Glenn's answer is, I'm sure, different than mine. I don't have any
rigorous evidence that the universe could be different than it is, in
terms of the physical laws that describe it. My main objection to
Glenn's probability calculations is based on the observation that the
parameters describing the laws of nature at the more phenomenological
levels are themselves determined by the deeper level theories and are,
thus, not freely adjustable to take on just any old value one supposes.
Since we currently do not have a worked out viable Theory of Everything
we do not know which of the 1 1/2 dozen or so remaining parameters (of
the so-called Standard Model of physics) are themselves determined and
calculable by that theory which is not yet in hand. Presumably if such
a theory exists and it is found that it is unique in that it is
eventually proved that there can be no other theory which is both
internally logically consistent and also accurately describes all the
facts then we would expect that all of the residual parameters of the
Standard Model would be, at least in principle, calculable from the
unique TOE. This would indicate that the would could not be any
different than it is in terms of the laws of nature describing it. As
things stand now the non-calculable parameters of the Standard Model are
just adjusted agree with experiment and there is no a priori reason for
one set of these parameters over another set. A functioning in hand TOE
would presumably change this situation drastically.
Even though I expect that a unique TOE may tend to fix all the parameters
of all the laws of physics, I think that it would still not necessarily
fix the exact state or appearance of the universe. This is because of
the built-in indeterminism in the outcomes of events and processes
described by those laws coming from a combination of fundamental quantum
uncertainty in the outcomes of measurement-like interactions and the
amplifying effect of tiny microscopic changes to huge macroscopic ones
produced by the sensitive dependence on the initial conditions of the
classical limit of some of the relevant classical phenomenological
theories (i.e. chaos effects). It is also entirely conceivable that the
same fundamental TOE can describe a universe (or many universes) with a
wildly different structure including the phase domain structure of the
vacuum than the one we have resulting in wildly different
phenomenological behaviors than the ones seen in our universe. A
different vacuum phase domain for the TOE may possibly result in
different low energy (relative to the TOE) Standard Model parameters and
gauge interactions and thus completely different phenomenological
theories describing the universe on more everyday energy and distance
scales.
So it seems that there is still may be a lot of slack in the necessary
appearance(s) of the universe or at least in our vacuum phase domain of
the universe. Therefore I do not completely discount anthropic
arguments. I just don't think that they are necessarily very
convincing. The naive applications of them, such as a priori probability
calculations based on changing the parameters of low energy
phenomenological theories, are incorrect because the considered
parameters are determined by the deeper level theories. And more
sophisticated applications involving deep-level (high energy scale)
theories tend to be fraught with uncertainties caused by the lack of a
useful in-hand TOE. In spite of my pessimism concerning these kind of
arguments I still do get the feeling (and I think it is mostly just a
feeling) that the universe seems to be made with the likes of us in mind.
Of course this feeling may result ultimately more from my prior religious
disposition than from the bare physical evidence. I'm not sure.
In response to my prior comment:
>I don't know about whether or not it is an "implicit probability
>calculation" but I, for one, *do* profoundly get the feeling (from
>natural theology) that the universe is somehow made *for us*, or at
>least that we are meant to be here. I don't know if natural theology
>can go much (or any) further than this though.
Glenn wrote:
>Of course it must be a probability argument. If it were not one why does
>the following statement (by you) lead ultimately to the feelings described
>above?
concerning my comment:
>There are very many ways for life (as we know it) to be impossible by
>making a slight adjustment of just a relatively few fundamental
>constants (e.g. number of dimensions of space & time, numbers of
>generations of elementary particles, coupling constants and mixing angles
>for the fundamental interactions, the masses of the elementary particles,
>etc.) whose values determine all the rest of the phenomenology of the
>physical world.
to which Glenn further responded:
>The usage of the word 'slight adjustment' implies that it doesn't take much
>change. And when you compare this to the possibility that it could have
>taken a huge change in the above parameters to kill off life, the concept
>of an implicit probability argument becomes clear. If it took a huge
>change in all the physical constants to prevent life, then we would say,
>'it is easy to create a universe compatible with life'. Any value would, in
>those circumstances lead to life. The constants could take on a wide range
>of values and the taking of any of those values would be compatible with
>life. But since only a slight change prevents life, the universe appears
>precariously balanced.
>
>So, in this sense I will defend the approach I used to calculate
>probabilites if not the example.
This argument *still* relies on the possibility that those parameters
can somehow be considered as freely adjustable. I'm not so sure of this
for the reasons stated in the first part of my post. It also implicitly
assumes an effectively more-or-less uniform distribution for the values
of the parameters that also are presumed to be essentially independent.
How do you know such a wide distribution (of independent parameters) is
supposed to be correct? I can imagine a prior distribution that is
sharply peaked around the values of the parameters that we happen to
have.
<Snip Glenn's stuff about the necessity of 3 *spatial* dimensions.>
>In other words if the universe can accomodate any dimensionality it would
>NOT be specially adjusted to our existence. It would be JUST the
>dimensionality chosen by historical accident. But what we have is a
>universe in which only one value allows life. It is like flipping a coin
>and having it not be heads nor be tails but land on the coin's edge. This
>is theoretically possible, but highly improbable. But mathematically we
>contemplate euclidian and non-euclidian spaces with from 0 to 3.5 billion
>dimensions (3.5 billion is the number of dimensions in the phase space of
>the human DNA). So there is no mathematical restriction on the
>dimensionality of any space we wish to contemplate. But only with a 3D
>universe can we exist. At the very least the odds against randomly
>choosing a 3d universe compatible with life from those mathematically
>contemplated (at least occasionally) is 1/3.5 billionths. And if any of
>those dimensionalities allowed for life, then the odds would be 1. And if
>the dimensionality probability were 1, then once again, we would say it is
>easy to create a universe with life. To me this is a probability argument.
But what if it can be proved that the dimensionality of spacetime must be
10 (as the most viable superstring theories claim) in order for any TOE
to be logically internally consistent and free of embarrassing
singularities that cause the theory to break down in any of various ways.
And further, what if the TOE predicts that 6 of those 10 dimensions
*must* be compactified into a well-defined tiny closed compact subspace
(whose effects cause all the nongravitational interactions in nature)
according to the built in logic of the TOE so that there *must* be 4
extended (noncompact) dimensions of spacetime left whose signature
requires that 1 of them be a temporal dimension and the other 3 be
spatial in character? In this case the spatial dimensionality of the
universe would *not* be freely adjustable from a choice of some
3.5 x 10^9 possibilities, but rather, would *necessarily* be 3. In this
case not only would a universe with other than 3 spatial dimensions be
impossible for life forms that wish to communicate with propagating
signals, but it would be impossible for the logical consistency required
of *any* universe that behaves according to the rules of logic.
>Thus I contend that the anthropic principle IS a probability argument and
>if used one is implicitly calculating probabilites to get the "feeling (from
>natural theology) that the universe is somehow made *for us*". If one can
>do this, then your's and Howard's objections to probability calculations
>would be inconsistent.
How so?
> So, if you feel that the universe is designed for
>us, then it must be possible to calculate probabilities.
Why?
> If you can't
>calculate probabilities, then the anthropic principle fails entirely and
>this universe is NOT designed for us--or at least there is no evidence of
>that design.
Huh? This seems to be a non sequitur unless I'm missing something. I'm
not necessarily claiming there must be evidence of design or not in such
a situation (i.e. me not being able to calculate various parameter
probabilities). I just don't see the logic of the statement.
David Bowman
dbowman@georgetowncollege.edu