Hidden Variables Read online

  Four hours of discussion between McAndrew and Wenig—with interruptions from Nina and me—had fixed the sequence for the vital half-second when we would be passing the Merganser. The ships would exert gravitational forces on each other, but that was useless for providing the lateral thrust on the life capsule system that McAndrew thought was needed. We had to give a more direct and harder push some other way.

  Timing was crucial, and very tricky.

  Whatever we threw at the other ship would have to pass through the drive exhaust region before it could impact the life-capsule column. If the drive were on, nothing could get through it—at those temperatures any material we had would be vaporized on the way, even if it were there for only a fraction of a second. The sequence had to be: launch mass from Dotterel; just before it got there, kill drive on Merganser; hold drive off just long enough for the Dotterel to clear the area and for the mass to impact the Merganser's support column; and back on with their drive, at once, because when the drive was off the Merganser's passengers would be feeling the full fifty gee of the mass plate's gravity.

  McAndrew and Wenig cut the time of approach of the two ships into millisecond pieces. They decided exactly how long each phase should last. Then they let the two on-board computers of the ships talk to each other, to make sure that everything was synchronized between them—at the rate things would be happening, there was no way that humans could control them. Not even Wenig, with his super-fast reflexes. We'd all be spectators, while the two computers did the real work and I nursed the abort switch.

  There was one argument. McAndrew wanted to use a storage tank as the missile that we would eject from our ship to impact theirs. It would provide high momentum transfer for a very brief period. Wenig argued that we should trade off time against intensity, and use a liquid mass instead of a solid one. Endless discussion and calculations, until Mac was convinced too. We would use all our spare water supply, about a ton and a half of it. That left enough for drinking water on a twenty gee return to the Inner System, but nothing spare for other uses. It would be a scratchy and smelly trip home for Dotterel's passengers.

  Drive off, we felt only the one-gee pull of our mass plate as we dropped in to close approach. On Merganser, McAndrew and Nina Velez were lying in water bunks, cushioned with everything soft on the ship. We were on an impact course with them, one that would change to a near-miss after we ejected the water ballast. It looked like a suicide mission, running straight into the blue furnace of their drive.

  The sequence took place so fast it was anti-climactic. I saw the drive cut off ahead of us and felt the vibration along the support column as our mass driver threw the ballast hard towards Merganser. The brief pulse from our drive that took us clear of them was too quick for me to feel.

  We cleared the drive region. Then there seemed to be a wait that lasted for hours. McAndrew and Nina were now in a ship with drive off, dropping towards HC-183. They were exposed to the full fifty gee of their mass plate. Under that force, I knew what happened to the human body. It had not been designed to operate when it suddenly weighed more than four tons. Membranes ruptured, valves burst, veins collapsed. The heart had never evolved to pump blood weighing hundreds of pounds up a gravity hill of fifty gee. The only thing that Mac and Nina had going for them was the natural inertia of matter. If the period of high gee were short enough, the huge accelerations would not have time to produce those shattering physical effects.

  Wenig and I watched on our screens for a long, long moment, until the computer on Merganser counted off the last microsecond and switched on the drive again. If the life-capsule was free to move along its column, the computer would now begin the slow climb out of HC-183's gravity well. No action was needed from the passengers. When we completed our own orbit we hoped we would see the other ship out at a safe distance, ready for the long trip home.

  And on board the ship? I wasn't sure. If the encounter had lasted too long, we might find no more than two limp and broken sacks of blood, tissue and bone.

  * * *

  It was another long day, waiting until we had been carried around in our orbit and could try to rendezvous the two ships. As soon as we were within radar range, Nina Velez appeared on the com screen. The drive was cut back, so we could get good visual signals. My heart sank when I saw the expression on her face.

  "Can you get over to this ship—quickly?" she said.

  I could see why all the professors at the Institute had lost their senses. She was small and slight, with a childlike look of trust and sad blue eyes. All a sham, according to everything I'd been told, but there was no way of seeing the strong personality behind the soft looks. I took a deep breath.

  "What's happening there?" I said.

  "We're back under low gee drive, and that's fine. But I haven't been able to wake him. He's breathing, but there's blood on his lips. He needs a doctor."

  "I'm the nearest thing to that in thirty billion miles." I was pulling a suit towards me, sick with a sudden fear. "I've had some medical training as part of the Master's License. And I think I know what's wrong with McAndrew. He lost part of a lung lobe a couple of years ago. If anything's likely to be hemorrhaging, that's it. Dr. Wenig, can you arrange a rendezvous with the mass plates at maximum separation and the drives off?"

  "I'll need control of their computer." He was pulling his suit on, too. I didn't want him along, but I might need somebody to return to the Dotterel for medical supplies.

  "What should I be doing?" Thank heaven Nina showed no signs of panic. She sounded impatient, with the touch of President Velez in her voice. "I've sat around in this ship for weeks with nothing to do. Now we need action but I daren't take it."

  "What field are you in now? What net field?"

  "One gee. The drive's off now, and we've got the life-capsule right out at the end of the column."

