Superdense Computers Hans Moravec The Robotics Institute Carnegie-Mellon University Pittsburgh, PA 15213 (412) 268-3829 Copyright 1986 by Hans P. Moravec In the large, computers are characterized by their speed (or power) and their memory capacity. At a next level of detail, the amount of parallelism is a key measure. Here's a helpful metaphor. Computing is like a sea voyage in a motorboat. How fast a given journey can be completed depends on the power of the boat's engine, while the maximum length of any journey is limited by the capacity of its fuel tank. Some computations are like a trip to a known location on a distant shore, others resemble a mapless search for a lost island. Parallel computing is like having a fleet of small boats - it helps in searches, and in reaching multiple goals, but not very much in problems that require a distant sprint. The calculation speed of computers has been increasing at a slightly accelerating pace averaging a thousandfold every twenty years. This can be sustained for a considerable time even without great increases in raw switching speed by increasing parallelism - almost all computations have parts that can be sped up somewhat by this strategy. But some destinations cannot be reached in a given time by any number of slowboats. What is the ultimate speed limit of computer logic? Quantum Mechanics demands a minimum energy to localize an event to a given time: $$ Energy = {h \over time} $$ where $h$ is Planck's constant, the basic scale of Quantum Mechanics. Higher speeds require greater energy. Above the frequency of light, about $10^{15}$ transitions per second, the energy reaches one electron volt, close to the energy of the chemical bonds holding solid matter together. Attempts to switch faster will tear apart the switches. The fastest switches, electronic or optical, in laboratories today operate at a mere $10^{11}$ transitions per second, so we can expect a further ten thousandfold speedup before our switches blow up. But, things will be increasingly difficult as the limit is approached (by the year 2010, if our projection holds), aggravated by the fact that in $10^{-15}$ second signals can cover a distance of only 30 atoms. Is there any hope of breaching this ``light barrier''? \sect{Neutronium and Heavy Electrons} The tendency of energetic signals to disintegrate matter can be overcome by increasing the restraining forces, internal or external. Necessarily the matter will be pulled (or pushed) closer together, and will become more dense, incidentally reducing the travel distances of signals. Conventional pressures, such as the three or four million atmospheres achieved in diamond anvil presses (large nutcrackers concentrating their force on sub millimeter faces of two opposing gem quality diamonds) make almost no difference. The additional forces are weaker than the chemical bonds. Much greater pressures are known to exist in the interior of large astronomical bodies. In normal stars the effects of extreme pressure are cancelled by equally extreme temperatures. This is not the case in the burnt out remnants of some supernovas. There, the fusion reactions that power the stars have ceased for lack of fuel, and the atoms in the interior are crushed to the size of their nuclei by the weight of the overlying layers. A star initially ten million kilometers in diameter may be squeezed into a ball ten kilometers across. In the interior protons combine with electrons to form neutrons, which, with the neutrons in the original nuclei, form an undifferentiated, superfluid, sea of neutrons, and a material that has been named {\it Neutronium}. If this matter, or the slightly looser packed nuclei on the surface, could be organized into some kind of integrated circuit, perhaps by high energy versions of present methods, we would expect to be able to switch a million times as fast, $10^{21}$ times per second, using photons that are hard gamma rays. The residual heat of the neutron star would provide some power, which could be augmented from outside by beaming in gamma rays, dropping fusion fuel or simple dead weight, or orbiting dense, tide raising, bodies. Someday neutron stars may be the preferred location for monster super computers since they are common and large. For the immediate future they are too far away, the nearest being thousands of lightyears from us. Is there any hope for smaller, more immediate, ultraspeed gadgets? After all, we're going to reach the speed limit of conventional matter in a mere 25 years. The size of an atom depends on the charge and mass of the electrons orbiting it. If electrons could be made twice as massive, atomic diameters would shrink by half and the density of matter would increase eightfold. Chemical binding energies, which depend on the inverse square law of electric forces, would quadruple, as would the maximum switching speed. Electrons are unlikely to get heavier, but perhaps something could be substituted for them? Heavier particles would bind to nuclei more tightly than electrons, and so would naturally displace them if introduced (just stand back so you're not fried by the liberated energy!). Protons, found in all atomic nuclei, weigh about 2000 times as much as electrons, but the have the wrong charge to also serve for electrons. Antiprotons, protons' mirror images, have the right charge, but combine catastrophically with protons in trillionth second fireballs of mutual annihilation. Particle physicists long ago discovered heavy cousins of electrons, the {\it mu} and (more recently) {\it tau} particles, 200 and 