Stephen P. King (stephenk1@home.com)
Wed, 09 Jun 1999 17:07:08 -0400
Dear Matti and Friends,
In [time 395] Constructing spacetimes, Matti wrote:
"There is also problem about information flow between different
LS:s. How can one define information current between LS:s if
these systems correspond to 'different spacetimes'?"
There is much to be discussed here!
If I am correct, "current" is defined as some quantity of change
occurring through a boundary of some sort.
(http://www.whatis.com/current.htm) It is usually assumed that some
particle or fluid is being transferred from one location to another and
a term "density" is associate with "Current per unit cross-sectional
area". So we are thinking of the concepts: "flow", "boundary",
"information", "different space-times", and "particle".
We need definitions that are mutually consistent, I am proposing to
using graph theoretic concepts since we can easily generalize them to
continua:
http://hissa.nist.gov/~black/CRCDict/termsArea.html#search
Flow: "A measure of the maximum weight along paths in a weighted,
directed graph" We could consider the "weight" as the degree to which a
given edge connects a pair of vertices, e.g. if a pair of vertices are
identical relative to their possible labelings the weight is 1, the
weight is 0 if their respective sets of labels are disjoint. (When
considering spinors as labels of the vertices we use alternative
notions.)
http://hissa.nist.gov/~black/CRCDict/HTML/flow.html
Boundary: I can not find a concise definition so I will propose a
tentative one: the boundary of a graph B{G} is the minimum set of
vertices |V_G| that have as incident edges that connect a pair of
points, one of which is an element of ~{G} and the other which is an
element of {G}; where {G} and ~{G} are a graph and its complement.
I am not sure that this notion is appropriate. :( I am thinking of the
way which traditional set theory defines a boundary of a set: "a point
is in the boundary of a set iff every neighborhood of the point
intersects both the set and its complement". So the boundary of a set of
these points. It looks like the only element involved would be the empty
set {0} in the usual way of thinking of sets in the binary logical
sense, this relates to my discussion of the Hausdorff property...
Information: Now here is the key problem: How to define "information"!
What is Information? Is is "meaning" as in "the semantic content of a
pattern of matter/energy"? Is it the bits that are recovered when a
string of bits is encoded or compressed by some scheme and then decoded
or decompressed by the scheme's inverse? Is it the value of a quantity
present at some arbitrary point?
Different space-times: This statement implies a plurality, a multitude
of configurations of distinguishable particles such that a basis of
three orthogonal directions is definable in conjunction with a dynamic
that alters the configurations in a uniform way.
Particle: An entity that in a given reference frame or framing is
indivisible. It should not be assumed that an entity that is indivisible
in one framing need be so in another framing. I am thinking of a framing
as a finite context or environment that acts as a "contrast" for the
entity in question.
The problem I see right away is that information is not a substance in
the normal sense, since it has the properties of compressibility and,
according to Bart Kosko, irrotability, which are in contrast with those
properties of matter which is, usually incompressible and rotateble....
But, I think that Peter's notions are the most relevant to this
conversation of "information flows" between LS, so we need a way of
bridging between the formalism of graph theory and the formalisms used
in Peter's papers.
We'll take that up after some discussion. :)
Later,
Stephen
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