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FQXI ARTICLE
July 19, 2018

Measuring Up the Multiverse
Alex Vilenkin and Jaume Garriga ponder how unusual our universe is and whether this is all just a quantum dream.
by Kate Becker
FQXi Awardees: Alex Vilenkin, Jaume Garriga
April 24, 2009
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ALEX VILENKIN
Tufts University
Credit: Jodi Hilton
How do you compare one infinity to another? Think fast: The fate of the universe just might depend on your answer.

That may sound a little dramatic to some, but not to Alexander Vilenkin of Tufts University, Massachusetts, and Jaume Garriga of the University of Barcelona, Spain. They believe that our universe is one of many—infinitely many. According to "multiverse" theory, our Big Bang was just one in an eternal rumbling of bangs, each of which brings a new universe into being. Vilenkin and Garriga want to work out how ordinary—or how unusual—the properties of our universe are when compared with its neighbors. What fraction could harbor life, for instance?

The trouble is that with an infinite number of universes propagating forever, "anything that can happen will happen an infinite number of times," says Vilenkin. The trick is weighing up these infinities.

To explain why the sums are so hard, Vilenkin poses a numerical brainteaser: "What is the relative number of even and odd integers?" If you think there are just as many evens as there are odds, that’s a good answer. After all, one pairs up with two; three pairs up with four; five pairs up with six; and so on, into infinity.

"But what if I write the numbers separately and take two odds for each even?" he asks. Now one is grouped with two and four; three is grouped with six and eight; and so on. You could conclude that there are twice as many evens as odds, and you wouldn’t be wrong. “I can reach any conclusion I wish! And that’s not good,” says Vilenkin.

Anything that can happen
will happen an infinite
number of times.
- Alex Vilenkin
Things get a little more complicated when you’re talking about universes. For one thing, universes don’t come in nice neat rows like numbers. Plus, they’re all different: Theorists believe that the fundamental constants could be set to different values in each universe. In Universe A, gravity could be ten times stronger than in Universe B. Meanwhile, in Universe B, atoms could be bound together only half as tightly as they are in Universe C.

Theorists have been searching for a natural prescription to make these infinities somehow finite for decades, says Vilenkin. One solution was to count infinities only up to a certain time cutoff: At 100 billion years, say, someone rings a bell and you start tallying up the universes, ignoring any universes that crop up later.

Quantum Hallucination

But nothing’s ever that easy. Many of the cutoffs, or "measures," that researchers examined led to logical paradoxes, and those that didn’t made predictions that were in glaring conflict with observations. Some were plagued by the "youngness paradox," that is, they predicted that intelligent life would be most likely to crop up close to the time of the Big Bang. That makes our very existence, 14 billion years post-Bang, a near–impossibility. Theorists crossed those measures off of their list.


"How do I know whether I am a normal
person...or a vacuum fluctuation?"

Alex Vilekin ponders Boltzmann brains.
Credit: Andrey Volodin
Other measures had downright bizarre implications, predicting that "normal," biologically–evolved human brains should be outnumbered by so–called Boltzmann brains—disembodied minds that float in space. Boltzmann brains could be complete human beings, just brains, or maybe even silicon chips—material objects with the thinking power to "hallucinate" the universe we think of as real. Pick the wrong measure, and poof: You’re a Boltzmann brain!

It might sound like crackpot cosmology, but Boltzmann brains are a serious sticking point for some measures. Quantum mechanics tells us that things can pop up from the fluctuating vacuum. These "things" could be as trivial as an electron–positron pair that blinks into existence and then disappears again a split–second later. Particle physicists are well aware of this phenomenon; it happens all the time. Less likely, a whole atom could perform this magic trick. Even more improbably, a whole human being—or Windsor Castle, or a Honus Wagner baseball card, or a fully–formed brain thinking exactly your thoughts—could spontaneously materialize.

"It’s ridiculously improbable!" says Vilenkin. But given an infinite amount of time, even things that are ridiculously improbable are bound to happen. "So how do I know whether I’m a normal person…or a vacuum fluctuation?"