3600 times as massive. Unfortunately they are unstable and so unsuitable for constructing long lasting matter. The muon lasts two microseconds, before decaying into an electron, the tau much shorter. In fact, no particle definitively observed so far will do. Stable charged particles should be very easy to detect in accelerator experiments, and since none have been seen, it's highly probable that none exist up to the energy range of present accelerators. This is over 50,000 times the electron's mass, unfortunately. It means the step beyond normal matter is likely to be big and difficult. \sect{Higgsinium} The theoretical physicists make some tentative promises. Supersymmetry is a class of theories that predicts ``spin-reflected'' analogs of all of the known (and some merely predicted) particles. The theories are not well enough along to assign exact masses to these new particles, but, constrained by already performed experiments, do set bounds. Accelerators being completed now may produce some of these before 1990. One possibility is that the peculiarly named {\it negative Higgsino} particle is stable, and has a mass about 75 times that of a proton (or 150,000 electrons). Suppose we start with a mass of Hydrogen, the simplest atom. In it one electron orbits one proton. Since Higgsinos are heavier than protons, substituting one for the electron will turn the atom inside out: the massive Higgsino will become the nucleus, and the proton will do most of the orbiting, and will set the size of the atom, about 2000 times smaller in diameter than a normal one. The force between adjacent atoms would be $2000^2$ or four million times as great - only astronomical temperatures would break those bonds - the material would remain a solid under any earthly conditions, and there would be $2000^3$ or eight billion times as many atoms per cubic centimeter. Because Higgsinos are heavy, each atom will weigh 75 times as much, so the density would be about $10^{12}$ times that of normal matter. But there's a surprise. Each Higgsino added will itself generate about 20,000 electron volts of energy as it captures a proton - enough to radiate gamma rays. That's minor. But then the exposed orbiting protons of adjacent resulting ``Higgsino Hydrogen'' atoms will be in an optimum position to combine with one another in fours to form Helium nuclei in a fusion reaction. Each fusion liberates a whopping 10 million electron volts, and frees the Higgsinos to catalyse more fusions. This will continue until the resulting nuclear explosion blows the material apart. The Higgsinos may cause fusion of heavier elements as well, and perhaps fission of very heavy nuclei. Great opportunities here, but not quite what we had in mind! Iron nuclei are prone neither to fusion nor fission - it takes energy to both break them down or to build them up - and so can (perhaps) be combined safely with Higgsinos. Each iron nucleus contains 26 protons, and must be neutralized by 26 negative Higgsinos. But it's unlikely that the Higgsinos can overcome their mutual repulsion to neatly form the right sized nuclei. A different, more condensed, arrangement is probable. Suppose we mix small amounts of hydrogen and Higgsinos very slowly and carefully, taking away waste energy (perhaps to help power the Higgsino manufacturing accelerator). The resulting mass will settle down to some lowest energy configuration, probably a crystal of Higgsinos and protons, electrically neutralizing each other, and some neutrons, bound by both electromagnetism and the strong nuclear force. If there are too many neutrons, some will decay radioactively until a stable mix is reached. The protons and neutrons, being the lighter and fuzzier of the particles, will determine the spacing: about that found in neutron stars. The millionfold speedups possible there will apply here also. The final material (let's call it Higgsinium) would be $10^{18}$ times as dense as water; a thimbleful has the weight of a mountain. It'll be a while before that much of it is manufactured. A cubical speck a micron on a side weighs a gram, and should be enough to make thousands of very complex integrated circuits - analogous to a cubic centimeter of silicon. Their speed would be a millionfold greater, as would their power consumption and operating temperature. It may be possible to build the circuits with high energy versions of the optical and particle beam methods used to construct today's ICs, though the engineering challenges are huge! And in the long run tiny machines of Higgsinium might be dropped onto neutron stars to seed the construction of immense Neutronium minds. \sect{Magnetic Monopoles} Higgsinos, and the rest of the supersymmetric stable, were ``invented'' only recently. An equally plausible, and even more interesting, kind of particle was theorized in 1930, by Paul Dirac. In a calculation that combined Quantum Mechanics with Special Relativity, Dirac deduced the existence of the positrons, mirror images of the electrons. This was the first indication of antimatter, and positrons were actually observed in 1932. The same calculation predicted the existence of a magnetic monopole, a stable particle carrying a charge like an isolated north or south pole of a magnet. Dirac's calculation did not give the monopole's mass, but it did specify the magnitude of its ``charge''. Recent ``gauge'' theories, in which the forces of nature are treated as distortions in higher dimensional spaces, also predict monopoles (as knots in spacetime), and even assign masses. Unfortunately there are competing