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

*Wed, 12 May 1999 09:09:27 +0300 (EET DST)*

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Dear Matti,

Matti Pitkanen wrote:

[SPK]

*> To say the truth, I am in awe of your knowledge of the math
*

*> involved! I am happy that critique is useful. :) I have a few silly
*

questions...

*>
*

*> Matti Pitkanen wrote:
*

*> >
*

*> > I have been pondering more and more seriously the problem of mapping
*

real

*> > spacetime surface and imbedding space to their p-adic counterparts.
*

*> > I proposed already earlier a possible solution of problem but it
*

*> > was not satisfactory: thanks for Stephen for critical comments.
*

*> > The basic problem that canonical identification mapping real
*

coordinates

*> > to their p-adic counterparts is not manifestly General Coordinate
*

*> > Invariant concept and one should be able to identify preferred
*

*> > coordinates of imbedding space, where canonical identification applies
*

*> > in some form, in order to achieve GCI.
*

[SPK]

*> Is it possible that there exist a class of pairs {M_i, I_p},
*

where

*> M represents the spacetime [hyper?]surface and I_p represents the p-adic
*

*> imbedding space, such that there is an asymptotic hierarchy of
*

*> inclusions of the {M_i, I_p} that, at the limit of +/- \inf, there is
*

*> isomorphism between M_i and I_p and a dismorphisms for any i, p > \inf.?
*

*> I hope this makes sense! ;)
*

*>
*

*> [MP]
*

*> I am not sure whether you regard M_i as real or p-adic manifold and
*

*> I could not quite understand what you mean by asymptotic hierarchy of
*

*> inclusions. Certainly this kind of sequence might exists but since
*

*> I do not know about motivations for the existence of sequence I cannot
*

*> imagine any concrete example.
*

I was trying to think of M_i as a real (analytic) manifold. By the

"asymptotic hierarchy of inclusions" I was thinking of how the p-adic

manifolds would contain as subsets other p-adic manifolds. I find the

means to map the reals into this nesting structure to cause problems

with the usual topology assumptions of the real manifold. I will try to

be more explicit: When we map a subset of R to another subset of R the

usual assumption seems to involve the Borel property, which, frankly, I

don't understand well :(. So I will use a simple example from elementary

algebra. We think of an open set of points from R^1 as a line segment

without the endpoints, conventional topology seems to be built from R^n

versions of there. Ok, if we were to take an arbitrary sized open set

and try to map it to a subset of a p-adic manifold, how would we know

that it "fit" exactly and uniquely? more on this below...

[Matti]

Your example is good. p-Adics are not well ordered and to speak

of the mapping of ordered real interval to p-adic *p-adic ordered

interval* is statement, which as such does not make sense.

Canonical identification

x_R= SUM x_np^n --> SUM_n x_np^(-n)

maps reals in continuous manner to p-adics (Here x_n has values 0, ...p-1

since pinary expansion is in question). Continuity can be checked by

direct

calculation.

One can however INDUCE the ordering of reals to p-adics just by saying

that p-adic x is smaller than y if the inverse image of x is smaller than

the inverse image of y. This ordering cannot be and is not global however

since two p-adics x_1 and x_2 can be mapped to same real and in this case

one

cannot distinguish between x_1 and x_2 since the real images of x_1 and

x_2 are

identical. This is related to the nonuqinuess of pinary expansions

of real numbers (counterpart of 1=.99999..).

This induced ordering is crucial in my proposal for

the definition of the p-adic version of definite integral reducing

the definite integral to the difference of integral function at

the endpoints of the integration interval whose ordering is induced

by canonical identification. This same ordering could make

possible to define the concept of differential forms but

this would require the touch of real mathematician.

[MP]

*> What I am considering is basically the problem of mapping real manifold
*

*> M_R to its p-adic counterpart M_p (in present case M is the
*

8-dimensional

*> space H where spacetimes are 4-surfaces). The idea is that this mapping
*

*> induces the mapping of submanifolds of M_R (spacetime surfaces)
*

*> to submanifolds of M_p somehow.
*

That is the relationship (explicitly!) between the 4-surface

subsets(?)

of M_R?

