The Great Escape Chapter 12, Part 8 of 10

The Great Escape
Chapter 12, Part 8 of 10

"I'll try to explain," Rosa said, having listened meekly all this time.

"No information-bearing signal can travel faster than light in special relativity."

"Yes, but the plume isn't traveling in space."

"The plume is an interface between space and hyperspace, so part of it is in normal space-time and, as such, obeys quantum theory and special relativity. Quantum theory says there's a minimum time for a signal to pass through the plume. Special relativity says that a signal that travels within the plume cannot contain information because the plume itself travels faster than light or it would be if it were traveling through normal space-time."

"I'm lost again," Roger confessed and returned to his history books. Danielle carried on:

"We've established that the plume's trajectory and energy cannot be precisely measured in real-time if the traveler is of any practical size; hence, we come to Li's method."

"I proposed a static hyperspace drive that sends out multiple plumes. If the traveler veers off-course, the next plume steers it back on track. As you can see, it's the inverse of Rosa's method."

"How does Li's hyperspace drive know that the traveler has veered off track?"

"Because it's in constant contact with the plume."

"Isn't the plume many light-years away in seconds?"

"Not in hyperspace. The plume is connected to the hyperspace drive until it collapses, and the traveler bounces back into normal space."

This was puzzling, and Herman stopped to think it over. Then:

"So why didn't Li's method work? If it can correct for anomalies, why was his traveler off-target?"

"For the same reason, Rosa's method failed. They both work perfectly for a traveler with zero mass and less well the more mass the traveler has. For a traveler with a few thousand tonnes, the calculations for Li's method are intractable and cannot keep up with the anomalies."

"So neither method will work?"

"Not as originally proposed, though Li's method may be easier to fix. We need a lot more power. Then, Li's method would be like what we already do. The permanent hyperspace pathways that take travelers from Earth to Capella Spaceport and onward to the inhabited galaxy are driven by large hyperspace drives with huge power sources."

"That's why Capella is so well-placed. Its 'star' is four stars. They are tapped for fuel by giant collecting stations, which beam the energy to a dozen or more hyperspace drives that power pathways in all directions. The other ends of the pathways also have hyperspace engines, making what we call 'tethered' pathways. The drives at each end are called 'beacons.' A pathway with powerful enough beacons can ignore almost all anomalies. It's like a compelling radio signal: it doesn't matter how much interference there is; so long as the signal is strong enough, it will get through."

Herman nodded his understanding.

"This is where we came in, isn't it?" he observed. "You showed that Rosa's method alone
wouldn't work, and then you tried to combine her method with Li's."

"Exactly. I wanted to use Rosa's method to make the corrections in trajectory and Li's method to make corrections in energy. It would simplify the calculation for her traveler and reduce the power Li needs, but it doesn't work, either. We're always stumped by the impossibility of getting Rosa's traveler to communicate with Li's beacon."

"Because of special relativity?"

"Correct. The traveler is effectively going faster-than-light relative to the beacon; so, while the traveler can talk to the plume and the plume can talk to the beacon, the traveler cannot talk to the beacon through the plume. The information always gets scrambled."

"All right. I think I'm clear now." Herman prepared himself for renewed mental effort, but Danielle said:

"Before we start, I have a question for Roger."

"Yes, Dear?"

"Why am I hungry?"

"Because it's two o'clock in the afternoon, and we haven't even had breakfast."

"How did it get to be 2 pm? Rosa and Herman only got here ten minutes ago."

"Three hours ago."

"Good Lord! Sorry, everyone. You must be starving. I'll make us some lunch. Are scrambled eggs all right?"

"Darling," Roger halted her. "Do you want Rosa and Herman to remain friends with us?"

"Of course I do!"

"Then do you think you should cook?"

"Oh, God! You're right."

Danielle was not a bad cook generally, but when her mind was distracted, she was a disaster.

"Rosa," she asked, "can you cook?"

"I'll cook," Roger said.

He retired to the kitchen to make scrambled eggs, toast, coffee, and fruit juice. He used almost every pan Danielle possessed, even though she had a robotic oven that would have done most of the work.

After the late lunch, Roger returned to his historical studies, leaving the others to ponder the problem of combining Rosa's method with Li's. He kept an ear open for signs of progress, but there were still none by four o'clock when Roger got up to perform more hosting duties by making tea. He forced them to stop work for five minutes to drink it, and then he left them alone for another marathon session.

At six o'clock, he called the restaurant to cancel the table and ask them to deliver the food instead. He ordered boeuf bourguignon for four and a bottle of wine, paying with Danielle's credit stick. He told her that she had lots of money and that it was better to spend it on good food than on clothes she would wear only once or, God forbid! Even more handbags.

She murmured something, which he took as an assent. The three of them worked in silence, at a holo-screen or tablet, or just staring into space, thinking.

Dinner arrived at 8 pm, a welcome surprise. Although they began eating mechanically, their minds winding down from intense activity, they followed Roger's advice to enjoy the food and rest their brains. Danielle and Rosa joined Roger in a glass of wine while Herman stuck to the water. Eventually, they relaxed, and their glazed expressions softened.

It was now that the large lump of information Roger had swallowed while Herman was having his lesson began to digest in his mind. Enquiries percolated up. He let the others sit in silence all through dinner, but when they finished their coffees and got up to resume working, he asked his question:

"Darling, can you explain something about what was said earlier?"

"I'll try."

"Rosa was quite specific in her language when she said, 'No information-bearing signal can travel faster than light.' Does that imply that signals that don't bear information can travel faster than light?"

"Faster than light in a vacuum, yes."

"Oh. But isn't light the fastest thing there is?"

"Yes, ignoring hypothetical particles with imaginary mass."

