POP. What are the chances that an everyday object 鈥 a rock, a chair, you name it 鈥 could suddenly appear out of thin air? Not zero, surprisingly. In fact, given enough space and time, it is conceivable that a conscious being could arise, even if only for a microsecond.
OK, such an event would be incredibly unlikely, but not impossible 鈥 at least in theory. Physicists have dubbed such hypothetical beings 鈥淏oltzmann brains鈥, after the 19th-century Austrian physicist Ludwig Boltzmann, a pioneer in thermodynamics and statistical mechanics. Boltzmann posed the question of whether the universe could have arisen from a thermal fluctuation; his work presaged the idea that a fluctuation could also give rise to a conscious entity that sees the universe. In this regard Boltzmann brains are not necessarily actual brains, but rather are a metaphor for observers of the universe that might appear spontaneously.
The idea sounds absurd, but it is helping cosmologists grapple with models of the universe, and our place in it. Cosmology, indeed most of science, assumes that we humans are typical observers in the grand scheme of things. Ever since the 16th century, when Polish astronomer Nicolaus Copernicus argued that the Earth is just a rock orbiting the sun, we have been dethroned from a unique position in the cosmos. The laws of physics seem to be the same in our neighbourhood as in the rest of the visible universe. So the idea has been enshrined that unless we have reason to think otherwise, we should assume that we are typical. 鈥淭his assumption is very essential to everything that we do,鈥 says Alex Vilenkin of Tufts University in Massachusetts. 鈥淚f we don鈥檛 assume that our observations are typical of observers, we wouldn鈥檛 be able to conclude anything.鈥
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That鈥檚 because if we aren鈥檛 typical, then whatever we see is not representative of the universe at large. So here鈥檚 the problem: some well-established cosmological models predict that, trillions of years in the future, Boltzmann brains could vastly outnumber 鈥渙rdinary observers鈥 like us, who depend on aeons of evolution and life support. If that is true, then over the lifetime of the universe, they 鈥 not we 鈥 might be the typical ones. That鈥檚 scary, because models suggest that their view of the cosmos would be strikingly different from ours.
Now Vilenkin and others are trying to figure out just how common Boltzmann brains could be and whether there is a way to banish them, or at least stop them from outnumbering us. Indeed, the Boltzmann brains problem is forcing cosmologists to revisit their most crucial assumptions about the structure of the universe. Either they must explain how the cosmos can produce enough ordinary observers to stay ahead of the 鈥減op-up鈥 brains, or we may have to accept that our ideas are wrong and that the ultimate fate of the universe is coming sooner than we thought.
All in their heads
Boltzmann brains reared their ugly heads in the late 1990s, when astrophysicists discovered that the expansion of the universe is accelerating, rather than slowing down as most had expected. One possible explanation for this 鈥渄ark energy鈥 has been known for decades: empty space could hold inherent energy that has a repulsive effect, driving space to expand and forcing matter apart. This effect goes by different names 鈥 the cosmological constant, or vacuum energy. Why it exists is one of the biggest mysteries in physics.
Regardless of its origins, vacuum energy is active and always subtly fluctuating 鈥 occasionally enough to transform into particles and matter. A photon might pop up here, an atom over there. The bigger and more complex the object, the less likely it is to appear. Wait long enough and a Boltzmann brain could pop up (see 鈥淲hat little brains are made of鈥). 鈥淚t looks like a miracle,鈥 says theorist Andrei Linde of Stanford University in California. 鈥淣ot entirely impossible, but just extremely improbable.鈥
A Boltzmann brain is so improbable, in fact, that there is essentially no chance that even a single one has appeared in the 13.7-billion-year history of our universe. But factor in the accelerating expansion of the universe, and the picture changes: it points to an infinitely large space that will last an infinitely long time, with ongoing fluctuations in the vacuum. This will be a cold, dark and inhospitable place for conventional creatures, but a perfect breeding ground for Boltzmann brains, which would see only empty space around them. 鈥淏rains and what-not will be popping out of this vacuum at some very low rate, but for a very long time,鈥 says Vilenkin.
