Egan, Greg - The Planck Drive

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Asimov's - The Planck Dive

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The Planck Dive by Greg Egan

This story first appeared in Asimov’s Science Fiction,

February 1998. Nominated for Best Novelette.

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

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Asimov's - The Planck Dive

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

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Asimov's - The Planck Dive

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.

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"The Planck

Dive" by Greg

Egan, copyright

Egan, used by

permission of the

author

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Asimov's - The Planck Dive

"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?"

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Asimov's - The Planck Dive

"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

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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

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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."

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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."

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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,

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Asimov's - The Planck Dive

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

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