Mach's Metric

by D. W. Patterson

  Elias and James hurried to the ship.

  Close up it had more damage than could be seen from a distance. The back of the ship was crushed and the girder complex that connected the crew wheel to the fusion engine was obviously bent. The wheel itself was shattered where it had come to rest on the moon's surface. The layers of the wormhole generator were exposed.

  Elias had a thought.

  “James, I wonder.”

  “What is it Elias?”

  “We can get to the actuator and Mach layer materials because of the damage. If we could build a wheel of some kind and recreate the generator's layers upon it, we could use it to signal Arn.”

  “Really, you can do that?”

  “Yeah, I think so.”

  “I know he can,” said Burgess.

  That evening Dag continued his tale of Robinson Crusoe:

  But something always returned swift upon me to check these thoughts, and to reprove me; and particularly one day, walking with my gun in my hand by the seaside, I was very pensive upon the subject of my present condition, when reason, as it were, expostulated with me the other way, thus: “Well, you are in a desolate condition, it is true; but, pray remember, where are the rest of you? Did not you come, eleven of you in the boat? Where are the ten? Why were they not saved, and you lost? Why were you singled out? Is it better to be here or there?” And then I pointed to the sea. All evils are to be considered with the good that is in them, and with what worse attends them.

  Then it occurred to me again, how well I was furnished for my subsistence, and what would have been my case if it had not happened (which was a hundred thousand to one) that the ship floated from the place where she first struck, and was driven so near to the shore that I had time to get all these things out of her; what would have been my case, if I had been forced to have lived in the condition in which I at first came on shore, without necessaries of life, or necessaries to supply and procure them? “Particularly,” said I, aloud (though to myself), “what should I have done without a gun, without ammunition, without any tools to make anything, or to work with, without clothes, bedding, a tent, or any manner of covering?” and that now I had all these to sufficient quantity, and was in a fair way to provide myself in such a manner as to live without my gun, when my ammunition was spent: so that I had a tolerable view of subsisting, without any want, as long as I lived; for I considered from the beginning how I would provide for the accidents that might happen, and for the time that was to come, even not only after my ammunition should be spent, but even after my health and strength should decay . . .

  Chapter 10

  Wormhole Physics 101 by Dr. Elias Mach

  Copyright 2393 C.E.- Chapter 11, Page 403

  Practical Applications

  The wormhole is very much a communication device, bridging light-years. A practical wormhole communication involves opening a small wormhole link to the destination and using an ordinary radio frequency transmitter to send the message. The communication is almost instantaneous.

  The distance achievable with this form of communication is much greater than that for wormhole transport. Wormhole communication links up to thirteen light-years have been achieved with a minimum of energy usage because it is only necessary to open the smallest of “bridges” in the wormhole dimension to communicate.

  To calculate the energy necessary to open a link we first write the metric . . .

  The work was slow and surprisingly hard considering the lower gravity of the moon. Even though the EVA suits and breathers did their job well the cold seemed to find its way in, especially the hands which would become almost numb after working for ten, twelve hours. Dag was immune but the toll it was taking on Elias and James was noticeable. James seemed particularly affected since he had no one to commiserate with as Elias had Burgess.

  They had partitioned the shuttle with Elias and Burgess taking the back area. Dag usually suspended for the day in the flight control area so as to be quickly available if something alerted. That left James to himself in the middle of the shuttle. He hadn't anyone to talk to after a long day's work and soon was keeping himself very quiet even during the evening meal they all shared. Elias had thought it was just weariness brought on by the hard work.

  It had taken over two weeks to build the makeshift generator and set it up. Dag had been a great help. If not for him Elias wasn't sure they would have succeeded. James, after a fast start, had begun to falter. He was slow to get started and would often quit work before Elias and Dag. He had also become more and more withdrawn.

  Elias and Dag cycled through the shuttle's airlock after a long “day”.

  “We should be able to try to signal tomorrow. Dag and I hooked up the isotopic reserves of the shuttle to the generator, it should fully charge overnight.”

  James looked up and said, “It's a waste.”

  “What's that James?” asked Elias.

  “We're wasting power. We could get another day or two of heat and light out of the energy you are wasting on this fantasy.”

  “James I can assure you that the power is not being wasted. The device will work. In fact it's our only chance to be rescued.”

  “Chance. That's exactly what it is, chance. And how great is that chance? Can you calculate it? No. But I can tell how much the power you're wasting means for our life support system.”

  “James we all agreed over two weeks ago that this was the way to proceed.”

  “I was wrong then and you are wrong now Elias. That power you're wasting would give us another day maybe two. I think we should save it.”

  “Again James I point out that this is the agreed-upon path we all decided to take. You must allow us to finish.”

  “I must this, I must that!” shouted James. “I was first-officer of a fusion ship! What are you Elias? Some fool that doesn't know his limitations, that's what. And you are to decide when we die? I think not.”

  With that James arose and went to the airlock before the others could move to stop him. He had started cycling the air while trying to put on an EVA suit. Elias ran to the airlock door. Through the window he could see James working feverishly to get the suit on and the breather in.

