CHAPTER Six
The Most Bang for Your Buck
Nothing Unreal Exists. Kir-kin-tha's First Law of Metaphysics (Star Trek IV: The Voyage Home,)
If you are driving west on Interstate 88 out of Chicago, by the time you are 30 miles out of town, near Aurora, the hectic urban sprawl gives way to the gentle Midwestern prairie, which stretches forward and flat as far as you can see. Located slightly north of the interstate at this point is a ring of land marked by what looks like a circular moat. Inside the property, you may see buffalo grazing and many species of ducks and geese in a series of ponds.
Twenty feet below the surface, it is a far cry from the calm pastoral atmosphere above ground. Four hundred thousand times a second, an intense beam of antiprotons strikes a beam of protons head on, producing a shower of hundreds or thousands of secondary particles: electrons, positrons, pions, and more.
This is the Fermi National Accelerator Laboratory, or Fermilab for short. It contains the world's highest-energy particle accelerator. But more germane for our purposes is the fact that it is also the world's largest repository of antiprotons. Here, antimatter is not the stuff of science fiction. It is the bread and butter of the thousands of research scientists who use the Fermilab facilities.
It is in this sense that Fermilab and the U.S.S. Enterprise bear a certain kinship. Antimatter is crucial to the functioning of a starship: it powers the warp drive. As I mentioned earlier, there is no more efficient way to power a propulsion system (though the warp drive is not, in fact, based on rocket propulsion). Antimatter and matter, when they come into contact, can completely annihilate and produce pure radiation, which travels out at the speed of light.
Obviously, great pains must be taken to make sure that antimatter is “contained” whenever it is stored in bulk. When antimatter containment systems fail aboard starships, as when the Enterprise's system failed after its collision with the Bozeman, or when the containment system aboard the Yamato failed due to the Iconian computer weapon, total destruction inevitably follows soon afterward. In fact, antimatter containment would be so fundamental to starship operation that it is hard to understand why Federation Lieutenant Commander Deanna Troi was ignorant of the implications of containment loss when she temporarily took over command of the Enterprise in the Next Generation episode “Disaster,” after the ship collided with two “quantum filaments.” The fact that she was formally trained only as a psychologist should have been no excuse!
The antimatter containment system aboard starships is plausible, and in fact uses the same principle that allows Fermilab to store antiprotons for long periods. Antiprotons and antielectrons (called positrons) are electrically charged particles. In the presence of a magnetic field, charged particles will move in circular orbits. Thus, if the particles are accelerated in electric fields, and then a magnetic field of appropriate strength is applied, the antiparticles will travel in circles of prescribed sizes. In this way, for example, they can travel around inside a doughnut-shaped container without ever touching the walls. This principle is also used in so-called Tokomak devices to contain the high-temperature plasmas in studies of controlled nuclear fusion.
The Antiproton Source for the Fermilab collider contains a large ring of magnets. Once antiprotons are produced, in medium-energy collisions, they are steered into this ring, where they can be stored until they are needed for the highest-energy collisions, which take place in the Tevatronthe Fermilab high-energy collider. The Teva-tron is a much larger ring, about four miles in circumference. Protons are injected into the ring and accelerated in one direction, and antiprotons are accelerated in the other. If the magnetic field is carefully adjusted, these two beams of particles can be kept apart throughout most of the tunnel. At specified points, however, the two beams converge and the collisions are studied.
Besides containment, another problem faces us immediately if we want to use a matter-antimatter drive: where to get the antimatter. As far as we can tell, the universe is made mostly of matter, not antimatter. We can confirm that this is the case by examining the content of high-energy cosmic rays, many of which originate well outside our own galaxy. Some antiparticles should be created during the collisions of high-energy cosmic rays with matter, and if one explores the cosmic-ray signatures over wide energy ranges, the antimatter signal is completely consistent with this phenomenon alone; there is no evidence of a primordial antimatter component.
Another possible sign of antimatter in the universe would be the annihilation signature of antiparticle-particle collisions. Wherever the two coexist, one would expect to see the characteristic radiation emitted during the annihilation process. Indeed, this is exactly how the Enterprise searched for the Crystalline Entity after it had destroyed a new Federation outpost. Apparently the Entity left behind a trace antiproton trail. By looking for the annihilation radiation, the Enterprise trailed the Entity and overtook it before it could attack another planet.
