Subject: Is our universe infinite, finite, or both?
From: Dimi Chakalov <>
Date: Fri, 10 Oct 2003 06:13:05 +0100
To: Neil J Cornish <>, David Spergel <>, Jean-Pierre Luminet <>, Jeffrey R Weeks <>

Dear Colleagues,

I read just two of the reports about your discussion, in New Scientist
[Ref. 1] and in New York Times [Ref. 2], and what I liked the most is the statement by Neil Cornish: "But I guess you've just got to take the Universe you're given."

I'm eagerly awaiting the report by David Spergel, hopefully next month, at . Einstein's GR does not tell us
whether the volume of space is finite or infinite, nor what is its
overall topology, but only that the sign of the curvature depends on the total density of matter and energy, 96 per cent from which is totally unknown,

I hope Dr. Spergel will say something new on these 96 per cent "dark
stuff", otherwise this whole debate might begin to resemble the old
story about the drunken man who had lost his key in the dark, but is
searching for it under the street lamp, simply because it is brighter there.

"Is space infinite or not?", asks Max Tegmark, gently reminding us that "this is what got Giordano Bruno burned at the stake" [Ref. 2].

Jain. It's both infinite and finite,

Let's not involve Giordano Bruno, he was a very open-minded person. We're old and biased, or at least some of us. It seems to me that there are quite many people who believe that the question about the topology of the universe should be cast in the format 'either-or', simply because Mother Nature could not have managed to employ all three possibilities, say, open and closed in the global mode of spacetime, and asymptotically flat in the local mode of spacetime.

What if Mother Nature is smarter? Let's take a good look at the 3-D
space in Einstein's GR. We, or at least some of us, believe that there
is 3-D space, but what if this is nothing but a wishful thinking?

Perhaps the mystery of 3-D space should be the starting point toward
understanding the topology of the universe,

Then comes the mystery of time,

All we need is math and clear mind. Surely nobody will got burned, like Giordano Bruno.

Kindest regards,

Dimi Chakalov
35 Sutherland St
London SW1V 4JU


[Ref. 1] Tantalising evidence hints Universe is finite, by Hazel Muir 19:00 08 October 03 
Special Report from New Scientist Print Edition,

Perplexing observations beamed back by a NASA spacecraft are fuelling debates about a mystery of biblical proportions - is our Universe infinite? Scientists have announced tantalising hints that the Universe is actually relatively small, with a hall-of-mirrors illusion tricking us into thinking that space stretches on forever.

However, work by a second team seems to contradict this, and scientists are now busy trying to resolve the conundrum. "Whether space is finite is something people have been asking since ancient times, and probably before that," says mathematician Jeffrey Weeks from Canton, New York. "If we resolved this and confirmed that space is finite, this would be an enormous step forward in our understanding of nature."

Weeks and his colleagues, a team of astrophysicists in France, say the WMAP results suggest that the Universe is not only small, but that space wraps back on itself in a bizarre way (Nature, vol 425, p 593).

Despite being finite, the Universe would not have any kind of edge. If a spacecraft blasted off in what we'd perceive to be a straight line - the line a beam of light would follow - it would eventually end up back where it started.

Because of this odd wraparound effect, the light from one galaxy could follow two different routes to the Earth, so the same galaxy would appear in two different parts of the sky. Effectively, the Universe would be like a hall of mirrors, with the wraparound effect producing multiple images of everything inside.


It would also banish the philosophical paradoxes of an infinite
Universe, such as the idea that every person on Earth has an infinite
number of alien doubles leading parallel lives. "If we could prove that
the Universe was finite and small, that would be earth-shattering," says David Spergel of Princeton University in New Jersey. "It would really change our view of the Universe."

However, in response to Weeks's report, Spergel and his colleagues have announced evidence that contradicts the findings. They showed previously that if the Universe does produce a hall-of-mirrors effect, it should be possible to find a pattern of matching circles in the microwave background around which the fluctuations are identical (New Scientist print edition, 19 September 1998, p 28).

