Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction

by Adler, Charles L.

  The origin of the idea of the spread of alien life through microbes is probably the “panspermia” theory of Fred Hoyle and Chandra Wickramasinghe, which postulated that life on Earth was seeded by comets carrying the basic building blocks of life. Bacteria and viruses were carried by radiation pressure from one star to another over cosmic timescales, ultimately landing by accident or design (as in the directed panspermia theory of Francis Crick) on a random world, beginning life there if the conditions were right. It’s worth taking a little time to evaluate the idea scientifically.

  As mentioned in previous chapters, light exerts a force on objects it falls onto. This is the basis of the matter-antimatter (or photon) rocket: the force exerted is given by the formula

  where I is the total intensity (power per unit area) of the light incident on the object, c is the speed of light, A is the surface area of the object, and k is a dimensionless parameter that describes how effective the object is in scattering light: k depends on the wavelength of the light and the exact shape of the object. If the object is large compared to the wavelength, k will be somewhere between about 1/2 to 2. We’ll simply assume it is 1 for now.

  If we assume that the microbe being sent through space is spherical, then its area is given by the formula

  where r is its radius. Its mass is its volume times its average density (ρ):

  The acceleration of the microbe will be the force exerted on it divided by its mass:

  The smaller the object, the greater the acceleration. In Earth’s orbit the solar constant (intensity of light from the Sun) is 1,360 W/m2; if we assume that our microbes have a density the same as water (1,000 kg/m3) and a radius of 1 µm (=10−6 m), we get an acceleration of about 0.01 m/s2. This doesn’t sound so high, and of course, the acceleration drops as it gets farther from the Sun, but with this acceleration over a distance of 1 AU, the speed of the bacterium will be 64 km/s—greater than the escape speed from the Solar System. It isn’t going anywhere fast, but it could make it to the Alpha Centauri system in about 20,000 years. One plausible invasion scenario would be genetically engineered bacteria or viruses, or even the basic genetic material needed to seed other planets with higher-order life, sent out by an alien race to colonize other worlds. This could be done at a tiny fraction of the cost of sending starships containing fully sized aliens: a bacterium moving at 86% of the speed of light has a kinetic energy of only about 400 J. Now, there isn’t any way I know to slow it down once it reaches its destination (though there might be). This might be the means by which the unseen alien intelligences managed the Chtorr invasion of the Earth in Gerrold’s series, although it hasn’t been revealed yet. Fast or slow, this invasion strategy is much more plausible than almost any other scenario because of the small amount of energy needed.

  16.2.2 Trade or “Enlightenment”

  When you trade among the stars, there is no repeat business.

  —LARRY NIVEN, “THE FOURTH PROFESSION,” IN ALL THE MYRIAD WAYS

  The issue of commerce between the stars is pretty simple: energetics and time effectively prevent it, or at least prevent physical trade. Consider the following: even traveling at 86% of the speed of light, travel to Alpha Centauri will have a round-trip time of 10 years. And that’s the nearest system. The cost is also horrific: the kinetic energy of anything with a mass of 1 kg moving at that speed is 9×1016 J. At current energy costs of about 10 cents per kW-hr this corresponds to about $300 million per kilogram. This isn’t the entire cost, however, as the relativistic rocket equation tells us that we need 1.4 kg of antimatter (combined with an equal amount of matter) to give 1 kg of payload this velocity. Plus more to slow down to a stop, reverse course with the goods, and slow to a stop again on return. It is hard to imagine anything that could be traded at a profit given the fundamental problems. This is where the fundamental premise of the movie Avatar breaks down: the cost of unobtainium, available only on Pandora, will probably be at least an order of magnitude higher than the quoted value of $20 million per kilogram.

  The exchange of information is orders of magnitude cheaper. Communication between alien civilizations via radio waves is faster and cheaper than any exchange of material goods: radio travels at the speed of light, faster than any material object can travel. Cocconi and Morrison showed in the 1950s that it would be possible to detect Earth’s radio transmissions, using then current radio telescope technology, from a distance of more than 10 light-years [60]. So communications between alien civilizations is possible, but is there anything we would want to say to them? I discussed this above: it is possible that aliens wouldn’t want to talk simply because they wouldn’t have much to say to us. However, merely saying “hi” and nothing more would immediately become the most important radio message ever received.

  16.2.3 Mars Needs Women!

  The successful cross between a human and a Vulcan … is about as likely as the successful mating of a Vulcan and a petunia.

  —CARL SAGAN, 1968 NEW YORK TIMES ARTICLE

  This is more of a joke than anything else: any competent science fiction writer understands the issue that interspecies “relations” are unlikely. The genetic information for most species on Earth is stored in deoxyribonucleic acid (DNA); it is unlikely that this is the only possible genetic molecule, so there is almost no chance that life evolved on another world would be “compatible” with ours. Even if it was DNA based, aliens would represent different species from humans. As Larry Niven put it in his essay “Man of Steel, Woman of Kleenex,” sexual relations between a human and an alien is what Tom Lehrer once called “animal husbandry” [178].

