From: Lee Corbin (lcorbin@tsoft.com)
Date: Tue Jun 24 2003 - 21:12:08 MDT
Our level one universe consists of infinitely many
of each of these items:
solar systems ~10^9 kilometer
galaxies ~10^6 ly = 10^22 m
inhomogeneous patches .1 x 10^9 ly
Hubble volumes 84 x 10^9 ly
where the quantities on the right suggest the scale of
the object. A lightyear (ly) is ~10^16 meters.
Perhaps our universe should be called Bruno, in honor
of the man "whose vision of space was homogeneous,
infinite, and populated by infinitely many worlds:
There is a single general space, a single vast
immensity which we may freely call Void: in it
are innumerable globes like this one on which
we live and grow; this space I declare to be
infinite, since neither reason, convenience,
sense-perception nor nature assign to it a
limit." [3]
There are about 10^11 stars in our galaxy, and there
are about 10^12 galaxies in our Hubble volume, which
is our visible universe [4]. An inhomogeneous patch
corresponds to what Tegmark calls "the largest coherent
structures astronomers have been able to identify".
Laid end to end, there are very roughly 1000 of these
patches across our Hubble volume, as in 500 to our
left and 500 to our right, and at this level "the
arrangement of matter gives way to dull uniformity".
I don't think that we should designate either
the inhomogeneous patches (or, as Tegmark does) the
Hubble volumes, as "universes" because unlike solar
systems and galaxies, there are no demarcation
lines from one to the next. Observers 20 million
light years from us see themselves at the center
of their inhomogeneous patch, and observers 20
billion light years from us see themselves at
the center of their Hubble volume.
I also would prefer not to call the level 1 universe
a multiverse for the same reason.
The shocking question is, "if our universe is only
13.7 billion years old, [2] then how is it possible for
it to have a radius of about 42x10^9 ly? How can we
possibly see that much? Our Hubble volume should only
be 14 billion ly in radius!"
The answer is that light got to cross certain regions
quickly when the universe was young; these regions are
now very much further apart. Thus this light carries
information to us about objects that are now at about
40 billion light years. When the light left them,
however, they weren't nearly so far away.
Here is a similar math problem. A worm on the right
end of a one meter rubber rod is determined to reach
the left end of the meter rod, which is fixed at the
point zero. But at the same instant the worm begins
to move (at one centimeter per second), the rod expands
uniformly to the right at one meter per second, carrying
the worm along with it. Does the worm finally manage to
reach the left end of the rod? Does the worm cross more
millimeter lines (which are moving farther apart each
second) near the beginning of his journey, or near the
end, or does it matter?
Imagine that the path of each galaxy in a spacetime diagram
follows a world line. These world lines diverge---there
are more light years between them at later times than at
earlier times. (The galaxies inside clusters don't move
farther apart from each other over time, so by "galaxies"
you may wish to think of clusters of galaxies.) These world
lines are like the millimeter lines in the math problem.
Thus when the light from the most distant galaxy we can see
began its journey, it crossed more of these worlds lines in
a given time than it is able to now.
Galaxies formed about 10 billion years ago: that is, about 4
billion years after the big bang. The matter making up our
Hubble volume was about six times smaller, so the space between
us and the theoretically furthest galaxy observable now has
enlarged by a factor of six since then [5].
But we can see much further than that. The cosmic background
radiation was emitted when the universe finally became transparent
to photons 300,000 years after the big bang, when the universe's
temperature was 3,000 degrees. The following discussion is based
mostly on Guth, pages 182-183 [6].
Suppose that we see coming towards us from opposite directions
two photons emitted at the time of transparency (300,000 AB).
They've been traveling in straight lines, and represent the
furthest distance from which information via photons can possibly
be available in this century. These photons were 90,000,000 light
years apart at the time of emission, and so was the matter, of
course, that emitted them. That matter is now separated by 80
billion light years! If we call X the atom that emitted the
photon coming at us from the left, and Y the atom that emitted
the photon coming at us from the right, then the space between X
and Y has expanded from 90M ly to 80G ly, or has expanded
approximately by a factor of one thousand.
Of course, X and Y were extremely close together in the big
bang. (The big bang was a process---there was no time zero,
though it is a handy reference point.) The photons emitted
from X and Y were swept along in the general expansion of space,
and did not reach their maximum separation for a long time.
