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

by Adler, Charles L.

  It seems clear that the more power a civilization uses, the more it will change the environment around it, and probably in many unforeseen ways. The global weather system is a classic example of a chaotic system—small changes to the inputs driving the weather can have big changes in its outputs. This has been known on some level since 1963, when Edward N. Lorenz put together a simple model of convection in Earth’s atmosphere [154]. To quote Lorenz, “When our results … are applied to the atmosphere … they indicate that the prediction of the sufficiently distant future is impossible by any method.” This is occasionally called the butterfly effect: the flapping of a butterfly’s wings in China can cause a hurricane to sweep across Texas. The Earth’s ecology is another example of a chaotic system, if one with a much longer response time: most mathematical models of small parts of Earth’s ecology, such as predator-prey models, involve strongly coupled nonlinear differential equations, the very hallmark of chaos. To make matters worse, the ecology is complex enough that it isn’t clear whether most of the current mathematical simulations of it are close to reality [231].

  20.5 TYPE II CIVILIZATIONS

  On the Kardashev scale, Type II civilizations control the resources of an entire solar system, or, using the formula given above, have access to power of order 1026 W, the power output of an “average” star like the Sun. Getting from Type I to Type II may present something of a problem. I’m not sure I know of any science fiction novels that have directly addressed this issue. The main problem is this: harvesting all the power from the Sun involves dismantling planets. The issue is creating a screen to capture the light from the star.

  Larry Niven’s novel Ringworld is an interesting example of this approach. The Ringworld, whose dynamics are discussed in chapter 19, is an enormous ring around a star with radius just about equal to Earth’s mean distance from our Sun. It’s spun at an enormous rate, and the scale of the thing implies that a Type II civilization built it. The Ringworld civilization controls the power of its star; there is a “shadow-square” system that not only provides day and night to the Ringworld, it also defends it against outside threats using controlled solar flares. In an odd way, Niven’s story provides an example of what I mentioned above: people might change in unexpected ways in order to survive in such an engineered environment. On the Ringworld, the fall of civilization leads to humans evolving into a variety of unoccupied ecological niches, including ghouls, a carrion-eating subspecies, who fill the roles of hyenas on Earth [183].

  Civilizations somewhere between Type II and Type III are common in the media and in older science fiction, even though not called by that name. Any Federation of Planets or Galactic Empire, so beloved of older writers, is by definition higher than Type II. Don’t believe me? Let’s consider a small point from the television show Star Trek: The Next Generation and its sequel series: the replicator.

  The replicator was presumably an offshoot of transporter technology. We’ve discussed teleportation in an earlier chapter. I tend to think it impossible, for various reasons, but what the heck: let’s assume it works somehow. As all fans of the series know, Captain Picard tells a little box sitting in his office, “Tea, Earl Gray, hot,” and moments later a cup materializes in it. (And contains, one is tempted to say, “a liquid that was almost, but not quite, entirely unlike tea.” Thank you, Douglas Adams! [19]) Whether the cup is prepared elsewhere and transported to the office or created whole is never said. Presumably the latter, as the Holodeck seems to work on the same principles. Now, a cup of tea has a mass of about 250 grams. This represents an energy equivalent of 2.25×1016 J. This is about the same amount of energy currently used by the entire United States in two and a half hours. If there are seven billion people in the Federation of Planets, each wanting a cup of tea, then this is about the same amount of energy that the Sun radiates in half a second! Of course, this is probably a low population estimate. In any event, the tiny little replicator indicates that the Federation is able to handle enormous amounts of energy. If we assume that all the food in the Federation is generated in this manner, then the amount of power required approaches the total output power of several stars.

