Planck Zero

A.D. 5653

Recently I've been poring over theoretical physics texts. My friends—those who can still stand to see me, since the Ghosts rebuilt me—can't understand it. Okay, they say, you were almost killed by the Ghosts' Planck Zero experiment. It was terrible. But isn't it all over now? Why brood? Why not walk—or rather, fly—out into the sunshine, and enjoy what's left of your life?

...But I have to do this. I need the answer to a specific question.

Is there any way out of a black hole?

When I heard of the Ghosts' experiment I made a lot of noise. Eventually their Sink Ambassador agreed to meet me—but they insisted the venue had to be the exposed surface of the Moon. Earth conditions wouldn't have made a damn bit of difference to a Silver Ghost, of course; it was all part of the Ghosts' endless diplomatic gavotte. As chief administrator of the Ghost liaison project, it was my precise job not to find such matters irritating.

I guess age—and Eve's death—were making it harder for me to stomach the pettiness of interspecies diplomacy.

Into Lethe with it.

I rode out on the Sahel Cable, then took a flitter to the Moon. We were to meet outside Copernicus Dome; I suited up and walked out briskly. If the Ambassador had been hoping that my sixty-five years would keep me at home it had another thing coming.

The Silver Ghosts' Ambassador to the Heat Sink floated a yard off the crisp Lunar regolith; the reflection of Earth was a distorted crescent sliding over its midriff.

We met without aides, as I'd requested, and spoke on a closed channel.

I came straight to the point. "Ambassador, I've asked to meet you because we suspect you are conducting unauthorized experiments on quagma material."

It bobbed up and down, a child's balloon incongruously dispatched to the airless Moon. "Jack, I would like to see evidence to support your allegation."

I was prepared for that. "I'll download the dossier to you. As soon as I'm satisfied you are being just as honest with me."

"Perhaps you are speculating. Perhaps this is a—" Pause. "—a shot in the dark? You are trying to extract valuable information from me on the threat of evidence which does not exist."

I shook my head. "Ambassador, think it over. Your race and mine have contacts at many levels, right down to the one-man traders. Security measures between our species are as porous as human flesh." A charming Ghost simile.

"Perhaps." Its bobbing evolved into a complex shimmering. "Very well. Jack Raoul, we have grown to know each other, these past decades, and I am aware that you are an honest man... if not always an open one, despite your present posture as an injured party. Therefore I must accept that you have such evidence."

I felt a surge of satisfaction. "Then you are conducting a covert project."

"Covert, perhaps, but not intentionally so from our human partners."

"Oh, really?..." I let it pass. "Then from whom?"

"The Xeelee."

I studied the Ambassador with a sneaking admiration. "I'll be impressed if you manage to keep secrets from the Xeelee. How are you doing it?"

The Ghost began to roll gently. "All in good time, Jack Raoul. We cannot be sure of secure communications, even here."

"This conversation has served its purpose, then. Our staff can proceed with the details—"

"But we would not allow the dissemination of any data. Only an inspection tour, at the highest level, would be acceptable."

"The highest level?"

"Perhaps you would care to visit the site yourself, Jack Raoul."

I laughed. "Perhaps... when I find out what the catch is."

The rolling accelerated. "We know each other too well. Jack, we would have to rebuild you."

There was no inflection in the artificial voice. The image of Earth rippled across Ghost skin.

I shivered.

"Ambassador, just give me one hint. You know I'm an inquisitive man."

"A hint?"

"What are you trying to do, with your quagma?"

The rolling stopped. "You have heard of the Uncertainty Principle..."

"Of course."

"We have violated it."

After my meeting with the Ambassador I returned to our New Bronx apartment, poured myself a malt, slumped on my favorite couch, and called up Eve.

One wall melted. Eve was heartbreakingly real, at least when she didn't move and the image stayed stable.

She looked around quickly, as if establishing where she was, then fixed me with an admonishing stare.

"You're looking good," I said, raising my glass at the wall.

She snorted, but pushed a hand through her grayed hair. "What do you want, Jack? You know this is bad for you."

"I want you to tell me about the Uncertainty Principle."

"Why?"

"I'll explain later."