While the Star Trek writers got this idea right, they got the details wrong. Dr. Marr and Data search for a sharp “gamma radiation” spike at “10 keV”a reference to 10 kilo-electron volts, which is a unit of energy of radiation. Unfortunately, this is the wrong scale of energy for the annihilation of protons and antiprotons, and in fact corresponds to no known annihilation signal. The lightest known particle with mass is the electron. If electrons and positrons annihilate, they produce a sharp spike of gamma radiation at 511 keV, corresponding to the mass of the electron. Protons and antiprotons would produce a sharp spike at an energy corresponding to the rest energy of the proton, or about 1 GeV (Giga-electron volt)roughly a hundred thousand times the energy searched for by Marr and Data. (Incidentally, 10 keV is in the X-ray band of radiation, not the gamma-ray band, which generally corresponds to radiation in excess of about 100 keV, but this is perhaps too fine a detail to complain about.)
In any case, astronomers and physicists have looked for diffuse background signals near 511 keV and in the GeV range as signals of substantial matter-antimatter conflagrations but have not found such signals. This and the cosmic-ray investigations indicate that even if substantial distributions of antimatter were to exist in the universe, they would not be interspersed with ordinary matter.
As most of us are far more comfortable with matter than antimatter, it may seem quite natural that the universe should be made of the former and not the latter. However, there is nothing natural at all about this. In fact, the origin of the excess of matter over antimatter is one of the most interesting unsolved problems in physics today, and is a subject of intense research at the present time. This excess is very relevant to our existence, and thus to Star Trek's, so it seems appropriate to pause to review the problem here.
When quantum mechanics was first developed, it was applied successfully to atomic physics phenomena; in particular, the behavior of electrons in atoms was wonderfully accounted for. However, it was clear that one of the limitations of this testing ground was that such electrons have velocities that are generally much smaller than the speed of light. How to accommodate the effects of special relativity with quantum mechanics remained an unsolved problem for almost two decades. Part of the reason for the delay was that unlike special relativity, which is quite straightforward in application, quantum mechanics required not just a whole new world view but a vast array of new mathematical techniques. The best young minds in physics were fully occupied in the first three decades of this century with exploring this remarkable new picture of the universe.
One of those minds was Paul Adrien Maurice Dirac. Like his successor Stephen Hawking, and later Data, he would one day hold the Lucasian Professorship in Mathematics at Cambridge University. Educated by Lord Rutherford, and later training with Niels Bohr, Dirac was better prepared than most to extend quantum mechanics to the realm of the ultrafast. In 1928, like Einstein before him, he wrote down an equation that would change the world. The Dirac equation correctly describes the relativistic behavior of electrons in fully quantum mechanical terms.
Shortly after writing down this equation, Dirac realized that to retain consistency, the mathematics required another particle of equal but opposite charge to the electron to exist in nature. Of course, such a particle was known alreadynamely, the proton. However, Dirac's equation suggested that this particle should have the same mass as the electron, whereas the proton is almost two thousand times heavier. This discrepancy between observation and the “naive” interpretation of the mathematics remained a puzzle for four years, until the American physicist Carl Anderson discovered, among the cosmic rays bombarding the Earth, a new particle whose mass was identical to the electron's but whose charge was the oppositethat is, positive. This “antielectron” soon became known as the positron.
Since then, it has become clear that one of the inevitable consequences of the merger of special relativity and quantum mechanics is that all particles in nature must possess antiparticles, whose electric charge (if any) and various other properties should be the opposite of their particle partners. If all particles possess antiparticles, then which particles we call particles and which we call antiparticles is completely arbitrary, as long as no physical process displays any bias for particles over antiparticles. In the classical world of electromagnetism and gravity, no such biased process exists.
Now we are left in a quandary. If particles and antiparticles are on an identical footing, why should the initial conditions of the universe have determined that what we call particles should comprise the dominant form of matter? Surely a more sensible, or at least a more symmetric, initial condition would be that in the beginning the
number of particles and antiparticles would have been identical. In this case, we must explain how the laws of physics, which apparently do not distinguish particles from antiparticles, could somehow contrive to produce more of one type than the other. Either there exists a fundamental quantity in the universethe ratio of particles to antiparticleswhich was fixed at the beginning of time and about which the laws of physics apparently have nothing to say, or we must explain the paradoxical subsequent dynamical creation of more matter than antimatter.
