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 could 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 details 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.
The implication of the accelerating universe is that it will never go through a “Big Crunch” in which the universe halts its expansion and recollapses. (I preferred Douglas Adams’s term “Gnab Gib” over “Big Crunch,” but the point is moot now.) These new discoveries invalidate narratives like Tau Zero that are predicated on a cycle of Big Bang–Big Crunch–Big Bang, and so on. Such a model was aesthetically pleasing, but it seems that the universe is just not like that.
Among science fiction writers, Olaf Stapledon was probably the first to consider the very long-term future history of the universe. We’ve discussed Star Maker in an earlier chapter [225]. Stapledon implicitly used the idea of the open universe in Star Maker; at the end of time, the universe consisted mostly of galaxies too far away to communicate with each other, each consisting of a few remnants of the once great stellar populations. The long-term evolution of the universe has made its way into a number of science fiction books since Stapledon. Most writers have seemed to favor the “closed universe,” or cyclical universe, as Tau Zero does, as it seems to envision an infinite future. Even if humanity can’t survive forever, perhaps some form of intelligent life can evolve in the next cycle of the universe.
Main-sequence lifetime is tied to stellar mass. For example, in about four or five billion years our Sun will move off the main sequence and swell into a red giant whose luminosity will exceed 100 times its present value. As it burns through its nuclear fuel, it will cool and contract to a white dwarf whose total luminosity will be initially about 10−3 what it is today, and will further cool over time. Higher mass stars than the Sun burn through their nuclear fuel quickly and end their lives in spectacular supernova explosions. Low-mass stars live significantly longer than high-mass ones. Luckily, most stars in the sky are low-mass M-class stars with low luminosity but very long lives. This allows the possibility (as in Asimov’s story) of moving to a new star once the Sun has evolved into a white dwarf. Stellar lifetimes are given by the approximate formula
where M is the stellar mass and L its luminosity. From chapter 14, an M7 star has M = 0.08 and L = 0.0025, leading to a main-sequence lifetime of 3.2 × 1011 (320 billion) years. The estimate is probably an underestimate of their true lifetime. Our Sun will run through only about 10% of its hydrogen before swelling into a red giant. This is because the Sun’s core isn’t convective, that is, it isn’t stirred around by currents created by temperature gradients. This means that the core, where fusion takes place, can’t get any new material to fuse once the core’s supply is gone. M-class red dwarf stars have fully convective cores, meaning that new fuel is mixed in constantly. This increases their main-sequence lifetime above our crude estimate [47]. Stars at the lowest end of the mass range may have lifetimes near 1013 years.
The long-term issue we face is similar to the short-term issue our civilization is facing today: resource depletion. We are rapidly using up the Earth’s reserve of fossil fuels now. In this imaginably distant future we will be using up the resources of the stars. If human civilization lasts for a few billion years, I feel confident in predicting that we will have some form of interstellar travel by then, because we will need it. Maybe we can move our entire planet to a new solar system. Both Freeman Dyson and Larry Niven have speculated on methods of doing this.
21.5 BLACK HOLE–POWERED CIVILIZATIONS
When all the stars die, that’s the end, right? All other sources of energy are gone, aren’t they? Well, maybe not. Black holes will be around for a long time after all the stars grow cold, and they offer the potential of providing energy in those end times (which may last for a much, much longer time than all of the other eras in the universe).
A black hole may seem like a bad source of energy. After all, the common conception of them is that they swallow everything that enters them, and nothing can come out. However, that’s not quite true: as we saw in an earlier chapter, black holes radiate away energy (Hawking radiation), even though it is too low to detect directly.
There are two ways to retrieve energy from things dropped into black holes:
1. By electromagnetic radiation from the things dropped into them via heating in the accretion disk; and
2. By gravitational radiation.
The first process is relatively straightforward: the radius for the event horizon of a (nonrotating) black hole is determined only by the mass of the black hole:
where Ms is the Sun’s mass. Therefore, a small black hole ten times the mass of the Sun would have an event horizon 15 km in radius. Imagine dropping a 1 kg object from a long distance away toward the black hole and abruptly stopping it three radii away. In its fall it would acquire kinetic energy approximately equal to 1/6 mc2 = 1.5 × 1016 J. I am using the Newtonian formula here, which is an approximation to the full relativistic formula. I chose three radii from the black hole for two reasons:
