"Since the universe in fact has four dimensions how does this affect your
argument?"
And I received the following answers:
David Bowman: "The universe has 3 *SPATIAL* dimensions even though its
spacetime manifold is 4-dimensional. Glenn specifically stated '3 spatial
dimensional universe'."
Glenn Morton: "I wrote 3 SPATIAL dimensions."
I appreciate the quick responses, but they do not really answer my question.
Instead, they assume that I either did not read Glenn carefully or that I
deliberately ignored his use of the term "spatial". Neither alternative is
the case. Rather my question was meant to suggest that our labeling three
dimensions as spatial and one as temporal may in fact be naive, based more
on how we perceive these dimensions than on real knowledge of their true
character.
In a later post Dave Bowman wrote what I feel is an excellent succinct
summary of what has been called the "hyperspace" model: "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 [theory of
everything] 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?"
I disagree that the "signatures" of the extended dimensions "requires" that
there be one temporal and three spatial. My reading of the hyperspace model
(admittedly from the popular scientific press -- _Scientific American_,
_Science News_, _Discover_ and the like -- including books like _Hyperspace_
and _Cosmic Questions_) indicates that the theorists for the most part view
the different dimensions as being equivalent. In fact many of them have
crudely referred to these dimensions as "spatial", in the sense that the
10-dimensional universe can be crudely visualized as a 10-dimensional
hyper-object (hence the term "hyperspace") within 10- or 11-dimensional
space. I have seen no attempt by any theorist to characterize these
dimensions on the basis of any kind of "signature" or "flavor" or whatever
else you want to call it. As a result I could be wrong, but my impression
is nonetheless that the dimensions of hyperspace in fact have all the same
"signature" (or very nearly so) and that our characterization of "temporal"
vs. "spatial" is subjective and naive based on perception and tradition, not
hard science.
So if this is true, I ask again: how does the fact that the universe is
made up of four dimensions affect Glenn's argument?
I should point out that I tend to agree with Dave on this issue. If in fact
the universe is a 10-dimensional "hyper-object" it may have no more choice
in what values to give to the universal constants than a cube has in
determining how many faces it should have or at what angle those faces
should connect.
Kevin L. O'Brien