She frowned. "The walls have plenty of popular science texts—"

"You know I can never understand a word of that stuff unless you explain it to me."

"Lethe, Jack; that's just sentimental—"

"Humor me. It's important."

She sighed and pulled at a stray lock of hair. "All right, damn it. But I'll keep it brief; and when it's over, that's it."

"It's a deal."

Now Eve changed, subtly, so that—without any obvious reworking of the image—she seemed younger, more comfortable on the couch. I guessed the wall was accessing an older part of her Notebooks. "To understand Heisenberg's Uncertainty Principle," she began, "you need to get a handle on quantum mechanics."

According to the quantum philosophy, particles like electrons don't exist as points of mass and charge. Instead each electron has a wave function which describes its position, velocity and other properties; it's as if the electron is spread over a small volume of space delimited by the wave function.

"So where does the Uncertainty Principle come in?"

Eve twisted my ring around her finger. "You can reduce the spread of an electron's position wave-volume—perhaps by inspecting it using very high frequency photons. But the catch is that the wave-volume associated with another variable—the electron's momentum—expands enormously. And vice versa.

"So you can never know both the electron's position and momentum; you can never reduce both wave-volumes to zero."

"Okay. What's the size of these volumes?"

"The scale is given by Planck's constant. Which is a small number; one of the fundamental constants of physics. But in real terms—suppose you measured an electron's position to within a billionth of an inch. Then the momentum uncertainty would be such that a second later you couldn't be sure where the damn thing was to within a hundred miles."

I nodded. "Then the principle is describing a fundamental fuzziness in reality—"

She waved her hand with exasperation. "Don't talk like a cheap data desk, Jack. There's nothing fuzzy about reality. The wave functions are the fundamental building blocks of the Universe; their governing wave equations are completely deterministic... well, never mind. The Uncertainty Principle is essentially an expression of the scale of those wave functions."

"How does this relate to your work?"

She sighed and sat back in her couch. "It was at the heart of it, Jack."

Eve had spent much of her working life trying to develop the principles of remote translation systems. Teleport beams, to you and me.

She said, "A translation device might work by scanning the position of every particle in an object. That information could be transferred somewhere else and a copy constructed of the original, exact down to the last electron."

"But the Uncertainty Principle tells us that's impossible."

"Correct. But the Principle says nothing about transferring exact data about the wave functions themselves... and that was the approach I was working on. Also, in some way we still don't fully understand, the quantum waves provide a connectivity to space. When two objects are once joined there is a sense in which they are forever linked, by quantum properties. It may be that unless full quantum functions are copied, remote translation is impossible."

"That which God has joined, let no man put asunder."

She looked at me suspiciously, as if expecting me to burst into tears. "Something like that. Jack, it may also be that consciousness is a quantum phenomenon. Without our defining quantum functions—without the anchorage they give us to reality, and to those around us—we are nothing."

I set down my glass, stood and walked to the wall. Hesitantly she got up and walked closer to her side. "And this wave-function mapping was the technical barrier you could never breach."

She shrugged. "Perhaps it's just as well. Because if this was a perfect image of me, Jack, stored in this wall, you'd never leave this damn apartment." She looked up at me, and I imagined her eyes softening. "Would you?"

"What would happen if you violated the Uncertainty Principle?"

The image wavered slightly; I imagined the wall frantically searching its datastores for a response. "You can't. Jack, haven't you understood a word I've said?"

"Just suppose."

She frowned. "If the uncertainty limit were lowered somehow then greater data compression would be possible. Better data storage."

"So sharper wall images. What else?"

"Faster, more compact computing devices." The image crumbled for a sudden, shocking moment into a storm of cubical pixels. "Jack, this is right at the edge of what I left in my Notebooks."

"Bear with me, please... it is important. How would you do it?"

She rubbed the bridge of her nose, as if her head was aching. "Assuming you're talking about the Universe we're living in—so the fundamental laws are the same—you'd have to find a way of reducing Planck's constant, over some region of space. The interface between Planck-differentiated regions would be kind of interesting. But it's impossible, of course." She looked up at me, troubled. "Jack, I don't like this. It makes me feel—odd."