  "Right. I want to you stay in that position, but set the drive at one gee acceleration. I want McAndrew in a zero-gee environment to slow the bleeding. Dr. Wenig, can you dictate instructions for that while we are rendezvousing?"

  "No problem." He was an irritating devil, but I'd choose him in a crisis. He was doing three things at once, putting on his suit, watching the computer action for the rendezvous, and giving exact and concise instructions to Nina.

  Getting ourselves from one ship to the other through open space wasn't as easy as it might sound. We had both ships under one gee acceleration drives, complicated by the combined attraction of the two mass plates. The total field acting on us was small, but we had to be careful not to forget it. If we lost contact with the ships, the nearest landing point was back on Triton Station, thirty billion miles away.

  Nina in the flesh was even more impressive than she was over the video link, but I gave her little more than a cursory once-over. McAndrew's color was bad and even while I was cracking my suit open and hustling out of it I could hear a frightening bubbling sound in his breathing. Thank God I had learned how to work in zero gee—required part of any space medicine course. I leaned over him, vaguely aware of the two others intently watching. The robodoc beside me was clucking and flashing busily, muttering a faint complaint at McAndrew's condition and the zero-gee working environment. Standard diagnosis conditions called for at least a partial gravity field.

  I took the preliminary diagnosis and prepared to act on it while the doc was still making up its mind. Five cc's of cerebral stimulant, five cc's of metabolic depressant, and a reduction in cabin pressure. It should bring Mac up to consciousness if his brain was still in working order. I worried about a cerebral hemorrhage, the quiet and deadly by-product of super-high gees. Ten minutes and I would know one way or the other.

  I turned to Wenig and Nina who were still watching the robodoc's silent body trace. "I don't know how he is yet. We may need emergency treatment facilities ready for us as soon as we get back to the System. Can you go over to Dotterel, cut the drive and try to make contact with Triton Station? By the time you have the connection we sho
uld have the full diagnosis here."

  I watched them leave the ship, saw how carefully Wenig helped Nina to the transfer, and then I heard the first faint noise behind me. It was a sigh, with a little mutter of protest behind it. The most wonderful sound I ever heard in my life. I glanced over at the doc. Concussion—not too bad—and a little more bleeding than I wanted to see from the left lung. Hell, that was nothing. I could patch the lung myself, maybe even start the feedback regeneration for it. I felt a big grin of delight spreading like a heat wave over my face.

  "Take it easy, Mac. You're doing all right, just don't try and rush yourself. We've got lots of time." I secured his left arm so that he couldn't disturb the rib cage on that side.

  He groaned. "Doing fine, am I?" He suddenly opened his eyes and stared up at me, "Holy water, Jeanie, that's just like a medic. I'm in agony, and you say it's a little discomfort. How's Nina doing?"

  "Not a mark on her. She's not like you, Mac, an old bag of bones. You're getting too old for this sort of crap."

  "Where is she?"

  "Over on Dotterel, with Wenig. What's the matter, still infatuated?"

  He managed a faint smile. "Ah, none of that now. We were stuck on Merganser for more than two weeks, locked up in a three meter living sphere. Show me an infatuation, and I'll show you a cure for it."

  The com-link behind me was buzzing. I cut it in, so that we could see Wenig's worried face.

  "All right here," I said, before he had time to worry any more. "We'll be able to take our time going back. How are you? Got enough water?"

  He nodded. "I took some of your reserve supply to make up for what we threw at you. What should we do now?"

  "Head on back. Tell Nina that Mac's all right, and say we'll see you both back at the Institute."

  He nodded again, then leaned closer to the screen and spoke with a curious intensity. "We don't want to run the risk of having a stuck life capsule again. I'd better keep us down to less than ten gee acceleration."

  He cut off communication, without another word. I turned to McAndrew. "How high an acceleration before you'd run into trouble with these ships?"

  He was staring at the blank screen, a confused look on his thin face. "At least forty gee. What the devil's got into Wenig? And what are you laughing at, you silly bitch?"

  I came over to him and took his right hand in mine. "To each his own, Mac. I wondered why Wenig was so keen to get here. He wants his shot at Nina—out here, where nobody else can compete. What did you tell her—some sweet talk about her lovely eyes?"

  He closed his eyes again and smiled a secret smile. "Ah, come on Jeanie. Are you telling me you've been on your best behavior since I last saw you? Gi' me a bit of peace. I'm not soft on Nina now."

  "I'll see." I went across to the drive and moved us up to forty gee. "Wait until the crew on Titan hear about all this. You'll lose your reputation."

  He sighed. "All right, I'll play the game. What's the price of silence?"

  "How long would it take a ship like this to get out to Alpha Centauri?"

  "You'd not want this one. We'll have the next one up to a hundred gee. Forty-four ship days would get you there, standing start to standing finish."

  I nodded, came back to his side and held his hand again. "All right, Mac, that's my price. I want one of the tickets."

  He groaned again, just a bit. But I knew from the dose the doc had put into him that it wasn't a headache this time.

  AFTERWORD: MOMENT OF INERTIA.

  It's not hard to reconstruct McAndrew's reasoning when he developed the specifications for designing the Dotterel and the Merganser. It must have run as follows:-

  Consider a thin flat circular plate of material, uniform in composition. Suppose its mass is M and its radius R, so that the mass density (σ) per unit area is σ = M/πR2.

