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Date: Mon, 10 Mar 2003 23:46:38 -0500
From: Ruben I Safir
Subject: [hangout] Everything in the Universe might not be what it seems
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March 11, 2003 Universe as Doughnut: New Data, New Debate By DENNIS
Long ago in the dawn of the computer age, college students often whiled
away the nights playing a computer game called Spacewar. It consisted of
two rocket ships attempting to blast each other out of the sky with
torpedoes while trying to avoid falling into a star at the center of the
Although cartoonish in appearance, the game was amazingly faithful to
the laws of physics, complete with a gravitational field that affected
both the torpedoes and the rockets. Only one feature seemed outlandish:
a ship that drifted off the edge of the screen would reappear on the
Real space couldn't work that way.
Or could it?
Imagine that the Spacewar screen is wrapped around to form a cylinder or
a section of a doughnut so that the two edges meet.
That is the picture of space, some cosmologists say, that has been
suggested by a new detailed map of the early universe. Their analysis of
this map has now provided a series of hints ? though only hints ? that
the universe may have a more complicated shape than astronomers
Rather than being infinite in all directions, as the most fashionable
theory suggests, the universe could be radically smaller in one
direction than the others. As a result it may be even be shaped like a
"There's a hint in the data that if you traveled far and fast in the
direction of the constellation Virgo, you'd return to Earth from the
opposite direction," said Dr. Max Tegmark, a cosmologist at the
University of Pennsylvania.
The new data have generated both buzz and skepticism among cosmologists
in recent weeks. Dr. Tegmark and other astronomers agree that the
measurements are far from conclusive, or even persuasive about the shape
of the universe.
But if true, the doughnut universe would force cosmologists to
reconsider their theories about what happened in the earliest moments
after the universe was born in the Big Bang; those theories predict an
The new findings have brought to center stage the hope that astronomers
may be able to test speculations about the shape, or topology, of the
universe that until recently have been relegated to the abstract
mathematical margins of cosmology.
The results are part of the bounty of data produced by a NASA satellite
known as the Wilkinson Microwave Anisotropy Probe, built and operated by
an international collaboration led by Dr. Charles L. Bennett of the
Goddard Space Flight Center in Greenbelt, Md. The satellite recorded the
pattern of heat, in the form of faint microwave radiation, that fills
This radiation is believed to be the afterglow of the Big Bang itself,
and thus constitutes a portrait of the universe when it was only 380,000
As the COBE satellite first confirmed in 1992, the microwave cloud is
laced with ripples and splotches ? lumps in the cosmic gravy ? from
which galaxies and other cosmic structures would ultimately form.
According to theory, these lumps are born as microscopic fluctuations
during the first instant of time and then amplified into sound waves as
the universe expands and matter and energy slosh around.
Now the new satellite has illuminated the findings of COBE (pronounced
KOE-bee, for Cosmic Background Explorer) in exquisite detail.
By analyzing these waves cosmologists can determine many of the
characteristics of the universe, which scientists have long debated,
like its age and density. To their delight, the first results from the
Wilkinson satellite, released last month, confirmed many of the strange
ideas that cosmologists entertained in the last decade, including the
notion that most of the universe consists of something called dark
energy, which is pushing space apart at an accelerating rate.
"Cosmologists have built a house of cards and it stands," said Dr. James
Peebles, a cosmologist at Princeton.
But to their even greater delight, perhaps, as they dig into the trove
released last month, cosmologists are finding hints of even more
In principle, in an infinite universe, the waves in the cosmic fireball
should appear randomly around the sky at all sizes. But, according to
the new map, there seems to be a limit to the size of the waves, with
none extending more than 60 degrees across the sky.
The effect was first noted as a puzzle in the COBE data, according to
Dr. Gary Hinshaw, an astronomer at the Goddard Space Flight Center and a
member of the Wilkinson probe team, and now seems confirmed.
If the universe were a guitar string, it would be missing its deepest
notes, the ones with the longest wavelengths, perhaps because it is not
big enough to sustain them.
"The fact that there appears to be an angular cutoff hints at a special
distance scale in the universe," Dr. Hinshaw said.
