So Ally went off to find Dag.
She found him in one of the coffee shops deeply involved with his calculations.
“Hello Dag, may I interrupt?”
“Oh hi Miss. Of course I'm finished. Just trying to find a mistake in my calculations.”
“You're trying to find a mistake, why?”
“Because if I haven't made a mistake then we, as well as everyone else, are stuck in place. You see, my calculations tell me the wormhole drive, even the modified version, is dead.”
“The changing constant? Have you told anyone else yet?”
“No I've just been going over and over my calculations.”
“Well it's not the end of the world.”
“No, not yet.”
“You mean if the constant . . .”
Dag started to interrupt. She changed her wording.
“If the former constant keeps changing then none of us are safe?”
“Yes Miss, it's only a matter of time if we can't stop the change.”
“Dag I don't understand something. If dark energy is the cause of the constant changing why are we seeing these effects locally only? I thought it would take billions of years for the effects we are seeing to make themselves known and the change would be uniform throughout space.”
“Somehow Miss dark energy is being localized. I'm convinced that was how the giant wormhole, a kind of tornado in spacetime was created. Over most of the universe, it is still constant or at least changing so slowly that we do not see these effects. Only in some local areas is it changing so quickly. It's like water pooling in a valley.”
“Dag how could that be natural?”
“I'm not sure it is.”
18
Dag was certain there was no reason to try and patch the wormhole drive. In a world where the cosmological constant could change at any time in some locale, the drive would always be subject to failure.
But what was the alternative?
It had been five hundred years since the invention of the wormhole drive and science had not advanced much further in the physics of advanced propulsion. In fact, as far as Dag was concerned the discipline had stagnated. Elias Mach had developed the theory and much of the technology to make the wormhole drive a reality. His granddaughter had extended it. Since then physicists had advanced many theories but achieved few results.
Indeed the manner in which Dag's original research into the enhanced wormhole drive, the way it was thwarted by committee and incompetence so that the politically connected could take credit was all too familiar in the recent history of science. And now that society needed a robust problem-solving physics discipline there was nothing but administrators and timid researchers. Dag hoped that there were others working on the transportation problem but as far as he knew he was the only one. And he felt the weight of that possibility.
At least Dr. Payne was supportive. And the Jump-Ships Corporation had all the manufacturing capabilities that Dag would need if he could come up with an idea. But that was the catch. How do you come up with an idea as brilliant as the famous Dr. Mach's? Dag wasn't sure but he determined to do what he usually did when he was stuck for an idea, loaf and let it come in its own time.
Dag was walking around the large Jump-Ships facility when he ran into Dr. Payne and a companion.
“Oh Dr. Mach,” said Dr. Payne, “I want you to meet Walker, he has been very instrumental in getting the facility running again after the trip from Adowan orbit.”
Dag was facing another robot. Walker, along with many other robots, was a part of the Jump-Ships' workforce. As Dr. Payne had explained once, the Corporation had lost many workers when the decision was made to leave Adowa. Many left the orbiting facility to stay with their families. So many in fact that Dr. Payne had to turn to Em-based robots to make up the loss.
“Hello Walker.”
“Hello Dr. Mach.”
“Dr. Mach, Walker here is also a student of physics. Perhaps you two would enjoy a discussion of common interests sometime?”
“Yes of course. Always enjoy discussing physics. Whenever it is convenient Walker.”
“Thank you Dr. Mach, I look forward to it.”
“As a matter of fact, you two could start now. Walker, I have a meeting I need to get to. Perhaps you could take Dr. Mach on a tour of the shops?”
“I would be delighted Dr. Payne.”
“Good I will see you two later.”
“Well Dr. Mach, is there anything that you would particularly like to see?”
“No whatever, I was just out for a stroll.”
“Very well then if you will follow me.”
“Lead on my dear Walker, lead on,” said Dag playfully.
After the tour Dag was sitting in the coffee bar when Ally showed up.
“Hi Dag where have you been?”
“I was being shown around the facilities by Walker Miss.”
“Whose Walker?”
“He's another Em-based robot. He pretty much has responsibility for everything as far as I can tell. Dr. Payne has no biases when it comes to capability.”
“So what did you learn?”
“I've been thinking about that Miss. You see Walker was showing me the cross-walks. Those tubes that run from the rim to the center of the facility. There is a pull-strap in there that will take you from one side of the wheel rim to the other. A short-cut kind of.”
“Yeah, I see. Why did you find that interesting?”
“Well, as of yet it's still just a crazy idea. I really don't know if it will work.”
“Well … let's hear it anyway,” said Ally as she tried to draw Dag out.
“Okay Miss but don't laugh. You know I think it is useless to continue refining the wormhole drive because we can't depend on the cosmological constant to stop changing, at least locally.”
She nodded her head.
