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Gisela was contemplating the advantages of being crushed–almost
certainly to death, albeit as slowly as possible–when the messenger
appeared in her homescape. She noted its presence but instructed
it to wait, a sleek golden courier with winged sandals stretching
out a hand impatiently, frozen in mid-stride twenty delta away.
The scape was currently an expanse of yellow dunes beneath a pale
blue sky, neither too stark nor too distracting. Gisela, reclining
on the cool sand, was intent on a giant, scruffy triangle hovering
at an incline over the dunes, each edge resembling a loose bundle
of straw. The triangle was a collection of Feynman diagrams, showing
just a few of the many ways a particle could move between three
events in spacetime. A quantum particle could not be pinned down
to any one path, but it could be treated as a sum of localized
components, each following a different trajectory and taking part
in a different set of interactions along the way.
In "empty" spacetime, interactions with virtual particles caused
each component’s phase to rotate constantly, like the hand of
a clock. But the time measured by any kind of clock traveling
between two events in flat spacetime was greatest when the route
taken was a straight line–any detours caused time dilation, shortening
the trip–and so a plot of phase shift versus detour size also
reached its peak for a straight line. Since this peak was smooth
and flat, a group of nearly straight paths clustered around it
all had similar phase shifts, and these paths allowed many more
components to arrive in phase with each other, reinforcing each
other, than any equivalent group on the slopes. Three straight
lines, glowing red through the center of each "bundle of straw,"
illustrated the result: the classical paths, the paths of highest
probability, were straight lines.
In the presence of matter, all the same processes became slightly
skewed. Gisela added a couple of nanograms of lead to the model–a
few trillion atoms, their world lines running vertically through
the center of the triangle, sprouting their own thicket of virtual
particles. Atoms were neutral in charge and color, but their individual
electrons and quarks still scattered virtual photons and gluons.
Every kind of matter interfered with some part of the virtual
swarm, and the initial disturbance spread out through spacetime
by scattering virtual particles itself, rapidly obliterating any
difference between the effect of a ton of rock or a ton of neutrinos,
growing weaker with distance according to a roughly inverse square
law. With the rain of virtual particles–and the phase shifts they
created–varying from place to place, the paths of highest probability
ceased obeying the geometry of flat spacetime. The luminous red
triangle of most-probable trajectories was now visibly curved.
The key idea dated back to Sakharov: gravity was nothing but the
residue of the imperfect cancellation of other forces; squeeze
the quantum vacuum hard enough and Einstein’s equations fell out.
But since Einstein, every theory of gravity was also a theory
of time. Relativity demanded that a free-falling particle’s rotating
phase agree with every other clock that traveled the same path,
and once gravitational time dilation was linked to changes in
virtual particle density, every measure of time–from the half-life
of a radioisotope’s decay (stimulated by vacuum fluctuations)
to the vibrational modes of a sliver of quartz (ultimately due
to the same phase effects as those giving rise to classical paths)–could
be reinterpreted as a count of interactions with virtual particles.
It was this line of reasoning that had led Kumar–a century after
Sakharov, building on work by Penrose, Smolin, and Rovelli–to
devise a model of spacetime as a quantum sum of every possible
network of particle world lines, with classical "time" arising
from the number of intersections along a given strand of the net.
This model had been an unqualified success, surviving theoretical
scrutiny and experimental tests for centuries. But it had never
been validated at the smallest length scales, accessible only
at absurdly high energies, and it made no attempt to explain the
basic structure of the nets, or the rules that governed them.
Gisela wanted to know where those details came from. She wanted
to understand the universe at its deepest level, to touch the
beauty and simplicity that lay beneath it all.
That was why she was taking the Planck Dive.
The messenger caught her eye again. It was radiating tags indicating
that it represented Cartan’s mayor: non-sentient software that
dealt with the maintenance of good relations with other polises,
observing formal niceties and smoothing away minor points of conflict
in those cases where no real citizen-to-citizen connections existed.
Since Cartan had been in orbit around Chandrasekhar, ninety-seven
light years from Earth, for almost three centuries–and was currently
even further from all the other spacefaring polises–Gisela was
at a loss to imagine what urgent diplomatic tasks the mayor could
be engaged in, let alone why it would want to consult her.
She sent the messenger an activation tag. Deferring to the scape’s
aesthetic of continuity, it sprinted across the dunes, coming
to a halt in front of her in a cloud of fine dust. "We’re in the
process of receiving two visitors from Earth."
Gisela was astonished. "Earth? Which polis?"
"Athena. The first one has just arrived; the second will be in
transit for another ninety minutes."
Gisela had never heard of Athena, but ninety minutes per person
sounded ominous. Everything meaningful about an individual citizen
could be packed into less than an exabyte, and sent as a gamma-ray
burst a few milliseconds long. If you wanted to simulate an entire
flesher body–cell by cell, redundant viscera and all–that was
a harmless enough eccentricity, but lugging the microscopic details
of your "very own" small intestine ninety-seven light-years was
just being precious.
"What do you know about Athena? In brief."
"It was founded in 2312, with a charter expressing the goal of
‘regaining the lost flesher virtues.’ In public fora, its citizens
have shown little interest in exopolitan reality–other than flesher
history and artforms–but they do participate in some contemporary
interpolis cultural activities."
"So why have these two come here?" Gisela laughed. "If they’re
refugees from boredom, surely they could have sought asylum a
little closer to home?"
The mayor took her literally. "They haven’t adopted Cartan citizenship;
they’ve entered the polis with only visitor privileges. In their
transmission preamble they stated that their purpose in coming
was to witness the Planck Dive."
"Witness–not take part in?"
"That’s what they said."
They could have witnessed as much from home as any non-participant
here in Cartan. The Dive team had been broadcasting everything–studies,
schematics, simulations, technical arguments, metaphysical debates–from
the moment the idea had coalesced out of little more than jokes
and thought experiments, a few years after they’d gone into orbit
around the black hole. But at least Gisela now knew why the mayor
had picked on her; she’d volunteered to respond to any requests
for information about the Dive that couldn’t be answered automatically
from public sources. No one seemed to have found their reports
to be lacking a single worthwhile detail, though, until now.
"So the first one’s suspended?"
"No. She woke as soon as she arrived."
That seemed even stranger than their excess baggage. If you were
traveling with someone, why not delay activation until your companion
caught up? Or better yet, package yourselves as interleaved bits?
"But she’s still in the arrival lounge?"
"Yes."
Gisela hesitated. "Shouldn’t I wait until the other one’s all
here? So I can greet them together?"
"No." The mayor seemed confident on this point. Gisela wished
interpolis protocol allowed non-sentient software to play host;
she felt woefully ill-prepared for the role herself. But if she
started consulting people, seeking advice, and looking into Athena’s
culture in depth, the visitors would probably have toured Cartan
and gone home before she was ready for them.
She steeled herself, and jumped.
The last person who’d whimsically redesigned the arrival lounge
had made it a wooden pier surrounded by gray, windswept ocean.
The first of the two visitors was still standing patiently at
the end of the pier, which was just as well; it was unbounded
in the other direction, and walking a few kilodelta to no avail
might have been a bit dispiriting. Her fellow traveler, still
in transit, was represented by a motionless placeholder. Both
icons were highly anatomical-realist, clothed but clearly male
and female, the unfrozen female much younger-looking. Gisela’s
own icon was more stylized, and her surface, whether "skin" or
"clothing"–either could gain a tactile sense if she wished–was
textured with diffuse reflection rules not quite matching the
optical properties of any real substance.
"Welcome to Cartan. I’m Gisela." She stretched out her hand, and
the visitor stepped forward and shook it–though it was possible
that she perceived and executed an entirely different act, cross-translated
through gestural interlingua.
