[time 669] Re: [time 660] Re: [time 659] Cylindrical But Locally Lorentzian Universes

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 4 Sep 1999 07:29:42 +0300 (EET DST)

On Fri, 3 Sep 1999, Stephen P. King wrote:

> Dear matti et al,
> A few questions...
> Matti Pitkanen wrote:
> snip
> > [MP] In TGD closed spacetime surfaces are possible absolute minima
> > of Kaehler action. They have necessarily finite extension in both
> > time and spatial directions. One can imagine of constructing them
> > by taking two finite pieces of Minkowski space in M^4_+xCP_2, slightly
> > deforming them in CP_2 directions, gluing along their boundaries,
> > smoothening resulting edges, and requiring that absolute minimum
> > of Kaehler action is in question. These surfaces decompose
> > to regions with Minkowskian signature and Euclidian signature
> > or have global Euclidian signature. They are not locally vacua:
> > globally they are: classical energies, momenta, etc are
> > of opposite sign on the two sheets. These surfaces are analogous
> > to vacuum bubbles appearing in perturbative quantum field
> > theories and contributing nothing to S-matrix elements.
> This is what I have been looking for! Thank you! Now, a question: You
> are saying that the cognitive and material space-time sheets have
> "opposite signs" of their "classical energies, momenta, etc". Would
> there be a CPT symmetry violation predicted from TGD to account for the
> statistics of neutral (?) kaons?

CPT is exact in TGD and experimentally. CP is broken. Breaking is caused
by the presence of classical Kaehler electric fields required by absolute
minimization of Kaehler action. CP breaking boils down at phenomenological
level to complex phases of Cabibbo-Kobayashi-Maskawa matrix
expressible V= UD^dagger, where U and D describe topological mixings
of quarks: quarks families correspond to different boundary component
topologies for CP_2 type extremal containing hole with boundary
which is sphere (e,nu_e) and (u,d), torus (mu,nu_mu), sphere with two
handles.... Last spring I constructed a detailed TGD based model to
explain CP breaking in K-antiK system in particular observed anomalous
behaviour: it almost made me mad. I will never, ever start making
numerical things at this age anymore!

The closed spacetime surfaces describe *'pure mind'*: enlightend
Buddhas staring at own navel. They could however
get glued to material spacetime sheets and interact with the world of
sinners. They have very nice nice properties: in particular, cognitive
fermion pairs are possible, not only cognitive neutrino pairs. It depends
on spectrum of induced Dirac equation how many of these are possible.
Finite number very probably. Right handed neutrinos are also in this case
in special position: if closed spacetime sheet is minimal surface,
covariantly constant right handed neutrino is certainly a solution if
induced Dirac. What is important is that absolute minimization of Kaehler
action almost predicts these objects: by Euclidicity they have negative
finite Kaehler action and this is favoured by absolute minimization of
Kaehjler action. Thus these enlightened Buddhas are there but are they
important for our brain functioning!?

An attractive idea is that the solutions of Dirac inside closed
spacetime surfaces interpretable as representations for logical thoughts
are identifiable as memes, pure ideas. They would hang aroud everywhere
and could also attach to our brain. [Basis of fermion Fock states<-->
Boolean algebra]

The second option for cognitive spacetime sheets is as spacetime sheets
with outer boundary and Minkowskian signature of induced metric: these
would *have time orientation which is same as that of material spacetime
sheets*. This is possible since cognitive neutrino pairs are possible in
this case too: the point is that neutrinos in condensed matter have
negative Z^0 binding energy much larger than their rest mass: creation of
cognitive neutrino pair with total energy=0 is possible. The fact, that
neutrinos are glued to spacetime sheets with size of epithelial sheets,
makes bell ringing inside me and I would bet that cognitive neutrinos are
characteristic for bio-consciousness.

To be honest, I do not know whether both of these two types of cognitive
spacetime sheets are important for understanding of brain.

> > Physical considerations pose no restrictions on the density of these
> > purely 'mindlike' objects (using the terminology of TGD inspired
> > theory of consciousness): they represent pure thought.
> > I have told about amusing structural isomorphism between the properties of
> > asymptotic selves (selves for which all subsystems have vanishing p-adic
> > entanglement) and between the closed Euclidian 4-surfaces.
> > I would identify them as liberated Buddhas! (Ontogeny recapitules
> > phylogeny.)
> > *****************
> But, Matti, these are mere geometric objects and do not follow the
> requirements of minds (e.g. boolean lattice-like structures).

They are geometric objects which correspond to certain selves: they form
cognitive representations by interacting with material spacetime sheets.
They contain cognitive fermion pairs (counterparts closed fermionic
bubbles) and fermionic Fock states provide physical representation for
Boolean algebra. And they correspond to conscious: even more,
ORP suggests that they correspond to asymptotic selves: end points of
evolution by quantum jump which cannot anymore reduce
their entanglement entropy by quantum jumps and are therefore
entanglement entropy=0 enligthened beings!

[ORP= Ontogeny ....]

> I see the
> "vacuum bubbles" are the objects of observation by other LSs. You see,
> all geometry, is cast as the content of an observation with the Chu
> space duality paradigm.

These vacuum bubbles glued to material background could be objects
of observation also. Gluing could transfer tiny energy inside bubble.

> The mind that does the observations is modeled
> in terms of the boolean (for 2-nary relations) structures that act as
> the "labels" of the geometries. This results from a consideration that
> the class of labels (or meanings) that can be attached to any given
> geometric object can not be trivially mapped to a geometry itself,
> unless one is considering the singleton case (it is self-dual, e.g. MIND
> = BODY for the Universe as a whole).

