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Appendix A:

In Which an Appendix is Provided

 

Collapsium

 

 

Perhaps it was novel, to imagine black holes not as highly compressed stars but as very heavy elementary particles, like protons massing a billion tons. Mega-particles, their surfaces able to devour light, to bend time and space, to tear energies loose from the zero-point field of the "empty" vacuum itself...

An enterprise worth pursuing!

Einstein may have changed the world with his famous equation linking mass and energy, but when you ask the more fundamental question -- just what is mass? -- you soon find yourself scribbling:

 

E = MC2

M = E/C2

E/C2 = E/C2

E = E

 

Mass is like energy because energy is like itself, just an electromagnetic vibration of the zero-point vacuum. Soon the quantum-age profusion of particles and forces falls away like a bad dream, leaving only charge, electromagnetism, and the vacuum. There is nothing else, no other force or substance required to construct the universe. And you wonder why you ever thought there was.

It all comes down to zitterbewegung vibrations, the "trembling motion" of charged particles buffeted by the very real energies of the zero-point field. Even the neutron is composed of quarks, charged +2/3, -1/3, and -1/3 proton-equivalents, and the secondary fields emitted by these trembling particles give rise to a net force which is always attractive, always infinite in range, always difficult to block or channel or deflect. Call it gravity -- Newton did. The experiment had been performed dozens of times before Bruno de Towaji came along: isolate a proton, subject it to oscillating electric fields at frequencies comparable to those of gravitation, and measure the increase in its mass. The Haisch effect. Bruno's "genius" was simply to dump in a neuble's worth of mass-energy, upping the frequency and amplitude of the oscillation, upping the illusory mass until the neuble was gone and the proton weighed a billion tons, enough to collapse it into a miniature black hole.

The rest had seemed obvious enough: two black holes, not only vibrating but vibrating each other, their interactions exactly 180 degrees out of phase with their zitterbewegung motions, gravities therefore canceling out. That turned out to be statically rather than dynamically stable, but eight holes arranged in a cube just so, at excruciatingly precise distances, would hold their positions indefinitely, for billions of years, for as long as the Hawking-bled holes themselves would last. A stiff cage, a "collapson," the elementary building block of a wholly new material: crystalline collapsium.

Obvious.

And once you did this, once you began bricking the collapsons together into three-dimensional structures, you were well on your way to the control of physical reality at its most fundamental levels.

 

 

 

 

Wellstone

 

 

Consider the humble semiconductor, which is an insulating substance which can nonetheless conduct electrons within a certain range or "band" of energies. The most common of these is silicon, whose native oxide is the main crustal component of every terrestrial moon and planet. Silicon's electrical properties are fixed by immutable physics, but through "doping," the carefully controlled introduction of impurities, its crystals can be tuned so that, for example, room-temperature electrons have a good chance of jumping up into the conduction band when a voltage is applied.

Now, by layering these doped silica in particular ways, we can trap conduction electrons in a membrane so thin that from one face to the other, their behavior as tiny quantum wave packets takes precedence over their behavior as particles. This is called a "quantum well." From there, confining the electrons along a second dimension produces a "quantum wire," and finally, with three dimensions, a "quantum dot."

The important thing about a quantum dot is that if it's the right size, the electrons trapped in it will arrange themselves as though they were part of an atom, even though there's no atomic nucleus for them to surround. Which atom they emulate depends on the number of electrons and the exact geometry of the wells confining them, and in fact where a normal atom is spherical, such "designer atoms" can be fashioned into cubes or tetrahedrons or any other shape, and filled not only with electrons but with positrons, muons, tau leptons, and other exotica to produce "atoms" with properties that simply don't occur in nature.

Lastly, the quantum dots needn't reside within the physical structure of our semiconductor; they can be maintained just above it through a careful balancing of electrical charges. In fact, this is the preferred method, since it permits the dots' characteristics to be adjusted without any physical modification of the substrate.

