He wandered over tundra moss and samphire, kedge and grass. Life on Mars. An odd business. Life anywhere, really. Not at all obvious why it should appear. This was something Sax had been thinking about recently. Why was there increasing order in any part of the cosmos, when one might expect nothing but entropy everywhere? This puzzled him greatly. He had been intrigued when Spencer had offered an offhand explanation, over beer one night on the Odessa corniche — in an expanding universe, Spencer had said, order was not really order, but merely the difference between the actual entropy exhibited and the maximum entropy possible. This difference was what humans perceived as order. Sax had been surprised to hear such an interesting cosmological notion from Spencer, but Spencer was a surprising man. Although he drank too much alcohol.
Lying on the grass looking at tundra flowers, one couldn’t help thinking about life. In the sunlight the little flowers stood on their stems glowing with their anthracyins, dense with color. Ideograms of order. They did not look like a mere difference in entropic levels. Such a fine texture to a flower petal; drenched in light, it was almost as if it were visible molecule by molecule: there a white molecule, there lavender, there clematis blue. These pointillist dots were not molecules, of course, which were well below visible resolution. And even if molecules had been visible, the ultimate building blocks of the petal were so much smaller than that that they were hard to imagine — finer than one’s conceptual resolution, one might say. Although recently the theory group at Da Vinci had begun buzzing about developments in superstring theory and quantum gravity they were making; it had even gotten to the point of testable predictions, which historically had been string theory’s great weakness. Intrigued by this reconnection with experiment, Sax had recently started trying to understand what they were doing. It meant foregoing sea cliffs for seminar rooms, but in the rainy seasons he had done it, sitting in on the group’s afternoon meetings, listening to the presentations and the discussions afterward, studying the scrawled math on the screens and spending his mornings working on Riemann surfaces, Lie algebras, Euler numbers, the topologies of compact six-dimensional spaces, differential geometries, Grassmannian variables, Vlad’s emergence operators, and all the rest of the mathematics necessary to follow what the current generation was talking about.
Some of this math concerning superstrings he had looked into before. The theory had existed for almost two centuries now, but it had been proposed speculatively long before there was either the math or the experimental ability to properly investigate it. The theory described the smallest particles of spacetime not as geometrical points but as ul-tramicroscopic loops, vibrating in ten dimensions, six of which were compactified around the loops, making them somewhat exotic mathematical objects. The space they vibrated in had been quantized by twenty-first-century theorists, into loop patterns called spin networks, in which lines of force in the finest grain of the gravitational field acted somewhat like the lines of magnetic force around a magnet, allowing the strings to vibrate only in certain harmonics. These supersymmetrical strings, vibrating harmonically in ten-dimensional spin networks, accounted very elegantly and plausibly for the various forces and particles as perceived at the subatomic level, all the bosons and fermions, and their gravitational effects as well. The fully elaborated theory therefore claimed to mesh successfully quantum mechanics with gravity, which had been the problem in physical theory for over two centuries.
All very well; indeed, exciting. But the problem, for Sax and many other skeptics, came with the difficulty of confirming any of this beautiful math by experiment, a difficulty caused by the very, very, very small sizes of the loops and spaces being theorized. These were all in the 10~33 centimeter range, the so-called Planck length, and this length was so much smaller than subatomic particles that it was hard to imagine. A typical atomic nucleus was about 1(T13 centimeter in diameter, or one millionth of a billionth of a centimeter. First Sax had tried very hard to contemplate that distance for a while; hopeless, but one had to try, one had to hold that hopelessly inconceivable smallness in the mind for a moment. And then remember that in string theory they were talking about a distance twenty magnitudes smaller still — about objects one thousandth of one billionth of one billionth the size of an atomic nucleus! Sax struggled for ratio; a string, then, was to the size of an atom, as an atom was to the size of … the solar system. A ratio which rationality itself could scarcely comprehend.
Worse yet, it was too small to detect experimentally. This to Sax was the crux of the problem. Physicists had been managing experiments in accelerators at energy levels on the order of one hundred GeV, or one hundred times the mass energy of a proton. From these experiments they had worked up, with great effort, over many years, the so-called revised standard model of particle physics. The revised standard model explained a lot, it was really an amazing achievement, and it made predictions that could be proved or disproved by lab experiment or cosmological observations, predictions that were so varied and had been so well fulfilled that physicists could speak with confidence about much of what had gone on in the history of the universe since the Big Bang, going as far back as the first millionth of a second of time.
String theorists, however, wanted to make a fantastic leap beyond the revised standard model, to the Planck distance which was the smallest realm possible, the minimum quantum movement, which could not be decreased without contradicting the Pauli exclusion principle. It made sense, in a way, to think about that minimum size of things; but actually seeing events at this scale would take experimental energy levels of at least 1019 GeV, and they could not create those. No accelerator would ever come close. The heart of a supernova would be more like it. No. A great divide, like a vast chasm or desert, separated them from the Planck realm. It was a level of reality fated to remain unknown to them in any physical sense.
Or so skeptics maintained. But those interested in the theory had never been dissuaded from studying it. They searched for indirect confirmation of the theory at the subatomic level, which from this perspective now seemed gigantic, and from cosmology. Anomalies in phenomena that the revised standard could not explain, might be explained by predictions made by string theory about the Planck realm. These predictions had been few, however, and the predicted phenomena very difficult to see. No real clinchers had been found. But as the decades passed, a few string enthusiasts had always continued to explore new mathematical structures, which might reveal more ramifications of the theory, might predict more detectable indirect results.
This was all they could do; and it was a very chancy road for physics to take, Sax felt. He believed in the experimental testing of theories with all his heart. If it couldn’t be tested, it remained math only, and its beauty was irrelevant; there were lots of bizarrely beautiful exotic fields of mathematics, but if they weren’t modeling the phenomenal world, Sax wasn’t interested.
Now, however, after all the decades of work, they were beginning to make progress in ways that Sax found interesting. At the new supercollider in Rutherford Crater’s rim, they had found the second Z particle that string theory had long predicted would be there. And a magnetic monopole detector, orbiting the sun out of the plane of the ecliptic, had captured a trace of what looked to be a fractionally charged unconfined particle with a mass as big as a bacterium — a very rare glimpse of a “weakly interacting massive particle,” or WIMP. String theory had predicted WIMPs would be out there, while the revised standard did not call for them. That was thought provoking, because the shapes of galaxies showed that they had gravitational masses ten times as large as their visible light revealed; if the dark matter could be explained satisfactorily as weakly interacting massive particles, Sax thought, then the theory responsible would have to be called very interesting indeed.