  This seems like a damn-fool way to make a cup of tea. No technology is 100% efficient; the waste heat generated from using a replicator would probably melt (or vaporize) any container one put it in. Most science fiction TV shows and movies don’t deal with these issues honestly, in my opinion. The movie Bladerunner, loosely based on Philip Dick’s Do Androids Dream of Electric Sheep?, features a 1940s noir world on the brink of collapse. However, there are advertisements in the film for volunteer colonists to other worlds, which implies a very energy-rich civilization. The two aren’t mutually exclusive, but they are difficult to reconcile.

  20.6 TYPE III CIVILIZATIONS

  Stanislaw Lem wrote a satirical story about aliens who had reached the HPLD, “highest possible level of development.” They basically sat around doing nothing, creating such miracles as square planets, and the like. They did nothing because, as they explained to one explorer, anything they did would represent a step down. I’m not sure it’s possible to write meaningful stories involving Type III civilizations for that reason: once you get to a certain point, Clarke’s dictum about sufficiently advanced civilization seems a bit tame. “Any really advanced technology is God-like” might be closer to the mark. In this book I have tried to stay close to what we know today and can extrapolate based on currently understood laws of physics. Any Type III Kardashev civilization, one that can effectively exploit the resources of an entire galaxy, must be long-lived on a scale that is unknown in human history. If we believe that the speed of light is the ultimate barrier, then it will take millions of years to spread across the galaxy. Even if we believe that faster-than-light travel is possible, this is still probably true. It also must be farsighted in a manner in which no contemporary human civilization is, and have clearer goals. This is because the only justification for such a society is the ultimate extreme long-term survival of that society. Nothing else makes sense. In earlier chapters we saw that any form of space travel is infinitely easier with unmanned probes: putting people on other planets is expensive to the point of insanity, and horrifically dangerous. However, it is the only means by which the human race can survive long term, meaning beyond a few million years. That is the subject of the next chapter.

  CHAPTER TWENTY-ONE

  A GOOGOL YEARS

  21.1 THE FUTURE OF THE FUTURE

  In this final chapter of the book I would like to examine the grandest theme in science fiction, the future of intelligent life in the universe. And by future I mean the far future. In previous chapters we’ve examined what truly advanced civilizations are capable of, and how they can potentially modify their environments in extreme ways. In this chapter I would like to examine how long such extraordinarily advanced societies can hope to last. It will dwarf all the history of the universe to this point by a long shot. Let us consider the long-term survival of humanity and intelligent life in the cosmos on the timescale of hundreds of millions of years to billions of years to even longer.

  21.2 THE “SHORT TERM”: UP TO 500 MILLION YEARS OR SO

  There is no guarantee that humanity will survive the next hundred years, let alone the next hundred million. Even if we don’t do ourselves in, natural climatological cycles may do the trick for us. Because of slow, periodic changes in the Earth’s orbit, Earth’s climate goes through cycles of glaciation followed by thawing over the course of about 100,000 years: about 80,000 years of glaciation, followed by about 20,000 years of interglacial periods. All of current human civilization has been encompassed by the last interglacial period, as stable human society is possible because of the invention of agriculture. This was only possible after the glaciers retreated some 15,000 years ago. The biggest shortterm threat to humanity is global warming. If we beat that, however, our descendants several thousand years from now will have to face global cooling. It isn’t entirely clear that humanity coul
d survive an ice age, although there are a lot of imponderables in that statement. There are no fundamental physical reasons why we couldn’t, however, so I’m going to take an optimistic view, and expand the timescale by a factor of 1,000. The problems happening over this time period are easier to discuss from a physics standpoint.

  Over the next few hundred million years, the biggest threat to humanity is expected to come from comet or asteroid impacts like the ones that led to the demise of the dinosaurs. The dinosaurs were killed off 65 million years ago when a comet or asteroid roughly 20 km in diameter hit the Earth. With a speed of roughly 40 km/s at impact and a mass of about 1015 kg, the kinetic energy of the event would have been about 1024 J. This is billions of times larger than all of the energy that would be liberated if all the world’s nuclear arsenals were exploded at once. These impacts have been the subject of fiction: Lucifer’s Hammer and the movies Deep Impact and Armageddon deal with impacts like this. In an earlier chapter we looked at the damage a nuclear war would do. The biggest problems would come from the nuclear winter caused by particulates blocking sunlight. An impact like this one would block sunlight for years, causing a massive dying off of most life on Earth. One theory of the history of mass extinctions in Earth’s paleontological history posits impacts like the dinosaur-killer happening roughly every 100 million years.