"I’m Cordelia. This is my father, Prospero. We’ve come all the
way from Earth." She seemed slightly dazed, a response Gisela
found entirely reasonable. Back in Athena, whatever elaborate
metaphoric action they’d used to instruct the communications software
to halt them, append suitable explanatory headers and checksums,
then turn the whole package bit-by-bit into a stream of modulated
gamma rays, it could never have fully prepared them for the fact
that in a subjective instant they’d be stepping ninety-seven years
into the future, and ninety-seven light-years from home.
"You’re here to observe the Planck Dive?" Gisela chose to betray
no hint of puzzlement; it would have been pointlessly cruel to
drive home the fact that they could have seen everything from
Athena. Even if you fetishized realtime data over lightspeed transmissions,
it could hardly be worth slipping one-hundred-and-ninety-four
years out of synch with your fellow citizens.
Cordelia nodded shyly, and glanced at the statue beside her. "My
father, really . . ."
Meaning what? It was all his idea? Gisela smiled encouragingly,
hoping for clarification, but none was forthcoming. She’d been
wondering why a Prospero had named his daughter Cordelia, but
now it struck her as only prudent–if you had to succumb to a Shakespearean
names fad at all–not to put anyone from the same play together
in one family.
"Would you like to look around? While you’re waiting for him?"
Cordelia stared at her feet, as if the question was profoundly
embarrassing.
"It’s up to you." Gisela laughed. "I have no idea what constitutes
the polite treatment of half-delivered relatives." It was unlikely
that Cordelia did, either; citizens of Athena clearly didn’t make
a habit of crossing interstellar distances, and the connections
on Earth all had so much bandwidth that the issue would never
arise. "But if it was me in transit, I wouldn’t mind at all."
Cordelia hesitated. "Could I see the black hole, please?"
"Of course." Chandrasekhar possessed no blazing accretion disk–it
was six billion years old, and had long ago swept the region clean
of gas and dust–but it certainly left the imprint of its presence
on the ordinary starlight around it. "I’ll give you the short
tour, and we’ll be back long before your father’s awake." Gisela
examined the bearded icon; with his gaze fixed on the horizon
and his arms at his sides, he appeared to be on the verge of bursting
into song. "Assuming he’s not running on partial data already.
I could have sworn I saw those eyes move."
Cordelia smiled slightly, then looked up and said solemnly, "That’s
not how we were packaged."
Gisela sent her an address tag. "Then he’ll be none the wiser.
Follow me."
They stood on a circular platform in empty space. Gisela had inflected
the scape’s address to give the platform "artificial gravity"–a
uniform one gee, regardless of their motion–and a transparent
dome full of air at standard temperature and pressure. Presumably
all Athena citizens were set up to ignore any scape parameters
that might cause them discomfort, but it still seemed like a good
idea to err on the side of caution. The platform itself was a
compromise, five delta wide–offering some protection from vertigo,
but small enough to let its occupants see some forty degrees below
"horizontal."
Gisela pointed. "There it is: Chandrasekhar. Twelve solar masses.
Seventeen thousand kilometers away. It might take you a moment
to spot it; it looks about the same as the new moon from Earth."
She’d chosen their coordinates and velocity carefully; as she
spoke, a bright star split in two, then flared for a moment into
a small, perfect ring as it passed directly behind the hole. "Apart
from gravitational lensing, of course."
Cordelia smiled, obviously delighted. "Is this a real view?"
"Partly. It’s based on all the images we’ve received so far from
a whole swarm of probes–but there are still viewpoints that have
never been covered, and need to be interpolated. That includes
the fact that we’re almost certainly moving with a different velocity
than any probe that passed through the same location–so we’re
seeing things differently, with different Doppler shifts and aberration."
Cordelia absorbed this with no sign of disappointment. "Can we
go closer?"
"As close as you like."
Gisela sent control tags to the platform, and they spiraled in.
For a while it looked as if there’d be nothing more to see; the
featureless black disk ahead of them grew steadily larger, but
it clearly wasn’t going to blossom with any kind of detail. Gradually,
though, a congested halo of lensed images began to form around
it, and you didn’t need the flash of an Einstein ring to see that
light was behaving strangely.
"How far away are we now?"
"About thirty-four M." Cordelia looked uncertain. Gisela added,
"Six hundred kilometers–but if you convert mass into distance
in the natural way, that’s thirty-four times Chandrasekhar’s mass.
It’s a useful convention; if a hole has no charge or angular momentum,
its mass sets the scale for all the geometry: the event horizon
is always at two M, light forms circular orbits at three M, and
so on." She conjured up a spacetime map of the region outside
the hole, and instructed the scape to record the platform’s world
line on it. "Actual distances traveled depend on the path you
take, but if you think of the hole as being surrounded by spherical
shells on which the tidal force is constant–something tangible
you can measure on the spot–you can give them each a radius of
curvature without caring about the details of how you might travel
all the way to their center." With one spatial dimension omitted
to make room for time, the shells became circles, and their histories
on the map were shown as concentric translucent cylinders.
As the disk itself grew, the distortion around it spread faster.
By ten M, Chandrasekhar was less than sixty degrees wide, but
even constellations in the opposite half of the sky were visibly
crowded together, as incoming light rays were bent into more radial
paths. The gravitational blue shift, uniform across the sky, was
strong enough now to give the stars a savage glint–not so much
icy, as blue-hot. On the map, the light cones dotted along their
world line–structures like stylized conical hour-glasses, made
up of all the light rays passing through a given point at a given
moment–were beginning to tilt toward the hole. Light cones marked
the boundaries of physically possible motion; to cross your own
light cone would be to outrace light.
Gisela created a pair of binoculars and offered them to Cordelia.
"Try looking at the halo."
Cordelia obliged her. "Ah! Where did all those stars come from?"
"Lensing lets you see the stars behind the hole, but it doesn’t
stop there. Light that grazes the three-M shell orbits part-way
around the hole before flying off in a new direction–and there’s
no limit to how far it can swing around, if it grazes the shell
close enough." On the map, Gisela sketched half a dozen light
rays approaching the hole from various angles; after wrapping
themselves in barber’s-pole helices at slightly different distances
from the three-M cylinder, they all headed off in almost the same
direction. "If you look into the light that escapes from those
orbits, you see an image of the whole sky, compressed into a narrow
ring. And at the inner edge of that ring, there’s a smaller ring,
and so on–each made up of light that’s orbited the hole one more
time."
Cordelia pondered this for a moment. "But it can’t go on forever,
can it? Won’t diffraction effects blur the pattern, eventually?"
Gisela nodded, hiding her surprise. "Yeah. But I can’t show you
that here. This scape doesn’t run to that level of detail!"
They paused at the three-M shell itself. The sky here was perfectly
bisected: one hemisphere in absolute darkness, the other packed
with vivid blue stars. Along the border, the halo arched over
the dome like an impossibly geometricized Milky Way. Shortly after
Cartan’s arrival, Gisela had created a homage to Escher based
on this view, tiling the half-sky with interlocking constellations
that repeated at the edge in ever-smaller copies. With the binoculars
on 1000 X, they could see a kind of silhouette of the platform
itself "in the distance": a band of darkness blocking a tiny part
of the halo in every direction.
Then they continued toward the event horizon–oblivious to both
tidal forces and the thrust they would have needed to maintain
such a leisurely pace in reality.
The stars were now all brightest at ultraviolet frequencies, but
Gisela had arranged for the dome to filter out everything but
light from the flesher visible spectrum, in case Cordelia’s simulated
skin took descriptions of radiation too literally. As the entire
erstwhile celestial sphere shrank to a small disk, Chandrasekhar
seemed to wrap itself around them–and this optical illusion had
teeth. If they’d fired off a beam of light away from the hole,
but failed to aim it at that tiny blue window, it would have bent
right around like the path of a tossed rock and dived back into
the hole. No material object could do better; the choice of escape
routes was growing narrower. Gisela felt a frisson of claustrophobia;
soon she’d be doing this for real.