  At a point P on the axis of the disc, distance z from its center, the gravitational potential is given by:

  where G is the gravitational constant ■

  The acceleration at P towards the disc is then:

  and the tidal effect (rate of change of acceleration) is:

  If we require that the rate of change of acceleration (i.e. the tidal effect) should be one gee per meter when the acceleration is 50 gee, from (2) and (3) we have:

  thus

  and this relation between R and z must hold independent of the mass M.

  An infinite number of (R,z) pairs will satisfy equation (4), and Table 1 lists some of them, together with the mass M, found from equation (3), and the distance, Z, where the gravitational acceleration towards the disc is one gee. Since we may as well use the most compact and lightest of the possible cases, we use the set: R = 50 meters, z = 0 meters, Z = 246.2 meters, GM = 62,500 square meters.

  This means a mass plate 50 meters in radius, and projecting from it we have a column at least 246.2 meters long. The life capsule will ride up and down this as the drive acceleration is varied.

  The only other thing that McAndrew needed to know was the gravitational acceleration and tidal effects at different distances from the plate. He would use these to decide how far away the life capsule should be positioned for different drive accelerations. Those values are provided from equations (2) and (3) and are shown in Table 2.

  This story has worried a number of readers. They say, in summary, how can a ship that can only generate fifty gee of thrust ever escape from a field where it is just balancing a fifty gee attraction? It's a hypothetical question, since the beginning of the story points out that the fifty gee limit applies not to the propulsion system, but to the balancing system that neutralizes the propulsive acceleration. Even so, it's a nice question, and one easily answered.

  If you are sitting balanced with a fifty gees thrust and a fifty gees attraction towards some central body, all you need do to escape is to turn the ship and direct the thrust at right angles to the direction of the attracting body. You then fall inwards at first, but the trajectory has a point of closest approach about 5,000 kilometers from the center of attraction—so we can only use this method for orbits about high-density and compact objects. If anyone is interested I can provide the actual trajectory and the profile of the escape spiral.

  There is, however, still a problem with the story, and one less easily answered. It concerns the drive itself. McAndrew's ship generates its fifty gees acceleration by expelling reaction mass—necessary for any propulsion system that wishes to satisfy the law of conservation of linear momentum. Unless we wish to throw overboard the most basic laws of modern physics, reactionless drives are out, as are drives that somehow convert angular momentum to linear momentum. We are stuck with a drive that consumes reaction mass to achieve its propulsive effect.

  Suppose that McAndrew's ship had a photon drive, in which matter is turned to radiation and the radiation, suitably directed, provides the thrust. That's the best we can imagine, if we accept today's physics. With a photon drive, it's easy to calculate that a sustained fifty gees drive will quickly consume the ship's own mass in order to keep on accelerating. Half the mass would be gone in a few days, and McAndrew's ship would disappear from under him.

  There is one loophole, a solution based on a known inconsistency between general relativity and quantum theory. To explore that loophole, see "All The Colors of the Vacuum," later in this collection.

  THE NEW PHYSICS: THE SPEED OF LIGHTNESS, CURVED SPACE, AND OTHER HERESIES

  Listwolme is a small world with a thin but permanently cloudy atmosphere. The inhabitants have never seen the stars, nor become aware of anything beyond their own planet. There is one main center of civilization which confined itself to a small region of the surface until about a hundred years ago, when an industrial revolution took place. For the first time, rapid transportation over substantial areas of the planet became possible.

  Orbital velocity at the surface of Listwolme is less than two kilometers a second. The meetings of the Listwolme Scientific Academy following the development of high-velocity surface vehicles
are chronicled below. The highlights of those meetings were undoubtedly the famous exchanges between Professor Nessitor and Professor Spottipon.

  * * *

  The first debate: In which Professor Nessitor reveals the curious results of his experiments with high-speed vehicles, and proposes a daring hypothesis.

  Nessitor: As Members of the Academy will recall, a few months ago I began to install sensitive measuring devices aboard the Tristee Two, the first vehicle to move at a speed more than ten times that of a running schmitzpoof. The work was not easy, because it was first necessary to suppress all vibration induced by the car's contact with the surface.

  One month ago we achieved the right combination of smooth suspension and vibration damping. It was with some excitement that I placed one of our instruments, a sensitive spring balance, within the vehicle and we began steadily to increase our speed. As you may have heard, there have been reports of "feeling light" from the drivers of these cars when they go at maximum velocity.

  Fellow scientists, those feelings are no illusion! Our instruments showed a definite decrease in load on the balance as our speed was increased. There is a relationship between weight and motion!

  (As Nessitor paused, there was a murmur of surprise and incredulity around the great hall. Professor Spottipon rose to his feet.)

  Spottipon: Professor Nessitor, your reputation is beyond question . What would arouse scepticism from another in your case is treated with great respect. But your statement is so amazing that we would like to hear more of these experiments. For example, I have heard of this "lightening" effect at high speeds, but seen no quantitative results. Were your balances sensitive enough to measure some relation between the lightness and the speed?