rather empty.

When a door at the front of the hall opened and a man entered, the cadets rose to their feet and stood at attention. The man was tall and slim, and wore a dark gray uniform that had the same simple cut as those of the cadets. He climbed the podium, walked to the lectern and ran his eyes over the cadets.

“Please be seated,” he said.

The class sat, while the lecturer activated the display screen on the lectern. He touched the display, and a large screen above and behind him displayed the words, Temporal Mechanics: Time Fields, at which a frisson of excitement went through the cadets.

Carl Obermeier, a sandy-haired cadet seated in the second tier, looked at the larger, dark-haired cadet seated next to him. This cadet, one Tom Remy, grinned back at him, eyebrows raised.

The screen at the front of the room changed, displaying the six fundamental equations of space-time dynamics, a synthesis of the Einstein theory of general relativity and the Maxwell equations of electromagnetism. Carl was familiar with these equations, which described how the two long-range forces of the universe interacted in the four dimensions of space and time. They did not include the two short-range forces that were important in atomic-level mechanics—the Strong and Weak forces—since those forces diminished at the distances of the macro world realm, and could therefore be eliminated in the equations by means of a mathematical procedure termed renormalization.

That, of course, was an approximation, and it struck Carl again that even with this simplification, how complex the equations listed on the screen were. Nevertheless, these equations were where the very nature of space and time was structured, and how each dimension could be manipulated—all presented of course in the language of physics: mathematics.

All of the cadets were familiar, if not comfortable with these equations by now; they had studied a number of terms in each equation during their first year at the Academy. Each term had required many hours of study in addition to the lectures. Now, seeing the full equations again, Carl was reminded how little they had actually explored of the seventy-two terms that comprised the equations, each term representing a significant aspect of the nature of space-time and the long-range forces that interacted with it.

The lecturer had been silent while Carl, and all the other cadets, re-familiarized themselves with this daunting mathematical behemoth. He was watching them, and smiling grimly.

He touched the lectern display again, and two additional equations appeared, surrounded by a red box, below the original six.

“And these,” he said, “are the Bose power equations, which you will at least have heard of.”

The response was an intense silence, as the cadets stared at them; they were even more complex than the others. The red box, indicating that the Bose power equations were classified, gave the equations an added aura of importance.

“As you probably know, the Bose power equations represent the operators we use to distort the fields of space-time, and therefore control the temporal dynamics by which we can engineer—that is, manipulate—the time fields. They represent the single greatest discovery of the past two hundred years—and, unfortunately, have been at the heart of the strife in society today—sometimes called the Time War.”

The lecturer paused again, allowing this information to be digested. The Academy, where recruits like these cadets were trained, had been founded by the government in order to wage the Time War.

Finally, the lecturer cleared his throat.

“We can,” he said, “extract from this set of eight equations the basis of the power coupling—in the following way.”

And now the lecturer began to direct the mathematical transformations via the lectern display, which manipulated the equations on the screen behind him. He did this with slow deliberation, commenting on how each step was accomplished, what each step represented. After several minutes the silence between his comments began to be disturbed by sounds of frustration from various members of the class, and at last the lecturer paused.

“This isn’t easy, I know. Some of you won’t be able to follow it, but some of you will. Those of you who don’t will have to study these elements on your own—because, I assure you, they are important.” He paused to scan the class, then looked back down at the display on the lectern. “I continue.”

The alterations and manipulations of the displayed equations continued for another ten minutes. Carl was one of the few who could follow them, though it took some effort. What helped was the excitement he felt as each new configuration either promised or actually showed directly some effect that he had studied.

“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 that means that stable, localized space-time realities can be 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, this was 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, and he 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 produce energy. 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.

The lecturer looked pleased. “Quite correct, Mr. Remy,” he said. “And in case anyone hasn’t put two and two together, what we have here is the configuration used by certain outlaws of the Ordered Society as a covert location for their nefarious activities. With what is in effect a built-in power source, they have a safe location in which they hide—in a most cowardly manner.” The man’s lips tightened as he spoke further, and his voice became slightly raspy with emotion. “And I think you are all familiar with what I am referring to.”

“The Time Pirates,” murmured voices around the lecture hall.

The lecturer nodded, appearing to have gotten hold of himself again.

“Now, these transformations are the fundamental basis of our modern engineering of the time gates as well. These gates are essentially transient space-time bubbles. The difference is that they do not create additional space-time, but comprise a shift in space-time coordinates, either to observe—as in the probe field—or to make physical connection with—as in the incursion field.

“The difference between the two is, as you can imagine, a question of power again. But these two are what might be called the first and second excited states—eigenstates, that is: stable energy states—of space-time.”

He paused again, then grinned. “I understand that you will be viewing your first real-time use of such gates—to observe, of course—after lunch. Now. I would like you to spend any free time studying what we covered this morning. Go over every transformation and, please, understand each one. Tomorrow we will continue on how the space and time shifts are generated. Any further questions before we adjourn?”

Ben put up his hand again and the instructor nodded at him. “Please Sir,” he began, “I don’t understand. This bubble is anti-space. Surely people can’t exist in such an environment.”

The lecturer’s thin smile returned and he shook his head slowly. “I’m sorry, Mr. Dohaney,” he said, “that you don’t appear to have fully understood the Assignment 12 problem set on The Basic Construction of Physical Space you were given in first year. Can anyone tell me how anti-space differs from regular space?”

Another cadet, Susan Connaught, raised her hand. “Please Sir,” she said, “the only practical difference is the parity effect.”

“Please demonstrate this. You have the board.”

The display at the front of the hall cleared, replaced a moment later by the contents of the student’s personal display unit work screen. Susan rapidly assembled the various terms of the existential spatial equations. Three separate elements she outlined in red.

“Please, Sir, if we change the signs associated with anti-space equations that you just showed us, the changed dynamic properties of all forces and dimensions all cancel out, except for a reversal through the origin in all dimensions.”

“And what effect does this have, practically speaking, on anything in that space-time?”

“I—I’m not certain, Sir,” Susan stammered, turning red. “But I shouldn’t think it would be significant.”

The lecturer nodded. “Yes, you are quite correct. But let us ask some of the biology experts in the room. Anyone? What is the effect of parity operation on biological systems?”

One of the Bio people raised a hand.

“Cadet Tippet.”

Doreen Tippet stood up. “Please Sir, the effect on physical processing would be undetectable, except for a slight glitch during passage into or out of such a space. This would be confined to the spatial sensory systems such as vision and balance. The person would experience a slight sense of dizziness and blurred vision.”

Again, the lecturer nodded, evidently pleased. “That is exactly correct,” he said, “although our testing with subjects have shown that this transient effect varies from person to person. In some it is actually undetectable. In others, especially if the person is taken unawares, there can be acute nausea for up to a minute or two, and in some cases even spasms of sudden regurgitation.”

There were suppressed murmurs of amusement at this description of vomiting. The lecturer nodded and came to attention, whereupon the cadets did the same, remaining motionless until the man had left the hall.

As he sat down and closed his personal display, pocketing the chip, Carl turned to Tom, who was already on his feet. “Neat stuff!”

Tom nodded, grinning. “Who said that math was dull?”

“Not me!” agreed Carl, laughing and rolling his eyes. Tom loved his math.

Tom laughed in turn. “You did too,” he said. Then they both filed along the row to the aisle, joining the other cadets to the doors at the back of the lecture hall.