  Even smaller impacts, which occur correspondingly more frequently, could destroy civilization and possibly all life on Earth. Astronomers have seen an impact like this one in 1993, when comet Shoemaker–Levy 9 hit Jupiter. This comet, which calved into several separate sections before impact, was smaller than the dinosaur-killer, but its impact energy was still larger than the world’s total nuclear arsenal.

  It seems likely that within the next few hundred million years Earth will suffer a similar impact. Large impactors still exist in the Solar System. The orbits of a large number of asteroids pass near Earth. There was a scare about a decade ago when the asteroid 99942 Apophis was predicted to have a non-zero chance of hitting Earth in the year 2031.

  21.3 THE “MEDIUM TERM”: UP TO ABOUT 1013 YEARS

  Perhaps a sufficiently advanced civilization will want to move the planet. If so, it can turn asteroid and comet impacts into a positive good. There are good reasons to want to move the Earth: in one billion years the luminosity of our sun will increase by 10% [130]. This will increase Earth’s temperature to the point that life will not be possible. Our descendants (or our replacements) might want to move Earth farther away from the Sun to keep it cool. At that stage, they would only need to move it outward by about .05 AU to keep the flux of light from the Sun about the same as it is now. Much later, five billion years or so from now, the Sun will exhaust the hydrogen in its core and swell into a red giant. The luminosity will then be many thousands of times what it is now, and the sun itself will swell until it is larger than the current orbit of Mercury. So, how do we move a planet?

  Interestingly enough, the energy it would take to move Earth farther from the Sun by 1 AU is comparable to the energy needed to dismantle it. If we want to move a planet of mass Mp from a circular orbit of radius r1 to radius r2, the change in the total energy of the planet-Sun system is given by

  The factor of 1/2 comes from what is called the “virial theorem.” Moving Earth from 1 AU to a distance of 2 AU has ΔE = 2×1033 J, equivalent to the Sun’s total energy output for two months. A few authors, including Freeman Dyson, have given some thought to how this might be done.

  One interesting paper on the subject uses a method similar to the gravitational slingshot method [142]. A planetoid of mass m falling from a large distance away from the Sun to a distance r away from it gains kinetic energy equal to

  Let r = 1.5 × 1011 m × a. That is, let’s express the distance in astronomical units. Then

  The velocity of the planetoid as it reaches a distance a from the Sun is

  In principle, the impact or near collision of such a planetoid with Earth would change its velocity by an amount of order

  where µ = m/ME. This is the same principle by which a spacecraft can increase its velocity in a close orbit around a planet. However, in this case the situation is reversed: we want to change the planet’s motion, not the spacecraft’s. In the original case, the speed of the spacecraft can be changed dramatically because the planet outweighs it by a factor of more than 1022. In this case, the change in the Earth’s orbital speed will be tiny, because even a very large planetoid will only have a small fraction of Earth’s mass.

  There is a lot of icy debris orbiting the Sun at distances from about 30 AU out to nearly 100 thousand AU. The Kuiper Belt, extending from about 30 AU to about 200 AU, is the home of the dwarf planets Pluto and Eris, both of which have masses of order 2 × 10−3 × ME. There are probably trillions of smaller pieces of ice and dust and rock; the total mass of the belt is estimated to be about 30 ME. One can imagine a sufficiently advanced civilization arresting most of the orbital motion of pieces of this debris and letting it “fall” into the inner Solar System. If one carefully chose its orbit so that it passed close to the Earth, it would be possible to increase Earth’s orbital speed, bringing it farther out from the Sun. It would take quite some time to do this. An object falling from a distance of 100 AU from the sun would take about 175 years to reach Earth’s orbit. The authors of the paper estimated that one would need about 106 such near collisions to move Earth’s orbit outward to 1.5 AU. This assumes an average value of µ = 1.7 × 10−6, or m = 1019 kg. The required net Δv change is of order 10 km/s. One issue mentioned in the paper is that the timing of the orbital approach of these planetoids as they passed Earth would need to be down to the minute. Again, each maneuver would take centuries, or even millennia [142].