“Then we need a new method of transport. The only long distance-method that I can think of would be something like teleportation.”
“But teleportation won't work Dag. You can't influence the distant particle unless that particle is already entangled with a local particle and then sent to a distant location. And you are talking about a lot of entanglements for a spaceship.”
“I know Miss, that's why I called it a crazy idea. And yet it is the only way I can think of to restore long-distance transport.
“We know that for hundreds of years quantum theory has hinted that locality is an illusion. That particles clear across the universe can somehow be linked.”
“Yeah, nonlocal links.”
“That's right. But how do we use that knowledge to transport a spaceship?”
Ally shrugged.
“Okay here's my crazy idea. We know that quantum mechanics in its present form predicts only statistical outcomes of experiments including those that would show nonlocality. This statistical nature of quantum mechanics is why sending a signal faster than light seems impossible.”
“Yes but you are thinking that quantum gravity, especially the old loop quantum gravity, has a loophole, so to speak.”
Dag was pleased. “You are a very sharp woman Miss. Yes, the old loop quantum gravity indicated that if we had more than a statistical theory of quantum mechanics, a more complete theory, an exact description of what happens in every quantum process, then for the theory to be consistent it would have to describe every quantum process including those that are nonlocal.”
“But that would destroy relativistic causality Dag. It would be like the butterfly effect except that there wouldn't have to be any physical causes linking the flapping of a butterfly's wings to the distant event.”
“Exactly Miss. And the speed of light would no longer be a limit to the physical transport of mass.”
“How many hundreds of years have people been trying to 'complete' quantum mechanics though?”
“I know. It's crazy.”
Ally smiled. “Well someone's got to do it.”
Dag knew what he w
as up against. Some of the greatest physicists in history had tried to “tame” the merger of quantum mechanics and general relativity. They had all failed, usually with the theory succumbing to physically impossible infinities.
But Dag had the time and the motivation. Dr. Payne had not required anything of him. He was held in reserve as an information resource for the others. There would be no better time than now to try.
Dag returned to his quarters and sat down to think. He often used analogies to guide his thought. In this case he began by comparing spacetime to a liquid. Although it may seem smooth and continuous, a liquid is just the collective motions of myriads of water molecules. At the atomic level it is discrete, it is only because of the huge numbers of molecules and their tiny size that we see a liquid as continuous.
Likewise thought Dag, if loop quantum gravity is correct, and there are reasons to think it is, then there is a quanta of volume which is extremely small, on the order of the Planck scale, and so numerous that spacetime appears smooth and continuous to our senses.
Now because of our difficulties dealing with such a large collection of objects, we must resort to statistics to describe their collective action. Like the temperature of a body of water is a thermodynamic property derived from the statistical spread of molecular motion. Some molecules are moving very fast while other molecules are moving very slow but the vast majority are moving at speeds around the mean which we call the temperature.
Something similar holds for quanta of volume but that is not the most interesting feature. What is most interesting is that the same distribution holds for the links, or the loops in LQG, that connect the volume quanta. Most of the links are around the mean, most are local and this is why we have the illusion that everything must be in contact, whether physically or through an intermediate field, to have a cause and effect.
But the links far from the mean, the ones we would consider nonlocal, are the interesting ones.
If I can figure out how to isolate and classify them then maybe I can use them to send or receive information. That would be the first test. Next, if that succeeds and considering that information sent in this way is just energy and energy is another word for mass ...
Dag stopped. He had the whole research program in his head. He took out his Emmie to record it.
19
Dag had been calculating non-stop for a week. So far the theory was holding up. He was hoping to present it to Ally and maybe Walker.
“So that's my theory. What do you think,” said Dag looking from Ally to Walker and back.
“Dag?”
“Yes Walker?”
“First I would like to say that what you have done is an amazing piece of work.”
“Thank you.”
“Specifically what I find interesting is how you plan to detect these nonlocal links.”
“You mean with modified entanglement detectors.”
“Exactly. If the theory is true we will be able to map the universe with such devices.”
“Yes, I believe you are right.”
“But think about it for a moment. Many of these links will be outside the observable universe.”
“You mean that part of the universe beyond the visible universe Miss? We'll be able to see things beyond forty-six billion light-years away?”
“That's right. Some of these links could be beyond the observable.”
“But one thing I don't understand Dag. Assuming these nonlocal links exist how will you use them for transportation or even communications?”
“Well Miss here's the thing. We know that these links exist because quantum mechanics demands it. Nonlocality is built into the quantum universe. We also believe that communications along these links is faster than light if not instantaneous because of quantum entanglement. So we know that happens.
“But what we don't know is why we can't use them to communicate with. Up until now people just invoke Einstein's law that information can not be transmitted faster than the speed of light.