They paused again to hover–implausibly–just above the horizon,
with the only illumination a pin-prick of heavily blue-shifted
radio waves behind them. On the map, their future light cone led
almost entirely into the hole, with just the tiniest sliver protruding
from the two-M cylinder. Gisela said, "Shall we go through?"
Cordelia’s face was etched in violet. "How?"
"Pure simulation. As authentic as possible . . . but not so authentic
that we’ll be trapped, I promise."
Cordelia spread her arms, closed her eyes, and mimed falling backward
into the hole. Gisela instructed the platform to cross the horizon.
The speck of sky blinked out, then began to expand again, rapidly.
Gisela was slowing down time a millionfold; in reality they would
have reached the singularity in a fraction of a millisecond.
Cordelia said, "Can we stop here?"
"You mean freeze time?"
"No, just hover."
"We’re doing that already. We’re not moving." Gisela suspended
the scape’s evolution. "I’ve halted time; I think that’s what
you wanted."
Cordelia seemed about to dispute this, but then she gestured at
the now-frozen circle of stars. "Outside, the blue shift was the
same right across the sky . . . but now the stars at the edge
are much bluer. I don’t understand."
Gisela said, "In a way it’s nothing new; if we’d let ourselves
free-fall toward the hole, we would have been moving fast enough
to see a whole range of Doppler shifts superimposed on the gravitational
blue shift, long before we crossed the horizon. You know the starbow
effect?"
"Yes." Cordelia examined the sky again, and Gisela could almost
see her testing the explanation, imagining how a blue-shifted
starbow should look. "But that only makes sense if we’re moving–and
you said we weren’t."
"We’re not, by one perfectly good definition. But it’s not the
definition that applied outside." Gisela highlighted a vertical
section of their world line, where they’d hovered on the three-M
shell. "Outside the event horizon–given a powerful enough engine–you
can always stay fixed on a shell of constant tidal force. So it
makes sense to choose that as a definition of being ‘motionless’–making
time on this map strictly vertical. But inside the hole, that
becomes completely incompatible with experience; your light cone
tilts so far that your world line must cut through the shells. And the simplest new definition of being
‘motionless’ is to burrow straight through the shells–the complete
opposite of trying to cling to them–and to make ‘map time’ strictly
horizontal, pointing toward the center of the hole." She highlighted
a section of their now-horizontal world line.
Cordelia’s expression of puzzlement began to give way to astonishment.
"So when the light cones tip over far enough . . . the definitions
of ‘space’ and ‘time’ have to tip with them?"
"Yes! The center of the hole lies in our future, now. We won’t
hit the singularity face-first, we’ll hit it future-first–just
like hitting the Big Crunch. And the direction on this platform
that used to point toward the singularity is now facing ‘down’
on the map–into what seems from the outside to be the hole’s past,
but is really a vast stretch of space. There are billions of light-years
laid out in front of us–the entire history of the hole’s interior,
converted into space–and it’s expanding as we approach the singularity.
The only catch is, elbow room and head room are in short supply.
Not to mention time."
Cordelia stared at the map, entranced. "So the inside of the hole
isn’t a sphere at all? It’s a spherical shell in two directions,
with the shell’s history converted into space as the third . .
. making the whole thing the surface of a hypercylinder? A hypercylinder
that’s increasing in length, while its radius shrinks." Suddenly
her face lit up. "And the blue shift is like the blue shift when
the universe starts contracting?" She turned to the frozen sky.
"Except this space is only shrinking in two directions–so the
more the angle of the starlight favors those directions, the more
it’s blue-shifted?"
"That’s right." Gisela was no longer surprised by Cordelia’s rapid
uptake; the mystery was how she could have failed to learn everything
there was to know about black holes long ago. With unfettered
access to a half-decent library and rudimentary tutoring software,
she would have filled in the gaps in no time. But if her father
had dragged her all the way to Cartan just to witness the Planck
Dive, how could he have stood by and allowed Athena’s culture
to impede her education? It made no sense.
Cordelia raised the binoculars and looked sideways, around the
hole. "Why can’t I see us?"
"Good question." Gisela drew a light ray on the map, aimed sideways,
leaving the platform just after they’d crossed the horizon. "At
the three-M shell, a ray like this would have followed a helix
in spacetime, coming back to our world line after one revolution.
But here, the helix has been flipped over and squeezed into a
spiral–and at best, it only has time to travel halfway around
the hole before it hits the singularity. None of the light we’ve
emitted since crossing the horizon can make it back to us.
"That’s assuming a perfectly symmetrical Schwarzchild black hole,
which is what we’re simulating. And an ancient hole like Chandrasekhar
probably has settled down to a fair approximation of the Schwarzchild
geometry. But close to the singularity, even infalling starlight
would be blue-shifted enough to disrupt it, and anything more
massive–like us, if we really were here–would cause chaotic changes
even sooner." She instructed the scape to switch to Belinsky-Khalatnikov-Lifshitz
geometry, then restarted time. The stars began to shimmer with
distortion, as if seen through a turbulent atmosphere, then the
sky itself seemed to boil, red shifts and blue shifts sweeping
across it in churning waves. "If we were embodied, and strong
enough to survive the tidal forces, we’d feel them oscillating
wildly as we passed through regions collapsing and expanding in
different directions." She modified the spacetime map accordingly,
and enlarged it for a better view. Close to the singularity, the
once-regular cylinders of constant tidal force now disintegrated
into a random froth of ever finer, ever more distorted bubbles.
Cordelia examined the map with an expression of consternation.
"How are you going to do any kind of computation in an environment
like that?"
"We’re not. This is chaos–but chaotic systems are highly susceptible
to manipulation. You know Tiplerian theology? The doctrine that
we should try to reshape the universe to allow infinite computation
to take place before the Big Crunch?"
"Yes."
Gisela spread her arms to take in all of Chandrasekhar. "Reshaping
a black hole is easier. With a closed universe, all you can do
is rearrange what’s already there; with a black hole, you can
pour new matter and radiation in from all directions. By doing
that, we’re hoping to steer the geometry into a more orderly collapse–not
the Schwarzchild version, but one that lets light circumnavigate
the space inside the hole many times. Cartan Null will be made
of counter-rotating beams of light, modulated with pulses like
beads on a string. As they pass through each other, the pulses
will interact; they’ll be blue-shifted to energies high enough
for pair-production, and eventually even high enough for gravitational
effects. Those beams will be our memory, and their interactions
will drive all our computation–with luck, down almost to the Planck
scale: ten-to-the-minus-thirty-five meters."
Cordelia contemplated this in silence, then asked hesitantly,
"But how much computation will you be able to do?"
"In total?" Gisela shrugged. "That depends on details of the structure
of spacetime at the Planck scale–details we won’t know until we’re
inside. There are some models that would allow us to do the whole
Tiplerian thing in miniature: infinite computation. But most give
a range of finite answers, some large, some small."
Cordelia was beginning to look positively gloomy. Surely she’d
known about the Divers’ fate all along?
Gisela said, "You do realize we’re sending in clones? No one’s
moving their sole version into Cartan Null!"
"I know." Cordelia averted her eyes. "But once you are the clone . . . won’t you be afraid of dying?"
Gisela was touched. "Only slightly. And not at all, at the end.
While there’s still a slender chance of infinite computation–or
even some exotic discovery that might allow us to escape–we’ll
hang on to the fear of death. It should help motivate us to examine
all the options! But if and when it’s clear that dying is inevitable,
we’ll switch off the old instinctive response, and just accept
it."
Cordelia nodded politely, but she didn’t seem at all convinced.
