**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Tue, 6 Jul 1999 17:51:06 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**WDEshleman@aol.com: "[time 434] Re: [time 406] Dissipation and quantum jumps between quantum histories"**Previous message:**Stephen P. King: "[time 432] Re: Cisc vs. Risc"

Why the Universe looks classical?

TGD predicts that quantum states are *quantum superpositions of classical

universes*: 3-surfaces Y^3 on lightcone boundary M^4_+xCP_2,

or equivalently, of the unique spacetime surfaces X^4(Y^3), defined as

absolute minima of Kaehler action.

[By the nondeterminism of Kaehler action the minima are actually

degenerate but one can modify the definition of 3-surfaces Y^3 by

allowing 'association sequences' consisting of the union of Y^3

on lightcone boundary and spacelike 3-surfaces X^3_i

not belonging to the lightcone boundary and having mutual time like

separations.]

This raises the question which is trouble for all theories in which one

makes spacetime dynamical objec.

*Why the universe looks so classical?*

Why our subjective experience suggests so strongly that spacetime is the

arena of physics and dynamical objects are particles in spacetime rather

than 3-surfaces themselves? A possible answer to this question came

almost accidentally, when I was pondering the precise definition of

subsystem concept crucial for the formulation of strong NMP..

1. Configuration space spinor fields

Configuration space spinor fields can be regarded as functions from

configuration space to the Fock space of fermions from which all known

elementary particles and a lot of exotics are constructed.

Very roughly: configuration space

spinor field assigns to each 3-surface Y^3 a state, which corresponds

to the many particle state of an ordinary quantum field theory.

One can hence write the state formally as

|TGD State> = SUM (Y^3) |Ordinary State(Y^3)> .

Here a formal continuous summation over Y^3 is understood. When only

single Y^3 is present state behaves like ordinary state of quantum field

theories since spacetime surface is now sharply defined.

2. Subsystem concept

Subsystem concept must be consistent with the definition used in

QFT. This requires that entangled subsystem corresponds to

*parallel superposition of subsystems* S(Y^3) entangled with

its complement. Thus one can say that subsystem a la TGD is function

assigning to Y^3 a subsystem a la QFT.

This means that one can write the initial state

UPsi_i of quantum jump

in entangled form as

UPsi_i = SUM(Y^3)C_nN(Y^3) |n(Y^3)>|N(Y^3)>

C_nN(Y^3) are entanglement coefficients depending on surface

Y^3.

[One can also imagine other, nonlocal manners to construct

superposition of entangled state, but the hypothesis that

*physics is local at configuration space level* suggests that this

expression has special significance.]

3. What quantum measurement means for configuration

space spinor fields?

Moments of consciousness mean quantum jumps to the eigenstates of

density matrix for some subsystem which defines entanglement structure

in the manner described above.

Hence the state UPsi_i *must become unentangled state* in quantum jump.

Since entanglement coefficients depend on Y^3 in general and since sum

is actually continuous integral there is only single possibility:

*Localization to single Y^3!*

This would mean that in each quantum jump localization to single

classical spacetime surface would occur and time development by

quantum jumps would effectively define hopping around

the configuration space! Thus the classicality of the world

of subjective experience would follow from the basic structure

of the configuration space spinor fields. Classical time development

would be like Brownian motion in infinite-dimensional

configuration space.

This looks nice but cannot be true. Complete localization

of the configuration space spinor fields is not consistent with

the basic symmetries of TGD (Super Virasoro, Super Kac Moody,

Super Canonical symmetries). It breaks also Poincare symmetry.

4. Localization in zero modes is enough for classicality

One must somehow milden the hypothesis about complete localization

and this is indeed possible. The point is that

configuration space of 3-surfaces has fiber space structure.

a) Fiber corresponds to ordinary quantum fluctuating degrees of freedom

and metric in these degrees of freedom is vanishing (contravariant metric

defines propagator for small perturbations of 3-surface).

b) Base space corresponds to *zero modes* in which configuration space

line element vanishes. Zero modes characterize size and shape

of 3-surface Y^3 and also the classical Kahler field associated

with it. Zero modes are purely TGD:eish concept resulting from

the nonpointlike nature of particles. Zero modes have the role

of fundamental order parameters in the spirit

of the Haken's theory of self organization. Configuration

space isometries act in the fiber and hence leave zero modes invariant.

A very attractive hypothesis is that quantum jumps involve only

*localization in zero modes*.