"I'm sorry." Without thinking I reached for her, through the wall; but my hand passed through her arm with little resistance.

"Jack. Don't." She stepped back, out of my reach. "It only hurts you."

"I have to go away."

"What?"

"I'm to make an inspection of a Ghost experiment. They say I must be physically modified... I might not come back."

"Well, why not," she said. "Lethe, Jack, I've been dead three years. You're getting morbid." Then she raised both hands to her head and said indistinctly, "If Planck's constant were taken to the ultimate, down to zero—"

"What? Eve, tell me."

She looked at me through a hail of pixels, her eyes wide. "Space could shatter—"

She dissolved. The wall became a wall again.

So I was made a Ghost.

My brain and spinal cord were rolled up and moved into a cleaned-out chest cavity. My circulatory system was wrapped into a complex mass around the brain pan. The Ghosts built a new metabolic system, far more efficient than the old and capable of working off direct radiative input. New eyes, capable of working in spectral regions well beyond the human range, were bolted into my skull; and I was given Ghost "muscles"—a tiny antigravity drive and compact actuator motors.

At last I was dipped in something like hot mercury.

The Sink Ambassador came to see me while I was being reconstructed. Its voice was like a bird hovering in the darkness. "How do you feel?"

I laughed—or sent appropriate impulses to my translator chips, at least. "How do you think I feel?"

"They tell me your spirits are high..."

"You're reducing Planck's constant. Aren't you? But I don't understand what quagma has to do with it."

The Ghost hesitated.

When its voice came through again it had a richer timbre. "I have established a closed channel. All right, Jack. You are aware that quagma is the state of matter which emerged from the Big Bang. Matter, when raised to sufficiently high temperatures, melts into a magma of quarks—a quagma. And at such temperatures the fundamental forces of physics unify into a single superforce. Quagma is bound together only by such a superforce. When quagma is allowed to cool and expand the superforce decomposes into the four sub-forces."

"So?"

"By controlling the decomposition, one can select the ratio between those forces."

"Ah." Eve, I wish you were here to help me with this... "And those ratios govern the fundamental constants—including Planck's constant."

"Correct."

I wanted to rub my face, but my head and hands had been taken away. "So you're building a model Universe, in which Planck's constant is lowered. Lethe, Ambassador. I'm surprised the Xeelee have let you get as far as you have."

"We have concealed well... Jack Raoul, are you still human?"

I would have shrugged. "I don't know."

"You don't sound as if you care."

"Why should you?"

"I have known you for a long time, Jack. Among my people there are analogies for the grief you felt at the loss of your wife."

"Ambassador, do you think this is some complicated way of committing suicide? You invited me to take the damn trip, remember."

"Human or not, you will still have friends."

"You can't imagine how much that comforts me."

They disconnected my new senses during the hyperspace flight. "I apologize," the Sink Ambassador said. "When we reach the quagma project site you will have freedom to inspect."

"But you don't trust me with the location."

"I do not have a free rein, my friend."

I spent the passage floating in a Virtual reality, trying not to think about what lay beyond my skin.

I emerged into a half-Universe.

I was in a Ghost intrasystem cruiser, a rough ovoid constructed of silvered rope. Instrument clusters were knotted to the walls. Perhaps a dozen Ghosts clung to the rope like berries on seaweed.

Above me I saw stars. Below me a floor of crimson mist, a featureless plane, extended to infinity.

A Ghost approached me.

"Ambassador?"

"We have arrived, Jack Raoul."

"Arrived where?" I gestured at the blood-red floor. "What's this?"

The Ambassador rolled, as if amused. "Jack, this is a red giant star. Are you familiar with astrophysics? This star is about as wide as Earth's orbit. We have emerged a million miles above its boundary."

I'm no small-town boy; I'd been off Earth before. But this was different. I felt the soft human thing inside my Ghost shell cringe.

I'd seen nothing yet.

The ship plunged into the interior of the star.

I cried out and grabbed at silvered rope. Glowing banks of mist shot upwards all around us. The Ghost crew floated about their tasks, unconcerned.

"Lethe, Ambassador."

"I could not warn you."