If you’d been raised in a polis that celebrated "the lost flesher
virtues," this probably sounded like cheating at best, and self-mutilation
at worst.
"Can we go back now, please? My father will be awake soon."
"Of course." Gisela wanted to say something to this strange, solemn
child to put her mind at ease, but she had no idea where to begin.
So they jumped out of the scape together–out of their fictitious
light cones–abandoning the simulation before it was forced to
admit that it was offering neither the chance of new knowledge,
nor the possibility of death.
When Prospero woke, Gisela introduced herself and asked what he
wished to see. She suggested a schematic of Cartan Null; it didn’t
seem tactful to mention that Cordelia had already toured Chandrasekhar,
but offering him a scape that neither had seen seemed like a diplomatic
way of side-stepping the issue.
Prospero smiled at her indulgently. "I’m sure your Falling City
is ingeniously designed, but that’s of no interest to me. I’m
here to scrutinize your motives, not your machines."
"Our motives?" Gisela wondered if there’d been a translation error.
"We’re curious about the structure of spacetime. Why else would
someone dive into a black hole?"
Prospero’s smile broadened. "That’s what I’m here to determine.
There’s a wide range of choices besides the Pandora myth: Prometheus,
Quixote, the Grail of course . . . perhaps even Orpheus. Do you
hope to rescue the dead?"
"Rescue the dead?" Gisela was dumbfounded. "Oh, you mean Tiplerian
resurrection? No, we have no plans for that at all. Even if we
obtained infinite computing power, which is unlikely, we’d have
far too little information to recreate any specific dead fleshers.
As for resurrecting everyone by brute force, simulating every
possible conscious being . . . there’d be no sure way to screen
out in advance simulations that would experience extreme suffering–and
statistically, they’re likely to outnumber the rest by about ten
thousand to one. So the whole thing would be grossly unethical."
"We shall see." Prospero waved her objections away. "What’s important
is that I meet all of Charon’s passengers as soon as possible."
"Charon’s. . . ? You mean the Dive team?"
Prospero shook his head with an anguished expression, as if he’d
been misunderstood, but he said, "Yes, assemble your ‘Dive team.’
Let me speak to them all. I can see how badly I’m needed here!"
Gisela was more bewildered than ever. "Needed? You’re welcome
here, of course . . . but in what way are you needed?"
Cordelia reached over and tugged at her father’s arm. "Can we
wait in the castle? I’m so tired." She wouldn’t look Gisela in
the eye.
"Of course, my darling!" Prospero leant down and kissed her forehead.
He pulled a rolled-up parchment out of his robe and tossed it
into the air. It unfurled into a doorway, hovering above the ocean
beside the pier, leading into a sunlit scape. Gisela could see
vast, overgrown gardens, stone buildings, winged horses in the
air. It was a good thing they’d compressed their accommodation
more efficiently than their bodies, or they would have tied up
the gamma ray link for about a decade.
Cordelia stepped through the doorway, holding Prospero’s hand,
trying to pull him through. Trying, Gisela finally realized, to
shut him up before he could embarrass her further.
Without success. With one foot still on the pier, Prospero turned
to Gisela. "Why am I needed? I’m here to be your Homer, your Virgil,
your Dante, your Dickens! I’m here to extract the mythic essence
of this glorious, tragic endeavor! I’m here to grant you a gift
infinitely greater than the immortality you seek!"
Gisela didn’t bother pointing out, yet again, that she had every
expectation of a much shorter life inside the hole than out. "What’s
that?"
"I’m here to make you legendary!" Prospero stepped off the pier, and the doorway contracted behind
him.
Gisela stared out across the ocean, unseeing for a moment, then
sat down slowly and let her feet dangle in the icy water.
Certain things were beginning to make sense.
"Be nice," Gisela pleaded. "For Cordelia’s sake."
Timon feigned wounded puzzlement. "What makes you think I won’t
be nice? I’m always nice." He morphed briefly from his usual angular
icon–all rib-like frames and jointed rods–into a button-eyed teddy
bear.
Gisela groaned softly. "Listen. If I’m right–if she’s thinking
of migrating to Cartan–it will be the hardest decision she’s ever
had to make. If she could just walk away from Athena, she would
have done it by now–instead of going to all the trouble of making
her father believe that it was his idea to come here."
"What makes you so sure it wasn’t?"
"Prospero has no interest in reality; the only way he could have
heard of the Dive would be Cordelia bringing it to his attention.
She must have chosen Cartan because it’s far enough from Earth
to make a clean break–and the Dive gave her the excuse she needed,
a fit subject for her father’s ‘talents’ to dangle in front of
him. But until she’s ready to tell him that she’s not going back,
we mustn’t alienate him. We mustn’t make things harder for her
than they already are."
Timon rolled his eyes into his anodized skull. "All right! I’ll
play along! I suppose there is a chance you might be reading her
correctly. But if you’re mistaken . . ."
Prospero chose that moment to make his entrance, robes billowing,
daughter in tow. They were in a scape created for the occasion,
to Prospero’s specifications: a room shaped like two truncated
square pyramids joined at their bases, paneled in white, with
a twenty-M view of Chandrasekhar through a trapezoidal window.
Gisela had never seen this style before; Timon had christened
it "Athenian Astrokitsch."
The five members of the Dive team were seated around a semi-circular
table. Prospero stood before them while Gisela made the introductions:
Sachio, Tiet, Vikram, Timon. She’d spoken to them all, making
the case for Cordelia, but Timon’s half-hearted concession was
the closest thing she’d received to a guarantee. Cordelia shrank
into a corner of the room, eyes downcast.
Prospero began soberly. "For nigh on a thousand years, we, the
descendants of the flesh, have lived our lives wrapped in dreams
of heroic deeds long past. But we have dreamed in vain of a new
Odyssey to inspire us, new heroes to stand beside the old, new
ways to retell the eternal myths. Three more days, and your journey
would have been wasted, lost to us forever." He smiled proudly.
"But I have arrived in time to pluck your tale from the very jaws
of gravity!"
Tiet said, "Nothing was at risk of being lost. Information about
the Dive is being broadcast to every polis, stored in every library."
Tiet’s icon was like a supple jeweled statue carved from ebony.
Prospero waved a hand dismissively. "A stream of technical jargon.
In Athena, it might as well have been the murmuring of the waves."
Tiet raised an eyebrow. "If your vocabulary is impoverished, augment
it–don’t expect us to impoverish our own. Would you give an account
of classical Greece without mentioning the name of a single city-state?"
"No. But those are universal terms, part of our common heritage–"
"They’re terms that have no meaning outside a tiny region of space,
and a brief period of time. Unlike the terms needed to describe
the Dive, which are applicable to every quartic femtometre of
spacetime."
Prospero replied, a little stiffly, "Be that as it may, in Athena
we prefer poetry to equations. And I have come to honor your journey
in language that will resonate down the corridors of the imagination
for millennia."
Sachio said, "So you believe you’re better qualified to portray
the Dive than the participants?" Sachio appeared as an owl, perched
inside the head of a flesher-shaped wrought-iron cage full of
starlings.
"I am a narratologist."
"You have some kind of specialized training?"
Prospero nodded proudly. "Though in truth, it is a vocation. When
ancient fleshers gathered around their campfires, I was the one
telling stories long into the night, of how the gods fought among
themselves, and even mortal warriors were raised up into the sky
to make the constellations."
Timon replied, deadpan, "And I was the one sitting opposite, telling
you what a load of drivel you were spouting." Gisela was about
to turn on him, to excoriate him for breaking his promise, when
she realized that he’d spoken to her alone, routing the data outside
the scape. She shot him a poisonous glance.
Sachio’s owl blinked with puzzlement. "But you find the Dive itself
incomprehensible. So how are you suited to explain it to others?"
