“Yes, although it’s a strange thing to say about a process that has taken so much brain power.”
“Tell me more about the ten dimensions,” Galileo requested. “Something more than their math. What do they mean? What can they mean?”
Aurora flew next to him, so closely that he felt they were intertwined. He dipped and turned, dropped or soared, stooped or gyred, always trying to stay next to her, and he found that she could make writing appear as clouds, or red ingots in the air before him. His body was a flock of bannering thoughts, flying around her in a dance. The landscape under them was a mountain range made of symbols and numbers piled one on the next, gnarled tectonically.
“Recall the Euclidean space that you know and sense,” she said, “having the three dimensions of length, breadth, and height. With Newton we added a different kind of dimension, which is time—”
“But I did that!” Galileo objected again. “Falling things accelerate as a square of the time passed! This I found out, and it meant time and space were bound together somehow.” Although, he recalled uneasily, the finding lay still unpublished, buried in his folios out in the workshop.
“All right, call it Galilean space,” Aurora said easily. “Whatever you call it, these four dimensions were understood as if they were an absolute, an underlying invisible gridwork through which physical phenomena moved. That’s when you have Laplace declaring that with a sufficient physics and database you could predict the entire past and future of the universe just by entering the numbers for the current moment, and running them through the equations either forward or back, as in an astrolabe. It was a thought experiment only, because no one would ever have the data set to do it. But the implication was that God, or something like it, could do it.”
“Yes. I can see that.”
“It implied a predetermined, clockwork universe that many found depressing to contemplate. We weren’t really choosing to do anything.”
“Yes. But your quantum mechanics destroyed all that.”
“Precisely.”
“Or imprecisely.”
“Ha, yes. With relativity and quantum mechanics we began to understand that the four dimensions we sense are artifacts of our perception of dimensions far more numerous than we knew. We began to see things that made it clear four dimensions were not adequate to explain what was happening. Baryons rotated 720 degrees before returning to their starting positions. Particles and waves both were confirmed even though they contradicted each other as explanations, as far as our senses and reason were concerned. In some cases our observations seemed necessary to make things exist at all. And something otherwise undetectable was exerting very marked gravitational effects, that if caused by a mass would outmass the visible matter of the universe ten to one. Then there appeared to be a kind of reverse gravity effect as well, an inexplicable accelerating expansion of space. People spoke of dark matter and dark energy, but these were names only—names that left the mysteries untouched. What they were was better explained by the existence of extra dimensions, first suggested by Kaluza and Klein, and then put to use by Bao.”
Galileo said, “Explain them to me.”
He felt himself become equations in the clouds inside him. Formulas described the motions of the minims, vibrating at the Planck distance and duration, thus small and brief beyond telling, and vibrating in ten different dimensions, which combined into what Bao called manifolds, each with its own qualities and characteristic actions.
“Investigations have by now found evidence for all ten dimensions,” Aurora said. “Even confirmation. The best way to conceptualize some of the extra ones is to imagine them enfolded or implicate in the dimensions we sense.” A long, flat red sheet appeared before him; it rolled lengthwise into a long thin tube. “Seen in two dimensions this looks like a ribbon, but in three dimensions it’s obviously a tube. It’s like that all through the manifolds. Dark matter has to be very weakly interacting but at the same time registering gravitationally at ten times the mass of all visible matter. That is an odd combination, but Bao considered it as a dimension we only were seeing part of, a hyperdimension or manifold that enfolds our dimensions. That manifold happens to be contracting, you could say, which gives the effect in our sensible universe of the extra gravity we detect. So that’s dimension four.”
“I thought you said time was the fourth dimension,” Galileo said.
“No. For one thing, what we call time turns out to be not a dimension but a manifold, a compound vector of three different dimensions. But put that aside for a second, and let’s finish with the spatial manifold. Dimension four we still call dark matter, as a gesture to our first awareness of it.”
“Four,” Galileo repeated.
“Yes, and dimension five in some ways counterbalances the action of four, as it is the perceived accelerating expansion of space-time. Aspects of this dimension are called dark energy.”
“Do these dimensions pass through each other, then?”
“Do length and breadth and height pass through each other?”
“I don’t know. Maybe they do.”
“Maybe the question as formulated does not have an answer, or maybe the answer is simply yes. Reality is composed of all the dimensions or manifolds, compounded or coexisting in the same universe.”
“All right.”
“Now let us come to time. Mysterious from the start, it seems mostly absent from our perception, but crucial as well. Past, present, and future are the aspects of time commonly spoken of as perceived by us, but they and other phenomena are the result of sense impressions compiled by living in three different temporal dimensions, which together make the manifold, in the same way our impression of space is a manifold. All three temporal dimensions impact on us even though we mostly have a very strong sense of moving forward in a manifold, so that we can only remember the past, and only anticipate the future, both of which remain inaccessible to us in any sensory way. Our senses are stuck in the present, which appears to move in only one direction—into the future, which does not yet exist, leaving behind the past, which exists only in memory but not in reality.
“But that present moment: how long is it, of what does it consist? How can it be as short as a single Planck interval, 1043 of a second, while even the briefest of phenomena that we are aware of takes much longer to happen than that theoretical minim? What can the present be? Is it a succession of Planck intervals, a clutch of them? Is it even real?”
“God knows,” Galileo said. “I count it in heartbeats. The beat of the moment is my present, I pray.”
“That’s a long durée, in effect. Well, look at Bao’s temporal equations, and see how neatly every present that we sense, like your long durée of a heartbeat, gets explained.”
They flew into something like a cathedral, or an immense snowflake, made of intersecting numbers and figures: a lacing of equations, the details of which now completely escaped Galileo. He tried to hold to the architectural shapes they made, but he was no longer following the math.
“Her equations postulate a temporal manifold made of three dimensions, so that what we sense as time passing, what we call time, is a compound with a vector made up of the three temporalities. We can see it here, in something like a Feynman drawing for elementary particles. Indeed we can fly in the drawing, see? The first temporality moves very fast—at the speed of light, in fact. This explains the speed of light, which is simply the rate of movement in this dimension if you consider it as a space. We call that time therefore speed of light time, or c time, from the old notation for the speed of light.”