So picture this: a diffuse lattice of crystalline silicon, superfine threads much thinner than a human hair crisscrossing to form a translucent structure with roughly the density of balsa wood, a structure which, like balsa wood, is mostly empty space. Except that with the application of electrical currents, that space can be filled with "atoms" of any desired species, producing a virtual substance with the mass of diffuse silicon, but the chemical, physical, and electrical properties of some new, hybrid material.

Being half-composed of silicon, wellstone iron is less strong than its natural cousin, less conductive and ferromagnetic, basically less ironlike, and if you bash it over and over with a golf club it will gradually lose any resemblance, reverting to shattered silicon and empty space. On the other hand, it's feather-light, wholly rustproof, and changeable at the flick of a bit into zinc, rubidium, or even imaginary substances like unobtanium, impossibilium, and rainbow kryptonite.

Well, half-kryptonite anyway; the rest is still silicon. However, since the theoretical properties of the "pure" substance will never occur outside a quantum well, the distinction is largely moot. The copyrighted element Bunkerlite, for example, is a million times stronger than the wellstone matrix which supports it. Together, they're merely half a million times stronger.

Wellstone can also form compounds, amalgams, admixtures, sinters, and even whole solid-state devices; a thin square of it can be a hypercomputer if you like, or a clear glass window, or a stunningly accurate painting of your sister.

So it's handy stuff to have around, particularly in conjunction with nanoassemblers and other semiadvanced technologies of the third millennium. The thing you need to remember is that by Bruno de Towaji's time it was also dirt-common, its infinite potential mainly in the hands of bored or inept programmers who'd rather be looking at counterfeit naked pictures of the Queen.

 

 

 

 

Semisafe Black Holes

 

 

A neuble-mass black hole -- precisely the size of a proton -- can absorb exactly two excess electrons before electrostatic repulsion overcomes gravitational attraction, by which time the hole's mass -- and therefore its Schwarzchild radius -- has become 9.1E-31 percent larger. This infinitesimal widening is sufficient that the hole can consume an unlucky proton that strikes it just right -- a statistical rarity but, given prolonged contact, an eventual certainty.

That second widening slightly increases the chance that another proton will fall in, which in turn increases the chances of still another, and a few billion iterations later the invading protons are free to crowd around the event horizon and spiral in, forming an ever-widening hole whose mass can eventually grow to disrupt -- and finally crush -- the collapsium lattice around it.

 

 

 

 

 

Feigenbaum's Number

 

When a system is in transition from a laminar (or "smooth") to a turbulent (or "messy") state, it passes through a condition known as "chaotic frequency doubling," in which cyclic events come more and more frequently, until finally they smear into a jumble we resignedly call "random." Examine the trail of smoke rising up from a burning ember or weed pipe in the absence of wind and you can see this phenomenon directly: near the source, the smoke is a thin, clean line, like a length of ribbon. Higher up, it's a rising and unpredictable snarl of overlapping vortex rolls and curls. In between lies the chaotic transition zone, where single vortices break into double vortices break into quadruple vortices, and so on. This zone leaps up and down as you watch, its position and dimensions malleable in the face of quite small perturbations, but understand that if all the variables were constant -- the air perfectly still, the embers' combustion perfectly uniform -- the transition zone would hang exactly so, its frequency doublings happening over and over at the same exact positions, as if rows of invisible knives hung there, cleaving the vortices in twain as they rose, doubling their number with each successive row.

Here's the kicker: the spacing of these invisible knives is known in advance, regardless of the nature or conditions of the experiment. The interval between the first and second row is larger than the interval between the second and third by a ratio of exactly 4.6692016090. The same ratio, always, for smoke curls or ocean waves or ripples through an electromagnetic field. Feigenbaum's number: one of the many mysterious constants that underlie our universe.

 

 

 

 

True Vacuum

 

 

Normal "empty" space is nothing of the kind, is in fact a catchpool of invisible energies at every possible wavelength, and it's only when these wavelengths are excluded -- by closely spaced conducting plates, by fierce applications of charge and vibration, or, best of all, by sheets or shells of static collapsium -- that anything like "emptiness" can actually be achieved. The physicist Hendrick Casimir had proved as much even before the age of spaceflight, and the Queendom's communication and transportation networks relied on the principle for their daily operation.