In the 1960s, the famous Soviet scientist and later dissident Andrei Sakharov made a modest proposal. He argued that it was possible, if three conditions were fulfilled in the laws of physics during the early universe, to dynamically generate an asymmetry between matter and antimatter even if there was no asymmetry to start with. At the time this proposal was made, there were no physical theories that satisfied the conditions Sakharov laid down. However, in the years since, particle physics and cosmology have both made great strides. Now we have many theories that can, in principle, explain directly the observed difference in abundance between matter and antimatter in nature. Unfortunately, they all require new physics and new elementary particles in order to work; until nature points us in the right direction, we will not know which of them to choose from. Nevertheless, many physicists, myself included, find great solace in the possibility that we may someday be able to calculate from first principles exactly why the matter fundamental to our existence itself exists.
Now, if we had the correct theory, what number would it need to explain? In the early universe, what would the extra number of protons compared to antiprotons need to have been in order to explain the observed excess of matter in the universe today? We can get a clue to this number by comparing the abundance of protons today to the abundance of photons, the elementary particles that make up light. If the early universe began with an equal number of protons and antiprotons, these would annihilate, producing radiationthat is, photons. Each proton- antiproton annihilation in the early universe would produce, on average, one pair of photons. However, assuming there was a small excess of protons over antiprotons, then not all the protons would be annihilated. By counting the number of protons left over after the annihilations were completed, and comparing this with the number of photons produced by those annihilations (that is, the number of photons in the background radiation left over from the big bang), we can get an idea of the fractional excess of matter over antimatter in the early universe.
We find that there is roughly one proton in the universe today for every 10 billion photons in the cosmic background radiation. This means that the original excess of protons over antiprotons was only about 1 part in 10 billion! That is, for every 10 billion antiprotons in the early universe, there were 10 billion and 1 protons! Even this minuscule excess (accompanied by a similar excess in neutrons and electrons over their antiparticles) would have been sufficient to have produced all the observed matter in the universethe stars, galaxies, planetsand all that we have come to know and love.
That is how we think the universe got to be made of matter and not antimatter. Aside from its intrinsic interest, the moral of this story for Star Trek is that if you want to make a matter-antimatter drive, you cannot harvest the antimatter out in space, because there isn't very much. You will probably have to make it.
To find out how to do this, we return to the buffalo roaming on the Midwestern plain above the Fermilab accelerator. When thinking about the logistics of this problem, I decided to contact the director of Fermilab, John Peoples, Jr., who led the effort to design and build its Antiproton Source, and ask if he could help me determine how many antiprotons one could produce and store per dollar in today's dollars. He graciously agreed to help by having several of his staff provide me with the necessary information to make reasonable estimates.
Fermilab produces antiprotons in medium-energy collisions of protons with a lithium target. Every now and then these collisions will produce an antiproton, which is then directed into the storage ring beneath the buffalo. When operating at average efficiency, Fermilab can produce about 50 billion antiprotons an hour in this way. Assuming that the Antiproton Source is operating about 75 percent of the time throughout the year, this is about 6000 hours of operation per year, so Fermilab produces about 300,000 billion antiprotons in an average year.
The cost of those components of the Fermilab accelerator that relate directly to producing antiprotons is about $500 million, in 1995 dollars. Amortizing this over an assumed useful lifetime of 25 years gives $20 million per year. The operating cost for personnel (engineers, scientists, staff) and machinery is about $8 million a year. Next, there is the cost of the tremendous amount of electricity necessary to produce the particle beams and to store the antiprotons. At current Illinois rates, this costs about $5 million a year. Finally, related administrative costs are about $15 million a year. The total comes to some $48 million a year to produce the 300,000 billion
antiprotons that Fermilab annually uses to explore the fundamental structure of matter in the universe. This works out to about 6 million antiprotons for a dollar!
Now, this cost is probably higher than it would need to be. Fermilab produces a high-energy beam of antiprotons, and if we required only the antiprotons and not such high energies we might cut the cost, perhaps by a factor of about 2 to 4. So, to be generous, let's assume that using today's technology, one might be able to get from 10 million to 20 million antiprotons for a buck, wholesale.
The next question is almost too obvious: How much bang for this buck? If we convert entirely the mass of one dollar's worth of antiprotons into energy, we would release approximately 1/1000 of a joule, which is the amount of energy required to heat up about 1/4 of a gram of water by about 1/1000 of a degree Celsius. This is nothing to write home about.
Perhaps a better way to picture the potential capabilities of the Fermilab Antiproton Source as the nucleus of a warp core is to consider the energy that might be generated by utilizing every antiproton produced by the Source in real time. The Antiproton Source can produce 50 billion antiprotons an hour. If all these antiprotons were converted into energy, this would result in a power generation of about 1/1000 of a watt! Put another way, you would need about 100,000 Fermilab Antiproton Sources to power a single lightbulb! Given the total annual cost of $48 million to run the Antiproton Source, it would cost at the present time more than the annual budget of the U.S. government to light up your living room in this way.