  “Dag can you stop the airlock cycle?”

  “No Elias there is no provision for manual override.”

  Elias watched as James now in an almost completed airlock cycle seemed to be holding his breath while attaching his breather tube. Finally, he had the tube in and the outer hatch opened.

  Elias sighed with relief. James disappeared into the mist and snow of falling carbon dioxide crystals.

  Elias moved to the communications console.

  “James this is Elias, do you read me?”

  There was no reply. Elias tried several more times before giving up.

  “I guess he will be back when he's ready to come back,” he said turning to the others.

  “I guess he just snapped,” said Burgess. “I would have thought with his training and experience he would be the last to yield to the stress.”

  “Maybe the training and experience worked against him. He was trained for duty on a fusion ship in space not a shuttle on the ground.”

  Burgess just nodded.

  “We should have dinner honey.”

  Later that evening they lay in the back of the shuttle on their makeshift bed while Dag was upfront in suspension.

  “I guess he's not coming back soon,” said Elias.

  “I hope he's alright,” said Burgess.

  “I'm sure he is honey. He knows how to take care of himself out there and the suit should have enough power to keep him warm for a couple of days anyway.”

  “Elias?”

  “Yes honey?”

  “Is it hopeless like James said? Do we really have a chance to be rescued?”

  “Yes honey, there is a chance. I'm sure the generator will work. I know the coordinates to cast the far mouth to. Someone there should pick up our signal and relay it to Arn. There's no doubt we have a good
chance of being rescued.”

  “Thank you Elias.”

  “For what Burgess?”

  “For telling me the truth and for your courage in this dreadful situation.”

  “Honey you know I've always been honest with you no matter the situation. And if anyone should be thanked it should be you for holding up so well under the circumstances. You give me courage.”

  “I love you Elias.”

  “I love you too.”

  Elias and Burgess got up late the next morning. Dag was already monitoring at the flight control console.

  “Good morning Dag,” said Elias.

  “Good morning sir.”

  “Any word from James?”

  “Nothing sir.”

  “Well he's got another day in that suit.”

  “I'm afraid not sir. You see I checked the status of that suit after James left. He had maybe six hours before the power failed.”

  “You mean he's gone Dag?”

  “Are you talking about James?” asked Burgess as she came out of the back of the shuttle.

  “Yes, I'm afraid so honey. According to Dag's figures, James's suit ran out of power sometime last night. He's not back so I'm afraid he's dead.”

  “I don't understand it Elias. I mean I know he was angry. But I didn't think he was suicidal.”

  Just then a look of understanding came over Elias.

  “I don't think it was suicide Burgess, it was sacrifice.”

  “What do you mean?”

  “You see James and I had talked about rescue. Once Arn receives our message the quickest he could be here would be ten to twelve days. After charging the wormhole generator overnight we figured we would only have six days of power and supplies for three people. But for two people that could be stretched for almost ten days.”

  “That's why James has been so preoccupied,” said Burgess. “He's been thinking about what he should do and he decided to sacrifice himself for us. Oh, Elias.”

  Burgess clutched to Elias as he put his arms tightly around her.

  “There's only one thing we can do for James now honey.”

  Burgess looked up to him.

  “Survive,” was all he said.

  They had the monitors trained on the small wormhole generator. It looked more like a windmill with small swatches of fabric stuck to the end of long poles than a technological marvel. Even so, Elias was convinced it would work.

  The arms of the generator were rotating slowly to provide the necessary change in momentum and therefore acceleration that the Mach effect needed. The layers of material while not smoothly abutted were electrically joined where necessary. The effect wouldn't be the smooth spherical wormhole mouth they were familiar with but it should still be sufficient.

  “Okay Dag,” said Elias. “Get the radio transmitter ready with the message I've prepared. When I tell you, transmit that message.”

  “Ready,” said Dag.

  Elias closed the buss bar that would take the power from the isotopics to the generator. There in front of the generator, a pinpoint of light appeared. The brightness and size of the light source began to grow. Unlike usual, the glowing light was far from spherical but looked more like a cloud of swarming insects changing its overall shape moment to moment.

  “Now Dag,” said Elias.

  Dag pushed a button and the message went out over the radio. A mixture of audio and mathematics that Elias hoped would bring Arn Strombecker and a rescue ship straight to them.

  Then the cloud of light extinguished. The generator spun down.

  “Did we get it all transmitted?” asked Elias.

  “Yes sir,” said Dag.

  Elias looked at Burgess with a hopeful smile.

  When I took leave of this island, I carried on board, for relics, the great goat-skin cap I had made, my umbrella, and one of my parrots; also, I forgot not to take the money I formerly mentioned, which had lain by me so long useless that it was grown rusty or tarnished, and could hardly pass for silver till it had been a little rubbed and handled, as also the money I found in the wreck of the Spanish ship. And thus I left the island, the 19th of December, as I found by the ship’s account, in the year 1686, after I had been upon it eight-and-twenty years, two months, and nineteen days; being delivered from this second captivity the same day of the month that I first made my escape in the long-boat from among the Moors of Sallee. In this vessel, after a long voyage, I arrived in England the 11th of June, in the year 1687, having been thirty-five years absent.