But still Bruno had brooded: this Casimir supervacuum wasn't really blank, empty, or null. Not completely, not in any fundamental sense. A particle placed within it didn't freeze in place, locked down by absolute zero, and Bruno had wondered just how much energy could be pulled from the vacuum before it finally did. An infinite amount for every possible wavelength? Unlikely. So he'd concocted a simple experiment: a spherical shell of collapsium, a kind of piñata of bright pinpoint holes, slowly bleeding their mass-energy off as blue-white light. Then he'd measured the difference in vacuum energy between the inside and outside of the sphere. Then he'd put another collapsium shell outside the first -- spaced carefully, so the gravitic frequencies would cancel and they wouldn't fall in on each other -- and measured the energies again.

And then, somehow, even though these steps were fantastically difficult and expensive and demanding of his deepest attention, he'd repeated them eleven times more.

And for what? To learn what? That the vacuum increased with every Onion layer? That the energy difference between layers shrank progressively as one moved inward? That the rate of this shrinkage was neither exponential nor logarithmic nor asymptotic, but spaced -- precisely! -- according to Feigenbaum's number? Pi he could maybe have accepted. With greater difficulty, "e" or "i" or, just possibly, "gnu." But 4.6692016090? What could such a thing mean to imply? That the universe was chaotic straight through to its core? That all of physics was mad?

How absurd.

 

 

 

 

Electromagnetic Grapple

 

 

Electrons, like fluids, resist acceleration, but resist compression even more. "Press" on them with voltages, and they flow through the conduits laid out before them, spill down waterfall diodes, choke through bottleneck resistors... Fluid pressure can also power reciprocating devices which slosh the flow back and forth through "alternating current" conduits.

Unlike fluids, though, electrons give rise to electromagnetic fields when accelerated, and give rise to oscillating fields when sloshed back and forth. These oscillations can, in turn, affect the motion of charged particles, such as the quarks of which protons and neutrons are made. So imagine an ultra-high frequency EM field of infinite range, a field whose tugging vibrations universally attract matter of all types. Newton's phantom "gravitation," inexplicable for centuries and misunderstood for centuries more.

Lumps of matter emit such fields naturally, in spherically-symmetric echo of the invisible "vacuum" energy storming around them, but even before the Queendom's rise it was possible -- even trivial -- to generate tightly focused beams of this "gravity" for industrial or agricultural or sexual purposes. The scene suddenly fell into place around Bruno; here were the power generators, slowly bleeding the dream of matter off into the much more pliable dreams of AC voltage and amperage. Here were the inductors, the accumulators, the LRC loops, exactly as they might appear in any of Bruno's own EM grapples, and down there at the far end of the station, the hazy forms of the revpic chambers themselves. But where Bruno's equipment was designed to move individual collapsons, or small collections of them -- hence his helplessness in the face of the careening Onion -- here around him was a device for holding up millions of black holes against the pull of Solar gravity.

Holding what on the other end? What kept the grapple station itself from falling? He tried to imagine the station's complement beam anchored to Jupiter, and almost laughed out loud at the idea of that giant planet being reeled in like a fish. No, the beam was probably anchored to some huge, distant star, was probably dragging that star sunward, and dragging the entire Queendom of Sol out toward it, altering the paths and positions of the two stars in their slow galactic orbits. Two boats joined by even a very long elastic cord were doomed, eventually, to collide, yes? In a million years, perhaps, if the cords weren't cut before then.

They would be cut if the Collapsiter were ever finished. If the Queendom managed to survive its construction.

 

 

 

Muon Contamination

 

 

"Muons are short-lived," Bruno noted, perhaps too gruffly. "Time dilation has extended their lifespans?"

"Indeed," Marlon said, "they're quite close to the event horizons, and moving at very nearly the speed of light. Plays hell with the collapsium, I'm afraid -- relativistic mass increase is enough to disturb the gravitational balance. For a while, I was seriously thinking the whole region might deconstitute and become a single, massive black hole."

"Hmm. You've since ruled this out?"