We emerged into a clear layer within the star. Far, far below was a dense ocean of fire, looking like some fantastic sodium-lit cityscape; beneath it something small, hot and yellow glowed brightly. We descended through slices of fire-cloud with startling speed.

The Ambassador said, "You are perhaps aware that this giant is a star in the latter part of its life. Its bulk is a gas whose density is only a thousandth that of Earth's atmosphere, and whose temperature is well below that at the surface of Sol. Easily managed by your new skin. So you see, there is nothing to fear."

Now the ship veered to the right, and we skirted a huge, blackened thunderhead. "A convection fount; complex products from the core," explained the Ghost.

"The core?"

"Like a white dwarf star, about the size and mass of Sol. It is mostly helium by now, but hydrogen fusion is still proceeding in a surface layer." The Ghost rolled complacently. "Jack, your visit—this project—is inspired by quantum mechanics. Do you understand the Pauli Exclusion Principle?—that no two quantum objects can share the same state? You may be amused to know that it is electron degeneracy pressure—a form of the Pauli Principle—which keeps that core from collapsing on itself."

"You're prepared to live inside a star, just to evade detection by the Xeelee?"

"We anticipate long-term benefits."

We dropped into another clear stratus. The core was a ball about as hot and bright as the Sun from Earth; it rolled beneath us. Starstuff drifted above us like smog.

The Ghosts had built a city here.

Once this must have been a moon. It was a hollowed-out ball of rock, a thousand miles wide. Ghost ships swept over the pocked landscape.

At the poles two vast cylindrical structures gleamed. These were intrasystem drives, the Ambassador explained, there to maintain the moon's orbit about the core.

Our ship approached the city-world's surface—there was negligible gravity, so that it was like hovering before some vast, slotted wall—and, at length, slid into an aperture.

I turned to the Ambassador. "I won't pretend I'm not impressed."

"Naturally, after this demonstration, I will provide you with any backup data you require for your report."

"Demonstration? Of what?"

A hint of pride shone through the thin, sexless tones of the translator chips. "We have timed your arrival to coincide with the initiation of a new phase of our project."

"I'm honored."

We hurtled along dimly-lit passages. Other craft dipped and soared all around us. Blocks of light tumbled from cross-corridors, reminding me irresistibly of pixels. I recalled Eve's strange, ambiguous warning, and wondered bleakly if I really wanted to be present at the dawn of a "new phase."

With a soundless rush we emerged into a spherical cavity miles wide. Beams of crimson starlight crossed the hollow, bathing its walls with a blood-red glow. At the heart of the chamber was a sphere. A couple of miles across, the sphere gleamed golden and was semi-transparent, like a half-silvered mirror. Platforms bearing Ghost workers hovered over its surface.

Some vast machine moved softly, within the confines of the mirrored sphere.

"Mr. Raoul, welcome to our experiment," the Sink Ambassador said.

"What is that sphere?"

"Nothing material. The sphere is the boundary between our Universe... and another domain, which we have constructed by letting quagma droplets inflate under controlled conditions. Within this domain the ratio you know as Planck's constant is reduced, to about ten percent of its value elsewhere. Other physical constants are identical."

"Why the half-silvered effect?"

"The energy carried by a photon is proportional to the Planck number. When a photon enters the Planck domain the energy it may carry is reduced. Do you understand? It therefore sheds energy at the boundary, in the form of a second photon, emitted back into normal space."

I asked if we were to enter the Planck space.

"I fear not," the Ambassador said. "Our fundamental structure is based on Planck's constant: the spacing of electrons around the nucleus of an atom, for example. If you were to enter the domain, you would be—adjusted. The device in there—an artificial mind—has been constructed to withstand such Planck changes. The device controls the regeneration of the domain from quagma; we are also using it to conduct computational experiments."

The machine in its golden sac turned, brooding, like some vast animal.

"Ambassador, what is your purpose?"

The Ghosts, the Ambassador said, had two objectives. The first was to use the Planck boundary conditions to build a perfect reflective surface, an age-old goal of the energy-hoarding Ghosts.

The second objective was more interesting.