The central problem is that as things stand today it requires far more energy to produce an antiproton than you would get out by converting its rest mass back into energy. The energy lost during the production process is probably at least a million times more than the energy stored in the antiproton mass. Some much more effective means would be needed for antimatter production before we could ever think of using matter-antimatter drives to propel us to the stars.
It is also clear that if the Enterprise were to make its own antimatter, vast new technologies of scale would be needednot just for cost reduction, but for space reduction. If accelerator techniques were to be utilized, machines that generate far more energy per meter than those of today would be necessary. I might add that this is currently a subject of intense research here on late-twentieth-century Earth. If particle accelerators, which are our only tools for directly exploring the fundamental structure of matter, are not to become too costly for even international consortiums to build, new technologies for accelerating elementary particles must be developed. (We have already seen that our own government has decided that it is too expensive to build a next-generation accelerator in this country, so a European group will be building one in Geneva, designed to come on line at the beginning of the next century.) Past trends in the efficiency of energy generation per meter of accelerator suggest that a tenfold improvement may be possible every decade or two. So perhaps in several centuries it will not be unreasonable to imagine a starship-size, antimatter-producing accelerator. Given the current reluctance of governments to support expensive fundamental research at this scale, one might not be so optimistic, but in two centuries a lot of political changes can occur.
Even if one were to make antimatter on board ship, however, one would still have to deal with the fact that to produce each antiproton would invariably use up much more energy than one would get out afterward. Why would one want to expend this energy on antimatter production, when one might turn it directly into propulsion?
The Star Trek writers, always on the ball, considered this problem. Their answer was simple. While energy available in other forms could be used for impulse propulsion and hence sublight speeds, only matter-antimatter reactions could be used to power the warp drive. And because warp drive could remove a ship from danger much more effectively than impulse drive, the extra energy expended to produce antimatter might be well worth it in a pinch. The writers also sidestepped the accelerator-based antimatter-production problems by inventing a new method of antimatter production. They proposed hypothetical “quantum charge reversal devices,” which would simply flip the charge of elementary particles, so that one could start with protons and neutrons and end up with antiprotons and antineutrons. According to the Next Generation Technical Manual, while this process is incredibly power-intensive, there is a net energy loss of only 24 percentorders of magnitude less than the losses described above for accelerator use.
While all this is very attractive, unfortunately simply flipping the electric charge of a proton is not enough.
Consider, for example, that both neutrons and antineutrons are neutral. Antiparticles have all the opposite “quantum numbers” (labels describing their properties) of their matter partners. Since the quarks that make up protons possess many labels other than electric charge, one would have to have many other “quantum reversal devices” to complete the transition from matter to antimatter.
In any case, we are told in the technical manual that, except for emergency antimatter production aboard starships, all Starfleet antimatter is produced at Starfleet fueling facilities. Here antiprotons and antineutrons are combined to form the nuclei of anti-heavy hydrogen. What is particularly amusing is that the Starfleet engineers then add antielectrons (positrons) to these electrically charged nuclei to make neutral anti-heavy-hydrogen atomsprobably because neutral antiatoms sound easier to handle than electrically charged anti-nuclei to the Star Trek writers. (In fact no antiatoms have yet been created in the laboratoryalthough recent reports out of Harvard suggest that we are on the threshold of producing an antihydrogen atom in this decade.) Unfortunately, this raises severe containment problems, since magnetic fields, which are absolutely essential for handling substantial amounts of antimatter without catastrophe, work only for electrically charged objects! Ah well, back to the drawing board. .. .