So if the universe can produce two kinds of observers 鈥 ordinary ones like us, and freakish Boltzmann brains 鈥 cosmologists have a problem. To preserve the assumption that we are typical, they need to show that their models of the universe do not allow Boltzmann brains to outnumber us.
How do we figure out which kind of observer is more common? Consider the theory of inflation, which most cosmologists regard as the best explanation of our universe (New 杏吧原创, 3 March, p 33). Developed in part by Linde and Vilenkin in the 1980s, inflation says that just after the big bang, our universe expanded enormously and rapidly, making it extremely 鈥渟mooth鈥 and homogeneous, but with just enough bumpiness early on to allow matter to clump together to form stars and galaxies.
Many cosmologists buy into the idea that inflation is continuing at various points in the universe 鈥 a theory known as eternal inflation. In this picture there is a vast backdrop of expanding space, out of which new 鈥減ocket universes鈥 are continually budding off (see Diagram). Some of these universes are like our own 鈥 going through a short period of explosive growth and then settling down 鈥 while others could have wildly different laws of physics. In this 鈥渕ultiverse鈥 scenario, pocket universes can grow infinitely large and contain an infinite number of stars and planets 鈥 and Boltzmann brains, which could outnumber ordinary observers.
To tame these infinities, researchers have been trying to figure out each type of observer鈥檚 likelihood of existing. 鈥淲hat we鈥檙e struggling with is the question of computing probabilities in such scenarios,鈥 says Raphael Bousso of the University of California, Berkeley. 鈥淵ou produce an infinite number of bubbles, and each of them is infinitely large, so you have to find a way of comparing infinities. Boltzmann brains are one of the constraints that help us figure out how to think about this kind of cosmology correctly.鈥
The most radical solution comes from Don Page of the University of Alberta in Edmonton, Canada. He argues that our universe must have a built-in self-destruct mechanism that will kill it off before Boltzmann brains can dominate ().
鈥淥ur universe must have a self-destruct mechanism to kill it off before Boltzmann brains can dominate鈥
How so? Just as the vacuum energy has quantum fluctuations that can generate Boltzmann brains, the energy itself can jiggle and 鈥渄ecay鈥 to a higher or lower level. In eternal inflation, this is how a pocket universe begins. The decay starts at a tiny point and releases an enormous amount of energy, creating a bubble that expands outward at nearly the speed of light (New 杏吧原创, 12 March 2005, p 29). This bubble of fire would eradicate us, along with all structure in the cosmos. 鈥淚t would be destroying the universe as we know it,鈥 Page says.
Such a decay would act like a cosmic reset button, preventing the universe from getting old enough to let Boltzmann brains take over. For this to work in our universe, says Page, it needs to happen within about 20 billion years from now. Wait any longer, he says, and our universe will be expanding so rapidly that such decay bubbles could never catch up: patches of the original universe would remain, forever spawning Boltzmann brains. Although it is nothing our grandchildren will need to worry about, this time frame is much shorter than most had expected.
Other researchers argue that taking a broader view can banish Boltzmann brains without requiring our universe to self-destruct at such a tender age. The multiverse, they claim, is evolving an infinite number of regular observers like us. The only problem is that an infinite number of Boltzmann brains are popping up too. However, not all infinities are equal. To see who is winning the race, physicists have begun counting up the observers. 鈥淭his is where people start fighting,鈥 says Linde.
Picking pockets
Linde鈥檚 approach looks across multiple pocket universes and counts the number of observers in a certain volume of space at any given moment. In this picture, many universes can support creatures like us for a short period of time, but in the long run give rise to Boltzmann brains. However, since new universes are always being created by eternal inflation, Linde says, when you add up all the observers at any given time, ordinary ones always outnumber Boltzmann brains because there is a continual supply of them (). 鈥淚f you use this measure,鈥 he says, 鈥渢hen this paradox with Boltzmann brains does not appear.鈥
Vilenkin has his own solution, also based on eternal inflation, but using a different method of counting up the observers. He instead compares the likelihood of new pocket universes forming with the likelihood of Boltzmann brains popping up. According to his calculations, too, regular observers are always appearing faster than Boltzmann brains ().