1. Three radii away is the closest distance at which stable orbits are possible [235].
2. It is also the closest radius at which I feel comfortable using Newtonian formulas to estimate the energy liberated.
This is an enormous amount of energy; we could power all of current-day America’s energy needs using 600 kg of trash, assuming we could reclaim the energy liberated at 100% efficiency. This is essentially the method that astronomers have used to find black holes that have evolved from large stars: if a black hole is in close orbit with a normal star, gases from the star will be funneled into the black hole. Frictional heating of the gases as they fall in leads to them reaching temperatures in the millions to hundreds of millions of degrees, radiating away enormous amounts of energy in the x-ray spectrum.
A more subtle way of generating energy using black holes is via gravitational waves. Gravitational waves are literally ripples in the fabric of space and time. It has been predicted that merging black holes are a strong source of gravitational waves. This is one of the key things the Laser Interferometer Gravitational-wave Observatory (LIGO) gravity wave detector is looking for. In principle, up to 50% of the mass-energy content of any junk dropped into a black hole can be recovered as useful energy [236]. This is a much higher efficiency than any other known source of energy.
The science fiction idea of powering objects using black holes dates back to the 1980s, if not earlier. The earliest use I know of is in the McAndrew chronicles, a series of stories written by Charles Sheffield centering on the eponymous astrophysicist [217]. In these stories, mini-black holes are used to power spacecraft, and presumably other things as well. The discovery of Hawking radiation makes the stories obsolete, as the mini-black holes of the stories would evaporate too quickly to use. The final episode of the new Battlestar Galactica series had the Cylons in orbit around a black hole, powering their civilization by throwing trash into it.
This is the method by which a civilization past the death of all of the stars could get energy: take your unused trash and toss it into the black hole. This leads to various baroque speculations and plot ideas. One can imagine some far-distant civilization powering their energy needs for the upcoming year by tossing a sacrificial virgin or two into the black hole. It would certainly work better than tossing them into a volcano.
21.6 PROTONS DECAY—OR DO THEY?
One thing that may cut short our joyous spree into the forever is the possibility that ordinary matter may softly and silently vanish away. This Boojum is the Snark of proton decay.
The proton is one of the three building blocks of ordinary matter. Of the other two constituents, the electron is the lightest—about 1,800 times lighter than the proton. It is a stable particle. The neutron is not: the neutron is a charge-neutral particle made up of one “up” quark, with charge +2/3 of the electron charge, and two “down” quarks, each with charge −1/3. When outside the nucleus, the neutron can decay into a proton, electron, and antielectron neutrino; the decay converts one of the down quarks into an up quark, which is what turns the neutron into a proton. The proton is two ups and one down, with net charge of +1. The neutron decay time is long by physics standards, taking tens of seconds. Because protons aren’t elementary particles either, the possibility exists that they could decay into lighter particles as well.
This has never been seen experimentally, but some theories of physics such as string theory predict it. If protons decay, they take a very long time to do so. The universe has been around for 13.7 billion years, so this puts a lower limit on the time it takes. If protons decayed much faster than this, we wouldn’t be around. Because it’s so hard to calculate anything using string theory, there are no very good predictions for the proton decay rate. However, experiments set the proton lifetime as being greater than 1034 years. A friend of mine once made the comment that that was a pretty good definition of forever, but it’s not good enough for our purposes!
21.7 A GOOGOL YEARS—ALL THE BLACK HOLES EVAPORATE
If protons don’t decay, then the ultimate lifetime of life in the universe may be set by the timescale it takes for black holes to evaporate. Black hole evaporation is a quantum mechanical phenomenon. If we attempt to put a particle inside a black hole, quantum mechanics tells us there is a small probability that one will find it outside the hole. This is because of the Heisenberg uncertainty principle. We work out the basics of this phenomenon in the web problems. The bottom line is that in 1974, Stephen Hawking showed that black holes aren’t completely black. They act as blackbody radiators, though at very low temperature. A small amount of energy leaks out, and one can even assign a temperature to them:
where M is the mass of the black hole, and the other terms have been defined previously in this book. A black hole with the mass of the Sun would have a temperature of only 6 × 10−8 K, and larger ones would have lower temperatures. Still, the standard formulas for blackbody radiation apply, even to such exotic objects. One can show that the rate at which the black hole radiates away energy is proportional to 1/M2. A completely isolated black hole will spontaneously radiate away energy. Its mass will decrease. As its mass decreases, it will radiate away energy at a higher rate, which will cause it to decrease in size more rapidly, leading to an explosion of energy in the last few seconds of its existence. One can calculate the time the black hole will last from this formula:
A black hole with the mass of the Sun will far outlast all of the stars. A more typical black hole with a mass ten times that of the Sun will last for 2 × 1070 years. But this is peanuts compared to the largest black holes around.
