Sfera
by Michael Crichton
(*)(*)(*)(*)( )(1,897)
A trecento metri di profondità, su un fondale del Pacifico meridionale, viene individuata un'enomre macchina. Sul luogo è immediatamente convocata un'équipe di scienziati, che è fatta discendere nelle profondità dell'oceano per studiare quella presenza enigmatica: una nave spaziale di dimensioni ina... More

All Quotations

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Ashwin NanjappaAshwin Nanjappa added a quotation
10
"Ted, remember back on the ship, when you said space and time are aspects of the same thing?"

"Space-time, yes."

"I’ve never really understood that."

"Why? It’s quite straightforward."

"You can explain it to me?"

"Sure."

"In English?" Norman said.

"You mean, explain it without mathematics?"

"Yes."

"Well, I’ll try." Ted frowned, but Norman knew he was pleased; Ted loved to lecture. He paused for a moment, then said, "Okay. Let’s see where we need to begin. You’re familiar with the idea that gravity is just geometry?"

"No."

"Curvature of space and time?"

"Not really, no."

"Uh. Einstein’s general relativity?"

"Sorry," Norman said.

"Never mind," Ted said. There was a bowl of fruit on the table. Ted emptied the bowl, setting the fruit on the table.

"Okay. This table is space. Nice, flat space."

"Okay," Norman said.

Ted began to position the pieces of fruit. "This orange is the sun. And these are the planets, which move in circles around the sun. So we have the solar system on this table."

"Okay."

"Fine," Ted said. "Now, the sun"—he pointed to the orange in the center of the table—"is very large, so it has a lot of gravity."

"Right."

Ted gave Norman a ball bearing. "This is a spaceship. I want you to send it through the solar system, so it passes very close to the sun. Okay?"

Norman took the ball bearing and rolled it so it passed close to the orange. "Okay."

"You notice that your ball rolled straight across the flat table."

"Right."

"But in real life, what would happen to your spacecraft when it passed near the sun?"

"It would get sucked into the sun."

"Yes. We say it would ‘fall into’ the sun. The spacecraft would curve inward from a straight line and hit the sun. But your spacecraft didn’t."

"No.

"So we know that the flat table is wrong," Ted said. "Real space can’t be flat like the table."

"It can’t?"

"No," Ted said.

He took the empty bowl and set the orange in the bottom. "Now roll your ball straight across past the sun."

Norman flicked the ball bearing into the bowl. The ball curved, and spiralled down the inside of the bowl until it hit the orange.

"Okay," Ted said. "The spacecraft hit the sun, just like it would in real life."

"But if I gave it enough speed," Norman said, "it’d go right past it. It’d roll down and up the far side of the bowl and out again."

"Correct," Ted said. "Also like real life. If the spacecraft has enough velocity, it will escape the gravitational field of the sun."

"Right."

"So," Ted said, "what we are showing is that a spacecraft passing the sun in real life behaves as if it were entering a curved region of space around the sun. Space around the sun is curved like this bowl."

"Okay…"

"And if your ball had the right speed, it wouldn’t escape from the bowl, but instead would just spiral around endlessly inside the rim of the bowl. And that’s what the planets are doing. They are endlessly spiralling inside the bowl created by the sun."

He put the orange back on the table. "In reality, you should imagine the table is made out of rubber and the planets are all making dents in the rubber as they sit there. That’s what space is really like. Real space is curved-and the curvature changes with the amount of gravity."

"Yes…"

"So," Ted said, "space is curved by gravity."

"Okay."

"And that means that you can think of gravity as nothing more than the curvature of space. The Earth has gravity because the Earth curves the space around it."

"Okay."

"Except it’s not that simple," Ted said.

Norman sighed. "I didn’t think it would be."

[...]

"Now," Ted said, "when you roll your ball bearing across the bowl, you notice that it not only spirals down, but it also goes faster, right?"

"Yes."

"Now, when an object goes faster, time on that object passes slower. Einstein proved that early in the century. What it means is that you can think of the curvature of space as also representing a curvature of time. The deeper the curve in the bowl, the slower time passes."

[...]

Ted held up the bowl. "Now, if you’re doing all this mathematically, what you find is that the curved bowl is neither space nor time, but the combination of both, which is called space-time. This bowl is space-time, and objects moving on it are moving in space-time. We don’t think about movement that way, but that’s really what’s happening."

"It is?"

"Sure. Take baseball."

[...]

"Okay. Imagine the batter hits a line drive to the center fielder. The ball goes almost straight out and takes, say, half a second."

"Right."

"Now imagine the batter hits a high pop fly to the same center fielder. This time the ball goes way up in the air, and it takes six seconds before the center fielder catches it."

"Okay."

"Now, the paths of the two balls—the line drive and the pop fly—look very different to us. But both these balls moved exactly the same in space-time."

"No," Norman said.

"Yes," Ted said. "And in a way, you already know it. Suppose I ask you to hit a high pop fly to the center fielder, but to make it reach the fielder in half a second instead of six seconds."

"That’s impossible," Norman said.

"Why? Just hit the pop fly harder."

"If I hit it harder, it will go higher and end up taking longer."

"Okay, then hit a low line drive that takes six seconds to reach center field."

"I can’t do that, either."

"Right," Ted said. "So what you are telling me is that you can’t make the ball do anything you want. There is a fixed relationship governing the path of the ball through space and time."

"Sure. Because the Earth has gravity."

"Yes," Ted said, "and we’ve already agreed that gravity is a curvature of space-time, like the curve of this bowl. Any baseball on Earth must move along the same curve of space-time, as this ball bearing moves along this bowl. Look." He put the orange back in the bowl. "Here’s the Earth." He put two fingers on opposite sides of the orange. "Here’s batter and fielder. Now, roll the ball bearing from one finger to the other, and you’ll find you have to accommodate the curve of the bowl. Either you flick the ball lightly and it will roll close to the orange, or you can give it a big flick and it will go way up the side of the bowl, before falling down again to the other side. But you can’t make this ball bearing do anything you want, because the ball bearing is moving along the curved bowl. And that’s what your baseball is really doing—it’s moving on curved space-time."

Norman said, "I sort of get it. But what does this have to do with time travel?"

"Well, we think the gravitational field of the Earth is strong—it hurts us when we fall down—but in reality it’s very weak. It’s almost nonexistent. So space-time around the Earth isn’t very curved. Space-time is much more curved around the sun. And in other parts of the universe, it’s very curved, producing a sort of roller-coaster ride, and all sorts of distortions of time may occur. In fact, if you consider a black hole—"

He broke off.

"Yes, Ted? A black hole?"

"Oh my God," Ted said softly.

Ashwin NanjappaAshwin Nanjappa added a quotation
10
"Ted, remember back on the ship, when you said space and time are aspects of the same thing?"

"Space-time, yes."

"I’ve never really understood that."

"Why? It’s quite straightforward."

"You can explain it to me?"

"Sure."

"In English?" Norman said.

"You mean,

... More