Other physicists are not convinced that anyone can yet justify the assumptions behind eternal inflation models clearly enough to make tallies across multiple universes, so they are wary of using these models to resolve the Boltzmann brain problem. Page, for one, argues that these solutions suffer from 鈥渢he ambiguity of taking ratios of infinite numbers鈥.
Bousso goes further. He says it is not possible, even in principle, to take an overview of the multiverse. In a universe like ours, there is only so much that any one observer can see. That鈥檚 because observers can鈥檛 travel any faster than the speed of light, and neither can any signals. Bousso recommends sticking with a local view rather than trying to calculate across multiple universes. 鈥淟et鈥檚 make our theories describe any possible history, but not pretend that they all have to fit together into some God鈥檚-eye view,鈥 he says. Taking Bousso鈥檚 approach seems to solve the Boltzmann brain problem but, like Page鈥檚 proposal, only if the universe as we know it self-destructs ().
In contrast to Page鈥檚 work, Bousso looks at a much smaller area of space: the volume inside a given observer鈥檚 horizon. Since this allows much less space for Boltzmann brains to pop up in, the universe could last much longer before self-destructing, though still decaying soon enough that Boltzmann brains won鈥檛 dominate. 鈥淭he only way that Boltzmann brains could win is if the vacuum lasts longer than it takes for a Boltzmann brain to appear,鈥 Bousso says. The time it would take to happen even once is 鈥渋nsanely long鈥, he says. Even if the universe self-destructed after an incredibly long time 鈥 10 to the power of 1020 years 鈥 that would still be soon enough to prevent Boltzmann brains from taking over.
So which approach is correct? And what does banishing Boltzmann brains ultimately tell us about the universe? There is no consensus yet, and experiments cannot test these proposals. Page says we鈥檙e still 鈥渂abes in the woods鈥 when it comes to grappling with the multiverse. So far he has been content just to point out the potential problem.
However, Boltzmann brains could indicate which ways of calculating probabilities in the multiverse are right or wrong. Vilenkin says that any decent method should give the answer 鈥渢hat the regular observers win over freak observers鈥. Linde has a similar outlook. 鈥淚f we suggest some probability measure in inflationary cosmology and it leads to this Boltzmann brain problem,鈥 he says, 鈥渢hen this is another way to learn that we are doing something wrong.鈥
Conversely, if a method for counting Boltzmann brains also provides insight into a different problem, that could be a sign that it鈥檚 on the right track. Bousso and his colleagues have recently extended their approach of working within a given horizon to calculate the strength of vacuum energy a typical observer would measure. Previous methods for predicting this energy density gave results larger than the observed value by factors of 10, 1000 or even many billions. Bousso鈥檚 result gets much closer to the measured value (). 鈥淲e didn鈥檛 know what the answer would be,鈥 he says, 鈥渂ut it just led to an enormous improvement.鈥
So cracking the conundrum of Boltzmann brains may do more than simply remove their threat, allowing cosmologists to continue assuming we are typical: it may also help us weed out models of the universe that fall short of explaining its strangeness. Then again, despite astronomical odds, there remains the unsettling possibility that we are all, in fact, Boltzmann brains鈥 POP.
What little brains are made of
As empty space contains a repulsive force known as vacuum energy, it can eventually spawn particles, atoms and even, in theory, conscious entities. These hypothetical 鈥淏oltzmann brains鈥 鈥 spontaneous observers of the space around them 鈥 challenge our place in the universe.
What exactly might these things be? In theory, they could take on almost any form, but the larger and more complex they are, the less likely it is that they will appear, according to the laws of probability and quantum mechanics. They could be disembodied brains with eyeballs, floating in outer space. They could consist of a whole body, encased in a space suit and equipped with an oxygen tank. They could be human brains, animal brains or an intelligent alien species made of gas. What matters is that they qualify as conscious 鈥 by whatever definition researchers agree on.
They need not even be actual brains. If computers could become complex enough to be considered conscious, for instance, they would qualify too. Since computer chips pack large amounts of processing power into a tiny space, silicon-based Boltzmann brains could be much smaller than biological brains. If so, that might make conscious computers more likely to pop out of the vacuum than biological entities, meaning they could be the ones to dominate the universe.
