[tt] Nature: Cosmic coincidence spotted

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Cosmic coincidence spotted
http://www.nature.com/news/2008/080220/full/news.2008.610.html
[Linked by Arts and Letters Daily, http://www.ald.com .]
Published online 20 February 2008
doi:10.1038/news.2008.610

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 10^122. 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
combined^1. 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 10^122. 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 10^122, 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 6x10^121.
And the number of ways in which the particles of the current
Universe can be arranged throughout space (a measure of entropy) is
2.5x10^122.

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 10^40.

Like Dirac, Funkhouser thinks that these large-number coincidences
can't be accidental. All the instances of 10^122, 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 10^122
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 coincidence^2.

Too many coincidences

The existence of two large-number coincidences (10^40 and 10^122)
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 10^122 is about equal to the cube of 10^40. 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 paper^3, 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).

Comments

* any chance at all that 10^122 can actually be related to, let's
say, 42^42? Via another costant may be? =)
+ 20 Feb, 2008
+ Posted by: Luca Fenu

* And here is another coincidence. Decimal 10 is
âEURœAâEUR in hex, 122 is 7A. So the combination of 7
and A. âEURœAâEURœ âEUR" is total number of
dimensions, and 7 âEUR" number of shrank dimensions! Further. A
âEUR" 7 = 3 ThatâEUR(TM)s our 3 dimensions! But 3 in binary is
11. And 7 is 111 ! Another coincidence? How about A in bin? Take
a guess. 1010. Now add those 3 numbers: A+7=11 (hex). Or 10001.
That is inverted 7 in the middle. Mind boggling
+ 20 Feb, 2008
+ Posted by: Simon Jinx

* Why was my input previous screwed? Something doesn't want us to
see this??? I am trying again. And here is another coincidence.
Decimal 10 is A in hex, 122 is 7A. So the combination of 7 and
A. But A - is total number of dimensions, and 7 âEUR" number of
shrank dimensions! Further. A-7=3 ThatâEUR(TM)s our 3
dimensions! But 3 in binary is 11. And 7 is 111 ! Another
coincidence? How about A in bin? Take a guess. 1010. Now add
those 3 numbers: A+7=11 (hex). Or 10001 in binary. That is
inverted 7 in the middle. Mind boggling
+ 20 Feb, 2008
+ Posted by: Simon Jinx

* Luca 42^42 ~ 1.5*10^68 42!*(42^42) ~ 2*10^119
+ 20 Feb, 2008
+ Posted by: Thomas R Toms