24 July 2014 sky & telescope
Big Bang Breakthroughreason the cosmos has to be arranged for the benefi t of
this generation of scientists and their testing capabilities.
And as Max Tegmark says, “Parallel universes are not a
theory — they’re predictions of certain theories.”
A bigger problem comes from the idea that if infl ation
goes on forever, it spawns not just a very large number
of big bangs, but an infi nite number of them. Nowhere
in the real world has any physical infi nity ever before
appeared. Infi nities come up all the time in math that
usefully describes the world (that’s why calculus was
invented). But no measurable physical quantity, such as
mass or distance, ever has an infi nite value. Unless infl a-
tion forces the issue.
And in fact, infl ation predicts a second, diff erent kind of
infi nity closer to home. Even if there is only a single bang
and nothing but our own bubble universe (theorists are try-
ing to fi nd a way to make this work), infl ation still requires
our own universe to be infi nite in extent. We can’t see far-
ther than our 13.8-billion-year horizon, but endless farther
reaches must exist beyond it, fi lled with stars and galaxies
pretty much like those nearby. Go far enough, and every
possible fi nite arrangement of atoms, each acting out every
quantum event available to it — including perfect, atom-
by-atom copies of Earth and its people — not only repeat,
but repeat an infi nite number of times. Tegmark calls this
more immediate version of infi nity the “Level I multi-
verse,” and the infi nity of other infi nite big-bang universes
spawned by eternal infl ation the “Level II multiverse.”
The crisis posed by infi nite space is a paradox called
the “measure problem.” If infi nite copies of you exist, for
instance, it becomes impossible to assign any probabilityat all to anything that might happen to you (or to any-
thing else) — because all things happen an infi nite num-
ber of times, and infi nities of this class are necessarily
identical. One such infi nity can’t be larger than another.
The naïve idea that you can just pick a “large enough”
fi nite region, and compare the numbers of things within
that, fails to work. In an infi nite context, every fi nite
region is itself duplicated an infi nite number of times,
with an infi nite occurrence of all possible outcomes.
This was just a matter of armchair philosophy before
the predictions of infl ation started making it press-
ingly real. Alan Guth, for one, is not very concerned. At
the March 17th BICEP press conference, he said that he
thinks the measure problem can ultimately be resolved
and will go away. Tegmark, on the other hand, says “The
measure problem is a terrible embarrassment for modern
cosmology.... Infl ation is saying, hey, there’s something
totally screwed up with what we’re doing. There’s some-
thing very basic we’ve assumed that’s just wrong....
It’s telling us that things aren’t just a little wrong, but
terribly wrong.” He predicts that, with the infl ationary
universe becoming more and more inescapable, coping
with the infi nities it requires will become the central
problem in cosmology and physics going forward.
Stay tuned. ✦S&T senior editor Alan M. MacRobert has been follow-
ing quantum proposals for the Big Bang’s origin, and their
suggestions of a multiverse, since the fi rst was published by
Edward Tryon in 1973.ETERNAL INFLATION In this symbolic representation,
separate big-bang universes (black) begin and expand forever in
an eternally infl ating outer matrix of superdense “false vacuum”
(blue). Time runs from bottom to top. There may or may not be a
particular start, but once the process gets going, it never ends.FURTHER READING
More news of cosmology’s “spring cleaning” after the
BICEP2 announcement keeps appearing. See our choice
of links, including the BICEP team’s original discovery
papers, at skypub.com/july2014infl ation.SOURCE: MAX TEGMARK,OUR MATHEMATICAL UNIVERSEYou are
here