At the center of each galaxy are ultramassive black holes whose mass can range from about a million times to several billion times the mass of our Sun. Our own galaxy has a relatively modest one with a mass of only 30 million Suns. A civilization in an artificial planet or Dyson net in orbit around this could potentially last for more than 1089 years. This dwarfs the current age of the universe by a huge margin, but we can do better.
The largest known black holes have a mass of more than 1010 solar masses. They are billions of light-years away, of course, but we have all the time we need to get there. A 70 billion solar mass black hole would have a lifetime of 10100 years—a googol years. There are currently no known black holes with this mass. The largest, discovered in April 2011, has a mass of 21 billion solar masses. However, I’m going to assume we can find a larger one, because writing a googol years is cooler than writing 1098 years.
To indicate how long a time this is, the current age of the universe is about 1010 years. If the age of the universe so far was represented by, say, the mass of a proton, a googol years would be represented by … what? The mass of all the grains of sand on all the world’s beaches? No. The mass of the Earth? No. The Sun? No. The mass of our universe? NO. A googol years would be represented by all of the visible mass in ten billion universes just like the one we are in right now. By the way, one great satisfaction in writing this section is that I have finally found a practical use for the term googol, which has not had much application in mathematics or physics to date, despite a fair amount of commercial (if badly spelled) success.
I am not the first person to have made these speculations. One of the interesting things about writing this book is that certain names keep popping up. Larry Niven and Poul Anderson are the two science fiction writers whom I have turned to for inspiration many times; among scientists, Freeman Dyson is the clear standout. In a 1974 paper he did the same thing that I am doing here: he calculated how long intelligent life in the universe could last [73]. His conclusions were more optimistic than mine: he concluded that life in the universe could last indefinitely by going through cycles of hibernation and activity, using less and less energy on each active cycle. One point: because of the paper’s date, a number of ideas in it don’t reflect current ideas in cosmology. In particular, the consensus model invalidates a number of his ideas. The paper “A Dying Universe: The Long-Term Fate of Astrophysical Objects” by Fred C. Adams and Gregory Laughlin is a more up-to-date analysis of this idea; I recommend it for the science fiction writer interested in very far-out ideas, as it contains a trove of data and formulas on the subject of the eventual fate of the universe [20]. The article is slightly out of date, as it predates the supernova measurements leading to the concept of the accelerating universe. However, its last section discusses the fate of the universe with non-zero cosmological constant.
My pen halts, though I do not. Reader, you will walk no more with me. It is time we take up our lives.
—GENE WOLFE, THE CITADEL OF THE AUTARCH
Jack Vance, Isaac Asimov, Gene Wolfe, Neil Gaiman, and many, many others have stories set at the end of time. This usually means at the end of the Earth’s lifetime, but some have gone much, much farther than that. As I said at the outset, this book is not meant to be predictive. The same can be said for science fiction itself. I do not expect humankind to last for a googol years; even if it does, it would not exist in any form recognizably human for even a tiny fraction of that time. However, even in the most far-flung stories, humans must remain human if we (as humans) are to sympathize with (or even understand) their actions. This is perhaps the greatest limitation of the literature: the hopes and dreams of one little species don’t amount to a hill of beans in this crazy universe. Or as Neil Gaiman put it, you can have happy endings as long as you end the story early enough.
I’m finishing this book with a quotation that speaks to me in a deep way. Let it be a metaphor for the best in science fiction as well as the best in humanity. It is from the great French mathematician Henri Poincaré:
Geologic history shows us that life is only a short episode between two eternities of death, and that even in this episode, conscious thought has lasted and will only last a moment. Thought is only a gleam in the midst of a long night.
But it is this gleam which is everything [192].