[astro] 10^122, the answer to everything

[Eugen Leitl]

(it's 10^122, not 10122 below, same 10^40, not 1040)

http://www.nature.com/news/2008/080220/full/news.2008.610.html

Published online 20 February 2008 | Nature | doi:10.1038/news.2008.610

News

Cosmic coincidence spotted

An absurdly large number could hold the key to universal mysteries.

Philip Ball

This unimaginably large number keeps popping up in descriptions of the
Universe.This unimaginably large number keeps popping up in descriptions of
the Universe.

The secret of the Universe is not 42, according to a new theory, but the
unimaginably larger number 10122. Scott Funkhouser of the Military College of
South Carolina (called The Citadel) in Charleston has shown how this number —
which is bigger than the number of particles in the Universe — keeps popping
up when several of the physical constants and parameters of the Universe are
combined1. This ‘coincidence’, he says, is surely significant, hinting at
some common principle at work behind the scenes.

The number first turned up when, more than a decade ago, physicists
discovered that the expanding Universe is accelerating. This implies that
there is a force that opposes gravity on very large scales, which physicists
call dark energy. It is quantified by a parameter called the cosmological
constant.

One interpretation of dark energy is that it results from the energy of empty
space, called vacuum energy. The laws of quantum physics imply that empty
space is not empty at all, but filled with particles popping in and out of
existence. This particle ‘fizz’ should push objects apart, just as dark
energy seems to require. But the theoretical value of this energy is immense
— so huge that it should blow atoms apart, rather than just causing the
Universe to accelerate.

Physicists think that some unknown force nearly perfectly cancels out the
vacuum energy, leaving only the amount seen as dark energy to push things
apart. This cancellation is imperfect to an absurdly fine margin: the unknwon
'energy' differs from the vacuum energy by just one part in 10122. It seems
incredible that any physical mechanism could be so finely poised as to reduce
the vacuum energy to within a whisker of zero, but it seems to be so.  Five
more times

Now Funkhouser says that this is not the only appearance of this vast number
among the parameters of the Universe. He lists five other instances in which
the ratios between various cosmic quantities turn out to be equal to 10122,
give or take a factor of ten (which matters very little at such huge scales,
and could be due to errors in our understanding of the numbers involved).

For example, the ratio of the mass of the observable Universe to that of the
smallest possible ‘quantum’ of mass is about 6x10121. And the number of ways
in which the particles of the current Universe can be arranged throughout
space (a measure of entropy) is 2.5x10122.

This isn’t just numerological number juggling. “If you take the basic
parameters of the Universe there are only so many ways you can put them
together to make ‘pure numbers’ with no units,” Funkhouser says — and less
still ones that have any obvious physical interpretation. So the fact that
even a handful of these give ratios that are so huge and yet so similar seems
significant. “It is unlikely for chance alone to be responsible for
generating so many pure numbers from just several fundamental parameters,”
says Funkhouser.  Logic behind the scenes

    “For the same basic set of parameters to produce two large-number
coincidence problems is essentially preposterous.”

Scott Funkhouser

A similar ‘large-number coincidence’ was noted in the 1930s by the astronomer
Arthur Eddington and the physicist Paul Dirac. They saw that several other
combinations, such as the ratio of the electrostatic attraction between an
electron and a proton to the gravitational attraction, are equal to about
1040.

Like Dirac, Funkhouser thinks that these large-number coincidences can’t be
accidental. All the instances of 10122, he argues, must stem from the same
basic reason. It’s rather like noticing that the recurrence of spring and
neap tides coincides with the phases of the Moon: both are due to the motions
of the Moon and Earth.

At the root of the issue, Funkhouser says, is the fact that the current
density of matter in the Universe is about the same as the observed vacuum
energy density — a puzzling fact that he calls the ‘cosmic coincidence’. The
vacuum energy density is thought to be constant, but the mass density changes
as the Universe expands. Why they happen to be equal right now — a balance
that helps us to detect dark energy amidst matter — is not known. Some have
suggested explanations based on the anthropic principle: basically, it’s only
under these conditions that life becomes possible, so if things were
otherwise, we wouldn’t be here to see it.

Given this single coincidence, Funkhouser shows, all the 10122 ratios
inevitably follow from the standard laws of physics and cosmology. “The major
parameters of the Universe are the cosmological constant and the total mass
and radius,” he says. “Due to the cosmic coincidence, they are related.” He
has shown previously that similar reasoning accounts for the Eddington-Dirac
large-number coincidence2.  Too many coincidences

The existence of two large-number coincidences (1040 and 10122) now presents
a puzzle in itself.

“It is remarkable enough that the parameters of nature should somehow produce
one large-number coincidence,” says Funkhouser. “For the same basic set of
parameters to produce two large-number coincidence problems is essentially
preposterous — unless the two problems are related.” But how?

Funkhouser notes that 10122 is about equal to the cube of 1040. Is there some
reason why the two sets of large numbers should be linked in that way? It
would follow, Funkhouser says, if there happens to be a certain mathematical
relationship linking the mass of a nucleon (a proton or neutron) with the
speed of light, the gravitational constant, Planck’s constant and the
cosmological constant.

That sounds pretty exotic, but in fact such a link was proposed in 1967 by
the Russian physicist Yakov Zel’dovich based on an entirely separate
argument. And he’s not the only one to suggest this.

“The interesting thing is that the relationship has been proposed before by
several different authors, each with a different explanation,” says
Funkhouser. And in a separate paper3, he’s come up with yet another
justification for it. “I have shown that a simple model for the origin of our
Universe involving ten spatial dimensions leads naturally to this relation,”
he says. It follows if seven of the dimensions shrank while the other three
“puffed out” to form the reality we observe today.

    * References

	 1. Funkhouser, S. Proc. R. Soc. A advance publication
doi:10.1098/rspa.2007.0370 (2008).

	 2. Funkhouser, S. Proc. R. Soc. A 462, 2076 (2006).

	 3. Funkhouser, S. Int. J. Theor. Phys. (in the press).