Prospero shook his head. "I have come to create enigmas, not explanations.
I have come to shape the story of your descent into a form that
will live on long after your libraries have turned to dust."
"Shape it how?" Vikram was as anatomically correct as a Da Vinci
sketch, when he chose to be, but he lacked the tell-tale signs
of a physiological simulation: no sweat, no dead skin, no shed
hair. "You mean change things?"
"To extract the mythic essence, mere detail must become subservient
to a deeper truth."
Timon said, "I think that was a yes."
Vikram frowned amiably. "So what exactly will you change?" He
spread his arms, and stretched them to encompass his fellow team
members. "If we’re to be improved upon, do tell us how."
Prospero said cautiously, "Five is a poor number, for a start.
Seven, perhaps, or twelve."
"Whew." Vikram grinned. "Shadowy extras only; no one’s for the
chop."
"And the name of your vessel . . ."
"Cartan Null? What’s wrong with that? Cartan was a great flesher
mathematician, who clarified the meaning and consequences of Einstein’s
work. ‘Null’ because it’s built of null geodesics: the paths followed
by light rays."
"Posterity," Prospero declared, "will like it better as ‘The Falling
City’–its essence unencumbered by your infelicitous words."
Tiet said coolly, "We named this polis after Elie Cartan. Its
clone inside Chandrasekhar will be named after Elie Cartan. If
you’re unwilling to respect that, you might as well head back
to Athena right now, because no one here is going to offer you
the slightest cooperation."
Prospero glanced at the others, possibly looking for some evidence
of dissent. Gisela had mixed feelings; Prospero’s mythopoeic babble
would not outlive the truth in the libraries, whatever he imagined,
so in a sense it hardly mattered what it contained. But if they
didn’t draw the line somewhere, she could imagine his presence
rapidly becoming unbearable.
He said, "Very well. Cartan Null. I am an artisan as well as an
artist; I can work with imperfect clay."
As the meeting broke up, Timon cornered Gisela. Before he could
start complaining, she said, "If you think three more days of
that is too awful to contemplate, imagine what it’s like for Cordelia."
Timon shook his head. "I’ll keep my word. But now that I’ve seen
what she’s up against . . . I really don’t think she’s going to
make it. If she’s been wrapped in propaganda about the golden
age of fleshers all her life, how can you expect her to see through
it? A polis like Athena forms a closed trapped memetic surface:
concentrate enough Prosperos in one place, and there’s no escape."
Gisela eyed him balefully. "She’s here, isn’t she? Don’t try telling
me that she’s bound to Athena forever, just because she was created
there. Nothing’s as simple as that. Even black holes emit Hawking
radiation."
"Hawking radiation carries no information. It’s thermal noise;
you can’t tunnel out with it." Timon swept two fingers along a
diagonal line, the gesture for "QED."
Gisela said, "It’s only a metaphor, you idiot, not an isomorphism.
If you can’t tell the difference, maybe you should fuck off to
Athena yourself."
Timon mimed pulling his hand back from something biting it, and
vanished.
Gisela looked around the empty scape, angry with herself for losing
her temper. Through the window, Chandrasekhar was calmly proceeding
to crush spacetime out of existence, as it had for the past six
billion years.
She said, "And you’d better not be right."
Fifty hours before the Dive, Vikram instructed the probes in the
lowest orbits to begin pouring nanomachines through the event
horizon. Gisela and Cordelia joined him in the control scape,
a vast hall full of maps and gadgets for manipulating the hardware
scattered around Chandrasekhar. Prospero was off interrogating
Timon, an ordeal Vikram had just been through himself. "Oedipal
urges" and "womb/vagina symbolism" had figured prominently, though
Vikram had cheerfully informed Prospero that as far as he knew,
no one in Cartan had ever shown much interest in either organ.
Gisela found herself wondering precisely how Cordelia had been
created; slavish simulations of flesher childbirth didn’t bear
thinking about.
The nanomachines comprised only a trickle of matter, a few tons
per second. Deep inside the hole, though, they’d measure the curvature
around them–observing both starlight and signals from the nanomachines
following behind–then modify their own collective mass distribution
in such a way as to steer the hole’s future geometry closer to
the target. Every deviation from free-fall meant jettisoning molecular
fragments and sacrificing chemical energy, but before they’d entirely
ripped themselves apart they’d give birth to photonic machines
tailored to do the same thing on a smaller scale.
It was impossible to know whether or not any of this was working
as planned, but a map in the scape showed the desired result.
Vikram sketched in two counter-rotating bundles of light rays.
"We can’t avoid having space collapsing in two directions and
expanding in the third–unless we poured in so much matter that
it collapsed in all three, which would be even worse. But it’s
possible to keep changing the direction of expansion, flipping
it ninety degrees again and again, evening things out. That allows
light to execute a series of complete orbits–each taking about
one hundredth the time of the previous one–and it also means there
are periods of contraction across the beams, which counteract
the de-focusing effects of the periods of expansion."
The two bundles of rays oscillated between circular and elliptical
cross-sections as the curvature stretched and squeezed them. Cordelia
created a magnifying glass and followed them "in": forward in
time, toward the singularity. She said, "If the orbital periods
form a geometric series, there’s no limit to the number of orbits
you could fit in before the singularity. And the wavelength is
blue-shifted in proportion to the size of the orbit, so diffraction
effects never take over. So what’s there to stop you doing infinite
computation?"
Vikram replied cautiously, "For a start, once colliding photons
start creating particle-antiparticle pairs, there’ll be a range
of energies for each species of particle when it will be traveling
so much slower than lightspeed that the pulses will begin to smear.
We think we’ve shaped and spaced the pulses in such a way that
all the data will survive, but it would only take one unknown
massive particle to turn the whole stream into gibberish."
Cordelia looked up at him with a hopeful expression. "What if
there are no unknown particles?"
Vikram shrugged. "In Kumar’s model, time is quantized, so the
frequency of the beams can’t keep rising without limit. And most
of the alternative theories also imply that the whole setup will
fail eventually, for one reason or another. I only hope it fails
slowly enough for us to understand why, before we’re incapable of understanding anything." He laughed.
"Don’t look so mournful! It will be like . . . the death of one
branch of a tree. And maybe we’ll gain some knowledge for a while
that we could never even glimpse, outside the hole."
"But you won’t be able to do anything with it," Cordelia protested.
"Or tell anyone."
"Ah, technology and fame." Vikram blew a raspberry. "Listen, if
my Dive clone dies learning nothing, he’ll still die happy, knowing
that I continued outside. And if he learns everything I’m hoping
he’ll learn . . . he’ll be too ecstatic to go on living." Vikram
composed his face into a picture of exaggerated earnestness, deflating
his own hyperbole, and Cordelia actually smiled. Gisela had been
beginning to wonder if morbid grief over the fate of the Divers
would be enough to put her off Cartan altogether.
Cordelia said, "What would make it worthwhile, then? What’s the
most you could hope for?"
Vikram sketched a Feynman diagram in the air between them. "If
you take spacetime for granted, rotational symmetry plus quantum
mechanics gives you a set of rules for dealing with a particle’s
spin. Penrose turned this inside out, and showed that the whole
concept of ‘the angle between two directions’ can be created from
scratch in a network of world lines, so long as they obey those
spin rules. Suppose a system of particles with a certain total
spin throws an electron to another system, and in the process
the first system’s spin decreases. If you knew the angle between
the two spin vectors, you could calculate the probability that
the second spin was increased rather than decreased . . . but
if the concept of ‘angle’ doesn’t even exist yet, you can work
backward and define it from the probability you get by looking at all the networks for
which the second spin is increased.
"Kumar and others extended this idea to cover more abstract symmetries.