“But I believe these nonlocal links, unlike the local links which are woven into spacetime, are not in this universe but the volume elements they link are. I hesitate to say extra-dimensional because of the fallout from the old string theory and its many dimensions. Still, I think that is the best way to look at it.
“For instance, we know that a wormhole can be created between distant locations and that travel through it, while locally less than the speed of light is nonlocally faster than the speed of light. In other words, we have operational proof that we can send information and mass over a distance faster than light can cover that distance. We say that the wormhole drive uses what we call the wormhole dimension.
“In this case, I think something very similar happens with these nonlocal links. They are similar to the wormhole dimension which we use, or used I should say, for transportation. A dimension that seems outside our ordinary four-dimensional spacetime.
“So in essence, you might say that I will be using nature's original long-distance network,” he finished feeling clever.
“That's interesting Dag and sounds doable. But how do we tap into this network?”
“You're talking applications now Miss. I don't have an answer to that yet. I do know it will involve somehow reaching into the sub-microscopic, the quantum spin foam, and opening a portal to the nonlocal network. Somewhat like the wormhole drive does.”
“Dag if I might ask. This quantum spin foam, I've heard that phrase before. Can you define it?”
“Well Walker it is somewhat involved but here goes. A spin foam in loop quantum gravity is an extension of the mathematics of spin networks to include time and space.
“Now a spin network consists of nodes and links which create a net-like graph. Kind of like a woven cloth with thread for links and nodes where the threads cross. Now if you associate the nodes with a small unit of volume and the links with a small unit of area then when time enters the picture the points get extended as lines and the lines extend as sheets. The whole thing creates something that resembles the borders between soap bubbles. This is where the term foam comes from.
“Now spin is related to quantum spin which is an intrinsic and unique property of sub-atomic particles, and is not the same as normal angular momentum. The quantum spin numbers are used in the mathematics that construct a valid spin network. Since spin is quantized, having only whole or half values the resulting spacetime is quantized leading to quantum gravity.”
“Spacetime then emerges from a spin network, a graph-like structure propagated through time then?”
“Yes, that's a succinct definition of spacetime Walker.”
“And it's important to remember that these links we are talking about are discrete quantum lines of force in quantum gravity. And they are not in space so much as they form space,” said Ally.
Walker agreed.
“Geometry is determined by gravity,” said Dag feeling clever again.
Walker tilted his head at the remark.
“So the graph that determines spacetime through its links is determined by the link's gravitational force?”
“That's right,” said Dag.
“The theory is somewhat densely recursive isn't it?”
“I guess you could say so,” said Dag, not quite as pleased with himself.
Ally was amused as she always was when someone tried to explain a physical theory without recourse to mathematics.
She said, “So these links of force. How do you expect to use the nonlocal links for transportation Dag?”
“Let me get back to you on that Miss, I haven't quite figured it out.”
The impromptu session broke up with Walker attending to his duties while Ally and Dag talked a bit more.
In the following weeks, Dag made progress in applying his theory. If his theory was correct he could modify a wormhole drive to create what he had come to call the quantum spin-two drive. Where spin-two is a reference to the particle of gravity, the graviton, although spin one-ha
lf particles were more important to the spin-two drive's operation.
Using the wormhole drive's ability to cast negative energy he would modify it to project that energy into a loop of points instead of a single point. The projected energy would cause a fermionic particle, particles with one-half quantum spin, to flip its spin as the light from the incident was measured by the ship. Nonlocal partners to these particles, entangled particles, would then assume the opposite spin state. By modulating the energy and resulting reading, a pulse of energy, equivalent to information, would travel down the nonlocal links at a frequency determined by the spin-two drive.
Dag then imagined a ship inserted into the “tunnel” of nonlocal links. Using the drive's ability to create negative mass-energy, the bubble inclusive of the ship, would be pulled and pushed along by the pulses, which were now decaying because the ship would no longer be supplying energy to the loop of points. Eventually the ship would emerge at the nonlocal loop of points before the loop closed. The loop portals would eventually decay and the nonlocal tunnel would collapse to its original minuscule size.
Anyway, that's the way Dag imagined it would work. There were still questions that would have to be solved by experiment. How much energy would be needed? Could the loop particles be synchronized well enough to create a coherent pulse of information? Would the link tunnel decay in an orderly fashion and if it did would it exist long enough for a ship to transit no matter the length of the nonlocal link?
Dag was preparing his notes to show Ally when the manufacturing wheel shuddered. The alarm clanged just like a ship's. Dr. Payne's voice came over his Emmie.
“Attention. The wheel has experienced a gravitational anomaly but should be stabilizing soon. I am calling a meeting of my department heads in ten minutes. Dr. Mach and Dr. Mekur please attend.”
The meeting was being held as usual in conference room two. Dag didn't know and was late. Ally was speaking when he entered the room.
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