"I don't get it."

"You're probably confused by a popular version of special relativity, which says, 'Nothing can go faster than the speed of light in a vacuum.' Microwaves travel faster than light in a waveguide, though they're made of light. In general, photons subject to the tunnel effect go faster than the speed of light in a vacuum."

Roger was mystified.

"So if light can travel faster, why can't you send information faster than light?"

"Because the way the tunnel effect works is that photons get through only randomly, so the information a signal carries in a collection of photons is scrambled."

"Oh, all right." Roger was glad he asked but wasn't sure he followed the answer.

He left them sitting comfortably, neglecting the holocoens, reviewing their calculations, and racking their brains for new ideas. Roger also pondered what they'd told him, trying to make sense of it as well as he could. He began looking things up on the computer, such as the difference between problems men can solve, problems only computers can solve, and problems neither men nor computers can solve.

An hour later, he thought he'd understood something and asked Danielle how they were getting on.

"We've made some progress, but we're still stuck on the main problem," Danielle admitted.

"With a powerful enough beacon, we can send a moderately massive traveler, but we cannot properly control the direction. The impossibility of communicating the effect of the anomalies beats us every time."

"I've been thinking. What about triangulation?" Roger asked.

"What do you mean?"

"Remember the three ways of checking a computer's calculation that I discussed with
Herman? There were empirical tests, the iterative method, and the third method, which compared information from different sources. I looked it up. I think it's the same as something called 'triangulation.'"

"Well, Li's method is like empirical tests because the beacon gets information from the plume and sends out corrections, like doing experiments and testing them. Rosa's method is iterative, and it makes corrections to corrections to corrections. So, the third one is triangulation, getting to the same answer by using different sources."

"Oh, Roger! It's pure coincidence that you mentioned only three mathematical methods. You might also have mentioned approximate methods, like finding cube roots."

Roger appeared deflated.

"I'm Sorry, Darling," she said in mollifying tones. There's no connection between the methods.

One is mathematical."

She paused and then carried on, just from inertia.

"The other is physical," she stopped again. She stared unthinkingly at him, her mind racing.

"Good God! He's right! Triangulation! Plume, traveler, and beacon. Do you see it? Good God!

My fiancé's a genius!"

"I don't see it," Herman said. Rosa stood up, eyes shut, and thought hard.

She babbled, squeezing her fists. "We know the energy from Li's method, and the traveler knows the direction by my iterative method, so we just need to get them to communicate, which is impossible. But we don't need to get them to communicate information. We need to keep them synchronized through the plume. So long as they're synchronized, we can adjust the plume according to what it experiences in hyperspace. The plume knows where it is. We need to triangulate the three sources of information."

Danielle beamed at her, summing up:

"The plume is like an automatic pilot that knows how to fly straight in a particular direction and height and corrects any deviation out of its path, but it doesn't know its actual destination."

"But can we keep the traveler and beacon synchronized if they can't send information to each other?" Herman asked.

"We don't need to send information; any signal will do. Rosa said it, and Roger implied it: 'The plume knows where it is!' So long as the traveler's on-course, we get a signal from the plume; when it veers off-course, the signal goes out-of-synch. No information passed, but being out-of-synch is enough to tell us to correct in the opposite direction from where the signal began to tail off. The signal can be random and travel through hyperspace as fast as it likes."

"The problem is," Danielle said, "it needs a new kind of hyperspace drive. It needs an inside-out engine for the traveler and a larger power source for the beacon than any that exists, but I don't see why it can't be done."

She sat down, exhausted but jubilant. They picked up their tablets and began to work. Roger returned to his armchair but watched them - a little smugly - as they wrote equations and did calculations.

A few minutes later, Rosa stopped. She looked at Danielle and said:

"What did you mean, 'my fiancé's a genius'?"

"Of course, I didn't tell you. Roger and I are engaged!"

Rosa and Herman were full of congratulations, which reminded Danielle of something. She put down her tablet and sat in Roger's lap.

"Well done, future husband," she said. "I'm glad I'm marrying you." Then she kissed him passionately, adoringly.

Herman looked down shyly, but Rosa thought it was very romantic. Eventually, Roger pushed his fiancé away.

"I love you, future wife, but we're embarrassing our guests."

Danielle planted a last defiant kiss on his lips and stayed in his lap.

"How did you think of it, Darling?"

"Well, as you said, comparing the mathematical methods with the astrophysical was a pure accident. But I was also thinking of something I learned about Isaac Newton."

"What was that?"

"The three-body problem."

"Good Lord! How do you know about that?"

"From my homework for yesterday's trip. I didn't understand it, and I knew it was a problem a computer can't solve."

"What is the three-body problem?" Herman asked.

Danielle explained:

"Newton's laws can predict all the future positions of a system with two gravitating bodies, like the sun and the Earth, but add a third body of non, negligible mass, and the predictions lose all precision. The results become chaotic, even though Newton's equations are deterministic."

"Another way of saying this is that the solar system is its fastest computer. Well, the same is true for the plume. The plume is its own fastest computer, and just as the bodies of the solar system know where they are before any computer can accurately predict their positions, the plume knows where it is before we can calculate its properties. That's what my brilliant fiancé meant."

Roger wasn't sure he understood this explanation of his insight, but he was happy to keep quiet and reap the credit.

Soon enough, Danielle returned to work with the others, and they worked until eleven o'clock when Roger interrupted them one last time. Rosa's eyes were dazed when she looked up, and Herman yawned wildly.

"It's late," Roger said. "You've been here twelve hours. It's time you went home. Come back tomorrow evening to continue."

They nodded.

"I've called for an antiseptic people-mover to take you to your digs."

"A what?" Herman asked.


To be continued