Stephen P. King (stephenk1@home.com)
Wed, 25 Aug 1999 20:03:59 -0400
Dear Bill,
I really appreciate these questions! I must admit that my answers are
only tentative as I am do fully cognizant of your meanings... :-)
WDEshleman@aol.com wrote:
>
> Stephen
>
> Here are some concerns I have:
>
> 1) Do a majority of other worlds differ only by tiny amounts
> from our world...or are close copies in the minority? That is,
> do the majority of other worlds contain close copies of our
> brains, bodies, etc...or do the majority of other worlds contain
> copies of our fermions spread out over solar systems and
> galaxies?
Well, I am not sure but if we consider that the Universe, as the
totality of existence, "contains" all possible finite and infinite
"versions" of itself; all that could be experienced and thus all that
must exist so that we can have some way to get logical consistent
chaining of observations, which is what define as our subjective
histories, there would have to be an innumerable number of different
worlds.
When we say "other worlds" it is assumed that we are referring to
worlds different from the "one" we think that we are experiencing. What
is the range of the possible differences, well, if we assume an infinite
Universe from which to construct experienced worlds as I do, then there
would be at least an infinite number of worlds that differed in at least
one aspect. We can discover differences when we map the objects in those
worlds to the numbers.
We could use the class (or set?) of the Integers as the "smallest"
infinity we have available. (We could restrict our selves to finite
numbers, but it is easy to see that this is automatically incomplete.)
Ok, let us label each world with an integer and let us assume that these
worlds can be decomposed and composed into "parts", say fermions,
bosons, brains, bodies, etc. Planck's constant aside, it is obvious that
any world can be composed from an infinite number of "parts" of other
worlds and this results, via Cantor's diagonalization into a proof that
there exist at least an uncountable (with integers) infinity of worlds.
Now, let us look for simplicity at worlds that differ just in terms of
their photons (and there there are inherent problems in figuring out
exactly how we can distinguish photons from different worlds, unless we
allow for a Weyl geometry with its real valued variation of gauge...).
Ok, the frequency of the electromagnetic wave can vary by infinitesimal
amounts, can it not? If so then the worlds that have infinitesimally
different EMF variations are separate. We could also consider
infinitesimal variations of the constants!
Are "close copies" a minority or majority? Well, there measure
theoretic properties of real valued labeled worlds is "measure one", in
other words it is certain that if we picked a pair of worlds out of an
urn that they would look almost alike! The article by F.W. Meyerstein
(http://www.cs.auckland.ac.nz/CDMTCS//researchreports/089walter.pdf) is
a good discussion of this!
> 2) Are the copies of our fermions, fermions or bosons and
> does this make a difference?
Well, this goes back to the difficulty that I see in figuring out how
to tell particles apart... Umm, according to QM, we can not make copies
of particles!
http://www.uibk.ac.at/c/c7/c704/qo/photon/_teleport/tpidea.html,
http://www.aip.org/physnews/preview/1997/qinfo/text.htm#4
Exactly what do we mean by this question? Umm, I am having trouble with
this one! :-(
> 3) Can observers ever get anything but a subjective view
> of things? That is, will we never have the ability to
> objectively distinguish a 3-D "entangled" universe from a
> MW multiverse?
I can't image how it will ever be possible to "get anything but a
subjective view of things" that is a "meaningful and communicable
experience". But, my imagination is finite and thus not an completely
trustworthy authority! :-) As I see it, the necessary requirements for a
truly "objective" view of the Universe are something we already have!
White noise is a good example of what is it like to experience the
"in-itself". It is all possibilities simultaneously and without bias.
The MW multiverse is exactly that by definition.
> 4) Are "splits" and "jumps" subjective and the same...or
> are one or both objective properties?
Umm, I think that the terms "slits" and "jumps" are complementary way
of explaining the same thing. If we assume the Schroedinger wave of a
particular unique world and measurements "cause" it to bifurcate, we use
the word split. If we consider that there is no bifurcation but instead
a global change in the space-time geometry and topology (subject to
restraints of course) then we say "jump". It is just a matter of
perspective. As to their being subjective or objective, well, since only
those "in" those worlds would experience the worlds and as they would be
"carried" along in the bifurcation or jump they would not be able to
directly perceive it. It is only in inferring from
communications/interactions between the worlds that any approximation to
"objectivity" can be obtained.
> 5) Would the interference connections with other worlds
> from observers in our world be identical...or would there more
> logically be a hierarchy of connections? Like the 2^LEVEL
> hierarchy I have suggested.
Umm, I am not sure. I lean toward the idea that there are a hierarchy
of connections as this is how I think of properties (!), but it appears
that both you and Matti are correct. I see "connections" as n-ary
relations. The 2^LEVEL hierarchy gives subsethood properties that in
turn give us the ability to have overlappings (and underlappings) in our
subjective observations and thus gives us an approximation to
"objectivity". Matti's p-adic hierarchy is different, it looks at the
connections in terms of phylogeny. The former appear to be related to
complexity of types and the latter to organization of types of
relations.
Could you elaborate some more about your thinking of 2^LEVEL hierarchy?
Onward!
Stephen
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