Stephen P. King (stephenk1@home.com)
Mon, 26 Jul 1999 11:46:06 -0400
Dear Matti,
Focusing on two notions...
Matti Pitkanen wrote:
snip
> [MP]
> > By the way, motion in zero modes occurs as hopping quantum jump by
> quantum
> > jump:
> >
> > x1-->x2--x3---
> >
> > Just like Brownian motion. In fact, I believe that Brownian motion
> > indeed corresponds to this kind of motion. The possibility to
> > Brownian motion to move faster than light would not be a
> > result of nonrelativistic approximation but real physical
> > effect.
[SPK]
> Yes! WE need to look at this very carefully! I say that the
> forward
> jumps ... -->x1 --> x2--> ...
> are dual to "backward jumps" ... i2 <-- i1 <-- ... of logical
> implication (following Pratt). It looks like this:
>
> ... -->x1 --> x2--> ... Time
> | |
> ... |g |h ...
> | |
> ... <--i2 <-- i1<-- ... Logic
>
> were g and h are infomorphic bisimulations...
>
> [MP] The problem is that logical causation and temporal causation
> seem to have different directions unless one replaces A--> B with
> not A <--- not B.
It is logical entailment or implication that "goes backwards" with
respect to time. This is discussed at length in Pratt's paper ratmech.ps
If we take the negation: "not A <--- not B", we are just reversing the
respective arrows. Umm, only in the strict binary boolean case is ~~A =
A, so it gets a bit complicated when we are using a Chu_[0,1] space to
represent the interactions of a given pair of LSs, since fuzzification
allows for ~A \intersect A =/= 0 under certain conditions!
> I would take only the upper part of the diagram:
>
> ... -->x1 --> x2--> ... Times for generation of subselves x1, x2
>
> and denote selves by x1, x2,.... Since x2 is subself of x1
> implication x1-->x2 is realized as set-theoretical inclusion.
> Subself is implied by self and in correct temporal order!
Yes, but I am trying to discuss how the ordering by inclusion is
constructed. If we just assume that the ordering is a priori, then we do
not have to deal with the question as to why the selves (or more
generally, observations) are ordered as they are. It is this assumption
that exists in the classical model of space-time and is in severe
contradiction with facts, such as those illustrated in the EPR and
delayed choice situations.
We can just say that temporal orderings are given by the MNP of the
quantum jumps, but I am trying to understand the details better. I think
of this as asking what decides the winner in a tournament; while we can
not say with certainty 1 who will win. All we can do is to set up
"pay-off matrixes", etc.
> There are several interpretations depending on the nature
> of quantum jump: interpretation as logical causation
> or as genuine set theoretic inclusions: selves as representation
> for objects of figure. Entire figure as big self, background and
> objects of figure as subselves containing smaller objects
> as subsubselves.... Or tree like
> structure of linguistic expression...
>
snip
> snip
> [MP]
> > > Actually the measurement can be said to be disjoint in well
> > > defined sense. Separate selves mutually unentangled.
> [SPK]
> > > Yes! This is why separate selves have separate indentities! I say that
> > > experiences are "almost disjoint" since they differ in at least the
> > > "point of identity". The notion of a fixed point under a given set of
> > > transformations is what I considered before I has educated by Peter's
> > > work. The Self, within Peter's formalism, is a greatest fixed point, I
> > > think. Umm, I need to review his paper:
> > > http://www.cs.brown.edu/~pw/papers/math1.ps
> [MP]
> > Quantum entanglement is what destroys selves. For instance, could
> > it be that the separate notes in chord correspond to
> > frequency-selves which have entangled to form chord-self?
> > This would explain why we do not hear separate notes but entire
> > chord.
>
> This is why we can not do a "Vulcan Mind Meld"! It would be
> impossible to unentangle the two minds!
>
> [MP] There are objections agains simple rule that unentangled
> subselves are experienced as average subself by self
> containing them. Probably the subselves must have large
> enough mutual resemblance before they are averaged. Perhaps
> they must have same p-adic prime, belong to same spacetime sheet:
> something like that. Must think about.
I think that a situation is required such that a "large enough"
sampling of the possible actions of the selves can be had so that a
winner can be reasonably predicted. We see an example of this in
political elections in a democratic country. The individual electorate
(representing the individual subselves) vote and a sample of these are
polled by the media to form a statistical sample of the whole and this
sample is used to predict the outcome "sooner than the actual counting
of the ballots can occur". I think that the situation involved with
"selves" is a continuous voting/polling situation since the "elections"
occur at every quantum jump!
The p-adic prime looks to me to well model the size of the sample
population!
snip
[SPK]
> > > How is the information content of this localization given? This is an
> > > infinite NP-Complete problem that requires ETERNITY to compute! It can
> > > not be given a priori!
> [MP]
> > TGD generously provides this eternity! The quantum computation defined
> > by informational time development operator lasts infinite amount
> > of lightcone proper time (not our psychological time which
> > is quite different thing).
>
> Yes! :-) I just try to think about how each observation involves
> its own lightcone of causality...
>
> [MP] In TGD framework causality is not involved at level of experiencing.
> It is involved at the dynamics determining spacetimes as
> absolute minima of Kahler action: that is at the level of configuration
> space geometry. In your approach situation is obviously different.
I say that since the determination of the particular experience is not
modelable locally, as it involves an entire light-like hypersurface, the
causality not considered as an experience itself. Only the results of
the determination enter into the "picture". So I agree this you here. My
only question is in the nature of the "absoluteness" of the minima of
the Kaehler action. Umm, what are the quantities involved in the Kaehler
action? Is there an associated Lagrangian or Hamiltonian? What
"information measures" are related to it?
snip
> [MP]
> > I understand what you are saying. This is probably the only possible
> > consistent philosophy in the framework in which one does not introduce
> > quantum jump and replace single objective reality with all
> > possible objective realities allowed by physical theory.
>
> Huh, how do you conclude that?
>
> [MP] Well, I don't know! Somehow I interpreted the idea about
> several almost non-intersecting spacetimes as geometric counterpart
> for giving up the notion of single objective reality, which
> is quantum concept.
Since we have many observers, it is natural to consider that there are
many observational experiences to be considered. The notion of a single
objective reality only makes sense IFF the class of observables is
strictly sharp (binary certainty). The problem I see is that only a
prediction can be made up to the accuracy allowed by the p-ary cut-off
(\epsilon of accuracy). So the smearing of "reality" that QM predict is
no surprise!
snip
> [MP]
> > I think that a lot of confusion is created by different views about
> > imbedding space. I do not regard its points as reprsentations of events:
> > it is quite too simple thing for that.
>
> Indeed! But, it is helpful as a concept to start out with...
>
> [MP]
> OK. It is certainly what Einstein believed. Classical geometric
> structures in spacetime would characterize entire physics.
Sure! Invariance structures are defined by geometry, so a physics = a
geometry.
Next I would like to better understand the problem you have with
Frieden's work...
Onward!
Stephen
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