Spooks in Space

POP. What are the chances that an everyday object - a rock, a chair, you name it - 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 - at least in theory. Physicists have dubbed such hypothetical beings "Boltzmann brains", 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. "This assumption is very essential to everything that we do," says Alex Vilenkin of Tufts University in Massachusetts. "If we don't assume that our observations are typical of observers, we wouldn't be able to conclude anything."

That's because if we aren't typical, then whatever we see is not representative of the universe at large. So here's the problem: some well-established cosmological models predict that, trillions of years in the future, Boltzmann brains could vastly outnumber "ordinary observers" like us, who depend on aeons of evolution and life support. If that is true, then over the lifetime of the universe, they - not we - might be the typical ones. That's 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 "pop-up" 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 "dark energy" 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 - 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 - 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 "What little brains are made of"). "It looks like a miracle," says theorist Andrei Linde of Stanford University in California. "Not entirely impossible, but just extremely improbable."

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. "Brains and what-not will be popping out of this vacuum at some very low rate, but for a very long time," says Vilenkin.

So if the universe can produce two kinds of observers - ordinary ones like us, and freakish Boltzmann brains - 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 Scientist, 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 "smooth" 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 - a theory known as eternal inflation. In this picture there is a vast backdrop of expanding space, out of which new "pocket universes" are continually budding off (see Diagram). Some of these universes are like our own - going through a short period of explosive growth and then settling down - while others could have wildly different laws of physics. In this "multiverse" scenario, pocket universes can grow infinitely large and contain an infinite number of stars and planets - and Boltzmann brains, which could outnumber ordinary observers.

To tame these infinities, researchers have been trying to figure out each type of observer's likelihood of existing. "What we're struggling with is the question of computing probabilities in such scenarios," says Raphael Bousso of the University of California, Berkeley. "You 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."

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 (www.arxiv.org/abs/hep-th/0610079).
“Our universe must have a self-destruct mechanism to kill it off before Boltzmann brains can dominate”

How so? Just as the vacuum energy has quantum fluctuations that can generate Boltzmann brains, the energy itself can jiggle and "decay" 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 Scientist, 12 March 2005, p 29). This bubble of fire would eradicate us, along with all structure in the cosmos. "It would be destroying the universe as we know it," 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. "This is where people start fighting," says Linde.
Picking pockets

Linde's 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 (Journal of Cosmology and Astroparticle Physics, DOI: 10.1088/1475-7516/2007/01/022). "If you use this measure," he says, "then this paradox with Boltzmann brains does not appear."

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 (Journal of High Energy Physics, DOI: 10.1088/1126-6708/2007/01/092).

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 "the ambiguity of taking ratios of infinite numbers".

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's because observers can't 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. "Let's make our theories describe any possible history, but not pretend that they all have to fit together into some God's-eye view," he says. Taking Bousso's approach seems to solve the Boltzmann brain problem but, like Page's proposal, only if the universe as we know it self-destructs (www.arxiv.org/abs/hep-th/0610132).

In contrast to Page's work, Bousso looks at a much smaller area of space: the volume inside a given observer's 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't dominate. "The only way that Boltzmann brains could win is if the vacuum lasts longer than it takes for a Boltzmann brain to appear," Bousso says. The time it would take to happen even once is "insanely long", he says. Even if the universe self-destructed after an incredibly long time - 10 to the power of 1020 years - 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're still "babes in the woods" 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 "that the regular observers win over freak observers". Linde has a similar outlook. "If we suggest some probability measure in inflationary cosmology and it leads to this Boltzmann brain problem," he says, "then this is another way to learn that we are doing something wrong."

Conversely, if a method for counting Boltzmann brains also provides insight into a different problem, that could be a sign that it's 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's result gets much closer to the measured value (www.arxiv.org/abs/hep-th/0702115). "We didn't know what the answer would be," he says, "but it just led to an enormous improvement."

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... POP.
Mason Inman is a science writer based in Boston, Massachusetts
From issue 2617 of New Scientist magazine, 18 August 2007, page 26-29