If canonical identification is applied in standard manner to all

coordinates of say 8-dimensional M_R ==H the p-adic image of X^4 in M_R

is fixed completely. But X^4_p is NOT smooth surface p-adically: this is

the

problem. I want smooth surfaces satisfying the field equations defined

by Kahler action. What follows could be also regarded as a manner to

loosen

the mapping so that the *discrete* image of X^4 could be completed to

smooth p-adic surface.

[MP]

*> > First some general comments on frames of reference question
*

*> > and then a brief description of how the concept of preferred
*

*> > frame appears as a purely technical concept in the formulation
*

*> > of quantum TGD.
*

*> >
*

*> > General Coordinate Invariance
*

*> >
*

*> > The Principle of General Coordinate Invariance states that the
*

*> > laws of physics cannot depend on frame of reference. A slightly
*

*> > different formulation says that diffeomorphisms of spacetime do
*

*> > not represent genuine physical degrees of freedom. You do not get
*

*> > new physical configuration by mapping various tensor quantities
*

*> > describing physical fields to their diffeomorphs.
*

*> > This means that GCI as a symmetry
*

*> > is like gauge invariance: there are not conserved quantum numbers
*

*> > associated with infinitesimal general coordinate transformations.
*

Is it absolutely necessary to assume that quantum number

conservation

is "external" to possible local observations? Would it not suffice to

show that for any sequence of observations is constructed such that in

any given transition in the sequence the total number of quantum numbers

is constant. This is a subtle but important difference. It shifts us

from a priori postulates to local logical consistency derivations.

[Matti]

Quantum numbers would be external to local observations in standard

approach

to quantum measurement theory, where observers are external agents

not described by quantum physics except phenomenologically by

state function collapse concept.

In TGD situation is different. TGD introduces theory of consciousness

as part of quantum physics: observation/observer is in quantum jump

between objective realities which as such are Zombies and do not observe

anything. This framework is much more ambitious: the theory should

predict when and where the observer and observation

are in given quantum jump, which subsystems can be said to observe

/be observed, etc...

[Stephen]

Weyl's original gauge theory made this explicit, but the lack of

imagination of other physicists at the time prevented proper

understanding. I have read and re-read Pauli and Einstein's critique of

"spectral indefiniteness" and Weyl's response of "unobservability". I

tell you that Weyl is correct! If we consider that each observer has its

own unique set of measuring tools, instead of some a priori egalitarian

handout from above, each observer would perceive a discrete spectra

-*relative to their local gauge*!

Thus the "smearing" of spectra from a so-called unique discrete

set to

a continuous one *would only be observable* to some ideal observer that

has the gauges of all others as explicit subsets of its own local gauge.

[MP]

I have kind of intuitive idea about Weyl's basic philosophy. For instance,

unit of length would not be universal and change with position.

This would require giving up the good old Riemannian geometry and

personally I am conservativist in this point: CP_2 size is the fundamental

length scale in my approach.

From my view point the introduction of ensemble of ideal

local observers looks phenomenological concepts: I am convinced that we

need the theory of consciousness which only talks about conscious

experiences: conscious

experience as quantum measurement is indeed attractive hypothesis

since it builds direct bridge between physics and psychology.

It might be a good idea to ponder the distinction between

what is measured and measurement itself. I would argue that

various structures of spacetime (metric, connections) describe what

is in principle measurable. Same applies to quantum numbers

characterizing quantum states and reducing to group theory.

The real measurements itself would not be describable by the model

of spacetime or physical system: quantum jump again!

Of course, I can only compare our basic assumptions (without

any claim for the correctness of my own ones: they are just assumptions!):

I do not put the observer to the world: observer and observations are

between two worlds: initial and final quantum histories of quantum jump.

This assumption would suggest that the theory of observers and local

systems should be based on quantum jump concept and use the concept of

quantum history pair: pair of two objective realities.

Perhaps at classical limit when quantum jump does not appreciabely

change the quantum state one would obtain description based

on single objective reality.

[SPK]

*> The use of infinitesimal (under any circumstance!) is suspicious
*

*> to me, since it tacitly assumes zero error (no uncertainty)
*

observations.