"The capacity of any computing machine is limited by the Uncertainty Principle," the Ambassador said. "The exploration of, say, high-value prime numbers has always been constrained by the fact that energy changes within a device must remain above the uncertainty level.

"With the reduction in Planck's constant we can go further. Much further. For example, we have already managed to find a disproof of an ancient human hypothesis known as Goldbach's conjecture."

Goldbach, it seems, speculated that any even number can be expressed as the sum of two primes. Twelve equals five plus seven; forty equals seventeen plus twenty-three. Centuries of endeavor had neither proved nor disproved the hypothesis.

The Planck machine had found a counterexample, a number in the region of ten raised to the power eighty.

"I guess I'm impressed," I said.

The Ghost rolled gently. "My friend, age-old problems melt before our Planck machine; already several NP-type problems have—"

I told the Ambassador I believed it, and to dump down the details later.

The science platforms were pulling away now, leaving the gold-silver sphere exposed and alone.

The Sink Ambassador continued its lecture. "But we want to go further. We see this Planck-adjustment technique as a means of probing—not just the very large—but the infinite. Our device will verify some of the most important theorems of our, and your, mathematics, simply by a direct inspection of cases, all the way to infinity."

I stared at the bobbing Ghost. "I think you're losing me. Won't an infinite number of cases still take an infinite amount of time?—and energy?"

"Not if the time and energy is allocated in decreasing amounts, so that the total converges to some finite value. And—if the Uncertainty Principle is removed completely—there is no limit to the smallness of energy allocations."

"Right. So you're going to take Planck's constant all the way to zero."

"That's right. And, Jack, mathematical conjectures are just the start. A training exercise. The artificial mind is heuristic—it is flexible; it can learn. With its infinite capacity at our disposal we anticipate the dawn of a new era of—"

There was a spark, dazzling bright, at the heart of the silvered Planck sac. The mind-device thrashed like some grotesque fetus.

I knotted my fingers in a length of silvered rope. "Ambassador, 'space could shatter.' "

"What?"

"What does that mean to you?"

"...Nothing. Jack, are you—"

The flame filled the sac, overwhelming the machine. For an instant the sac glowed brighter than the star core.

Then the sac turned silver. It looked like some huge Ghost. Images of the crowding science platforms, of the slotted walls of the city-world cavity, shivered over its flanks.

"Ambassador, what's happening?"

"...I'm not certain."

"Have you achieved Planck Zero?"

"Yes. But the device should be signaling to us—"

The walls of the sac contracted by a few hundred feet, trembling; it was as if the sac were a living creature, breathing in.

My ship lurched away from the sac and towards the walls of the chamber. One crewman was left tumbling in space, like a drop of mercury in freefall. I clung grimly to my rope.

The walls were still miles away.

The sac's surface billowed out and overwhelmed us.

I was utterly alone.

Lonely.

Darkness.

...Dark because photons could carry no energy, here at Planck Zero; nothing to excite my optic sensors...

Cold. How could I be cold? I rubbed my hands together. I could feel my fingers break up like ancient, crumbled paper.

Electron orbits in an atom are proportional to Planck's constant. At Planck Zero the orbits must collapse... right? So, no more chemistry. How long before the crumbling process reached my brain pan?

How would it feel?

And quantum wave functions, linking me to the rest of the Universe, had all turned to dust at Planck Zero.

I could feel it. I was alone in this shattered space.

What about the ship? Was it still heading for the wall?... Something else, in here with me. The Ghosts? No; something larger, more powerful.

Infinite.

The mind-device was without limit. It was stranded in this discontinuous space, and it was enraged.

Enraged by a pain I recognized.

Now I made out other minds. Ghosts. They were like tiny stars, shining out, falling away from each other.

The Planck mind lashed out. Ghosts were overwhelmed, insects in fire.

...The ship burst out of the sac; quantum functions rushed over me (for a precious moment visible, like prismatic waves lapping around me) and I was bound into the Universe once more.

The ship hurtled through a city-world passage, trailing ragged fragments. Ghosts lay dying all around me, their proud bodies deflated.

I looked back down the passage. A silver half-dome peered after us like some vast eye.

"...Sink Ambassador?"

"I'm still here, Jack."

