“You have time for it, too,” he pointed out, bolder. “Okay, if you don’t want a cocktail, what about a cup of coffee? Maybe a stroll through the gardens— Look, I don’t aim to make a pass. I’d just like to get better acquainted.”

She swallowed before she smiled, but then she gave him warmth. “Very well, Norbert. I would like that myself.”

* * *

A year after she started, Leonora Christine was close to her ultimate velocity. It would take her thirty-one years to cross interstellar space, and one year more to decelerate as she approached her target sun.

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=mc².

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.