versions with different mass predictions ranging from $1000$ to $10^{16}$ times that of a proton. These masses are beyond the energy of existing and planned particle accelerators. Some cosmic rays are energetic enough. For over forty years searches for monopoles all came up empty handed, and there was great skepticism about their existence. But they may have been fleetingly observed three times in the last decade, though none has yet been caught for extended observation. In 1973 a Berkeley cosmic ray expirement was lofted above most of the scattering atmosphere in a high altitude balloon. In 1975, after two years of study, a very heavy track bearing the stigmata of a monopole was noted in the lexan sheets that served as three dimensional detecting film. Calculations suggested it had twice Dirac's predicted charge, and a mass over 600 times that of a proton. Since monopoles had never been observed before, there was much skepticism. Other, more elaborate but more conventional possibilities were devised, and the incident was shelved. On Valentine's day in 1982, a modest experiment in Blas Cabrera's Stanford physics lab registered a clean, persistent, steplike jump in the current in a superconducting loop. The size of the step was just what a monopole with Dirac's quantum of magnetic charge would have caused had it passed through the loop. The only alternative explanation was mechanical failure in the experimental apparatus. Subsequent prodding and banging produced no effect - everything seemed shipshape. The result was so exciting many groups around the world, including Cabrera's, built larger detectors, hoping to confirm the observation. For four years there was silence. By then the cumulative experience of the new detectors (collecting area multiplied by time) was over a thousand times that of Cabrera's original experiment. Once again the possibility of monopoles faded. Then, on May 22, 1986, a detector at Imperial College, London, whose experience was over four hundred times as large as Cabrera's original, registered another event. Until a monopole is caught and held, its existence will be in question. Yet, each additional detection greatly increases the odds that the others were not mistakes. Magnetism and electricity are right angle versions of the same thing. A monopole waved up and down will cause a nearby electric charge to move side to side (and vice versa). A current of monopoles flowing in one wire will induce an electric current at right angles to itself. An electric current in a loop of conductor will flow in lockstep with a current of monopoles in a monopole-conducting loop chain linked with it. Two coils of wire wrapped around a monopole loop make a DC transformer - a current started in one coil will induce a monopole current in the loop, which will produce an electric current in the other coil's circuit. If good DC transformers had existed in the late nineteenth century, Thomas Edison and George Westinghouse would have had less to fight about, and all our electrical outlets would produce direct current. With monopoles we might refrain from making electrical connections at the plug at all, and draw power simply by passing the two ends of our power cords through a partially exposed monopole loop. But let's get serious. If there are monopoles, they're not very common, and few will be simply picked out of the air. If they're very heavy, they will be hard to stop. Perhaps a few can be found already trapped here and there, and can be coaxed out (such a search was conducted worldwide by Kenneth Ford of Brandeis University, armed with a portable electromagnetic solenoid, in the early 1960s). Many things are possible given a few monopoles. Physicists routinely build superconducting solenoids with powerful magnetic fields several hundred thousand times as strong as Earth's. A monopole accelerates along magnetic field lines (for instance, a ``North'' monopole is strongly attracted to the south pole of a magnet). A monopole riding the field lines down the center of a powerful solenoid will gain an energy equivalent to the mass of several protons for every centimeter of travel. Ten meters of solenoid will impart an energy matching that of the most powerful existing accelerators. A few kilometers of solenoids will produce energies equal to millions of proton masses. The fireball resulting from a head on collision of two monopoles moving thusly is intense enough to produce some number of additional monopoles, in North/South matching pairs. These can be sorted out magnetically, and so monopoles can be harnessed to breed more monopoles. Detectors of the Cabrera type do not measure the mass of passing monopoles, and the theories are little help. Monopoles can't be too light or they would have been created in existing accelerators. As mentioned above, the theoretical range of uncertainty is enormous. Things are especially interesting if there are at least two kinds of non mutually annihilating stable monopole, analogous to the proton and electron in normal matter (the North/South pairs mentioned above don't count - the two are antiparticles of each other, and annihilate when brought in contact). Here's a real leap of ignorance: let's suppose there are two kinds and that they are near the low end of the possible mass range. Let's suppose the lighter variety weighs $1000$ protons, and the the heavier $1,000,000$ protons. If two kinds don't exist, or if monopoles turn out to be much heavier many of the following proposals will become more extreme, or impossible. Others may open in their place. An