Another analysis of the new map suggests that there is a special
direction, as well as a special scale in the universe. While reanalyzing
the Wilkinson data to eliminate radio noise from stars and our own
galaxy, Dr. Tegmark, Dr. Angélica de Oliveira-Costa, also at
Pennsylvania and married to Dr. Tegmark, and Dr. Andrew J. S. Hamilton
of the University of Colorado have discovered that the universe appears
lumpier in one direction through space than it does in another. When
they combed finer variations out of the map, the remaining large-scale
variations formed a line across the sky.
It could be a chance alignment, a statistical fluke, Dr. Tegmark said,
or contamination from radio noise from the galaxy.
But in a paper posted on the physics Web site (at arXiv.org/pdf
/astro-ph/0302496) late last month, the three cosmologists wrote that it
was "difficult not to be intrigued" that their results bore all the
earmarks of what are variously called small, compact, finite or periodic
If the universe is finite in one dimension, like a cylinder or a
doughnut, Dr. Tegmark said in an interview, there is a limit to the size
of clumps that can fit in that direction. They couldn't be bigger than
the universe in that direction, just as a guitar string can only play a
note so low, depending on its length. So the biggest blobs would have to
squish out in a plane in other directions. The way home around the
doughnut would be perpendicular to that plane.
Nobody is yet claiming that this is a revolution. The notion of a
special direction is on less firm ground than the discovery of a cutoff
of large structures. "More detailed work in needed to clarify what's
going on," Dr. Tegmark said.
Dr. Martin Rees, a cosmologist at Cambridge University," said he didn't
think there was evidence for "anything crazy" in the data.
Even aficionados of finite universes are guarded. Dr. David Spergel, a
Princeton cosmologist and Wilkinson satellite team member, called the
results "intriguing," but cautioned that they could also be due to
Dr. Hinshaw called the findings of Dr. Tegmark's team "surprisingly
robust," but added, "I'm not sure it says something profound about the
Dr. Alexei Starobinski, a theorist at the Landau Institute in Moscow,
proposed in 1984 with his mentor, Dr. Yakov B. Zeldovich, that the
universe could have been born as a doughnut. Dr. Starobinski emphasized
that an infinite universe with ordinary Euclidean geometry was the most
natural universe and still favored by theory.
"However, theory is theory, but observations might tell us something
different," he said in an e-mail message.
The Science of Shapes A Compact Universe Like Mirrored Halls
The new work involves topology, the branch of mathematics that deals
with shapes. Topologists are often accused of not knowing the difference
between a coffee mug and a doughnut; because each object has one hole,
the two can be deformed into each other and are thus topologically
equivalent. In a similar vein, a figure 8 and a pair of eyeglass frames
are also the same to a topologist. The more holes, the more complicated
The simplest topology is just the infinite space of the Euclidean
geometry taught in high school. But some cosmologists have a hard time
calculating how an infinite universe could have appeared in that kind of
space. Nature, they contend, might have had an easier time making a
small "compact" universe than an infinite one, and they assume Nature
would take the easy way out.
"The basic idea is that God's on a budget," said Dr. George Smoot, a
physicist at the University of California's Lawrence Berkeley Laboratory
and a leader on the COBE team.
The simplest of these compact universes is something called a 3-torus, a
doughnut wrapped in three different dimensions. This object is
essentially impossible to visualize: it is the equivalent, in a way, of
a cube whose opposite sides are somehow glued together. In two
dimensions it works just like the Spacewar screen.
Living in such a universe would be like being inside a hall of mirrors,
Dr. Tegmark said. Instead of seeing new stars deeper and deeper in
space, you see the same things over and over again as light travels out
one side of your cube and back in the other.
This mirror game is not limited to cubes and doughnuts. Over the years
mathematicians, particularly Dr. William Paul Thurston, now at the
University of California at Davis, and Dr. Jeffrey Weeks, an independent
mathematician, have speculated about universes composed of various
polyhedrons glued together in various ways.
In 1996 the French astronomer Dr. Jean-Pierre Luminet of the Paris
Observatory and his colleagues Dr. Roland Lehoucq and Dr. Marc
Lachieze-Rey, both of the Center for Astrophysical Studies in Saclay,
France, developed a method called "cosmic crystallography," using galaxy
statistics to detect and diagnose the repeating periodic patterns that
would be created in the sky by light going around and around in
differently shaped universe.
