If you look one level higher in the periodic table, at lithium, you find that its three electrons have two precisely like a helium atom’s, but the third must occupy a higher energy state; it cannot ape either of the others.
One can build up all the elements this way, requiring that each added electron be different. That explains the difference in chemistry between atoms, and therefore, the whole periodic table. This was the revolutionary understanding that quantum mechanics brought.
Quarks run afoul of Pauli’s Principle because you cannot pack apparently identical quarks into a larger particle. Yet there were particles that demanded such an explanation. To explain completely the confusing swarms of observed particles, and still obey the Pauli Principle, physicists had to invoke a new quantum number, which described an added property, called color. An unfortunate choice of words, perhaps, because this facet of quarks has nothing to do with what you and I call color.
This lets quarks crowd into a larger particle, determining its properties, because the quarks could always happily differ in their color quantum number. At first the three choices of color were red, white and blue. Some Europeans correctly pointed out that white was not a color, and suggested a change to yellow. I always wondered if they secretly objected because these were the colors in the US flag (and the British), but I suppose that is an unprofessional suspicion. Even yellow wasn’t used by everybody, though, for the prosaic reason that green shows up better during talks using an overhead projector.
This color-coded theory worked well, successfully predicting particles. Interestingly, all observed particles are “colorless”—the three colors add together to yield no color at all. Now, all this seemed like a bookkeeping device, and many physicists regarded color and even quarks themselves as mathematical conveniences, mere recipes. Successful predictions, though, in a variety of detailed experiments, have convinced most physicists. But an annoying question kept popping up: Why don’t we see individual, naked quarks?
Here again, color saved the day. It turns out that color is as basic a facet of particles as their charge. We all know that charge permits particles to experience the electric and magnetic forces, which we see acting daily in everything from pop-up toasters to lightning. Color is more subtle, though. It regulates the “strong” force, which holds together tiny, sub-nuclear particles. It is the underpinning of our whole world, and we obliviously rely on it to hold matter itself together for our convenience.
The difference is that electric forces don’t have to exchange charge, even though they use them. When a radio signal travels from a commercial station to your receiver, it doesn’t convey charge. Instead, it wiggles the electrons in your antenna, and your receiver amplifies this wiggling, to draw out the message. There is no net charge transmission.
Color is more demanding than charge. It has to flow from one spot to another before the strong force will work. This simple difference makes it impossible to see free quarks.
Electrons, which have charge, make simple fields. We can draw these field lines from the electron, spreading out spherically.
The strength of the electric force is proportional to how many of these lines cross a given area. Far away from the electron, there are fewer lines in a given neighborhood, so the force is weaker. Gravitation works the same way. That’s why the Earth, which is nearby, attracts us more powerfully than does the Sun, even though the Sun has much more mass.
Two electrons nearby have field lines that link them, running from one to the other:
Again, the strength of the force is determined by the number of field lines which cross a given area.
Now take two quarks, Q and Q, which have color, not charge. The color must flow steadily between the quarks, like a current. We can make an analogy by saying this color flow is like electrical charge flow (currents), which produce magnetic fields. We can imagine wires between the two quarks, which carry electrical currents. These cause magnetic fields, and the fields squeeze the wires closer together (called the “pinch effect”). The wires crowd together, making a tight group of field lines:
Now the number of lines crossing a given area is larger than in the electrical case. In fact, the number is constant, since they squeeze together along the cramped axis between the quarks. Since the number of field lines lancing through an area is constant, the force between the quarks is constant, too, independent of how far apart they are.
Suppose we try to pull two quarks apart. We work hard against the force, and it never gets any easier, because the force doesn’t diminish as we separate the quarks. In fact, it isn’t merely difficult to separate two quarks so we can see them, it’s impossible.
All this pulling adds energy to the system, until finally there is enough to create more quarks—another QQ′ pair that appears, poof!, out of the vacuum. Then the tube of wires breaks, and we have:
Two sets of closely bound quarks again! Trying to separate a QQ′ pair—which are really a pair made up of a quark and an anti-quark, to be technical—is like trying to isolate one pole of a magnet. Chop a bar magnet in half and you don’t get a “north” end and a “south” end—you just end up with two smaller magnets, each with two poles.
Similarly, pulling quarks apart—say, by ramming an electron and an anti-electron together and watching the wreckage—gives you quark-antiquark pairs. In such an experiment, we see narrow jets of particles flying apart in opposite directions. They started as a single QQ′ pair that in turn decayed into a lot of other debris.
You can think of the electric field as a swarm of “photons” surrounding a charge. Similarly, around a quark there is a “gluon” swarm. (“Gluon” because they glue strongly interacting objects together; the terminology of physics isn’t all that high-falutin’, after all.) But gluons don’t let quarks get free, where we can see them.
Or rather, they’re not free on a scale that humans can see. The strong force is so powerful that quarks can’t get more than an infinitesimal distance away from each other.
So I began to think…. What if there was a force regulating very, very heavy particles? If it was weak enough, it would allow the heavy particles to separate quite a bit. Was this possible?
Square Forces in a Round World
The first trouble crops up immediately. For a weak, though quarklike force, the mass of the particle must be large—say, a ton or so. Yet it is one particle—and quantum mechanics tells us that particles can also be considered as wavelike. The wavelength of a particle is smaller, the larger the mass. A one-ton particle would have a wavelength so small that its mass would be compressed into an unimaginably small volume. Its density would be so high that its gravitational attraction would be enormous at its surface—so strong that light itself could not escape. That is, it would be a mini-black hole.
