Poul Anderson - Tau Zero

But that is an incomplete statement. It takes no account of relativity. Precisely because there is an absolute limiting speed (at which light travels in vacuo; likewise neutrinos) there is an interdependence of space, time, matter, and energy. The tau factor enters the equations. If v is the (uniform) velocity of a spaceship, and c the velocity of light, then tau equals

The closer that v comes to c , the closer tau comes to zero.

Suppose an outside observer measures the mass of the spaceship. The result he gets is her rest mass — i.e., the mass that she has when she is not moving with respect to him — divided by tau. Thus, the faster she travels the more massive she is, as regards the universe at large. She gets the extra mass from the kinetic energy of motion; e=mc 2.

Furthermore, if the “stationary” observer could compare the ship’s clocks with his own, he would notice a disagreement. The interlude between two events (such as the birth and death of a man) measured aboard the ship where they take place, is equal to the interlude which the observer measures … multiplied by tau. One might say that time moves proportionately slower on a starship.

Lengths shrink; the observer sees the ship shortened in the direction of motion by the factor tau.

Now measurements made on shipboard are every bit as valid as those made elsewhere. To a crewman, looking forth at the universe, the stars are compressed and have gained in mass; the distances between them have shriveled; they shine, they evolve at a strangely reduced rate.

Yet the picture is more complicated even than this. You must bear in mind that the ship has, in fact, been accelerated and will be decelerated in relation to the total background of the cosmos. This takes the whole problem out of special and into general relativity. The star-and-ship situation is not really symmetrical. The twin paradox does not arise. When velocities match once more and reunion takes place, the star will have passed through a longer time than the ship did.

If you ran tau down to one one-hundredth and went into free fall, you would cross a light-century in a single year of your own experience. (Though, of course, you could never regain the century that had passed at home, during which your friends grew old and died.) This would inevitably involve a hundredfold increase of mass. A Bussard engine, drawing on the hydrogen of space, could supply that. Indeed, it would be foolish to stop the engine and coast when you could go right on decreasing your tau.

Therefore, to reach other suns in a reasonable portion of your life expectancy: Accelerate continuously, right up to the interstellar midpoint, at which point you activate the decelerator system in the Bussard module and start slowing down again. You are limited by the speed of light, which you can never quite reach. But you are not limited in how close you can approach that speed. And thus you have no limit on your inverse tau factor.

Throughout her year at one gravity, the differences between Leonora Christine and the slow-moving stars had accumulated imperceptibly. Now the curve entered upon the steep part of its climb. Now, more and more, her folk measured the distance to their goal as shrinking, not simply because they traveled, but because, for them, the geometry of space was changing. More and more, they perceived natural processes in the outside universe as speeding up.

It was not yet spectacular. Indeed, the minimum tau in her flight plan, at midpoint, was to be somewhat above 0.015. But an instant came when a minute aboard her corresponded to sixty-one seconds in the rest of the galaxy. A while later, it corresponded to sixty-two. Then sixty-three … sixty-four … the ship time between such counts grew gradually but steadily less … sixty-five … sixty-six … sixty-seven…

The first Christmas — Chanukah, New Year’s, solstice festival season — that the crew spent together had come early in their voyage and was a feverish carnival. The second was quieter. People were settling down to their work and their fellows. Nevertheless, improvised ornaments glittered on all decks. The hobby rooms resounded, the scissors and needles clicked, the galley grew fragrant with spice, as everybody tried to make small gifts for everybody else. The hydroponics division found it could spare enough green vines and branches for an imitation tree in the gymnasium. From the enormous microtape library came films of snow and sleighs, recordings of carols. The thespian contingent rehearsed a pageant. Chef Carducci planned banquets. Commons and cabins rollicked with parties. By tacit agreement, no one mentioned that each second which passed laid Earth three hundred thousand kilometers farther behind.

Reymont made his way through a bustling recreation level. Some groups were stringing up the most newly made decorations. Nothing could be wasted, but aluminum-foil chains, blown-glass globes, wreaths twisted from bolts of cloth, were reclaimable. Others played games, chattered, offered drinks around, flirted, got boisterous. Through the chatter and laughter and shuffling, hum and crackle and rustle, music floated out of a loudspeaker:

Iwamoto Tetsuo, Hussein Sadek, Yeshu ben-Zvi, Mohandas Chidambaran, Phra Takh, or Kato M’Botu seemed to belong with it as much as Olga Sobieski or Johann Freiwald.

The machinist bellowed at Reymont: “ Guten Tag, mein lieber Schutzmann! Come share my bottle!” He waved it in the air. His free arm was around Margarita Jimenes. Suspended above them was a slip of paper on which had been printed MISTLETOE.

Reymont halted. He got along well with Freiwald. “Thank you, no,” he said. “Have you seen Boris Fedoroff? I expected him to come here when he got off work.”

“N-no. I would expect it too, as lively as things are tonight. He’s become a lot happier lately for some reason, hasn’t he? What do you want of him?”

“Business matter.”

“Business, forever business,” Freiwald said. “I swear your personal amusement is fretting. Me, I’ve got a better one.” He hugged Jimenes to him. She snuggled. “Have you called his cabin?”

“Naturally. No response. Still, maybe—” Reymont turned. “I’ll try there. Later I’ll come back for that schnapps,” he added, already leaving.

He took the stairs down past crew level to the officers’ deck. The music followed. “— Iesu, tibi sit gloria. ” The passageway was deserted. He pushed Fedoroff’s chime button.

The engineer opened the door. He was clad in lounging pajamas. Behind him, a bottle of French wine, two glasses, and some Danish-style sandwiches waited on the dresser top. Surprise jarred him. He took a backward step. “ Chto — you?”

“Could I speak with you?”

“Um-m-m.” Fedoroff’s glance flickered. “I expect a guest.”

Reymont grinned. “That’s obvious. Don’t worry, I won’t linger. But this is rather urgent.”

Fedoroff bridled. “It cannot wait until I am on duty?”

“The thing is, it had better be discussed confidentially,” Reymont said. “Captain Telander agrees.” He slipped around Fedoroff, into the cabin. “An item was overlooked in the plans,” he went on, speaking fast. “Our schedule has us changing over to high-acceleration mode on the seventh of January. You know better than I how that takes two or three days of preliminary work by your gang and considerable upsetting of everybody else’s routine. Well, somehow the flight planners forgot that the sixth is important in West European tradition. Twelfth Night, the Eve of the Three Holy Kings, call it what you will, it climaxes the merrymaking part of the holidays. Last year celebrations were so riotous that nobody thought about it. But I learn that this year a final feast and dance, with the old rituals, is being talked of, as something that would be pleasant if only it were possible. Think what such a reminder of our origins can do to help morale. The skipper and I wish you’d check the feasibility of postponing high acceleration a few days.”