There had to be a point at which, despite their frantic motion
towards each other, the distance between them was neither
increasing nor decreasing. (Had they not been swept up, of
course, then it would have taken but 45,000,000 years for them
to cross paths in the vicinity of matter that would later form
the Earth.)
What is profound about this "sweeping up" process is that although
from the point of view of an extremely remote galaxy that is
just now emitting photons in our direction everything is normal,
it's peculiar that the photons are nonetheless becoming further
from us each second, and if the universe is accelerating, may
never start to close the gap. This would never occur in ordinary
special relativity: a photon emitted towards one non-accelerating
object by another always closes the gap, regardless of reference
frame.
Note that the first expansion described above---from a time when
the galaxies formed (about 4 billion AB) to now---represents an
expansion by a factor of 6, whereas *this* expansion is from a
much earlier time, when everything in the universe was a thousand
times closer together than now. (Of course, by "everything",
I mean only the atoms currently residing in different galaxy
clusters. Within clusters and within galaxies, the distance
between atoms has not increased since galaxy formation.)
>From its own point of view, each galaxy is approximately at rest
with respect to the big bang. To its inhabitants, the universe
appears to be centered on that galaxy, with all the other galaxies
flying away from it. All the observers in all the infinitely many
galaxies have this impression. No galaxy, nor any Hubble volume,
was formed before all the others. Space and matter beyond 100
million light years is statistically homogenous so far as we know.
(One aspect to the expanding universe is that images of remote
objects---although necessarily very dated because of the time at
which light left them---appear larger than they "should" be.
If we (in coming decades) get pictures of extremely remote galaxies
just after their formation, about ten billion years ago, they'll
look six times as large as they would appear if light could
instantaneously cross from them to us now. That's because they
were six times closer then.)
If you are eager to become precisely at rest with respect to the
big bang, you can in principle do so within a factor of 100,000
or so. If you measure the frequency of the cosmic background
radiation, you'll find it almost the same in any direction except
for the slight random residual speed of your galaxy. You'll
obtain figures that agree to within 1 in 1000 in every direction,
so all you have to do is change your velocity by a few hundred
kilometers per second, and voila!, you are now at rest with
respect to the big bang.
It does seem strange that while you find yourself precisely
at rest with respect to the big bang, another observer moving
half the speed of light relative to you in a faraway galaxy
can also determine that he is at rest with respect to the big
bang!
Our whole universe is a single inflationary "bubble". But
discussion of any bubble besides our own, i.e., besides our
own universe, should wait until level two.
In our universe, in our bubble, there exist infinitely many
regions the size of our Hubble volume. Within our universe,
the laws of physics are the same everywhere, and thus Tegmark
and many others assume there exist other regions, also about
80 billion light years wide, that are completely identical
to ours. After all, QM dictates that there are only so many
states that can obtain in a volume of definite size. The
number of possible states is so vast, however, that it's
safe to say that there is probably no volume identical to
ours closer than 10^10^118 away. (Remarkably, it turns out
that it's unnecessary to specify whether you are
speaking of light years or meters, because in megamathematics
---my term for the study of phenomena arising in the consideration
of quite large integers---factors hardly matter at all. Even
the base used in, for example 10^10^118, hardly matters. If one
substituted ten billion for 10 as the bottom base, this would
only cause an increase to 10^10^119.)
A cautionary note concerning identity should be made. According
to one principle advocated as far back as Leibniz, it might be
more accurate to refer to the set of all identical Hubble volumes
when we speak of "ours". No possible observer, except for a God
who stands outside our universe and is able to specify, somehow,
a volume at random, can refer to a particular region in isolation,
because even that observer is replicated infinitely many times in
the universe. Although an individual person may find it helpful
to go about referring to "we" and "us" when discussing future
possibilities involving his or her own future, a digression into
this interesting topic isn't relevant here.
[1] Max Tegmark, Scientific American, April 2003, or
http://it.arXiv.org/abs/astro-ph/0302131
[2] http://map.gsfc.nasa.gov/m_mm/mr_age.html
[3] "The Measure of Reality", by Alfred W. Crosby, 1997, p.105
[4] "The Cosmological Anthropic Principle" by Barrow and Tipler
[5] http://spaceflightnow.com/news/n0008/17galaxyform/
[6] "The Inflationary Universe", by Alan H. Guth, 1997
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