Re: OT: Many Worlds Probability Problem

rev.goetz <jimgoetz316@xxxxxxxxx> wrote:

carlip-nospam@xxxxxxxxxxxxxxxxxxx wrote:

[...]
Here are the basics:

1. Certain physical constants have to fall within a range of values
for life (at least something close to "life as we know it") to
be possible.
2. Without a specific model that tells you how and why a given physical
constant can vary, there is no way to tell whether this allowed
range is "large" or "small," "probable" or "improbable." This is
because there are many different ways to describe the same set of
physical laws and processes; by choosing your description, you can
make any given range look as small or as large as you like.
3. If you have a *particular* model for the variation of physical
constants, you may be able to determine whether the range that
allows life is likely or unlikely to occur. Your conclusion,
though, will only hold in the context of that particular model;
the conclusion for a different model will, in general, be very
different.

Steve Carlip

I know what you mean by a range of values, which some people call
intervals. Is that correct?

Close enough.

But I am not sure what you mean about the how and why.

You are postulating a model in which there are many universes,
each of which has a different value of some physical constants.
Suppose a new universe is "born." What determines the values
of these constants in the new universe? Unless you have a
theory that answers this question, you have no way to tell
whether a given value is likely or unlikely.

I will take some values for constants from Carroll
(http://arxiv.org/abs/hep-th/0512148), and add an arbitrary range of
values for them (give or take), and we will hypothetically assume that
the following ranges are a prerequisite for the formation of galaxies
and DNA-based life:

Plank Energy = Ep = 10^27 eV give or take 10^26 eV
Fermi Energy = Ef = 10^11 eV give or take 10^10 eV
QCD Energy = Eqcd = 10^8 eV give or take 10^7 eV

And to keep it simple for this calculation, we will assume that nothing
but these 3 ranges are the prerequisites for the formation of galaxies
and DNA-based life.

OK, let me try some simple math one more time. You are assuming that
Eqcd must lie between 90000000 eV and 110000000 eV, and you are asking
whether this is a likely range of values. Let me define a new variable
x = 1/(Eqcd - 10^8). Then the range for Eqcd you've written down is
equivalent to a range of x from -.0000001 to infinity. Note that in
any given universe, Eqcd and x give you exactly the same information
-- any physical law or process that can be written in terms of Eqcd can
be written equally well in terms of x. We happen to choose to write
our physical laws in terms of Eqcd (or actually, more commonly, the
logarithm of Eqcd), but this is a statement about the history of science,
not about physics.

If you have a model in which, in each new universe, Eqcd is a randomly
selected number, then the range of Eqcd you've chosen is very improbable.
If you have a model in which, in each new universe, x is a randomly
selected number, then the probability of finding the range that allows
life is 50%. Unless you know the physics -- unless you know whether the
laws of nature pick a random value of Eqcd, or x, or one of the infinite
number of other variables that contains the same information -- you can
say nothing about likelihood.

(As yet another example, you can postulate a model in which new universes
form from black holes in existing universes, and have a value of Eqcd that
is close to, but different from, that of their "parent" universe. In such
a model -- proposed by Smolin -- the number of "baby" universes will be
largest when the constants are such that the "parent" contains a large
number of black holes. Smolin has argued that this tends to give constants
that are quite close to those needed for the existence of life.)

Does this make any sense? If yes, we will assume the Aquirre and
Gratton (http://arxiv.org/abs/gr-qc/0301042) model of timeless
inflation and an infinite number of universes. Based on this simplified
model of Ep and Ef and Eqcd, how many universes will have the
prerequisite for the formation of galaxies and DNA-based life?

In the Aguirre and Gratton model, none of these energies varies from
universe to universe, so your question is meaningless.

But even if they did, your question is still not very well formulated.
Suppose you had a model in which, say, Ep varied from universe to
universe. You want to determine the likelihood of various values by
just counting universes. But suppose that for some values of Ep, you
get a universe that grows very large and lasts for a long time, while
for other values you get a universe that grows only to a very small
size and then collapses -- a reasonable assumption, given what we know
about cosmology. Do you really want to count these the same? Or do
you want to look at "amount of space" instead of "number of universes"?

Or suppose you find that some universes form only a few galaxies, while
others form an enormous number. Do you want to count "number of universes"
or "number of galaxies"?

You can make a choice, but I think you'll have a hard time really justifying
any of these alternatives over any other, unless you have a *much* more
precise formulation of your question.

Steve Carlip


.

Relevant Pages