The online magazine The Edge has a set of "hard questions" by experts
and notables in a variety of fields, some of which discuss multiverse

Paul Davies critiques the multiverse+anthropic_principle explanation
for what we see, in

   Sir Martin raises the question of whether what we consider to be
   fundamental laws of physics are in fact merely local bylaws applicable
   to the universe we perceive. Implicit in this assumption is the
   fact that there are laws of some sort anyway. By definition, a law
   is a property of nature that is independent of time. We still need to
   explain why universes come with such time-independent lawlike features,
   even if a vast and random variety of laws is on offer. One might try to
   counter this by invoking an extreme version of the anthropic theory in
   which there are no laws, just chaos. The apparent day-by-day lawfulness
   of the universe would then itself be anthropically selected: if a
   crucial regularity of nature suddenly failed, observers would die and
   cease to observe. But this theory seems to be rather easily falsified.

   As Sir Martin points out, if a particular remarkable aspect of the laws
   is anthropically selected from a truly random set, then we would expect
   on statistical grounds the aspect concerned to be just sufficient to
   permit biological observers. Consider, then, the law of conservation
   of electric charge. At the atomic level, this law is implied by the
   assumed constancy of the fine-structure constant. (I shall sidestep
   recent claims that this number might vary over cosmological time
   scales.) Suppose there were no such fundamental law, and the unit of
   electric charge varied randomly from moment to moment? Would that
   be life-threatening? Not if the variations were small enough. The
   fine-structure constant affects atomic fine-structure, not gross
   structure, so that most chemical properties on which life as we know
   it depends are not very sensitive to the actual value of this number.

   In fact, the fine-structure constant is known to be constant to better
   than one part in a hundred million. A related quantity, the anamolous
   magnetic moment of the electron, is known to be constant to even
   greater accuracy. Variations several orders of magnitude larger than
   this would not render the universe hostile to carbon-based life. So
   the constancy of electric charge at the atomic level is an example of
   a regularity of nature far in excess of what is demanded by anthropic
   considerations. Even a multiverse theory that treated this regularity
   as a bylaw would need to explain why such a bylaw exists.

It seems that this point can be addressed pretty well by the flavor
of multiverse theories we consider here, in which "simple" universes
are inherently more likely than more complex ones.  In this model we
would predict that the universe would be just as complex as necessary
to support our kind of life, but no more so.

For a constant to be stable to better than 1/100,000,000 is not that
surprising; it is plausible that the simplest theory has that constant
being absolutely stable.  It would take more information to specify
a formula for variation of some physical unit than to specify a single
value which never varies.

The "Sir Martin" article being responded to above is interesting in its
own right, as an attempt to justify exploring the multiverse concept
despite some complaints that it is metaphysics rather than physics.
In Martin Rees gives his own
example of an apparent departure from simplicity: the fact that our
universe seems to have a considerable portion of its mass in dark matter,
which doesn't do anything obviously useful.  Of course it may well be
that dark matter plays an important role in the formation of galaxies,
which allow for the formation of 2nd-generation stars which have enough
heavy elements that they can have planets.


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