Finite or Infinite? Problems Are Posed For Favored Theory
Why would the universe want to do this to us? Partly to avoid the
difficulties of the infinite, said Dr. Glenn Starkman, an astronomer at
the Case Western Reserve University in Cleveland. Besides being
difficult to create, an infinite universe is philosophically
unattractive. In an infinite volume, he pointed out, anything that can
happen will happen.
"Somewhere there are two guys having this same conversation," Dr.
Starkman said in a telephone interview, "except that one of them has a
Moreover, the idea that dimensions could be curled in loops occurs
naturally in theories that try to unite gravity and particle physics,
several physicists pointed out. For example, according to string theory,
the leading candidate for a theory of everything, the universe actually
has 10 dimensions ? 9 of space and 1 of time ? rather than the 4 we are
familiar with. The extra dimensions are curled up into submicroscopic
loops, like the threads in an uncut carpet pile, so that we don't notice
them in ordinary life.
"This is the same idea on a very large scale," Dr. Smoot said.
Knowing that all nine of the spatial dimensions predicted by string
theory are finite and thus on the same footing could help string
theorists decide among the nearly endless possibilities allowed by the
theory, scientists say.
But a finite universe would create big problems for the reigning theory
of the Big Bang, inflation theory. It posits that the universe underwent
a burst of hyperexpansion in its earliest moments. Among other things,
it implies that the observable universe today, a bubble 28 billion
light-years in diameter, is only a speck on the surface of a vastly
greater realm trillions upon trillions of light-years across.
"There's no natural way yet proposed to get the inflation to stop and
give a space that's big enough to house all the galaxies but small
enough to see within the observable horizon," said Dr. Janna Levin, a
Cambridge University cosmologist who wrote about finite universes in her
1992 book, "How the Universe Got Its Spots, Diary of a Finite Time in a
Dr. Spergel added, "If the universe were finite, then this would rule
out inflation and require something new."
The Search for Patterns One Convincing Sign Of the Doughnut
So far, sporadic searches for repeating patterns of quasars or distant
galaxy clusters that would occur in a hall of mirrors universe have been
For finite universe aficionados, the first encouragement of note was
COBE's discovery that the universe appeared to be deficient in
large-scale fluctuations. There were no structures extending more than
about 60 degrees across the sky. But the finding was subject to large
statistical uncertainties, astronomers said.
There are other possible explanations for the cutoff in fluctuation
size, Dr. Starkman explained. According to inflation the biggest longest
waves are created first, and thus the missing notes are the earliest
ones that would have been strummed by inflation's guitar. Perhaps, he
said, this is telling us something about the beginning of inflation.
Dr. George Efstathiou of Cambridge University has pointed out in a
recent paper submitted to the Monthly Notices of the Royal Astronomical
Society that the Wilkinson satellite data are also marginally consistent
with yet another finite shape, namely a sphere. In that case,
fluctuations larger than the radius of the sphere might be dampened, he
said, producing the observed cutoff.
The most convincing sign of a doughnut universe, if it exists,
astronomers say, could come from a search of the satellite data now
being performed by Dr. Spergel, Dr. Starkman and Dr. Neil J. Cornish of
Montana State University. "We're looking for circles in the sky," Dr.
In a 1998 paper they point out that if the universe is small enough,
part of the cosmic background radiation, which essentially fills the sky
surrounding us, will hit the sides of the "box" or the space war screen
we are in and appear on the other side. The result, in the simplest
case, would be identical circles on opposite sides of the sky with the
same patterns of hot and cold running around them.
In the simplest case, the size of the circles would depend on the
distance between the "walls" of the universe: the smaller the universe,
the bigger the circles.
Success or even a definitive failure is not guaranteed. "It would be
fantastic if something like that was found," Dr. Hinshaw said of the
But success or even a definitive failure is not guaranteed. If the
universe is finite but still much larger than today's observable
universe ? 28 billion light-years in diameter ? the circles will not
show. "Usually in science when we see an intriguing pattern that appears
to contradict existing theory we do a better experiment," Dr. Spergel
wrote in an e-mail message, but in this case, "Ultimately we will be
limited by the fact that we can only observe the `visible' universe."
Dr. Levin was doubtful, "I suspect every last one of us would be
flabbergasted if the universe was so small," she said in an e-mail
message. When she first heard about the new satellite data, she
reported, "I tried on the idea that we were really and truly seeing the
finite extent of space and I was filled with dread.
"But I'm enjoying it too."
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