On 9/27/2011 8:07 PM, nihil0 wrote:
On 9/27/2011 4:18 PM, nihil0 wrote:

1) There is an infinite number of Hubble
volumes in our universe, which are all casually disconnected (as the
theory of inflation implies). 2) There is a limit on how much matter
and energy can exist within a region of space of a given size, such as
a Hubble volume. 3) There is only a finite number of possible
configurations of matter, due to the Uncertainty Principle.
I can explain any of these ingredients in more depth if you'd like me
to, but I hope you see that they lead to the conclusion that all
quantum-physical possibilities in our universe are realized infinitely
many times.
On Sep 27, 7:47 pm, meekerdb<meeke...@verizon.net>  wrote:

No they don't.   There's an implicit assumption that what happens in these 
other universes
has the same or similar probability distribution as we observe in ours.  A 
reasonable
assumption, but not a logically necessary one.  I think it's what Bruno means by
"homogeneous".  It's logically possible that all but a finite number of these 
universes
are just exact copies of the same completely empty universe, for example.

Brent
You imply that it's logically possible that there is only a finite
number of universes that are filled with matter, and you seem to think
few will resemble ours.

I don't think that. I just noted it's logically possible, contrary to assertions that our universe must be duplicated infinitely many times.

However, according to Vilenkin, Greene, and
Tegmark, a generic prediction of the theory of inflation is that there
is an *infinite* number of Hubble volumes (what you are calling
universes).  Let's call the hypothesis that all quantum-physical
possibilities are realized infinitely many times "the hypothesis of
Cosmic Repetition". Brian Greene argues for this hypothesis quite
persuasively. He says, "In an infinitely big universe, there are
infinitely many patches [i.e., Hubble volumes]; so, with only finitely
many different particles arrangements, the arrangements of particles
within patches must be duplicated an infinite number of times." (The
Hidden Reality, pg. 33)
It's plausible - but not logically required. Suppose all the infinite universes are number 1, 2, ... Number 1 is ours. Number 2 something different. Numbers 3,4, ...inf are exact copies of number 2. So there are only two arrangements of particles; in spite of there being infinitely many universes.


As for the probability distribution of matter and/or outcomes, I'll
let Tegmark do the explaining:

"Observers living in parallel universes at Level I observe the exact
same laws of physics as we do, but with different initial conditions
than those in our Hubble volume.

This is questionable. Most theories of the universe starting from a quantum fluctuation or tunneling from a prior universe assume that the universe must start very small - no more than a few Planck volumes. This limits the amount of information that can possibly be provided as initial conditions. So where does all the information come from? QM allows negative information (hidden correlations) so that one possibility is that the net information is zero or very small and the apparent information is created by the existence of the hubble horizon.

The currently favored theory is that
the initial conditions (the densities and motions of different types
of matter early on) were created by quantum fluctuations during the
inflation
epoch (see section 3). This quantum mechanism generates initial
conditions that are for all practical purposes random, producing
density fluctuations described by what mathematicians call an ergodic
random field. Ergodic means that if you imagine generating an ensemble
of universes, each with its own random initial conditions, then the
probability distribution of outcomes in a given volume is identical to
the distribution that you get by sampling different volumes in a
single universe. In other words, it means that everything that could
in principle have happened here did in fact happen somewhere else.
Inflation in fact generates all possible initial conditions
with non-zero probability, the most likely ones being almost uniform
with fluctuations at the 10^5 level that are amplified by
gravitational clustering to form galaxies,
stars, planets and other structures. This means both that pretty much
all imaginable matter configurations occur in some Hubble volume far
away, and also that we should
expect our own Hubble volume to be a fairly typical one — at least
typical among those that contain observers. A crude estimate suggests
that the closest identical copy
of you is about ∼ 10^(10^29)m away. . ." (The Multiverse Hierarchy,
section 1B, http://arxiv.org/abs/0905.1283)

Do you still disagree with the hypothesis of Cosmic Repetition? Which
parts of the argument do you accept or deny?

See above.

Brent

Best regards,

Jon


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