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Many readers will be unfamiliar with the physical/ cosmological theories on which this story is based, and may find the apparent contradictions jarring. Research into zero-point fields and forces has produced a growing and quite impressive body of literature which, as of this writing, has received little attention outside the astrophysics community. The situation vis a vis "quantum dot" technology is somewhat better, but the implications may still sound a bit magical to some.

The gravitational theories which gave birth to this book are some of the most fascinating and cutting-edge science being performed today. As far as I know, "collapsium" is my own invention, although I've since encountered the word in different context in a couple of places. For helping deduce and refine the mechanism by which collapsium could actually work, I'm deeply indebted to Drs. Richard M. Powers, The Right Reverend Gary E. Snyder, Bjorn Ostman, Boris Gudiken, Arthur C. Clarke, and especially Bernhard Haisch of the Lockheed Martin Solar and Astrophysics Laboratory in Palo Alto.

For those wanting to learn more about this body of work, three of Haisch's papers on the subject, coauthored with Doctors A. Rueda and H.E. Puthoff, include Physics of the Zero-Point Field: Implications for Inertia, Gravitation and Mass (Speculations in Science and Technology, 1996), Inertia as a Zero-Point Lorentz Force (Phys. Review A, Feb 1994), and the wonderfully for-dummies Beyond E=mc2 (The Sciences, Nov/Dec 1994, available online at

In discussions of charge-derived gravitation, the most common objection is usually "why do neutrons have mass?" The answer is simply that neutrons are composed of quarks whose charges cancel out. The quarks themselves are charged, and therefore exhibit the zitterbewegung motions which give rise to gravity and inertia. The neutron's "mass" is therefore a derived, rather than fundamental, property.

A more difficult objection to answer is, why does gravity affect photons and neutrinos? Current theory has a hard time explaining this, but I believe the short answer is probably "because charge warps spacetime." For a detailed explanation of this concept, I'll refer you to Steven C. Bell of Lockheed Martin Astronautics, whose On Quantized Electronic Schwarzchild and Kerr Relativistic Models for the Sperical Orbitals of Hydrogen can be found online at

A formal unification of these theories has yet to be completed; while Bell makes a compelling case for charge as a general-relativistic influence on spacetime curvature, no one has yet approached it as the only such influence. Still, I think at least one road is clearly leading in that direction.

As for collapsium itself, the "Haisch effect" of Appendix A-1 has never been tested in the laboratory. I doubt the necessary technology will exist for at least the next several decades. Nonetheless, assuming the effect is real, it should be possible to collapse a proton into a black hole by increasing its apparent mass. Collapse occurs when the Schwarzchild radius of the increased mass equals or exceeds the proton's radius:

Rs 1.5E-15 m

Rs = 2m/C2 = (2)(6.672E-11)(M)/(3.0E+08)2

\ M=8.768E11 kg

Hence the mass of 1 billion metric tons for the "neubles" which feed the process. Gravitational effects of such a tiny hypermass are indicated by the following equations:

Gravity at 6 cm Range:

gR = m/R2 = (66.72)/(0.06)2 = 18533.3 m/sec2

(approximately 1900 times Earth surface gravity, ge)

Gravity Gradient:

dgR/dR = -2m/R3 = (-2)(66.72)/(0.06)3 = -6.18E+05 sec-2

or, dgR/dR = -6.3E+04 ge/m

(changes by 630 Earth gravities in 1st centimeter)

meanwhile, only four meters away...

Gravity at 4.06 m Range:

gR = m/R2 = (66.72)/(0.06+4.0)2 = 4.23 m/sec2

(approximately 0.4 times Earth surface gravity, ge)


Gravity Gradient:

dgR/dR = -2m/R3 = (-2)(66.72)/(0.06+4.0)3 = -1.99 sec-2

or, dgR/dR = -0.203 ge/m

(changes by 0.2 Earth gravities in 1st meter)


So it's certainly nothing you'd want to be standing very close to. For anyone who's read my 1995 novel FLIES FROM THE AMBER or who is otherwise familiar with the spacetime effects of a hypermass, the question of gravitational time dilation naturally occurs. Sorry, the math will disappoint you:

g = 1-2m/(RC2) = 1-(2)(66.72)/(0.06)(3.0E+08)2

g = 2.47E-14

In other words, even at the lethal 6 cm range, time passes only 0.0000000000025% more slowly than in the outside universe. So for human beings, collapsium does not constitute a forward-only time machine unless, like Marlon's cage de fin, it's moving at relativistic velocity. C'est la vie. As for the obvious "why don't the collapsium's black holes fall into each other?" the answer lies in sympathetic vibrations. This is the same principle that lets "stealth" helicopters fly silently: the sounds produced by the engine and blades are measured, and a "negative" of the wave pattern -- a set of equivalent sound waves 180 degrees out of phase -- is produced to cancel it. If gravity is truly the result of vibration, an equivalent damping mechanism is quite plausible.

The terms "supervacuum" and "True Vacuum" are my own; however, information on the well-studied Casimir effect and its influence on vacuum energy can be found in Phillip Gibbs' online Physics FAQ at, or in Dr. Robert L. Forward's FUTURE MAGIC (Avon Books, 1988), or any of countless other sources.

Given the existence of neubles, building small planets around them is a natural -- albeit hideously expensive -- idea. Bruno's world contains 1500 neubles, at the core of a soil-and-rock sphere 636 meters across, yielding a surface gravity of

g = m/R2 = (6.672E-11)(1.5E16)/(636/2)2 = 9.9 m/sec2

almost exactly one gee.

For information about the theory and practice of quantum wells, wires, and dots, the best reference I've found is Richard Turton's THE QUANTUM DOT (Oxford University Press, 1995), although for the past several years Science News magazine has run occasional short articles on the subject which have also been important in shaping my speculations. The term "wellstone" was supplied by Gary Snyder of Pioneer Astronautics.


There are, of course, innumerable technical details in this book, both major and minor, only a handful of which are directly (and sketchily) addressed in this appendix. However, readers with additional questions are encouraged to pursue them. The answers may well enrich us all.