We emerged from the city-world. Ghost paramedics floated onto our ship and tended the wounded.

The city-world was changing.

A light, clear and white, shone out of the hundreds of portals, illuminating the murky giant star material. The massive drive assemblies at the poles had been damaged; I saw sparks fizzing across the surface of the nearer. A flotilla of heavy Ghost ships approached the drive units.

"Ambassador, what are they doing?"

"We must endeavor to repair the drive units, or the moon will fall into the core... Jack, the growth of the Planck sac in that cavity was not controlled. We are afraid."

"I bet you are."

"We are going to try to move the moon out of the giant star."

"And then what?"

"We must find some way to restrain the sac."

I stared down at the core of the giant. "Ambassador, it will overwhelm you. What are the limits to its growth?"

"There are no limits. Perhaps the Xeelee will intervene."

"The Xeelee aren't gods." I thought fast. "Sink Ambassador, listen to me. Do you have any influence over operations here?"

"Why?"

"Stop the efforts to repair the drives."

"...I do not have the authority."

"Then find someone who does. As acting human ambassador here, I formally request this. Sink Ambassador, have you recorded that?"

"Yes, Jack. Why do you want this?"

"Because I'm frightened, too. But I think there is a way out."

The Ghosts cut the drive assemblies loose from the city-world. Within an hour the Planck sac had overwhelmed the battered moon; it hung in the giant star glow, perfectly silver. They got us out of there. I could see reflections in the sac's surface, chains of ropy Ghost ships heading for safety. It took about a day for the Planck sac to impact the star core. By that time it was ten thousand miles wide and still growing. Huge ripples crossed its monstrous surface. It slid inside the star core, fusing hydrogen closing smoothly over the shining ovoid, vacuoles flaring.

An hour later the core started to implode.

Disembodied, the Sink Ambassador and I floated over Virtual images of the collapsing core. I said, "I wish Eve could see this."

"Yes."

By now, of course, the Ghosts had figured it out for themselves; but I couldn't resist rubbing it in. "It was your chance comment about electron degeneracy pressure that gave me the key. Suppose Planck were reduced to zero in the star core. The higher quantum states would collapse—spin values, for instance, would fall from Planck multiples to zero."

The Pauli Exclusion Principle could not work, and electron degeneracy pressure would fail. The star core must implode... all the way, past the neutron star compaction limit, on to become a black hole.

"Actually," the Ambassador said smoothly, "there are technicalities you didn't consider. For example, no electron can have zero spin value. Nor can any fermion. Presumably the core fermions are collapsing to bosons, like photons... The physics must be interesting in there."

"Whatever. It worked, didn't it?"

"Yes. We have contained the Planck Zero sac expansion. Within an event horizon, for all time."

"And we've locked away your Planck Zero AI."

The Ghost thought that over. "That is important to you?"

"What did you sense, inside the sac?"

"Infinite power... and anger."

"There was more, Ambassador. In discontinuous space, without the anchorage of quantum wave functions, it was utterly alone. And lonely. And it was furious. Do you see?"

Quantum loneliness.

I had recognized a fellow sufferer. In my loneliness I can only hurt myself, but the mind-device had an infinite capacity for destruction. Still, it was trapped now...

Then I began to wonder, and I haven't been able to stop. Is there any way out of a black hole?

The images conjured up by Eve had been like reflections in the glimmering walls of the Planck sac.

I brooded, for a while unable to speak.

Eve asked, "Are you all right?"

"I don't know."

I'd relived it all again. The rebuilding. The horror of that quantum loneliness.

"Nobody should have to go through that twice," I said angrily.

"I know, Jack. And I'm sorry. But it's important that—"

"—I understand. I know. What next, Eve?"

"Next," she said, "we'll look ahead..."

"Ahead? Into the future? How is that possible?"

"Watch," she said. "Just watch."


...Five thousand years in the future, and ten thousand years after its first eruption from Earth, humanity's colonization wavefront spread at lightspeed through the Galaxy.

Its experiences, at the hands of the Qax and others, had changed humanity.

Never again would humanity be made to serve at the behest of some alien power.

As humans grew in power, the conquest of other species became an industry. A new era began.