Saibal Mitra writes:
> From: ""Hal Finney"" <[EMAIL PROTECTED]>
> > The real problem is not just that it is a philosophical speculation,
> > it is that it does not lead to any testable physical predictions.
> > The string theory landscape, even if finite, is far too large for
> > systematic exploration.  Our ideas, with an infinite number of possible
> > universes, are even worse.
>
> I'm not so sure that our ideas are worse.

I should clarify, I meant that our ideas are even worse in terms of
systematic exploration of all the possibilities, because we generally
consider an infinity of possible universes, while the string theory
landscape predicts (some people say) about 10^500 possible universes.

> If you read some recent articles,
> e.g.:
>
> http://arxiv.org/abs/astro-ph/0607227
>
> you see that they haven't really formulated rigorous theories about measure,
> probabilities etc. of the multiverse. It's still very much in the
> "handwaving" stage.

This is actually a very interesting paper, by Starkman and Trotta.  I had
seen some mention of it but hadn't tracked it down.  Here is the abstract:

"We revisit anthropic arguments purporting to explain the measured value
of the cosmological constant. We argue that different ways of assigning
probabilities to candidate universes lead to totally different anthropic
predictions. As an explicit example, we show that weighting different
universes by the total number of possible observations leads to an
extremely small probability for observing a value of Lambda equal to or
greater than what we now measure. We conclude that anthropic reasoning
within the framework of probability as frequency is ill-defined and
that it cannot be used to explain the value of Lambda, nor, likely,
any other physical parameters."

The paper is pretty technical but I thought I could understand the gist
of it.  The cosmological constant ("Lambda") is a repulsive force which
drives galaxies apart in the Big Bang model.  Until a few years ago it was
thought to be entirely theoretical, but since then observations indicate
that it is real, and that the universal expansion is accelerating.
The question then becomes what would happen in universes with different
values of the CC.

The paper basically shows that observers (or civilizations) can last
longer in universes with smaller CC's.  The CC eventually puts an end
to the observations that can be made, because the expansion gets too
fast and there is no longer enough energy density.  The higher the CC,
the sooner this happens.  With CC's as high as what we observe, the
theoretical lifetime of civilization is much shorter than in universes
with smaller CC's.

The authors choose to use as their measure, the number of times the
CC can be measured in a given universe.  This makes low-CC universes
have a much higher measure, because the window for CC observations is
longer in those.  Hence they conclude that the highest probability is
for a CC much smaller than we observe, and so our own CC value cannot
be explained anthropically.

This is in contrast to earlier results which used different measures, such
as the number of galaxies, and found that our CC results were consistent
with anthropic considerations.  The authors argue that their measure is
at least as philosphically justifiable as those earlier papers, and their
real point is that no measure can be justified as better than another,
hence all anthropic reasoning is just hand-waving.

In our terms we might put it like this.  The new paper essentially uses a
measure which is the number of possible observer-moments in the universe.
Universes with a high CC go through a "big rip" process eventually,
accelerating to a super-expansion mode and presumably putting an end
to observers.  Universes with a low or zero CC go through this much
later or not at all, allowing for more observer-moments.  Hence this
measure gives a bonus to universes that last a long time.

Earlier papers apparently looked at a snapshot of time similar to the
present day, and in effect based the measure on the number of observers
(assumed to be proportional to the number of galaxies).  So we have a
distinction between an observer-moment measure and an observer measure.
The two apparently give very different results, the OM measure preferring
long-lasting universes while the observer measure is more interested in
the size of the universe.

I guess I'll stop here and see if there is more interest.  To leave with
a few questions: Is there any fundamental way to decide which measure
is "best"?  Do the OM measure and the observer measure really give
different results, and is that significant?  Are there other measures
that might be used, and what results would they get?  And finally, will
this apparent failure of anthropic reasoning discredit the concept among
working physicists?  As I mentioned, I've already seen it used in a blog
common on Woit's blog that I pointed to the other day, in just that way.

Hal Finney

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