sci.physics

>From Osher Doctorow

Let's examine the statement: "The Universe is expanding." Not only
intuitively (physics intuition rather than just naive intuition of
anybody, hopefully, although also mathematics intuition arguably) but
logically, for this to mean anything there should be somewhere and
sometime for the Universe to expand to and somewhere and sometime from
which it has expanded. After all, if the Universe does not expand
from anywhere to anywhere, then I doubt whether the reader can
maintain a consistent conversation or even quantitative analysis of
that expansion.

It doesn't really help to make an "arbitrary cut" somewhere and say
that we'll "pretend that the Universe at a particular time ends
there".

So what is left? Well, we're assuming when we naively say that the
Universe is expanding that the Universe is "everything" and its
"opposite" or complement is "nothing", but are we entitled to make
this asumption? We really can only speak of the Universe in "our
phase", which in the Multiverse and similar theories is the one that
we're familiar with or that has similar properties in some specific
sense to ours. Maybe it's one that obeys "our" Laws of Nature or one
that we can detect by current technology or one that has a certain
radius (principal radius, etc.) at a particular time but outside of
which there is another Multiverse at that particular time!

Let's ask what this means. If the Universe at time t_o (to for
short) where to is an arbitrary time is taken to have (principal)
radius r_o (ro for short), then what is outside ro at tme to? The
answer "nothing" doesn't quite compute. Even if there were some way
of expressing this, there is some "potential" radius outside of radius
> ro to which the Universe will eventually arrive. At the very least
we could call this "potential" Universe minus the Universe of radius
ro as a different Universe or different Multiverse. We don't actually
have to go to this extreme arguably, but in our new understanding of
Phase in this thread, we might well choose to regard "potential" as a
Phase.

In actuality, however, it is much simpler to be honest and say that
our Universe is one Universe among many in a Multiverse and that
beyond radius ro is another Universe or Multiverse at time to.

Doesn't this change computations? It may change some of them, but it
can also leave some of them unchanged. When we use Probability as a
scale for continuous variables, then since Probability is always
between 0 and 1, there is no temptation to regard the variables as
bounded by finite values like c or h or M_P (Planck mass), etc. The
value 1 in Probability corresponds to "complete certainty" except for
possible subsets of Probability 0, which for all practical purposes
means that a variable translated into Probability (assuming that this
can be done) doesn't stop at some finite "certainty" but at "infinite
certainty". There may be Probabilities of more generalized scales in
other Universes or Multiverses, say going from 1 to 2, 2 to 3, etc.
In fact, I discussed such scenarios in several posts not long ago.
But if we qualify our conclusions as referring to a scale that
corresponds to our Universe, then most of our computations arguably go
through unchanged. (By the way, the scale of 2 to 3 could correspond
to a higher order infinity, etc. - see Cantor's theory of Transfinite
Mathematics which, contrary to what many physicists may believe, is
mostly accepted today by mathematicians.)

Osher Doctorow