The total antimatter fuel capacity of a starship is approximately 3000 cubic meters, stored in various storage pods (on Deck 42 in the Enterprise-D). This is claimed to be sufficient for a 3-year mission. Just for fun, let's estimate how much energy one could get out of this much antimatter if it were stored as anti-heavy-hydrogen nuclei. I will assume that the nuclei are transported as a rarefied plasma, which would probably be easier to contain magnetically than a liquid or solid. In this case, 3000 cubic meters could correspond to about 5 million grams of material. If 1 gram per second were consumed in annihilation reactions, this would produce a power equivalent to the total power expended on a daily basis by the human race at the present time. As I indicated earlier in discussing warp drive, one must be prepared to produce at least this much power aboard a starship. One could continue using the fuel at this rate for 5 million seconds, or about 2 months. Assuming that a starship utilizes the matter-antimatter drive for 5 percent of the time during its missions, one might then get the required 3 years' running time out of this amount of material. Also of some relevance to the amount of antimatter required for energy production is another fact (one that the Star Trek writers have chosen to forget from time to time): matter- antimatter annihilation is an all-or-nothing proposition. It is not continuously tunable. As you change the ratio of matter to antimatter in the warp drive, you will not change the absolute power-generation rate. The relative power versus fuel used will decrease only if some fuel is wastedthat is, if some particles of matter fail to find antimatter to annihilate with, or if they merely collide without annihilating. In a number of episodes (“The Naked Time,” “Galaxy's Child,” “Skin of Evil”) the matter-antimatter ratio is varied, and in the Star Trek technical manual this ratio is said to vary continuously from 25:1 to 1:1 as a function of warp speed, with the 1:1 ratio being used at warp 8 or higher. For speeds higher than warp 8, the amount of reactants is increased, with the ratio remaining unchanged. Changing the amount of reactants and not the ratio should be the proper procedure throughout, as even Starfleet cadets should know. Wesley Crusher made this clear when he pointed out, in the episode “Coming of Age,” that the Starfleet exam question on matter-antimatter ratios was a trick question and that there was only one possible rationamely, 1:1.
Finally, the Star Trek writers added one more crucial component to the matter-antimatter drive. I refer to the famous dilithium crystals (coincidentally invented by the Star Trek writers long before the Fer-milab engineers decided upon a lithium target in their Antiproton Source). It would be unthinkable not to mention them, since they are a centerpiece of the warp drive and as such figure prominently in the economics of the Federation and in various plot developments. (For example, without the economic importance of dilithium, the Enterprise would never have been sent to the Halkan system to secure its mining rights, and we would never have been treated to the “mirror universe,” in which the Federation is an evil empire!)
What do these remarkable figments of the Star Trek writers' imaginations do? These crystals (known also by their longer formula 26 dilithium 21 diallosilicate 1:9:1 heptoferranide) can regulate the matter-antimatter annihilation rate, because they are claimed to be the only form of matter known which is “porous” to antimatter.
I liberally interpret this as follows: Crystals are atoms regularly arrayed in a lattice; I assume therefore that the antihydrogen atoms are threaded through the lattices of the dilithium crystals and therefore remain a fixed distance both from atoms of normal matter and one another. In this way, dilithium could regulate the antimatter density, and thus the matter-antimatter reaction rate.
The reason I am bothering to invent this hypothetical explanation of the utility of a hypothetical material is that
once again, I claim, the Star Trek writers were ahead of their time. A similar argument, at least in spirit, was proposed many years after Star Trek introduced dilithium-mediated matter-antimatter annihilation, in order to justify an equally exotic process: cold fusion. During the cold-fusion heyday, which lasted about 6 months, it was claimed that by putting various elements together chemically one could somehow induce the nuclei of the atoms to react much more quickly than they might otherwise and thus produce the same fusion reactions at room temperature that the Sun requires great densities and temperatures in excess of a million degrees to generate.
One of the many implausibilities of the cold-fusion arguments which made physicists suspicious is that chemical reactions and atomic binding take place on scales of the order of the atomic size, which is a factor of 10,000 larger than the size of the nuclei of atoms. It is difficult to believe that reactions taking place on scales so much larger than nuclear dimensions could affect nuclear reaction rates. Nevertheless, until it was realized that the announced results were irreproducible by other groups, a great many people spent a great deal of time trying to figure out how such a miracle might be possible.
Since the Star Trek writers, unlike the cold-fusion advocates, never claimed to be writing anything other than science fiction, I suppose we should be willing to give them a little extra slack. After all, dilithium-mediated reactions merely aid what is undoubtedly the most com-pellingly realistic aspect of starship technology: the matter-antimatter drives. And I might add that crystalstungsten in this case, not dilithiumare indeed used to moderate, or slow down, beams of anti-electrons (positrons) in modern-day experiments; here the antielec-trons scatter off the electric field in the crystal and lose energy.
There is no way in the universe to get more bang for your buck than to take a particle and annihilate it with its antiparticle to produce pure radiation energy. It is the ultimate rocket-propulsion technology, and will surely be used if ever we carry rockets to their logical extremes. The fact that it may take quite a few bucks to do it is a problem the twenty-third-century politicians can worry about.