Weeks's theory predicts six specific pairs of matching circles in the
sky, but Spergel's team has had no luck finding them in WMAP data.
"Weeks's team has a very powerful model that's nice because it makes a very specific prediction about the pattern we should see on the sky," says Spergel.

"However, we've looked for it, and we don't see it."

Spergel and his team are now working with Weeks to see if they might somehow have missed the circles. And there is a further test of the dodecahedron model. It predicts that a key measure of the density of matter in the Universe, which governs its curvature, is equal to 1.013.

Completely flat space corresponds to 1, while values greater than or
less than 1 would create a curved Universe. Observations of the
microwave background radiation so far suggest the value lies somewhere between 1.00 and 1.04. Further observations by WMAP and other instruments should give a more accurate answer within the next few months.

Computers at two universities and at NASA's Goddard Space Flight Center are scanning the WMAP results for all the possible patterns of circles that might exist on the microwave background.

"We're burning up a lot of supercomputer cycles on this," says Spergel's colleague Neil Cornish of Montana State University in Bozeman.

Cornish says his team believes it has already ruled out almost half of
the possible small-Universe shapes - including football and doughnut
shapes - and he suspects the work will probably turn up nothing, meaning that the Universe is either very large or infinite.

"We're disappointed because we favoured the small-Universe idea," says Cornish. "But I guess you've just got to take the Universe you're given."

[Ref. 2] New Model of the Universe: It's Shaped Like a Soccerball
(Cosmic Soccer Ball? Theory Already Takes Sharp Kicks), by Dennis Overbye, New York Times, Sec. Science, October 8, 2003;ei=5062&en=76b88024b23fc8c5&partner=

In a paper being published in the journal Nature, Dr. Jeffrey Weeks, an independent mathematician in Canton, N.Y., and his colleagues suggest, based on analysis of maps of the Big Bang, that space is a kind of 12-sided hall of mirrors, in which the illusion of infinity is created by looking out and seeing multiple copies of the same stars.

But other astronomers, including a group led by Dr. David Spergel of
Princeton, said that an ongoing analysis of the same data had probably already ruled out the soccerball universe.

For now, the two groups, which have been in intense communication the last few days, disagree on whether the soccerball universe has been refuted. What is amazing about this debate, they all agree, however, is that it will actually be settled soon, underscoring the power of modern data to resolve issues that were once considered almost metaphysical.

"This is what got Giordano Bruno burned at the stake," said Dr. Max
Tegmark, a cosmologist at the University of Pennsylvania. "Is space
infinite or not?"

In the model proposed by Dr. Weeks and his colleagues, three-dimensional space has 12 sides, like a soccerball, or more technically a dodecahedron. Each face is "glued" to its opposite number (don't try this at home). A spaceship crossing one face or panel of the soccerball, about 37 billion light years from here, would find itself entering the other side of the soccerball; after traveling 74 billion light years it would find itself back where it had started. For comparison, the light from the Big Bang has expanded over the course of cosmic time to fill a sphere 46 billion light years across, Dr. Weeks said.

Meanwhile, a more thorough analysis of the data, looking for all
possible circles, has been undertaken by Dr. Spergel, who was part of the original Wilkinson team, Dr. Cornish and Dr. Glenn Starkman of Case Western Reserve University in Cleveland. The study, about two-thirds complete, had already eliminated many simple models of so-called "small universes," including a dodecahedron, when the Nature paper hit their desks last week, Dr. Spergel said.

"No soccerball, no doughnuts, no bagels," he said.

Dr. Cornish said that although it was the community that would
ultimately decide, his team was confident of its results. "I don't see
any wiggle room," he said.

But because it is such a "truly spectacular claim," he said, they are
planning to run a special test in the next few days focused on the
particular model. The test could detect very small circles. "We can push it to where there's no chance," Dr. Cornish said.

The prospects for the finite universe, he added, look bleak."