Marlon shrugged uneasily. "There are a lot of variables. What equilibrium the system has found is chaotic equilibrium -- the collapson nodes wander in and out of phase at irregular intervals. So far, they haven't wandered far enough to lose gravitational rigidity, but the margin is slim, about twenty percent. It seems to be holding -- that's about all I can say."

"You've considered beaming antimuons in to annihilate the contamination?" He inquired.

"Of course," Marlon replied. "Simulations indicated that the resultant gamma radiation would destabilize the lattice almost as rapidly as gravitic radiation. Our one limited experiment matched the predictions perfectly, so I saw little point in pursuing the matter further."

"What's the half-life of the particles?"

"Half life? Most of them are gone already; they'd've decayed almost immediately. It's only the ones that fell into orbits around the collapson nodes that lingered, and most of those are gone as well. It's only the ones that fell in close that remain, all swollen with relativistic mass. So the half-life was probably about a second, although I don't think that's what you're really asking. What you want to know is when the remaining muons will be decayed and gone, or close enough to gone that the Ring Collapsiter's lattice structure regains stability."

"You see through the murk of my thoughts," Bruno agreed.

"Well, unfortunately, I don't have an answer. Again, there are too many variables to construct an accurate prediction. I can guess intelligently: the maximum stable orbit for a particle around a neuble-mass black hole is around a third of the way to the next node in the lattice, a little over one centimeter. Any further than that and the particle will simply be ejected, or else captured by a neighboring hole. The minimum stable orbit is around 1.14 proton radii, and that's where the long-lived particles mostly are. That would put the orbital velocity within, let's see..."

He tapped some calculations into his slate; they appeared, solved, on Bruno's own. Marlon said, "That puts them at about seventy percent of lightspeed, which would mean only minor time dilation if they weren't sitting in this trememdous gravity field. The gravitational time dilation factor would be... three times ten to the thirteenth. At that rate, a muon's lifetime would be--" he tapped some more numbers in "-- three times ten to the seventh seconds. Very approximately, of course."

 

 

 

 

Defeating Inertia

 

 

He began with the basics: a standard collapsium lattice spaced its cube-shaped nodes a little more than two centimeters apart. Denser and looser arrangements were possible, all manner of crystalline symmetries, hexagonal and gyroidal and orthorhombic, with stability islands occurring like spectral lines, seemingly random, at a number of different scales. But that one was the "standard" composition, the one he'd selected for the Iscog's first primitive collapsiters. By chance? By intuition? Many other crystals had been tried over the years, but that one still yielded the greatest blending of stability and mechanical/industrial usefulness.

This zpf-damping foam, though, would need to be a thousand times denser. Were there stability islands anywhere in the proper range for the foam to work? He crafted a series of simulations to confirm it, then backed them up with a rigorous mathematical proof. But the foam's structure was another major problem -- not a simple lattice at all, but something more akin to a quasicrystal of supercooled fluid packets, spiderwebbed in four dimensions. A vacuogel hypercollapsite? More math was needed to prove that wasn't a ridiculous idea. He fretted through the whole process, gnawing absently on the end of his thumb, but one by one the answers all came back affirmative: the material was physically possible.

Relieved, he called for a toilet, some coffee, a weed pipe and a tray of bagels, then indulged in a few minutes of stretching and smoking and refueling his body, before diving back in to tackle the issues of construction. Were there valid intermediate states the collapsium could pass through to reach the hypercollapsite state? A proof confirmed that there ought to be, but he needed a whole chain of them -- stepping stones from the large and simple to the tiny and intricate -- and his initial searches turned up only a single state on anything like the proper pathway.

He grumbled and fretted for a while, converting greater and greater swaths of his study walls into hypercomputer blocks. Finally, when the entire room -- right down to the floor beneath his feet -- was one giant computing device, he hit on a prime-number sorting algorithm that enabled the wellstone to spit out the whole series for him in the space of an hour. It even pointed to some alternate reaction paths and a handful of quite interesting dead-ends, which he resolved to investigate further when time permitted.

The robots sneaked in with more food and drink, which he paused once more to consume, and then fell -- most unwillingly -- asleep.