  The net energy needed for this maneuver is of order 1033 J. We have about one billion years in which to move the Earth. This means the average rate at which we need to expend this energy is

  This is three orders of magnitude above the net energy expenditure of our current civilization, or an energy expenditure rate of a Kardashev Type I civilization. This makes sense: one cannot conceive of moving a planet without access to vast reserves of energy.

  This maneuver was meant to protect the Earth’s climate from the Sun’s luminosity changes as the Sun evolved along the main sequence. After it leaves the main sequence, things get trickier. As the Sun turns into a red giant star, its luminosity will temporarily increase to over 1,000 times what it is currently. However, its luminosity will then decrease after the “helium flash” to about 100 [130, pp. 468–470]. At the high value of the luminosity, the Earth would need to be moved to 30 AU from the Sun (roughly the orbital distance of Pluto). After that, it would need to be moved back to 10 AU. This would take place on a timescale of hundreds of thousands or millions of years, not billions. This means that the power expenditure rates would need to be thousands of times higher than what we just considered. To a very long-lived observer, Earth would appear to be in some cosmic Ping-Pong game. The power expenditure rates would require a Kardashev Type II civilization, although at that point it might just be easier to move everyone to a new star system.

  21.4 THE “LONG TERM”: UP TO A GOOGOL YEARS

  And AC said, “LET THERE BE LIGHT!”

  —ISAAC ASIMOV, “THE LAST QUESTION”

  I want to make my underlying assumptions here clear: to discuss the far future of the universe, one must have a model for the evolution of said universe in mind. The model I am considering is the best one astronomers currently have. It is referred to as the “inflationary Big Bang consensus model.” The main ideas of this model are:

  1. The universe began in a big bang some 13.7 billion years ago. We do not know if there was anything before this (if that word has meaning) or if there are other universes like our own.

  2. Shortly after the universe began, it went through period in which it expanded rapidly from the size of a proton to the size of a basketball. This is known as “inflation.” Most of the detail
s of inflation aren’t well understood, but there seems to be very good evidence that it happened.

  3. The mass-energy content of the universe is distributed as follows: about 3% of the matter in the universe is ordinary matter, such as we are familiar with on Earth. About 90% of that is hydrogen. Of the other 97%, about 23% is “dark matter”; scientists don’t know what it is, except that it apparently doesn’t act much like regular matter (i.e., it doesn’t interact strongly with other matter except via gravitational interactions). The other 74% is “dark energy”; we really don’t know what that is.

  4. The universe is “flat,” in the sense that the total amount of matter/energy in the universe (apart from gravitational self-attraction) exactly balances out the gravitational self-energy of the universe.

  5. However, even though the universe is balanced so precisely, the dark energy is accelerating the expansion of the universe so that instead of slowing down owing to gravity as it expands out, it is accelerating at an ever-increasing rate.

  This consensus model has been developed since 1998 when observations of far-away supernovas led to the measurement of the dark energy and the acceleration of the universe. This isn’t the place to go into the evidence for the consensus model. Suffice it to say that there is a lot of it. If you are interested, I would suggest either a basic astronomy textbook such as 21st Century Astronomy or a popular book such as Mario Livio’s The Accelerating Universe [130][153]. Make sure that any astronomy textbook you read was published after 1998! The cosmology section of any textbook published before then is completely out of date.