From a list of rules about what constitutes a valid network, and
how to assign a phase to each one, we can now derive all known
physics. But I want to know if there’s a deeper explanation for
those rules. Are spin and the other quantum numbers truly elementary,
or are they the product of something more fundamental? And when
networks reinforce or cancel each other according to the phase
difference between them, is that something basic we just have
to accept, or is there hidden machinery beneath the mathematics?"
Timon appeared in the scape, and drew Gisela aside. "I’ve committed
a small infraction–and knowing you, you’ll find out anyway. So
this is a confession in the hope of leniency."
"What have you done?"
Timon regarded her nervously. "Prospero was rambling on about
flesher culture as the route to all knowledge." He morphed into
a perfect imitation, and replayed Prospero’s voice: "‘The key
to astronomy lies in the study of the great Egyptian astrologers,
and the heart of mathematics is revealed in the rituals of the
Pythagorean mystics . . .’"
Gisela put her face in her hands; she would have been hard-pressed
not to respond herself. "And you said–?"
"I told him that if he was ever embodied in a space suit, floating
among the stars, he ought to try sneezing on the face plate to
improve the view."
Gisela cracked up laughing. Timon asked hopefully, "Does that
mean I’m forgiven?"
"No. How did he take it?"
"Hard to tell." Timon frowned. "I’m not sure that he’s capable
of grasping insults. It would require imagining that someone could
believe that he’s less than essential to the future of civilization."
Gisela said sternly, "Two more days. Try harder."
"Try harder yourself. It’s your turn now."
"What?"
"Prospero wants to see you." Timon grinned with malicious pleasure.
"Time to have your own mythic essence extracted."
Gisela glanced toward Cordelia; she was talking animatedly with
Vikram. Athena, and Prospero, had suffocated her; it was only
away from both that she came to life. The decision to migrate
was hers alone, but Gisela would never forgive herself if she
did anything to diminish the opportunity.
Timon said, "Be nice."
The Dive team had decided against any parting of the clones; their
frozen snapshots would be incorporated into the blueprint for
Cartan Null without ever being run outside Chandrasekhar. When
Gisela had told Prospero this, he’d been appalled, but he’d cheered
up almost immediately; it left him all the more room to invent
some ritual farewell for the travelers, without being distracted
by the truth.
The whole team did gather in the control scape, though, along
with Prospero and Cordelia, and a few dozen friends. Gisela stood
apart from the crowd as Vikram counted down to the deadline. On
"ten," she instructed her exoself to clone her. On "nine," she
sent the snapshot to the address being broadcast by an icon for
the Cartan Null file–a stylized set of counter-rotating light
beams–hovering in the middle of the scape. When the tag came back
confirming the transaction, she felt a surge of loss; the Dive
was no longer part of her own linear future, even if she thought
of the clone as a component of her extended self.
Vikram shouted exuberantly, "Three! Two! One!" He picked up the
Cartan Null icon and tossed it into a map of the spacetime around
Chandrasekhar. This triggered a gamma-ray burst from the polis
to a probe with an eight-M orbit; there, the data was coded into
nanomachines designed to re-create it in active, photonic form–and
those nanomachines joined the stream cascading into the hole.
On the map, the falling icon veered into a "motionless" vertical
world line as it approached the two-M shell. Successive slices
of constant time in the static frame outside the hole never crossed
the horizon, they merely clung to it; by one definition, the nanomachines
would take forever to enter Chandrasekhar.
By another definition, the Dive was over. In their own frame,
the nanomachines would have taken less than one-and-a-half milliseconds
to fall from the probe to the horizon, and not much longer to
reach the point where Cartan Null was launched. And however much
subjective time the Divers had experienced, however much computing
had been done along the way, the entire region of space containing
Cartan Null would have been crushed into the singularity a few
microseconds later.
"If the Divers tunneled out of the hole, there’d be a paradox,
wouldn’t there?" Gisela turned; she hadn’t noticed Cordelia behind
her. "Whenever they emerged, they wouldn’t have fallen in yet–so
they could swoop down and grab the nanomachines, preventing their
own births." The idea seemed to disturb her.
Gisela said, "Only if they tunneled out close to the horizon.
If they appeared further away–say here in Cartan, right now–they’d
already be too late. The nanomachines have had too much of a head
start; the fact that they’re almost standing still in our reference
frame doesn’t make them an easy target if you’re actually chasing
after them. Even at lightspeed, nothing could catch them from
here."
Cordelia appeared to take heart from this. "So escape isn’t impossible?"
"Well . . ." Gisela thought of listing some of the other hurdles,
but then she began to wonder if the question was about something
else entirely. "No. It’s not impossible."
Cordelia gave her a conspiratorial smile. "Good."
Prospero cried out, "Gather round! Gather round now and hear The Ballad of Cartan Null!" He created a podium, rising beneath his feet. Timon sidled up
to Gisela and whispered, "If this involves a lute, I’m sending
my senses elsewhere."
It didn’t; the blank verse was delivered without musical accompaniment.
The content, though, was even worse than Gisela had feared. Prospero
had ignored everything she and the others had told him. In his
version of events, "Charon’s passengers" entered "gravity’s abyss"
for reasons he’d invented out of thin air: to escape, respectively,
a failed romance/vengeance for an unspeakable crime/the ennui
of longevity; to resurrect a lost flesher ancestor; to seek contact
with "the gods." The universal questions the Divers had actually
hoped to answer–the structure of spacetime at the Planck scale,
the underpinnings of quantum mechanics–didn’t rate a mention.
Gisela glanced at Timon, but he seemed to be taking the news that
his sole version had just fled into Chandrasekhar to avoid punishment
for an unnamed atrocity extremely well; there was disbelief on
his face, but no anger. He said softly, "This man lives in Hell.
Mucous on the face plate is all he’ll ever see."
The audience stood in silence as Prospero began to "describe"
the Dive itself. Timon stared at the floor with a bemused smile.
Tiet wore an expression of detached boredom. Vikram kept peeking
at a display behind him, to see if the faint gravitational radiation
emitted by the inflowing nanomachines was still conforming to
his predictions.
It was Sachio who finally lost control and interjected angrily,
"Cartan Null is some ghostly image of a scape, full of ghostly
icons, floating through the vacuum, down into the hole?"
Prospero seemed more startled than outraged by the interruption.
"It is a city of light. Translucent, ethereal . . ."
The owl in Sachio’s skull puffed its feathers out. "No photon
state would look like that. What you describe could never exist,
and even if it could it would never be conscious." Sachio had
worked for decades on the problem of giving Cartan Null the freedom
to process data without disrupting the geometry around it.
Prospero spread his arms in a conciliatory gesture. "An archetypal
quest narrative must be kept simple. To burden it with technicalities–"
Sachio inclined his head briefly, fingertips to forehead, downloading
information from the polis library. "Do you have any idea what
archetypal narratives are?"
"Messages from the gods, or from the depths of the soul; who can
say? But they encode the most profound and mysterious–"
Sachio cut him off impatiently. "They’re the product of a few
chance attractors in flesher neurophysiology. Whenever a more
complex or subtle story was disseminated through an oral culture,
it would eventually degenerate into an archetypal narrative. Once
writing was invented, they were only ever created deliberately
by fleshers who failed to understand what they were. If all of
antiquity’s greatest statues had been dropped into a glacier,
they would have been reduced to a predictable spectrum of spheroidal
pebbles by now; that does not make the spheroidal pebble the pinnacle
of the artform. What you’ve created is not only devoid of truth,
it’s devoid of aesthetic merit."
Prospero was stunned. He looked around the room expectantly, as
if waiting for someone to speak up in defense of the Ballad.
No one made a sound.
This was it: the end of diplomacy. Gisela spoke privately to Cordelia,
whispering urgently: "Stay in Cartan! No one can force you to
leave!"
