Matti Pitkanen (email@example.com)
Mon, 7 Jun 1999 11:35:43 +0300 (EET DST)
On Sun, 6 Jun 1999, Stephen P. King wrote:
> Dear Hitoshi and Matti,
> Hitoshi Kitada wrote:
> > Dear Stephen,
> > If you argue in LS theory, the inner products are of an infinite
> > number, proper to each Local System. I.e. LS theory considers an
> > infinite number of Hilbert spaces describing the inner state of each
> > observer's system. The outside of an observer's system is not
> > described by Hilbert spaces. Only a part of the outside that is an
> > object of an observation is described by a Hilbert space structure.
> I am very much interested on how acts of observation select a finite
> partially ordered subset of the infinite number of Hilbert spaces. I am
> wondering if the 4-vectors of GR are contractible from some part of
> these Hilbert spaces. Perhaps my words are incorrect here, I am trying
> to understand how consciousness, as a specific type of measurement, can
> be modeled. :)
> > In LS theory, the phenomena arise by the participation of the
> > observer. In this sense, my standpoint is the same as the Wheeler's
> > "participatory universe."
[MP] Also I agree if phenomenon is quantum jumps between two realities.
> Yes! This is my understanding. :) I am wondering how to model the
> "clocking" and "gauging" behavior of the LSs, e.g. the mechanisms of
> observation. It looks like a mapping between sets, but one that has
> hierarchical orderings involved.
> > The total state \phi of the universe is not considered in a Hilbert
> > space. It represents just the state of the total universe, which
> > does not evolve. No inner product is considered regarding \phi.
> Thus by definition there are no measurements of this \phi, no
> projection postulates in the ordinary sense? It is only the All...?
> > Neither the "observer" nor the "jumps" are "fundamental", as I see it;
> > they are complementary. Having one without the other renders
> > them meaningless! Existence is the grundlagen.
> > I think that I disagree. The use of single phi means
> > materialistic (sorry!(;-)) world view with single objective reality.
> > Materialism leads to problems with inner product besides all these social
> > problems(:-).
> > Single \phi does not need any inner product. By materialism, what do
> > you mean?
> To me, materialism means that the Universe is made up of a single
> substance and that information is merely patterns of matter. I question
> the root notions of "substance" since it tacitly posits the properties
> of a priori synthetics (existing with definite properties independent of
> observation). Thus I agree with Matti! ;) This is a very subtle issue
> that we do need to discuss further. :)
> URLs on materialism:
> compare to idealism (information monism):
> I think that the Universe U is, in it-self, Existence and as such it is
> One. Any subset of U that is distiguishable from the whole, is so
> because it is dual by the definition of distinguishability. This duality
> it the duality of complementarity, the duality of the subject-object
[MP] All depends what means with U. If U is space of all possible
quantum histories from which moments of consciousness give only
two-point glimpses then one can say that U is ONE. If U is quantum history
then there are very many U:s.
> > In TGD I allow all possible phis, quantum histories. TGD is
> > nonmaterialistic theory in strong sense.
> Matti, do you mean that TDG is not a model based on "atoms" in the
> origional sense?
I am not sure what 'atoms' means in original sense. What is clear
is that TGD breaks also the reductionistic dogma: many-sheeted spacetime
concept implies this. Various 'physics', nuclear, atomic, etc...
correspond to the p-adic hierarchy of spacetime sheets. The most
interesting new physics predictions are in bio length scales. For
instance, our body as kind of elementary particle, performing quantum
jumps as a single quantum whole. The new degrees of freedom are those
characterizing size, shape etc of 3-surface: not present in quantum field
theory based physics.
Rather interestengly, Mersenne primes are
expected to be especially interesting p-adic primes
from the point of view of elementary particle physics and the hierarchy of
Mersennes stops at electron length scale: next Mersenne corresponds
to super astronomical length scale. Thus reductionism becomes good
approximation as far as elementary particle physics is considered.
> > In the observable world for an observer, all histories are possible.
> > \phi does not appear in observations. The universe \phi is different
> > from the observed universe.
> Histories might be considered as finite portions (subsets) of streams.
> This is were I think that we need to understand Peter's work better...
> > > Thus I am proposing many \phi! :)
> > To each obsevation, there corresponds a proper universe. In this
> > sense, there are many \phi, where \phi is used in different meaning
> > from the \phi in the above.
> Have you ever taken a look at the infinitesimals in non-standard
> analysis as a means to model the relationships between the \phi_U^T (the
> Totality) and the \phi_U^i: i = 1, 2, ..., N? They are "actual" and
> opposed to the "potential" infinitesimals of normal maths....
> I will try to write up a note on this...
I have looked at them. Infinite primes (and hence also infinite rationals
and infinite reals) lead automatically also to infinitesimals.
Our entire cosmology 0<=t< infty would be just an infinitesimal duration
of cosmological time from the point of view of conscious beings with
infinite p-adic prime! I do not know whether there is relationship
between infinite primes and real number concept inspired by them and
non-standard analysis: the axioms of latter are so frustratingly abstract
In any case, in infinite prime business the new element is
number theory for infinite numbers (primeness, divisibility etc).
Division, multiplication, etc... become possible as operations
very similar to those performed in real context since one has
concrete representation of infinite numbers. I do not know
what the situation is non-standard analysis.
p-Adic number fields associated with infinite prime
seem to resemble reals to very high degree.
p-Adic Quantum theory makes sense also for infinite primes and S-matrix
is finite. The physical effects related to differences between infinite
primes would be probably extremely small and delicate: perhaps
moral choices involve choice between infinite primes; perhaps delicate
changes in mood(;-) involve the new math of infinite primes!
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