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

*Sat, 21 Aug 1999 11:13:03 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 589] parallel worlds"**Previous message:**Matti Pitkanen: "[time 587] Comments on plasma cosmology"

Hi Stephen et all,

I read the paper of Smolin et al and found it quite interesting.

1. Disappearence of time

a) The problem of the disappearing time in quantized General Relativity is

familiar to me and I have used it as one argument in favour of 3-space

as surface identication.

b) In fact, also in TGD all calculations of S-matrix elements reduce

effectively to functional integrals over 3-surfaces belonging to the

lightcone boundary. This is due to General Coordinate Invariance and the

determinism of Kaehler action: the determinism is broken by degeneracy of

absolute minima (cognitive spacetime sheets) but this implies only

additional summation in functional integral.

c) Cognitive spacetime sheets and evolution by quantum jumps however

save psychological time. Actually the necesssary anatomizing of cognitive

spacetime sheets forces to leave boundary of lightcone even if one could

calculate everything else without leaving it.

d) Although calculation of S-matrix elements reduces to functinal

integral on 'lightcone boundary', entire spacetime surfaces are

absolutely essential for construction of theory and for Poincare invariant

S-matrix: this is one of the latest results.

i) Diff^4 does not commute with ordinary Poincare:

absolute minima associated with translates of 3-surfaces are not

translates of absolute minima.

ii) The so called Diff^4 invariant representations of Poincare

transformations translate/rotate 3-surface X^3 in lightcone proper time

a=constant hyperboloid infinitesimally to Y^3 and replace spacetime

surface X^4(X^3) by X^4(Y^3).

iii) For finite values of lightcone proper time a X^4(Y^3) is

deformation of X^4(X^3) instead of pure Poincare transform having same

shape.

iv) Diff^4 invariant Poincare algebra closes and reduces to ordinary

Poincare algebra only at the limit a--> infty (lightcone boundary is

infinitely far in past). This algebra acting on 3-surfaces in infinite

future must be used to define momentum eigenstates and makes Poincare

invariance possible. The price paid for is that theory cannot be

constructed on lightcone boundary alone.

2. Computational nonconstructability as loophole of no-time arguments

Smolin saw the (computational) nonconstructibility of spate spaces of GRT

as a loophole killing the argumentation leading to the disappearence of

time in GRT. Smolin suggests that the theory should be discretized to

overcome the difficulty. I think that models are necessary discrete but

that theories are unavoidably computationally nonconstructible but

must allow computational models as approximations.

Smolin also suggests that standard quantum mechanics fails in

quantization of GRT. It is easy to agree with this.

I however see deeper reason for the disappearence of time: the

assumption that spacetime surface is abstract pseudo-Riemannian manifold

leads automatically to the disappearence of time in quantized theory.

The hypothesis that spacetime is 4-surface saves the situation.

Geometric time corresponds more or less to cm time coordinate of

3-surface.

3. Basic ideas and concepts

The following concepts and ideas appear in paper.

1. Non-constructibility of state spaces.

2. Spin networks

3. Discrete time evolution: successor of spin net work state:

emergence of discretized time.

4. Evolution at the level of state space

5. Self-organization

There are surprisingly many resemblances with my own approach

and somewhat self-centeredly I will compare Smolin's approach to

my own in the following.

a) Non-constructibility of state spaces

I would not be surprised if also the real state space of quantum TGD

would have this property. Of course, the reduction of state

construction to that of representations of infinite-dimensional

symmetry groups might help here. On the other hand, all possible

topologies 3-topologies imbeddable to M^4_+x CP_2 are involved.

b) Spin networks

My point of view is that theories and models are different

thing. It is possible to discover general principles of theories

although calculation requires discretization and approximations.

Pinary cutoff is basic feature of reals to p-adics correspondences

and it could be that pinary cutoff might be what makes things

calculable and makes possible models of arbitrarily high accuracy.

Pinary cutoff means replacement of 3-surfaces, spacetime surfaces,

configuration space,... with lattice analogous to spin network.

c) Discretization of time evolution

The discrete evolution of spin networks suggested by Smolin et al

resembles time evolution by quantum jumps although I understood that

this was meant to be more like discrete time evolution of Schrodinger

equation (although it was mentioned that next state need not be unique).

Time would be measured as number of steps occurred but there is very long

way to the geometric time and spacetime of General Relativity from this.

d) Evolution of state space and self-organization

Smolin et al suggested also evolution of state space

and self-organization at cosmological scales. This indeed what TGD

predicts. The effective p-adic topology characterizing p-adicized state

space increases in the long run. The maximal accuracy of the

representation of world prodived by the experiences determined by pinary

cutoff becomes better and better and discretization becomes more and more

precise. Self-organization by quantum jumps is basic feature of also TGD

approach: entire geometric time development is replaced with a new one so

that self-organization is not property of single geometric time evolution

In TGD however the real configuration space and configuration space

spinor fields are on the background: every quantum jump

involves the steps Psi_i-->UPsi_i--Psi_f and UPsi_i representes

real configuration space spinor field dispersed in entire

configuration space, superposition of all possible parallel spacetime

surfaces. Final state Psi_f is located in single sector D_p of

configuration space and spacetimes in superposition are macroscopically

equivalent.

Best,

MP

**Next message:**Matti Pitkanen: "[time 589] parallel worlds"**Previous message:**Matti Pitkanen: "[time 587] Comments on plasma cosmology"

*
This archive was generated by hypermail 2.0b3
on Sat Oct 16 1999 - 00:36:30 JST
*