Cordelia turned to her with an expression of open astonishment.
"But I thought–" She fell silent, reassessing something, hiding
her surprise.
Then she said, "I can’t stay."
"Why not? What is there to stop you? You can’t stay buried in Athena–"
Gisela caught herself; whatever bizarre hold the place had on
her, disparaging it wouldn’t help.
Prospero was muttering in disbelief now, "Ingratitude! Base ingratitude!"
Cordelia regarded him with forlorn affection. "He’s not ready."
She faced Gisela, and spoke plainly. "Athena won’t last forever.
Polises like that form and decay; there are too many real possibilities
for people to cling to one arbitrary sanctified culture, century
after century. But he’s not prepared for the transition; he doesn’t
even realize it’s coming. I can’t abandon him to that. He’s going
to need someone to help him through." She smiled suddenly, mischievously.
"But I’ve cut two centuries off the waiting time. If nothing else,
the trip did that."
Gisela was speechless for a moment, shamed by the strength of
this child’s love. Then she sent Cordelia a stream of tags. "These
are references to the best libraries on Earth. You’ll get the
real stuff there, not some watered-down version of flesher physics."
Prospero was shrinking the podium, descending to ground level.
"Cordelia! Come to me now. We’re leaving these barbarians to the
obscurity they deserve!"
For all that she admired Cordelia’s loyalty, Gisela was still
saddened by her choice. She said numbly, "You belong in Cartan.
It should have been possible. We should have been able to find
a way."
Cordelia shook her head: no failure, no regrets. "Don’t worry
about me. I’ve survived Athena so far; I think I can see it through
to the end. Everything you’ve shown me, everything I’ve done here,
will help." She squeezed Gisela’s hand. "Thank you."
She joined her father. Prospero created a doorway, opening up
onto a yellow brick road through the stars. He stepped through,
and Cordelia followed him.
Vikram turned away from the gravitational wave trace and asked
mildly, "All right, you can own up now: who threw in the additional
exabyte?"
"Freeeeee-dom!" Cordelia bounded across Cartan Null’s control scape, a long
platform floating in a tunnel of color-coded Feynman diagrams,
streaming through the darkness like the trails of a billion colliding
and disintegrating sparks.
Gisela’s first instinct was to corner her and shout in her face:
Kill yourself now! End this now! A brief side-branch, cut short before there was time for personality
divergence, hardly counted as a real life and a real death. It
would be a forgotten dream, nothing more.
That analysis didn’t hold up, though. From the instant she’d become
conscious, this Cordelia had been an entirely separate person:
the one who’d left Athena forever, the one who’d escaped. Her
extended self had invested far too much in this clone to treat
it as a mistake and cut its losses. Beyond anything it hoped for
itself, the clone knew exactly what its existence meant for the
original. To betray that, even if it could never be found out,
would be unthinkable.
Tiet said sharply, "You didn’t raise her hopes, did you?"
Gisela thought back over their conversations. "I don’t think so.
She must know there’s almost no chance of survival."
Vikram looked troubled. "I might have put our own case too strongly.
She might believe the same discoveries will be enough for her–but
I’m not sure they will."
Timon sighed impatiently. "She’s here. That’s irreversible; there’s
no point agonizing about it. All we can do is give her the chance
to make what she can of the experience."
A horrifying thought struck Gisela. "The extra data hasn’t overburdened
us, has it? Ruled out access to the full computational domain?"
Cordelia had compressed herself down to a far leaner program than
the version she’d sent from Earth, but it was still an unexpected
load.
Sachio made a sound of indignation. "How badly do you think I
did my job? I knew someone would bring in more than they’d promised;
I left a hundredfold safety margin. One stowaway changes nothing."
Timon touched Gisela’s arm. "Look." Cordelia had finally slowed
down enough to start examining her surroundings. The primary beams,
the infrastructure for all their computation, had already been
blue-shifted to hard gamma rays, and the colliding photons were
creating pairs of relativistic electrons and positrons. In addition,
a range of experimental beams with shorter wavelengths probed
the physics of length scales ten thousand times smaller–physics
that would apply to the primary beams about a subjective hour
later. Cordelia found the window with the main results from these
beams. She turned and called out, "Lots of mesons full of top
and bottom quarks ahead, but nothing unexpected!"
"Good!" Gisela felt the knot of guilt and anxiety inside her begin
to unwind. Cordelia had chosen the Dive freely, just like the
rest of them. The fact that it had been a hard decision for her
to make was no reason to assume that she’d regret it.
Timon said, "Well, you were right. I was wrong. She certainly
tunneled out of Athena."
"Yeah. So much for your theory of closed trapped memetic surfaces."
Gisela laughed. "Pity it was just a metaphor, though."
"Why? I thought you’d be overjoyed that she made it."
"I am. It’s just a shame that it says nothing at all about our
own chances of escape."
Each orbit gave them thirty minutes of subjective time, while
the true length and time scales of Cartan Null shrank a hundredfold.
Sachio and Tiet scrutinized the functioning of the polis, checking
and rechecking the integrity of the "hardware" as new species
of particles entered the pulse trains. Timon reviewed various
methods for shunting information into new modes, if the opportunity
arose. Gisela struggled to bring Cordelia up to speed, and Vikram,
whose main work had been the nanomachines, helped her.
The shortest-wavelength beams were still recapitulating the results
of old particle accelerator experiments; the three of them pored
over the data together. Gisela summarized as best she could. "Charge
and the other quantum numbers generate a kind of angle between
world lines in the networks, just like spin does, but in this
case they act like angles in five-dimensional space. At low energies
what you see are three separate subspaces, for electromagnetism
and the weak and strong forces."
"Why?"
"An accident in the early universe with Higgs bosons. Let me draw
a picture . . ."
There was no time to go into all the subtleties of particle physics,
but many of the issues that were crucial outside Chandrasekhar
were becoming academic for Cartan Null anyway. Broken symmetries
were being restored as they spoke, with increasing kinetic energy
diluting differences in rest mass into insignificance. The polis
was rapidly mutating into a hybrid of every possible particle
type; what governed their future would not be the theory of any
one force, but the nature of quantum mechanics itself.
"What lies behind the frequency and wavelength of a particle?"
Vikram sketched a snapshot of a wave packet on a spacetime diagram.
"In its own reference frame, an electron’s phase rotates at a
constant rate: about once every ten-to-the-minus-twenty seconds.
If it’s moving, we see that rate slowed down by time dilation,
but that’s not the whole picture." He drew a set of components
fanning out at different velocities from a single point on the
wave, then marked off successive points where the phase came full
circle for each one. The locus of these points formed a set of
hyperbolic wavefronts in spacetime, like a stack of conical bowls–packed
more tightly, in both time and space, where the components’ velocity
was greater. "The spacing of the original wave is only reproduced
by components with just the right velocity; they trace out identical
copies of the wave at later times, all neatly superimposed. Components
with the wrong velocity scramble the phase, so their copies all
cancel out." He repeated the entire construction for a hundred
points along the wave, and it propagated neatly into the future.
"In curved spacetime, the whole process becomes distorted–but
given the right symmetries, the shape of the wave can be preserved while the wavelength shrinks and
the frequency rises." Vikram warped the diagram to demonstrate.
"Our own situation."
Cordelia took this all in, scribbling calculations, cross-checking
everything to her own satisfaction. "Okay. So why does that have
to break down? Why can’t we just keep being blue-shifted?"
Vikram zoomed in on the diagram. "All phase shifts ultimately
come from interactions–intersections of one world line with another. In the Kumar model,
every network of world lines has a finite weave. At each intersection,
there’s a tiny phase shift that makes time jump by about ten-to-the-minus-forty-three
seconds . . . and it’s meaningless to talk about either a smaller
phase shift, or a shorter time scale. So if you try to blue-shift
a wave indefinitely, eventually you reach a point where the whole
system no longer has the resolution to keep reproducing it." As
the wave packet spiraled in, it began to take on a smeared, jagged
approximation of its former shape. Then it disintegrated into
unrecognizable noise.