  When I came to England I was as perfect a stranger to all the world as if I had never been known there. My benefactor and faithful steward, whom I had left my money in trust with, was alive, but had had great misfortunes in the world; was become a widow the second time, and very low in the world. I made her very easy as to what she owed me, assuring her I would give her no trouble; but, on the contrary, in gratitude for her former care and faithfulness to me, I relieved her as my little stock would afford; which at that time would, indeed, allow me to do but little for her; but I assured her I would never forget her former kindness to me; nor did I forget her when I had sufficient to help her, as shall be observed in its proper place. I went down afterwards into Yorkshire; but my father was dead, and my mother and all the family extinct, except that I found two sisters, and two of the children of one of my brothers; and as I had been long ago given over for dead, there had been no provision made for me; so that, in a word, I found nothing to relieve or assist me; and that the little money I had would not do much for me as to settling in the world.

  By the time Dag finished with his reciting it was almost the end of the story. Burgess seemed to be asleep and Elias was also. It had been fourteen days since they had sent the message. The food though rationed was almost gone. Elias and Burgess did not rise for anything but what they absolutely had to do. Dag had been able to generate a little water from the atmosphere but that too would be gone soon. Dag was now essentially a nursemaid.

  Chapter 11

  Wormhole Physics 101, 5th Edition by Dr. Elias Mach

  Copyright 2393 C.E.- Appendix 1, Page 554

  Extending the Wormhole's Reach

  The speed of a ship which casts a far wormhole mouth has an effect on the far coordinates. The usual 7.5 light-year limit for the cast mouth is increased slightly by the kinetic energy of the moving ship without the usual breakdown of spacetime due to energy concentration.

  The relationship is logarithmic, so after the initial increase in distance, a practical limit is reached. The safest distance a far mouth can be cast is 7.86 light-years. The speed of the ship needed for this distance can be found from the equation . . .

  Arn Strombecker had problems. The Starway 1 had entered the wormhole mouth at speed. They had eluded the Federation vessel chasing them but had ended up way off course. Instead of the relatively short jump to Luhman 16 they had expected, they had ended up nearly ten light-years away, somewhere near the star Sirius.

  Some of the crew had died during the jump. The doctor wasn't sure why. But to Arn, these weren't just dead crew members they were old friends. People that he had relied on for years. It was difficult to accept.

  “I just can't believe it,” said Arn to Al Hunt. “Jim, Dave and Jack, all gone.”

  “I know what you mean Arn but we've got to decide what to do now.”

  “Yeah I know. Okay, I say first we head for Sirius since we are close. But in the meantime I want to divert some of the fusion power to the isotopic's.”

  “For what?” asked Al.

  “I want to call the Luhman 16 office and see what their status is and whether they've heard anything from Elias.”

  “Then what?”

  “Then we can decide our next step.”

  Arn alone in his room began to think over the last few days.

  He was older than any of the others aboard Starway 1. He knew the history of the Corporation and the Centauri habitats and he was worried. The people were acting almost as a stampeding mob.
That man Mason kept them worked up continually with fears and anxieties. Warnings of doom and destruction filled the news almost nonstop. The effect was debilitating.

  Arn was surprised that the inhabitants could so easily be manipulated. He had thought of them as himself, independent with a love of freedom. But it seemed they would give it all up for a promise of safety. The whole edifice of the civilization he knew seemed to be cracking and groaning under the weight of fear. A dark time was coming and Arn was feeling too old to hold it back. But still, maybe he could rescue Elias and Burgess. Elias was the one man in two systems that could defy the odds.

  Arn was interrupted from his thoughts by a call over his Emmie.

  “This is Arn.”

  “Arn this is Al. We got a reply from Luhman 16 to our inquiry, you want to come here or have me read it.”

  “Go ahead and read it Al.”

  “Message from Elias Mach received here. Message indicates that Elias and others are stranded on a moon of the Epsilon Eridani system. He estimates twelve days of supplies, maybe a few more. The rest of the message is a technical document concerning making a longer than usual jump ...”

  Arn interrupted.

  “Send the rest to my Emmie immediately Al.”

  Arn had finished reading the tech doc from Elias. It explained what had happened to the crew of the Starway 7 which was similar to what had happened aboard Arn's ship. It had also suggested how to make a slightly longer than usual jump, a jump that would be needed to reach Epsilon Eridani from Sirius.

  What a coincidence. We're headed for Sirius now. We may have lost three lives but maybe we can save three.

  Arn didn't know about James Tiberius yet.

  “Damn,” said Arn.

  He and Al were trying to calculate the time it would take to reach Elias.

  “Almost fourteen days from know. That's too long Al.”

  “What can we do? That's the physics.”

  “We charge up the isotopics again as fast as possible while we are traveling. By the time we get to Sirius that should save a day or two of recharging in that system.”