"I have an idea of my own about the reason why Kaluza was particularly attracted to the Einstein theory. I think it might have been because he knew that Einstein, too, had started out as a privatdocent, and look where the man was now! Anyway, Kaluza tried to figure out just how Einstein's relativity theory worked when expressed in formal mathematical terms.
"It seemed to him that it worked best if you brought in some extra dimensions.
"With all his best efforts, it didn't work as well as he might have hoped, though. The equations wouldn't quite balance. What Kaluza didn't know was that there was a flaw in his theorizing. The place where he went wrong was that all of Kaluza's ideas had been unquestioningly based on the classical view of the universe.
"You can't blame him for that—after all, so were Einstein's! But, as time went on and scientists began to get a better handle on what 'reality' was like, it became obvious that the classical view was wrong somewhere.
"For instance, take the way light is generated by electrons changing orbit within an atom. That was an observable fact, but the classical theories about it didn't square with the observations. Classical theory said white light should be emitted—a mixture of all colors, all across the rainbow, uniting to form what we perceive to be Svhite.' It didn't happen that way, though. Each excited atom produced its own specific colors— you know that's true if you remember that that's basically how we can tell what elements are in a star, when we turn the spectroscope on it, by the particular colors associated with each excited atom.
"Then along came quantum mechanics.
"Quantum theory told us that electrons couldn't revolve in just any old orbits. There were certain forbidden orbits, and the electrons were restricted only to the permissible ones. Then it all began to make sense, and it became possible to understand why sodium atoms, for instance, radiated only yellow light instead of all the colors of the rainbow mixed together as white.
"So, as quantum mechanics got popular, a Swede named Oskar Klein tried putting Kaluza's ideas of extra dimensions in quantum mechanical form . . . and, voila, the Kaluza-Klein theories were born. About a million theorists have been playing with them ever since.
"That's what a Kaluza-Klein theory is. It is a quantum mechanical theory which invokes extra spatial dimensions to explain the relations among particles and forces. In a Kaluza-Klein theory there aren't any zero-dimensional points. Each 'point' that we perceive as a simple location, without extension in any direction at all, is actually something that we might try to visualize as a litde circle; and the circle goes in other dimensions.
"How many dimensions are involved?
"Ah, well, let's not limit ourselves here. We don't quite know how many we have to have. There are some theories which require twenty-six spatial dimensions to work. They don't all need that many. Kaluza himself only needed four spatial dimensions—plus the dimension of time, making his formulation five-dimensional in all.
"Personally, I like the ones that have nine spatial dimensions—plus time, making ten spacetime dimensions in all— but a lot of people who are just as intelligent as I am—well, almost, anyway—prefer eleven. So take your pick. There isn't any right answer—or, anyway, if there is one, no one knows what it is. So you don't have to worry. I promise that you'll never get that question on any quiz from me."
To all of that the aiodoi listened, tenderly amused; but there was one aiodos who sang strongly of something else: "The song of elsewhere is a good song. "But for those who live in no elsewhere, "There is an elsewhere that can do harm. "And we are part of their elsewhere." And the rest of the aiodoi were troubled as they sang.
14
What was certain was that the voyage to that pale, distant Turtle beacon was going to be a long one. A day or two at least, Krake told Sue-ling, and did not dare to tell her how many years of "imaginary" time those days would encompass.
Now that there was time to spare, Krake took up some unfinished business. He had not forgiven Thrayl—or Thrayl's mistress. Although he tried to keep his tone level, there was an edge to it as he turned to Moon Bunderan. "Now I want you to answer some questions for me. Why did you let that animal keep me from saving us?"
The Taur only gazed gently at him. Moon said staunchly: "Thrayl had a reason. Thrayl always has a good reason for everything he does, only he can't always explain what they are."
"Good reason! What good reason could he have for risking my ship—not to mention all our lives?"
"Do not address this Taur in that fashion," Chief Thunderbird said severely.
"If it were not for the Taur," Litlun seconded, "we would not have found the trail of the Mother planet. One knew one was right to bring the Taur along. It is proper to praise him now."
Sue-ling blinked at the Turtles. Something was going on that she had not expected—and something that Chief Thunderbird was finding interesting, too, because she saw one of the huge Turtle's eyes slowly revolve to fix on his Younger Brother. Krake, however, was not interested in subtleties. He opened his mouth to address them, but was distracted by what he saw behind them. He craned his neck to see Daisy Fay, seated at the control board and looking agitated.
"What's the matter?" he demanded.
The machine-woman waved a few tentacles at the display. "I don't know, Francis. What do you make of this?"
The captain pushed his way between the giant Turtles to bend over her. "What is it?"
Daisy Fay stabbed out with three or four arms, pointing to several different readings on the chart. "I'm trying to establish reference points, Francis—you know, distant galaxies to use as benchmarks, to compare nearer stars with. But they—"
"Foolish human woman!" Chief Thunderbird snarled. "Why do you bother with such things? It is the sacred Mother planet you should be seeking!"
"I know, but—"
"Do not dispute!" the Turde said peremptorily. "It is simple! You must find a single planet. It cannot be far from the wormhole."
"And you must find it quickly," Litlun put in, shivering with a sudden thought, "because if the planet came through by itself it is in terrible danger—it has lost its sun! No radiation to feed the Mother and her young!"
Krake looked at him sourly. "With all the radiation from all those stars? Anyway, there's nothing like a solitary planet in the range of our instruments," he told them, his face drawn.
"And look at what Daisy Fay has discovered. Those benchmark galaxies? The navigation instruments have been marking them, and do you see what the frequency analyzers say? Each one of them is shifted into the blue."
There was total silence from everyone in the chamber. Moon dared to break it. "I don't understand. What difference does it make what color a distant galaxy is?"
"It means," Sork said hollowly, "that this is a dying universe. The blue-shift means it is not expanding; it is collapsing."
Captain Krake said tightly, "Worse than that. This whole space is flooded with dangerous radiation."
Sue-ling watched the captain critically as he tried to control himself—there was a good chance of a cerebrovascular accident there, she thought, if he didn't calm down. She put her hand on his arm in sympathy, but he seemed not to notice.
"We of the Brotherhood do not fear this," Chief Thunderbird said in contempt.
"But we do! It would kill us. If those old lectures mean anything, this whole universe is collapsing, and as it does it is heating up, producing more and more radiation—"
Chief Thunderbird turned both burning eyes on Captain Krake. "Weak wet things," he said, dismissing them. "That is of no importance. We will not stay here for billions of years, to watch it contract to the single point again, as your legends would have it. We will not be here any longer than we must to find the Mother planet!"