Cordelia examined the diagram carefully, tracing individual components
through the final stages of the process. Finally she said, "How
long before we see evidence of this? Assuming the model’s correct?"
Vikram didn’t reply; he seemed to be having second thoughts about
the wisdom of the whole demonstration. Gisela said, "In about
two hours we should be able to detect quantized phase in the experimental
beams. And then we’ll have another hour or so before–" Vikram
glanced meaningfully at her–privately, but Cordelia must have
guessed why the sentence trailed off, because she turned on him.
"What do you think I’m going to do?" she demanded indignantly.
"Collapse into hysterics at the first glimmering of mortality?"
Vikram looked stung. Gisela said, "Be fair. We’ve only known you
three days. We don’t know what to expect."
"No." Cordelia gazed up at the stylized image of the beam that
encoded them, swarming now with everything from photons to the
heaviest mesons. "But I’m not going to ruin the Dive for you.
If I’d wanted to brood about death, I would have stayed home and
read bad flesher poetry." She smiled. "Baudelaire can screw himself.
I’m here for the physics."
Everyone gathered round a single window as the moment of truth
for the Kumar model approached. The data it displayed came from
what was essentially a two-slit interference experiment, complicated
by the need to perform it without anything resembling solid matter.
A sinusoidal pattern showed the numbers of particles detected
across a region where an electron beam recombined with itself
after traveling two different paths; since there were only a finite
number of detection sites, and each count had to be an integer,
the pattern was already "quantized," but the analysis software
took this into account, and the numbers were large enough for
the image to appear smooth. At a certain wavelength, any genuine
Planck scale effects would rise above these artifacts, and once
they appeared they’d only grow stronger.
The software said, "Found something!" and zoomed in to show a
slight staircasing of the curve. At first it was so subtle that
Gisela had to take the program’s word that it wasn’t merely showing
them the usual, unavoidable jagging. Then the tiny steps visibly
broadened, from two horizontal pixels to three. Sets of three
adjacent detection sites, which moments ago had been registering
different particle counts, were now returning identical results.
The whole apparatus had shrunk to the point where the electrons
couldn’t tell that the path lengths involved were different.
Gisela felt a rush of pure delight, then an aftertaste of fear.
They were reaching down to brush their fingertips across the weave
of the vacuum. It was a triumph that they’d survived this far,
but their descent was almost certainly unstoppable.
The steps grew wider; the image zoomed out to show more of the
curve. Vikram and Tiet cried out simultaneously, a moment before
the analysis software satisfied itself with rigorous statistical
tests. Vikram repeated softly, "That’s wrong." Tiet nodded, and
spoke to the software. "Show us a single wave’s phase structure."
The display changed to a linear staircase. It was impossible to
measure the changing phase of a single wave directly, but assuming
that the two versions of the beam were undergoing identical changes,
this was the progression implied by the interference pattern.
Tiet said, "This is not in agreement with the Kumar model. The phase is quantized, but
the steps aren’t equal–or even random, like the Santini model.
They’re structured across the wave, in cycles. Narrower, broader,
narrower again . . ."
Silence descended. Gisela gazed at the pattern and struggled to
concentrate, elated that they’d found something unexpected, terrified
that they might fail to make sense of it. Why wouldn’t the phase
shift come in equal units? This cyclic pattern was a violation
of symmetry, allowing you to pick the phase with the smallest
quantum step as a kind of fixed reference point–an idea that quantum
mechanics had always declared to be as meaningless as singling
out one direction in empty space.
But the rotational symmetry of space wasn’t perfect: in small
enough networks, the usual guarantee that all directions would
look the same no longer held up. Was that the answer? The angles the two beams had to take to reach the detector were
themselves quantized, and that effect was superimposed on the
phase?
No. The scale was all wrong. The experiment was still taking place
over too large a region.
Vikram shouted with joy, and did a backward somersault. "There
are world lines crossing between the nets! That’s what creates phase!" Without another word, he began furiously
sketching diagrams in the air, launching software, running simulations.
Within minutes, he was almost hidden behind displays and gadgets.
One window showed a simulation of the interference pattern, a
perfect fit to the data. Gisela felt a stab of jealousy: she’d
been so close, she should have been first. Then she began to examine
more of the results, and the feeling evaporated. This was elegant,
this was beautiful, this was right. It didn’t matter who’d discovered
it.
Cordelia was looking dazed, left behind. Vikram ducked out from
the clutter he’d created, leaving the rest of them to try to make
sense of it. He took Cordelia’s hands and they waltzed across
the scape together. "The central mystery of quantum mechanics
has always been: why can’t you just count the ways things can happen? Why do you have to assign each alternative
a phase, so they can cancel as well as reinforce each other? We
knew the rules for doing it, we knew the consequences–but we had
no idea what phases were, or where they came from." He stopped
dancing, and conjured up a stack of Feynman diagrams, five alternatives
for the same process, layered one on top of the other. "They’re
created the same way as every other relationship: common links
to a larger network." He added a few hundred virtual particles,
crisscrossing between the once-separate diagrams. "It’s like spin.
If the networks have created directions in space that make two
particles’ spins parallel, when they combine they’ll simply add
together. If they’re anti-parallel, in opposing directions, they’ll
cancel. Phase is the same, but it acts like an angle in two dimensions,
and it works with every quantum number together: spin, charge,
color, everything–if two components are perfectly out-of-phase,
they vanish completely."
Gisela watched as Cordelia reached into the layered diagram, followed
the paths of two components, and began to understand. They hadn’t
discovered any deeper structure to the individual quantum numbers,
as they’d hoped they might, but they’d learnt that a single vast
network of world lines could account for everything the universe
built from those indivisible threads.
Was this enough for her? Her original, struggling for sanity back in Athena, might take
comfort from the hope that the Dive clone had witnessed a breakthrough
like this–but as death approached, would it all turn to ashes
for the witness? Gisela felt a pang of doubt herself, though she’d
talked it through with Timon and the others for centuries. Did
everything she felt at this moment lose all meaning, just because
there was no chance to carry the experience back to the wider
world? She couldn’t deny that it would have been better to know
that she could reconnect with her other selves, tell all her distant
family and friends what she’d learnt, follow through the implications
for millennia.
But the whole universe faced the same fate. Time was quantized; there was no prospect of infinite computation before
the Big Crunch, for anyone. If everything that ended was void,
the Dive had merely spared them the prolonged false hope of immortality.
If every moment stood alone, complete in itself, then nothing
could rob them of their happiness.
The truth, of course, lay somewhere in between.
Timon approached her, grinning with delight. "What are you pondering
here by yourself?"
She took his hand. "Small networks."
Cordelia said to Vikram, "Now that you know precisely what phase
is, and how it determines probabilities . . . is there any way
we could use the experimental beams to manipulate the probabilities
for the geometry ahead of us? Twist back the light cones just
enough to keep us skirting the Planck region? Spiral back up around
the singularity for a few billion years, until the Big Crunch
comes, or the hole evaporates from Hawking radiation?"
Vikram looked stunned for a moment, then he began launching software.
Sachio and Tiet came and helped him, searching for computational
shortcuts. Gisela looked on, light-headed, hardly daring to hope.
To examine every possibility might take more time than they had,
but then Tiet found a way to test whole classes of networks in
a single calculation, and the process sped up a thousandfold.
Vikram announced the result sadly. "No. It’s not possible."
Cordelia smiled. "That’s all right. I was just curious." |
Terry Bisson: 
