Infinity

Before ER, House and even Marcus Welby, a TV-doctor show called Ben Casey opened each week with a hand drawing symbols, as the voice of Sam Jaffe identified them one by one: “Man, Woman, Birth, Death … Infinity.”

Those five symbols supposedly encapsulated what medicine was all about. But they could equally well have summarized the story of the universe. Cosmologists, the scholars of cosmic existence, generally concur that the universe is probably infinite. And they are consumed with understanding the universe’s birth, the prospects for its death and whether the presence within it of men and women has anything to do with it all.

Of course, the men and women don’t have to be human. Basically any sentient life-form capable of contemplating the cosmos will do. The question is whether life has a starring role in the cosmic drama or is merely an extra, permitted by prevailing conditions but not required to explain them. If the physical laws governing the observable universe reflect mathematical truths, specifying nature’s properties without regard to any inhabitants, then life would be the lucky outcome of chance events within a hospitable habitat, not a clue to why the habitat is so hospitable to begin with.

It’s not a new debate. Long ago, astronomers argued similarly about the Earth itself — why it orbited so pleasantly around its source of warmth. Perhaps some unknown mathematical law required such a fortuitous location, some savants averred. But it turned out that there was no one law — rather there were lots of planets. People simply populated the one of those planets that offered a congenial environment.

Today many believe that the same principle applies to the congeniality of the universe. There may be no law determining its properties — rather there may be many universes, and life occupies one with congenial conditions. In other words, the properties of the universe that physicists measure are “selected” by the fact that physicists exist to begin with. It’s a notion generally known as the anthropic principle, and it evokes intransigent opposition from those who condemn it and unflagging enthusiasm from those who espouse it.

Opponents of anthropic reasoning argue that it cannot be tested, rendering it at best interesting philosophy that doesn’t qualify as science. But lately, anthropic advocates have sought ways to calculate values for cosmic characteristics that standard theory cannot explain, suggesting that science may need anthropic reasoning to answer some important questions. Such calculations encounter a major impediment, though: To test whether the universe is the way it is because it’s a good place for men and women to be born and die, scientists must learn how to cope with infinity.

Inflation goes on and on

Once defined as everything that exists, the term “universe” now often refers to just one of an infinite number of space-time bubbles.

“What we’ve all along been calling the universe,” says Arizona State University cosmologist Paul Davies, may be “just an infinitesimal fragment in a much larger, more elaborate system for which want of a better word we call the multiverse.”

A generation ago, such multiple universes existed only in science fiction, not science textbooks. Nowadays, the multi-verse is a hot topic at real-world scientific conferences, including a recent symposium on “Origins” at Arizona State, in Tempe. There Davies and other experts explored the anthropic implications of a multiplicity of universes, which owe their newfound importance to a popular astrophysical theory called inflation.

Among the Origins symposium’s speakers was Alan Guth of MIT, who invented the inflation idea in 1980. It explained several mysteries about the Big Bang, the cosmic explosion 13.7 billion years ago marking the birth of today’s one known universe.

For a tiny fraction of a second, Guth proposed, the universe expanded exponentially, explaining why the visible cosmos is now so uniform in temperature and structure. That exponential inflation would have stretched spacetime enough to eliminate all but the tiniest lumps in the original amalgamation of matter and energy, resulting in smooth skies today. Inflation would also have provided the impetus for the universe to grow to its current size from its minute origin.

“Inflation explains how the universe got to be so big, which is something we might take for granted, but there isn’t really any other theory I know of which comes close to actually explaining it,” Guth said at the Arizona conference.

Inflation is driven, Guth explains, by a repulsive form of gravity, generated by an energy field residing in space. As spacetime inflates, some of that field loses its strength — so a local region can expand more gradually, allowing stars and galaxies to develop and stick together. But at the same time, other regions of the inflating field continue to grow exponentially. There is always more inflating material available to spawn new spacetime bubbles — Guth calls them “pocket universes” — and no way for that process to ever stop.

“So once started, inflation goes on literally forever, with pieces of the inflating region breaking off and producing these pocket universes,” Guth says. “And if this is right, we would be living in one of these infinity of pocket universes.”

Goldilocks bubbles

Most experts today believe that inflation is the best explanation available for the visible universe’s appearance and contents. And if it’s the right explanation for the one known universe, there must be an infinite number of others.

“The question arises as to whether all these other universes are going to be like ours,” says Davies, “or whether they may have different laws and the laws in our universe are in some sense special.”

Arguments based on string theory, a favorite candidate (although unsubstantiated by experiment) for explaining all of physical law, suggest that the multiverse encompasses bubbles hosting various sorts of physics. Andrei Linde of Stanford University, another pioneer of inflation theory, noted at the Arizona symposium that string theory predicts the existence of an enormous number of different “vacuum states,” or spacetime bubbles with different properties, such as physical constants or particle masses. Of an infinite number of bubbles, Linde says, there could be 10⁵⁰⁰ different varieties. And though any underlying basic law of physics would remain the same, the bubbles could nonetheless exhibit vast physical diversity. “It is the same fundamental law of physics, but different realizations,” Linde says.

Some of those bubbles would not have lasted long enough for life, inflating but then shrinking before any interesting chemistry commenced. Others would expand forever, as seems the case with the bubble that humans occupy. In some, the local laws of physics would have welcomed living things; others would have permitted none of the particles and forces that conspire to build atoms, molecules and metabolic mechanisms. It seems that universes come in all sizes and flavors, with the human bubble being the Goldilocks version, just right for life.