Have you considered possibility of representing Boolean algebra by
fermions? Cognitive fermion pairs inside these Buddhas are solutions of
induced Dirac and form representations for geometry. Each statement
about spacetime geometry would be represented by many fermion state.
These statements are certainly very abstract.

> One the other hand, the phylogenic hierarchical ordering of the sheets
> is very important! I see it as the "vertical" organization of a self,
> just as you think of it. But, it is a mistake to assume that the mind is
> geometries or fields of matter/energy. (Bohm has pointes out that they
> are the same thing really!)

No, I would never claim this: cognitive spacetime sheets only contribute
dominantly to the constents of experiences of selves and
this makes practical to identity self with cognitive spacetime sheet!
ORP suggests very strongly that the closed spacetime
surfaces are geometric counterparts of S=0 selves. The correspondences are
rather impressive.

a) S=0 self as asymptotic of subjective time evolution<-->closed absolute
minimum as asymptotic of Kahler evolution (perhaps very much like
blackhole). [BTW, elementary particles reprsented by CP_2 type extremals
are closed vacua with hole drilled in them to carry elementary particle
vacuum numbers.] S=0 selves could be the blackholes of TGD.

b) S=0 self <--> closed vacuum.
Closedness is the geometric counterpart for the trait of Buddhas
to stare in their navels!

c) Extended free will of S=0 selves<--> extended classical nondeterminism
of closed spacetime surfaces. One can take discrete sequence of 3-surfaces
with arbitary short timelike separations belonging to closed
local vacuum extremal and find absolute minimum
going through them. There is this kind of absolute minimum since there
is vacuum extremal with vanishing action going through them.

d) S=0 selves must be stable against generation of entanglement which
means falling asleep and snoring Buddhas! Join along
boundaries bonds with external world make generation of entanglment
probable (to form join along boundaries bond is to touch). But if there
are no boundaries, there can be no join along
boundary bonds and hence no entanglement is generated.

> > We might imagine that a flat, closed, unbounded universe of this
> > type would tend to collapse if it contained any matter, unless a
> > non-zero cosmological constant is assumed. On the other hand, I'm
> > not sure what "collapse" would mean in this context. It might
> > mean that the R parameters would shrink, but R is not a dynamical
> > parameter of the model. The 4D field equations operate only on
> > x,y,z,t. Also, any "change" in R would imply some meta-time
> > parameter T, so that all the R coefficients in the embedding
> > formulas would actually be functions R(T).
> All of this applied, but to the "what" is observed by an LS. The
> difference in properties between the "inside" and "outside" of an LS are
> very important! Umm, the idea of mapping (or identifying) the perceived
> behaviour of objects in a given observer's universe (which is a finite
> subset of The Universe) with the "internal" dynamics of the quantum
> propagator is what I call "clocking and gauging"...
> The key notion is that we must understand that we can not ever observe
> The Universe, only "our version of it"!
> > It seems that the flatness of the 4-space is independent of the
> > value of R(T), and if the field equations are satisfied for one
> > value of R they would be satisfied for any value of R.
> This, I see as the "free fall" frame of the observer. The "forces" are
> given when comparisons of pairs of frames like Bill's NOW/PAST pairs!
> > But I'm not sure how the meta-time T would relate to the internal time
> > t for a given observer. It might require some "meta field
> > equations" to relate T to the internal parameters x,y,z,t.
> > Possibly these meta-equations would allow (require?) the value
> > of R to be "increasing" versus T, and therefore indirectly
> > versus our internal time t = f(T), in order to achieve stability.
> How could meta-time T be observable? Why is it even necessary to
> consider such an idea? Is "stability" really necessary to assume? (think
> of dissipative systems!)
> > [MP] In critical Robertson-Walker cosmology one has somewhat
> > similar situation. 3-space is Euclidian and could be compactified to
> > 3-torus. Allowing R to on t one obtains curved 4-space as is clear from
> > the fact that mass density (G^tt component of Einstein tensor) is
> > nonvanishing. In special case one would have the
> >
> > ds^2= t^2(dt^2 -dx^2-dy^2-dz^2)
> >
> > I checked from general formula for mass density in RW cosmology
> > that mass density goes like 1/t^4, that is scales. This is to be expected
> > since line element is Weyl equivalent to flat metric. It seems
> > that this is nothing but the radiation dominated critical cosmology which
> > is scale invariant (massless particles dominate).
> > In this case R indeed increases with t linearly.
> So this is a quantification of "what can be observed" given a
> particular "mass density"

What I intented to say that 4-torus like line element with over-all
scaling factor depending on one of the coordinates seems to repreresent
radiation dominated critical cosmology. The criticality and high
symmetries force critical radiation ominance.

> >
> > [MP] It is often believed that quaternions and octonions are inherently
> > Euclidian objects. This is actually not true as I discovered for year or
> > two ago. The point is that one can define inner product as
> > real part Re(z1z2) of z1z2: the resulting inner product is standard
> > Minkowskian inner product. If one defines inner product as Re(z1^*z2)
> > one obtains the usual Euclidian inner product.
> What is the relationship between Re(z1z2) and Re(z1^*z2)? Are they
> orthogonal?

[MP] Sorry for not establishing notation. Re means real part. Consider
instead of quaterions and octonions complex numbers.
z=x+iy and Re(z1z2) = x1x2-y1y2 which is nothing but Minkowski inner
product in plane. Re(z^2)= x^2-y^2. In case of quaterions Re
can be regarded as real number or as a real quaternion: in latter
case one can speak about orthogonality but Re(z12) and
Re(z1^*z2) are not orthogonal.

> Later,
> Stephen

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