Don’t have an identity crisis just yet. Theorists agree that our universe must contain more "normal" brains than it does Boltzmann brains. "The world around a typical Boltzmann brain looks very different from the world around us," says Garriga. Plus, a Boltzmann brain likely wouldn’t stick around for long, so the mere fact that we all continue to think coherent thoughts from one moment to the next should be some assurance that we’re real.

Counting Universes

Once measures burdened by Boltzmann brains and other paradoxes were crossed off the list of contenders, says Vilenkin, a frontrunner emerged: a measure called the scale–factor cutoff.

Rather than measuring time using some synchronized cosmic clock, the scale–factor cutoff uses the expansion of the universe as a stopwatch. Instead of stopping the clocks and counting up universes after a certain amount of time passes, you stop after a set amount of expansion, so all regions are treated equally.

What makes the scale–factor cutoff stand out is that it seems to be the only simple cutoff that avoids paradoxes and pitfalls, says cosmologist Alan Guth, who has also studied measures.


JAUME GARRIGA
University of Barcelona
Problem solved? Well, almost. Not everyone agrees that the scale–factor cutoff is the best basket in which to place the universe’s infinite eggs. I–Sheng Yang, a graduate student at the University of California, Berkeley, is part of a team exploring an alternative measure based on a universal time cutoff.

"These two measures may have phenomenological differences, and their inventers may have different physical pictures in mind, but to me they are quite similar," says Yang. With so much yet to be learned about each cutoff, picking a winner "is actually quite about personal tastes," he says.

Ideally, cosmologists would prefer to derive a measure from fundamental principles, rather than simply endorsing the measure that happens to avoid the most paradoxes or making choices based on taste. Leaving such big questions to a process–of–elimination should only be "an exercise of last resort," says Guth, adding that theorists are now meeting the "limitations of trying to determine the correct measure simply by what works."

With that in mind, Vilenkin and Garriga are rebuilding their measure from the ground up, aiming for a precise version that is truly fundamental.

The Boundary of the Universe

But where to start? How about with a hologram?

There is an intriguing concept in physics, called the "holographic principle," which says that problems that are mathematically difficult in four dimensions (our three spatial dimensions plus a fourth dimension, time) can be more elegantly recast in three dimensions. By "going down a dimension," formerly intractable problems can be reduced to "some very beautiful mathematics," says Vilenkin.

The holographic principle offers up a lifeline, Vilenkin explains. "Since we cannot come up with a good motivation for our measure in four dimensions, maybe three dimensions will work."

"I really do consider the work to be extremely important," says Guth. If they succeed, "it would be a tremendous breakthrough."

This theory lives at the
future boundary of spacetime;
the place where everything has
been said and done.
- Jaume Garriga
If Vilenkin and Garriga can derive their measure by taking the number of spatial dimensions down a notch, what exactly does that mean? How will their two–dimensional theory relate to our three–dimensional space?

"This theory lives at the future boundary of spacetime," says Garriga. "The place where everything has been said and done."

In that place, theorists like Vilenkin and Garriga have already considered every possibility, derived everything there is to derive, and solved the universe’s puzzles a million times over. But in this universe, Vilenkin and Garriga are still at their desks, paper and pencils in hand, taking it one infinity at a time.

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Recent Comments


Since consciousness is the one thing that physics can't explain, we can make it a fundamental characteristic of spirit. Then, when we die, our physical body falls away (like the leaves on a tree fall away in Autumn). There is no mathematical description of love. Yet that is exactly what we experience when we die (or have a near death experience).

When we die, all that scientific cynicism dies with the physical body; true pure consciousness (the ability to witness) survives in spirit...


Here is an easy way to organize a multi-verse. Wave-functions exist. Wave-functions interpenetrate every boson, fermions and space-time. In fact, the big bang of this universe and other universes is just an expansion from this central ocean of wave-functions.

To look at it another way, wave-functions are what some people call "spirit". All universes that explode into existence are tied to spirit, what some people might call God.


The multiverse theory of space

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