  There is also no reason for them to look much like us. TV shows feature humanoid aliens because it is easier to make human actors look like humanoid aliens than protoplasmic blobs. Perhaps the Anna Karenina principle comes into play here, too: there may be issues that force intelligent, tool-wielding aliens to look more or less humanoid. Until we find examples, of course, we can’t know.

  16.2.4 Utterly Alien Motives

  A large genre of science fiction concerns alien contact in which the motives for contact are unknown and to a large extent unguessable. The authors of these stories tend to be non-U.S. or non-UK writers, many of them from the former Soviet bloc countries. In the Russian novel Roadside Picnic, by Arkady and Boris Strugatsky, the alien contact is invisible in addition to being inscrutable [230]. In this novel, the “Visitation” has altered several areas of Earth: in them, the laws of physics break down, miracles happen (usually deadly ones), and there are treasures for intrepid explorers to find. The aliens are entirely offstage (if they were ever there in the first place). The only evidence that they ever came is the “Pillman radiant,” an imaginary line in space along which the Visitation seems to have come. Dr. Pillman, the discoverer of the radiant, likens the Visitation to a roadside picnic in which visitors to a picnic site leave their trash without bothering to pick it up, but it isn’t clear that this is the motivation for the Visitation. Stanislaw Lem in Microworlds gives a more honorable motive for the Visitation, but it isn’t clear that his explanation is correct, either [150]. I suspect that Roadside Picnic was a primary motivation for the excellent TV miniseries The Lost Room, but cannot prove it; the “Event” of that series is very similar to the Visitation of the novel.

  Stanislaw Lem has two novels premised on alien contact with unknowable motives, Solaris and His Master’s Voice, and a third, Fiasco, in which the tables are turned: humanity attempts to contact an alien race but our motives are completely misunderstood [151]. In Solaris an intelligent planet attempts experiments on astronauts investigating it, for completely unknown reasons. [148]. In His Master’s Voice, scientists intercept an alien message and are completely unable to decipher it; various attempts lead to interesting discoveries, but the content of the message remains completely unknown [147].

  Philip K. Dick is one of relatively few American writers who have attempted stories constructed on unknowable alien motives. In Galactic Pot-Healer the protagon
ist (a “pot-healer,” or ceramics mender) is dragged into a conflict on a distant planet where he understands only the vaguest of the motives or powers of the beings fighting one another to raise a sunken cathedral [68], I find stories like this plausible, in that it is very difficult to communicate with members of species as close to humans as chimpanzees. What luck would we have with aliens? But putting all this aside, let’s get down to Earth and think about how likely it is for us to be able to make contact, whether we can understand them or not.

  16.3 DRAKE-EQUATION MODELS AND THE MATHEMATICS OF ALIEN CONTACT

  If we were to receive a greeting from an alien civilization tomorrow, we could be pretty confident it was within 50 light-years of us. Our world has been broadcasting radio signals for only about a century, so to receive a signal from aliens would indicate they found our signal and sent us back a reply within that time. This implies a certain density of alien civilizations in our galaxy of roughly one per every (50 LY)3, or 8×10−6 LY−3. The Milky Way Galaxy is a spiral galaxy composed of 3×1011 stars, some 1×105 light-years across and 1,000 light-years thick, so the total volume is approximately that of a cylinder with radius R = 5×104 light-years and thickness 1,000 light-years; this implies that the total volume is ≈ 8×1012 LY3. If such civilizations are distributed uniformly throughout the galaxy (which is not necessarily a good assumption), then the reception of such a message would imply about 64 million advanced civilizations currently in the galaxy. This seems like an incredibly large number. Of course, the fewer civilizations there are, the longer it will take to talk to them.

  Let’s make a simple model for this. Let’s hypothesize that the average number of alien civilizations currently in our galaxy can be expressed as

  Here, g is a “generation rate,” which indicates the number of galactic civilizations that achieve a technological level suitable for interstellar communication; this is a certain number per year being “born.” N is the number of such civilizations in the galaxy at any given time, and L is the lifetime of the civilization. Let me give an analogy for what is going on here: Imagine standing in a dark meadow in the middle of the countryside in summer. All around you, you see fireflies flicker on and off. How often do you see more than one firefly lit up? That depends: if a lot of fireflies on average “light up” every second, or if they stay lit for long periods of time, then your odds are good that you will see more than one. If, on the other hand, very few light up every second and they stay lit up only briefly, then the odds aren’t good. The number of fireflies lighting up every second corresponds to g; the amount of time they stay lit up corresponds to L. Intelligent life in the cosmos may be akin to those fireflies—brief flashes lighting the darkness.

  All three quantities, N, g, and L, are unknown. The astute reader will recognize this as a version of the Drake equation. In 1960 Frank Drake proposed a statistical model to estimate the number of alien civilizations in the galaxy. In his original version of the equation,

  It’s worthwhile considering the variables here:

  • G: the rate at which stars form. This is the only variable that is known with any precision: G ≈ 7 per year.