This means things are getting very exotic, indeed. On the other hand, this links up with our ideas about quarks. There are theories of gravity which may apply when the quantum nature of matter acts on the same dimensions as does gravity. These “supergravity” theories have quantum numbers similar to color.
Suppose supergravity is right. Then in the future, characters like John Bishop and Sergio Zaninetti could determine the quantum numbers by known methods of calculation. Instead of the boring old gravitational force law, out pops an attractive force which is quarklike.
At first, John and Sergio know only that the particle is awfully massive. They then realize that it warps the spacetime around it in a cubic way—another exotic property! Everything in our ordinary experience is dominated by spherical forces, like gravity. But this object doesn’t pull with equal force in all directions. How to reconcile these facets?
John remembers his boyhood experience with a strange, moving water wave. It was a soliton, and in fact seeing one move down a canal was how they were discovered in the 1830s. These “solitary waves” are concentrations of energy which stay confined and do not dissipate.
It is easy to miss soliton-type solutions in the equations of mathe
matical physics. Solutions revealing wavelike motions are technically easier to extract, so historically they have been favored. Only lately have we begun to find the harder solutions, and many suspect that such exotic animals lurk in the Einstein equations for gravitation.
So far, few soliton solutions have been pursued in gravitation. Although the compressed notations of Einstein’s equations are elegant, they conceal a bewildering complexity—a set of ten coupled, nonlinear differential equations. To make these manageable, mathematicians nearly always assume spherical symmetry. After all, stars and planets are spherical, and perhaps the universe is too, in a more generalized sense.
The equations don’t tell you how to solve them. So far they have rewarded simple assumptions, like spherical symmetry in the resulting objects. But it is quite plausible that cubic symmetry is also “natural,” and is allowed by the equations. No one has yet looked for it. There is no evidence either way for these types of solutions, so I imagined that they were there. It fitted nicely into the “fact” that the artifact itself was cubic, and not merely by whim of the artisan who made it.
John proceeds from this assumption. The cubic forms he finds allow a mass of a ton or so. Mathematically, the force arises from a conserved quantity John terms “fashion,” which plays a similar role to “color” in the strong force. His conversations with Sergio further reveal the quarklike nature of the force he has discovered, but neither takes the hint. After all, they see a single particle. Nobody sees naked quarks, though. They both think this is a flaw, a puzzle.
Seeing the artifact hanging by a cable, pulled toward the northeast, they both see the solution. The force is quarklike, but it’s so weak that the “quarks” can be separated enough for humans to see them. In fact, they can wander around as they like, attracted to each other.
From the angle of the cable, they estimate the force is about a tenth of Earth’s gravity. The energy required to separate two of them is then the product of this constant acceleration (0.1G) times their separation. To make a new pair of these singularities (mathematically indivisible points) requires 2Mc of energy. Dividing this by the energy of separation, they find that to make a new pair takes a separation of ten light years.
This means they’ll never see a new pair pop out of nothingness. But the two singularities can recombine, yielding a lot of energy—perhaps hundreds of megatons.
Indeed, as John and Sergio study matters further, this new force doesn’t seem so crazy after all. The singularity mass is about a ton, which means the force between them is roughly one percent of the force between quarks. So considering the force alone makes the two theories not so wildly different; they differ primarily in the masses involved. This allows the particles to be seen on a human scale of distances.
Another crucial clue for John was the fact that passing a hand over the artifact gave a peculiar, rippling sensation. The rippling of the gravitational field near the singularity caused this, and was direct evidence that the strength of the cubic gravitational potential far exceeded that of the net mass of the singularity.
Put technically, the octopole term in the potential (i.e., that which describes forces which have poles, like the magnetic force) exceeded the monopole term (that which describes spherical forces, like gravity) by orders of magnitude. This could only be true of a distorted, soliton-type solution.
To sum up, the physics surrounding this narrative requires only a few assumptions, none of which we know to be false:
A soliton solution to the gravitational equations, with cubic symmetry, exists.
The force involved has a quantum number similar to quark-style color.
It yields a large mass (a ton).
The force is about a tenth of gravity.
I have played as fairly as I know how—all the rest of the story follows from these conditions.
Yet see what a richness of circumstance can flow from so seemingly abstract a set of assumptions! Human history is based on assuming a rather humdrum world in which we know all the rules. Change one aspect, and—presto! We are perched on a precarious world view.
I have played rather more circumspectly with the archeology in the story. My only major deception lies in my implication that servants were buried with their masters in Mycenaean tombs. There is no evidence for or against this practice. Indeed, this assumption is not really necessary for my narrative, though it does add a bit of spice.
In all this I am much indebted to Dr. Marc Sher for numerous discussions of the physics involved, and his contribution to this Afterword in particular. Professor Hara Georgiou, a Greek archeologist, caught my errors in an early draft of the manuscript. They have my thanks, though of course they are not responsible for any mistakes which made it through to the final version.
Gregory Benford
Athens-Laguna Beach-Cairo
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This book is a work of fiction. The characters, incidents, and dialogue are drawn from the author’s imagination and are not to be construed as real. Any resemblance to actual events or persons, living or dead, is entirely coincidental.
ARTIFACT. Copyright © 1985 by Abbenford Associates. All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins e-books.
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