If one can assume that entanglement coefficients C_nN quite generally

*depend on zero modes only*, then localization in zero modes is enough

to achieve final state of required type. Localization in zero modes

sharpens the hypothesis about localization into definite sector D_p

of configuration space obeying effective p-adic topology since sectors

D_p are induced by the division of zero modes to corresponding sectors.

If localization in zero modes indeed occurs, then one can understand

classicality. The macroscopic parameters characterizing 3-surface

are sharply defined after quantum jump. For instance, the

sizes, shapes and mutual distances of spacetime sheets characterizing

material objects are fixed compeletely. Also Kahler field is fixed. Only

small quantum fluctuations are possible. The world of conscious

experience

looks essentially classical. Localization also implies that QFT based

subsystem concept applies to the the final states of the quantum jumps but

not for the initial states U Psi_i.

As far as the application of strong NMP is considered, all that is

needed is to compare negentropy gains for states located at Y^3:

this means enormous simplification of the theory. The probability that

localization occurs in Y^3 is given by the modulus squared of

configurations space spinor field and sequence of quantum

jumps is expected to lead to those regions of configurations space

whether this probability density is largest.

5. Symmetries--> independence of entanglement coefficients on

fiber degrees of freedom

The independence of the entanglement coefficients C_nN

on fiber degrees of freedom very probably follows from the symmetries

of the theory: I do not have any real proof for this however.

If the states |n> and |N> are gauge invariant, then isometry invariance

of entanglement coefficients means essentially that coefficients

are invariant under the infinite dimensional group of Super Canonical

transformations and this very probably implies that they can depend

on zero modes only since fiber is coset space defined by the group of

canonical transformations of the lightcone boundary M^4_+ xCP_2.

6. Connection with Haken's theory of self organization and Higgs

mechanism

What is important that quantum jumps define hopping motion

in zero modes defining the universal order parameter space

and thus the dynamics for the world of conscious experience can be

modelled as hopping around in the space of zero modes. This means

that Haken's classical theory of self organization generalizes almost

as such. The hopping around zero modes corresponds to dissipation leading

gradually to those values of zero modes for which configuration

space spinor field is very large and corresponds

to a maximum of vacuum functional, which is exponent for the

absolute minimum of Kaehler action. This justifies the construction

of QFT limit of TGD in spacetime surfaces which correspond to

maxima of vacuum functional.

Order parameters are parameters completely analogous to Higgs fields

and localization means that the values of these fields are sharp

in any final state of the quantum jump instead of being

quantum superpositions over several values. The drift to

the maximum of Kaehler function provides mechanism

analogous to that leading to the minimum of Higgs potential.

Symmetry breaking mechanism associated with self organization

generalize directly to TGD context.

Thus localization in zero modes is consistent with the standard

quantum description of order parameters. There is also connection

with Joel Henkel's theory in which one introduces

state spaces parametrized by zero modes and assumes that states

are localized in zero modes. TGD however provides fundamental

mechanism describing the motion in order parameter space without

introducing unitarity breaking but replacing real unitarity with

p-adic unitarity. Note however that real unitarity is broken also

in TGD.

7. Are parameters characterizing various degenerate absolute

minima of Kaehler action zero modes?

There are some discrete parameters characterizing the various

degenerate absolute minima associated with a surface Y^3 on lightcone

boundary. It seems that also these parameters must be identified

as zero modes. In these degrees of freedom the complete localization

of configuration space spinor field is not however necessary.

The point is that these degrees of freedom are *discrete* and

quantum jump can quite well occur to superpositions of degenerate

3-surfaces X^4(Y^3) such that entanglement coefficients in this

subset are constant. This would make possible partial localization

essential for the earlier argument for the arrow of psychological time

in which volitional quantum jumps at time t selects one branch

from the superposition of branches of the multifurcation.

Localization in zero modes might help to understand

the arrow of psychological time. Psychological time could be perhaps

identified as an order parameter, which more or less gives center of

mass time for cognitive spacetime sheet with finite time duration.

Physical time arrow could be related to a gradual drift of cognitive

spacetime sheet on lightcone: there are of course also other

possibilities and one must keep mind open.

With Best,

Matti Pitkanen

**Next message:**WDEshleman@aol.com: "[time 434] Re: [time 406] Dissipation and quantum jumps between quantum histories"**Previous message:**Stephen P. King: "[time 432] Re: Cisc vs. Risc"

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