*>
*

*> [MP]
*

*> Infinitesimal is convenient physics shorthand: there is
*

*> rigorous group theory behind this all. One defines
*

*> conserved charges as variational derivatives of action with respect
*

*> to the action of various abelian subgroups generated by Lie-algebra
*

*> elements of symmetry group. For instance, angular momentum in
*

*> specific direction corresponds to the action of rotation around
*

*> the direction of angular momentum in that direction.
*

But is it not true that the Lie groups, for example, assume

infinitesimal changes x -> x within points \subset S^1? or what ever

analytic manifold that is used...

[Matti]

You are right. This goes to the basis of calculus: manifold

theory relies on calculus and which is the proper definition of

calculus. The concept of derivative can

be formulated without notion of infinitesimal and derivatives are all

that is needed.

[Stepen]

What does "specific direction" mean? Do we assume a unique basis

of

independent vectors for all possible measurements of angular momentum? I

am reminded of the thought: "In space you can't tell up from down..." Is

this "specific direction" assuming a preferred frame for all?

[MP]

Sorry for unclear sentence. It should have read 'For instance, the

component

of angular momentum in given direction corresponds to the action of

rotation

around the axis defined by that direction'.

The 'specific direction' was bad choice of words. There is

no selection of specific frame involved yet.

*> [Stephen]
*

*> I believe that these are *very* special cases, and need to be better
*

*> understood! One thing that infinitesimals do is that they create the
*

*> illusion that all observations use the exact same measuring 'rod'. This
*

*> may not be the case. I have been trying to explore Weyl's gauge theory
*

*> to understand how we can do physics when each observer has its own
*

*> unique measuring rod and clock, as opposed to assuming that an absolute
*

*> standard is imposed "from above"!
*

*>
*

*> [MP]
*

*> Noether theorem makes the symmetry thinking of physicists mathematically
*

*> rigorous. The concept of Noether charge as completely independent
*

*> of any measurement theory: it is purely group theoretical concept:
*

*> infinitesimals are only bad linguistic habit of physicists (or who
*

*> knows!?). This group theoretical aspect becomes decisive in quantum
*

*> mechanics which to large extend reduces to a representation theory for
*

*> symmetry groups.
*

This rigor can only come at a high price of ideality! Umm, I do

need to

understand what is being written about Noeter charge, could you give me

an elaboration on it or a good explicit (with examples) reference? :)

[Matti]

Noether's theorem from the nonrigorous point of view of physicists can

be found from most books on quantum field theory or variational

calculus.

a) What is done is to study variation of action S= int Ld^x

under symmetries: it must vanish by definition.

b) Variational principle states that under arbtrary variation of

fields the change of action reduces to total divergence and hence

to a mere boundary term. Boundary term contains contributions

from boundaries with spacelike and timelike normals, usually

at spatial and temporal infinities. The spatial boundary term

is required to vanish but no conditions on the latter term are posed.

c) The variation under symmetry for

a solution of field equations reduces to mere timelike

boundary term which no vanishes since symmetry is in question.

This expresses conservation of classical charge. Charge is the integral

over time=constant section.

*> My personal belief that the concept of measurement comes into play only
*

*> at the level of quantum measurement theory, which is the poorly
*

*> understood part of quantum mechanics and involves
*

*> the concept of quantum jump and basically consciousness. On the other
*

*> hand, Riemannian geometry is classical theory of length and angle
*

*> measurement, and I take it as God given and go on to postulate that
*

entire

*> QM with quantum jump excluded is just infinite-dimensional Riemannian
*

*> geometry. I could be wrong!!
*

*> Somehow I however believe that Riemannian geometry is something final.
*

Should we not consider a geometry with a maximum amount of

possible

properties to be the most "primitive"? This is why I think Weyl's

geometry is more primitive that Riemann's as the former contains the

latter as a special case! The point you make: "Riemannian geometry is

classical theory of length and angle

measurement, and I take it as God given..." is what bothers me. :( I am

reminded of Lee Smolin's discussion of "ideal elements" in his paper

"Space and Time in the Quantum Universe" found in "COnceptual Problems

of Quantum Gravity" A. Ashtekar & J. Stachel eds. Birkhauser QC 178.C63

1991, pg. 228-288

[Matti]

You might be right about 'primitive'. I have not strong preconvictions

about the correctness of any philosophy: the only test is whether

philosophy

leads to working physical theory.

I have indeed made the assumption about special nature

of Riemann geometry, this is nothing but a naive belief of poor physicists

to the Godly intuition of geometers(;-) and perhaps motivated partly my

laziness!