It’s not possible, or at least it’s very unlikely (SN: 6/7/08, p. 22), for any of those other universes to make its presence physically known. So at first glance there is no obvious way to prove that they exist apart from inflation’s equations. But in fact, Guth and others argue, applying anthropic reasoning to the multiverse allows calculations of some observable properties of the known universe, otherwise inexplicable. Success in such calculations would validate the assumption that the multiverse is real.

“Whether you like it or not, we may be living in a multiverse —the question is whether or not it will be possible to tell one way or the other,” says Alex Vilenkin of Tufts University in Medford, Mass. “Some people complain that this theory is completely untestable. I think it can be tested.”

His reasoning is based on the belief that people aren’t special. In other words, if the multiverse offers multiple bubbles that permit life to evolve, humans would most likely live in an average bubble. If, for instance, you throw out all the bubbles that wouldn’t allow life anyway, and then calculate the average temperature of space in those that remain, humans should measure a cosmic temperature that is not very far off from that average.

But computing that average is not simple enough that a caveman could do it. Even after discarding the bad universes, an infinite number of good ones remain. So calculating the probability of measuring a particular temperature would involve dividing an infinite number of observations by an infinite number of universes. Try it. You can see why it’s a problem.

Vilenkin, Guth and others have attempted to circumvent the infinity problem by devising “measures” that permit an estimate for probabilities even in an infinite multiverse. One idea, which looked promising at first, was to define a finite sample of the multiverse, restricted to a limited time period. Just imagine a clock starting up at every point in space and allow the clocks to run until a specified cutoff time.

Calculations based on the finite region of space thus monitored could be extrapolated to infinity.

But a cosmos measured in this way would be deceiving. New bubble universes emerge every 10^-37 seconds; consequently whenever you stopped the clocks, fully half the bubbles would be only 10^-37 seconds old, and many more would also be very young. This “youngness bias” distorts the calculations, so that most of the universes that did grow old enough for life to evolve would still be much younger than the one that humans occupy. Because the universe cools as it expands, younger universes are hotter, and the most likely temperature of habitable universes in this scenario would be much higher than observed, cosmologist Max Tegmark of MIT has calculated.

So Guth and colleagues are now pursuing a measure of infinite space that largely avoids the youngness bias. Instead of watching the multiverse grow over time, this method (called the scale-factor cutoff) follows the cosmos as it grows by a certain amount of size. This approach still entails some youngness bias, but not very much. And actually, a little youngness is a good thing. For if the average universe age is too old, humans would not be the most likely sentient forms of matter. There would be many, many more Boltzmann brains than people.

Brains in space

Boltzmann brains are named for the 19th century physicist Ludwig Boltzmann, a pioneer in explaining probabilistic processes in physics. In an infinite universe, all things are possible, even random accumulations of atoms that precisely mimic objects that evolved by cause-and-effect processes — such as brains. Somewhere in the cosmos, such a random mix of molecules has produced a brain identical to yours in every respect, neurons in identical configurations, with all your memories and perceptions. If enough matter and energy is around to make them, Boltzmann brains could become quite populous, making them, rather than humans, the typical observers of the cosmos.

It is clear that you are not a Boltzmann brain, though. Close your eyes and clear your mind of all unpleasant thoughts. Then open your eyes, and you see all the same stuff, not the newly randomized world that a Boltzmann brain would see.

If Boltzmann brains dominated the cosmos, humans would be rare, so your very existence implies that the average habitable universe must be young enough to restrain the odds of Boltzmann brain formation. Guth believes the scale-factor cutoff approach may succeed in limiting the likelihood of those Boltzmannesque impostors, as spelled out in a paper by Andrea De Simone of MIT and collaborators (including Guth, Vilenkin and Linde) posted online at arxiv.org/abs/0808.3778.

In any case, the new approach seems to allow calculations relevant to one of the thorniest problems that physicists face today: the amount of energy in the vacuum of space. This “dark energy” exerts a repulsion that drives the universe to expand at an accelerating rate, yet its strength is much less than the best estimates available from standard theory. No known math can specify why the dark energy has the strength that it does.

But a multiverse offers an answer — there is no one right answer. Dark energy’s strength would differ from bubble to bubble. Anthropic reasoning suggests, then, that humans should occupy a bubble with something like a typical intensity of dark energy — based on the average dark energy expected for all the bubbles where life would be possible. Using the scale-factor cutoff to evade the infinities in such calculations, Guth, Vilenkin, De Simone and Michael Salem of Tufts show that sure enough, the expected dark energy intensity is rather close to the calculated average, as shown in a paper appearing last year in Physical Review D.

“The agreement of this prediction with the measurement is very good,” Vilenkin said at the Arizona conference. “So this may be our first evidence that there is indeed a huge multiverse out there.”

To be sure, these calculations are still crude. They rely on a rather gross estimate of the number of observers in the multiverse, for example, using the expected number of galaxies as a proxy for people (or other comparable life-forms). But these aren’t the only results that point in an anthropic direction. Another group of MIT physicists, in the March issue of Physical Review D, analyzes the masses of quarks and ascertains that they lie comfortably in the range to be expected for a universe congenial to complex life.

Still, die-hard opponents remain unconvinced. David Gross, a Nobel laureate and director of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, argues passionately against anthropic reasoning every chance he gets.

“Eternal inflation is technically and conceptually shaky,” he said in Arizona. And string theory is an unfinished project. “We still don’t know what string theory is,” he points out.

In the past, Gross notes, apparently unexplained features of physics eventually succumbed to efforts to find a single correct answer, rather than resorting to the anthropic approach. Perhaps, he suggests, some fundamental insight, now missing from conventional theory, will someday show the way to solving nature’s riddles with mathematical rigor.

But perhaps that missing insight is merely realizing the need to master the inconveniences of infinity to resolve the cosmic conundrums. In other words, an infinite number of universes could be just what the doctor ordered.