atom of {\it Monopolium} has a light monopole of one polarity (let's say North) bound to a heavy monopole of the opposite pole. Its size is set by the fuzzier light monopole. We assumed this has a mass of 1000 protons (or two million electrons), making the monopole atom about two million times smaller than a normal one. The particle spacing in Monopolium is thus comparable to that in Neutronium or Higgsinium. Its density, however, will be a million times beyond those because of the great mass of the central heavy monopole. This makes it $10^{25}$ times as heavy as normal matter. A thimbleful weighs as much as the Moon. Dirac's calculation found the magnetic quantum of charge to be $68.5$ times as intense as the electric quantum. Two monopoles a certain distance apart would attract or repel each other $68.5^2$ or $4,692$ times as strongly as two equally separated electric particles. Combining this with the (inverse square) effects of much closer spacing and the increased density, makes Monopolium ten thousand times as strong for its weight as normal matter, though this number changes radically with changes in the assumed masses of the two kinds of monopole. The limiting switching speeds may be a thousand times higher than those we found for Higgsinium. \sect{Other Applications} If Higgsinium or Monopolium can be made they may have applications beyond circuitry. Both materials are very tightly held together, and have no mechanism for absorbing small amounts of energy such as those found in photons, even soft gamma rays. This should make the materials very transparent. Yet the internal electromagnetic fields are huge, making for a tremendous index of refraction. Submicroscopic gamma ray microscopes, telescopes and lasers merely hint at the possibilities. In larger optics, gravitational effects will become important. If the materials can host loose electric or magnetic charges, they would be almost certainly be superconductors up to very high temperatures. because the tremendous binding forces would limit the number of states that the conducting particles can assume. To them the surface of the sun would is still very close to absolute zero in temperature. Superconducting versions of the materials should be nearly perfect mirrors, again up to gamma ray energies. Macroscopic extents of these substances are possible in {\it very} thin fibers or sheets. An (utterly invisible) Higgsinium strand one conventional atom ($= 10^6 particles$) in diameter masses 100 grams per centimeter of length. It may be able to support a 100 million tonnes, being about ten thousand times stronger for its weight than normal materials. Although it would slice through conventional matter as through a cloud (but sometimes the extremely thin cut would heal itself immediately), properly mounted it would make gargantuan engineering projects such as orbital elevators trivial. A single particle thick layer of Higgsinium would weigh about ten kilograms per square centimeter. Overlayed on structures of conventional matter the superconducting version especially would make powerful armor that would shield against essentially all normal matter projectiles, temperatures into the nuclear range, and all but the highest energy radiation. (But it could be penetrated by even denser Monopolium tipped bullets. Arms races are relentless!) The same armor could be used to line the combustion chamber and expansion bell of a matter-antimatter rocket. Normal matter is instantly disintegrated by the violence of the reaction, but Higgsinium would easily bounce the pions, gamma rays and X rays produced when hydrogen meets antihydrogen. Single particle thick Monopolium, at a hundred tonnes per square centimeter, may be too heavy to use as a veneer at macroscopic scales. But it might be just the thing for constructing microscopic interstellar ships. A ship with two tiny tanks crammed with ultra compressed hydrogen and antihydrogen could rapidly propel itself at high acceleration to a few percent of the speed of light. Unaffected by either protons or antiprotons, Monopolium it would be better for building the engine and tanks than Higgsinium. The ship's front end might house a superfast mind, and tiny robot arms. It could probably land on a neutron star and start raising Neutronium crops and children. Combining electrically conducting matter and Monopolium is interesting. Our Monopolium is about $10,000$ times as strong for its weight as normal matter. Properly exploited, it can store $10,000$ as much energy in mechanical or electromagnetic form. Monopolium superconductor plated in a ring around a copper rod should make a lovely storage battery. To charge it, pass a current through the rod, thus setting up a monopole supercurrent in the ring. The magnetic current remains when you break the electrical connection, and causes the ends of the rod keep the voltage you had applied. When you connect a load to the rod ends, a current flows, and the voltage gradually drops towards zero as the monopole current slowly converts to electrical power. A kilogram of Monopolium should be able to store a fantastic one million watt hours. {\it Caution: Do Not Overcharge!} If the monopole current becomes too large, the electric field it generates will burst the ring, and all of the stored energy will be released at once in an explosion equal to a ton of TNT. There are other possibilities, especially involving intimate mixtures of monopoles and electrically charged matter (intertwined, like links of a chain), but we're out far enough on this limb for now. \end{document}