On the other hand, the attempts

to construct quantum geometries have not been very successful: the reason

is that 'quantization' is application of ad hoc rules.

My basic philosophy is mirror image of Smolin and others:

it is simply 'Do not quantize but classically geometrize instead'.

What gives support for my approach is that one can indeed geometrize

basic structures of QFT: oscillator operator algebras reduces nicely

to Kahler geometry. Even fermionic anticommutation relations have

nice interpretation in terms of gamma matrix algebra in

infinite-dimensional

context.

[Stephen]

Smolin discusses the Principle of Sufficient Reason of Leibnitz:

"...in

a complete theory of the universe, every question of the form: 'why is

the world this way rather than that way?' must have an answer." (pg.224

ibid.) He goes on to show that this implies that any measurement (or

answer to such questions!) must be done relative to some subset (my

paraphrasing) of the whole and not some "external unobservable", such as

Newton's God Clock and Ruler and Ordering. These infinitesimals are an

explicit example of Newton's attempt to eliminate the finite subjective

observer and impose an absolute apartheid upon the Universe. Suffice it

to say, he is wrong! The subjective view is *all* that is accessible to

any, any observer! We must not forget, ever!

[Matti]

Here I warmly agree: measurement involves always subsystem-complement

division

and Newtonian picture about observer is quite too simplistic.

But I go even further: I do not regard measurement done by some

continuous stream of consciousness, observer. Quantum measurement is the

moment of

consciousness and contains conscious information like

'I am doing measurement now in lab X and the reading of measurement

apparatus is this and that' or my personal version

' There is conscious experience about existence of observer doing .....'

Subjective views are indeed what exist subjectively. I however assume that

the

quantum states=quantum histories exist objectively but change quantum jump

by quantum jump so that there is no unique objective reality.

This is just assumption: the alternative, completely logical,

possibility is to assume no objective realities and finish doing physics.

[MP]

*> I have make little quantitative progress... :(
*

YOu are not alone, The above mentioned book is full of despondent

physicists!

[MP]

*> > This is in fact leads to the basic conceptual problem of General
*

*> > Relativity: one does not have any GCI definition of energy and
*

momenta

*> > since Noether theorem gives identically vanishing conserved diffeo
*

*> > charges.
*

[SPK]

*> One thing that I have always wondered about Noeter's theorems,
*

*> which relate conservations to symmetries, is that the symmetries are
*

*> always considered using "time" as a parameter; but it is a "time" that I
*

*> would call exactly "periodic". Ben discusses a spiral/fractal time in
*

*> http://goertzel.org/ben/timepap.html that IMHO is possibly more
*

*> realistic. We must remember that the Noeter theorems are phrased in
*

*> classical thinking, and as such are ideal.
*

*>
*

*> [MP]
*

*> What Noether theorem says that variation of action for a volume of
*

*> space vanishes and by equations of motion the variation reduces to
*

*> a surface integral. What happens under suitable
*

*> additional assumption is that the surface integral reduces
*

*> to contributions from two time=constant surfaces and these
*

contributions

*> must cancel: this says that classical charges at these t=constant
*

*> surfaces are identical: charge is conserved. Metric signature
*

*> does not matter: only the idea that there is cylinder like region such
*

*> that charges do not flow out from the sides of the cylinder.
*

"Infinitesimal variation of action"? Action = ? "Integration" with

what

measure?

[MP]

Choice of action depends on theory. For instance, in TGD

action is what I call Kahler action and integration

measure is volume element defined by induced metric and is general

coordinate invariant with respect to spacetime and imbedding space.

Infinitesimal variation is change of action under small variation

of field quantities. In TGD field quantities are replaced by imbedding

space coordinates as function of spacetime coordinates so that

there are only 4 primary field variables since GCI eliminates four

of them: this is to be compared to the number of dynamical

field variables in typical unification of basic interactions.

[Stepthen]

I think that your "additional assumptions" are correct! It

localizes and normalizes the measure to "between" synchronous observers

only. We can define space-like hypersurfaces relative to these two

time=constant surfaces. But notice what happens if we parametrize the

norm to the phase difference between observer "motions"! As observers

become asynchronous in their motions, their norms diverge from each

other until they can no longer perceive each other! This is the essence

of the bisimulation model of interaction (communication).