  • fp: the fraction of all stars in the galaxy with planets. In 1960 there were no known exoplanets; now there are more than 700 known ones. The value of fp is probably somewhere between 0.05 and 0.2 (5% and 20%) based on the statistics of stars with planets. As discussed in previous chapters, the probability of a given star having detectable planets increases with increasing metallicity, and is also a function of stellar class.

  • ne: the average number of Earth-like planets circling the star. This figure is highly problematic. As discussed earlier, a planet being “Earth-like” depends on a number of factors, some of which are interrelated. Depending on how you define it, there are between one and three Earth-like planets in our own Solar System, but the average number per solar system is likely to be much lower.

  • fl: the fraction of Earth-like planets that develop life. This and the next two variables are completely unknown. It might be high, as Earth developed life only about 700 million years after it formed.

  • fi: the fraction of planets developing intelligent life.

  • fc: the fraction of intelligent life that develops technology able to communicate over interstellar distances (i.e., radio).

  Needless to say, the equation and its interpretation have engendered much controversy. In response to criticism, Drake has called it a way to “organize our ignorance.” The formula is valid for estimating the number of intelligent alien races only if the variables are statistically independent of one another. This is unlikely to be true. In particular, when we look at ne, what exactly do we mean by an Earth-like planet? That number, ne, could be estimated by a mini-Drake equation of its own: we could estimate the average number of planets in the habitable zone times the number whose orbital eccentricities are small enough times the number that are the right size times.…

  In any event, we don’t know most of the factors that go into g. We also don’t know L. Remember, L is the lifetime of the “typical” advanced civilization. However, “advanced” means “being able to receive and transmit communications over interstellar distances”—otherwise we couldn’t communicate with them. On Earth we have had this capability for less than 110 years, depending on how you define it. We’ve been listening for alien signals for only about 50 years. This probably represents a lower bound on L, but it isn’t clear what an upper bound should be.

  Michael Shermer in an article in Scientific American estimated the average life span of a human civilization as 420 years; these civilizations were all preindustrial, but if this is a reasonable estimate for the life span of a technological civilization, there is no hope of contacting aliens [218]. There has been heated debate over this article on the web, but Shermer’s reasoning isn’t stupid. For one thing, any advanced technological society implies a wealth of energy. The generation of energy in our society rests almost entirely on nonrenewable resources, which will probably be depleted in less than a century if their use continues at the same rate as today. We’ll take up the issue of how long human civilization can last in later chapters. For now, is there anything at all we can say about the possibility of alien contact, given our lack of knowledge of all of the variables above?

  Well, first of all, we want the product g L>2, so that there is someone else to talk to. This is not a hard-and-fast rule, as these numbers represent averages, but it seems like a reasonable criterion. Unfortunately, this is a necessary but not sufficient condition. We also need to be able to communicate, which will be impossible to do within the lifetime of our civilization if the alien worlds are spread too far apart.

  If galactic civilizations are uniformly distributed, then we can imagine them as being spread over the volume of a cylinder with a very high aspect ratio (i.e., 100:1) between radius and height. Therefore, if these civilizations are separated by distances larger than about 1,000 light-years, it makes more sense to discuss them in terms of the number per unit area spread over a disk representing the galaxy with radius R = 50,000 light-years. If we send a radio signal from Earth and expect it to be intercepted by aliens after a time t, then we can relate N to t as follows:

  This is a straightforward probability argument: the expected number of civilizations that receive the signal is equal to the area the signal spreads over (ignoring the thickness of the galactic disk) multiplied by the area density of such civilizations. (From here on, I’ll work in units in which c = 1, to make life easier).

  If we want to receive a signal in return, then t ≤ L/2. That is, if our advanced technological civilization has a finite life, the aliens had better be close enough to signal us back before it ends. From this, we can put a lower bound on the lifetime required for us to be able to talk to the aliens. Using N = g L, we can derive

  Figure 16.1. Minimum values of L if we want to make contact.

  So we have two criteria:

  and

  Both cri
teria must be satisfied in order to be able to talk with the aliens. Figure 16.1 shows what this implies. Note that g decreases to the right.

  The graph is separated into two regions. Above the line, contact is possible. There are enough aliens out there to talk to and our civilizations will endure for a long enough time to make contact. Below the line, contact is unlikely, as either there are no other civilizations in the galaxy or they are separated by such a large distance that contact will not be made within the lifetime of the civilization.

  For low values of g, the harder criterion to satisfy is the first one; the odds of having any other civilizations in the galaxy at a given time are low no matter what you do. However, as g gets larger, for a value of g around 3×10−5 per year, it is now harder to satisfy the criterion that the civilization must last long enough for a conversation to happen. It is very likely that g < 10 per year, as the stellar generation rate is less than this, and all the other factors going into g tend to decrease it. The implication is that no matter what, the minimum lifetime for advanced civilizations is about 1,000 years if we want contact to be even a bare possibility. This leads us into the final section of the book: how long can an intelligent species hope to last?

  Note

  1. Gibson is an interesting example of an author who has gradually removed many of what people think of as science fiction trappings (alien contact and space travel, to name two things) from his novels while still keeping a very science fiction feel to his writing.