[Matti]

This idea about synchrony and asynchrony might have counterpart in

neurophysiology and also in my model of EEG. In my approach EEG

corresponds to spatially independent collective oscillations in some

region of

brain. Two brain regions oscillating in resonance would form

a single observer: their conscious experiences bind to single

experience. When the regions oscillate as separate units, they

are two separate observers with their own experiences.

[MP]

*> Since Noether theorem relies on group theory, one can generalize
*

*> the concept of Noether charge straightforwardly to quantum theory
*

context.

*> Formulas are the same: now Noether charges become Hermitian operators
*

*> whose real eigenvalues correspond to quantum mechanical charges, quantum
*

*> numbers such as spin and momentum.
*

Yes, but the problems of the diffeomorphisms remains for QGR! The inner

product goes from unique to smeared over all possible. It is interesting

that in p-adic math, the metric is glocal, since it is defined in terms

of a prime number, and since there are \inf of them, we have \inf

different metrics, but they are disjoint! (I think ;) ) "Ultrametric

balls either have each other as subsets or are mutually disjoint."

[Matti]

You are talking about metric in sense of p-adic norm, a I right?.

To build p-adic physics one is however forced to construct p-adic

version of Riemann geometry. To generalize the expression of line element,

to generalize the concept of line length, area, etc...

Also the concept of tensor, in particular, the concept of form

must be generalized. This all is nontrivial because p-adics are

not well ordered and the concept of boundary, crucial

for integration and differential geometry and theory of forms,

is not sensical in PURELY p-adic context. Canonical identification is what

makes possible integral calculus and gives hopes of lifting

these concepts to p-adic context. But all this involves all kinds

of tricky problems.

[MP]

*> > Most importantly: it does not make sense to speak about 'active
*

*> > diffeomorphisms'. One can however speak of
*

*> > isometries of spacetime as symmetries: in this case the action to
*

*> > fields is different: one can say that fields are replaced
*

*> > with general coordinate transformed counterparts but *coordinate
*

system

*> > is not changed*. This transformation creates genuinely new field
*

*> > configuration and in case of isometries of spacetime. This new field
*

*> > configuration solves the field equations.
*

[SPK]

*> One question, how would an observer *know* that their fields
*

have

*> changed if their tools of measurement change also? As we consider a
*

*> transformation of fields, we must understand that the observer is *not*
*

*> independent of the transformations, as would the classical "external
*

*> observer".
*

*> [MP]
*

*> You are certainly right. I see however this question as a problem of
*

*> quantum measurement theory or basically problem of consciousness theory.
*

*> The classical theory of fields (absolute minimization of Kahler action
*

in

*> TGD) as well as 'Schrodinger equation' are completely observer
*

dependent:

*> there are no observers or observations in classical world nor in single
*

*> quantum mechanical time evolution/quantum history (so I believe).
*

Quantum

*> histories are dead: life and observations are in quantum jumps between
*

*> these quantum evolutions. To answer your questions is indeed a great
*

*> challenge but a challenge to consciousness theory, which we should
*

*> construct first(;-).
*

That is what we are discussing! ;) Whether we assume QM or GR to

be the

primitive and the other contingent is a matter of taste. Either method

works, maybe. Hitoshi's model casts QM as the primitive and GR as

contingent, you seem to reverse this. But the final predictions should

be equivalent. :) I am reminded of how Schroedinger and Heisenberg's

formalisms for QM show this same kind of duality! :)

[Matti]

I would claim that infinite-dimensional Kahler geometry is primitive:

perhaps everything follows from the requirement that infinite-dimensional

Kahler geometry allowing spinor structure exists(;-): spacetimes as

surfaces in H, etc...would be properties of this geometry.

Dualities might be possible. I am, and most of us are victims of our

formulations unable to see that same things can be said in different

manner.

[Stephen]

Your point that "Quantum histories are dead", to me illustrates

how,

from the GR view, Quantum histories" are static bound states spread

across space-like hypersurfaces, and have no absolute "extension" in the

time direction! I agree!

[Matti]

Actually I claim even more: entire deterministic time developments from

big bang to infinite future are dead, not just hypersurfaces.

[Stephen]

Your point that "life and observations are in

quantum jumps between these quantum evolutions" I also agrees with! How

we map features on one such surface to another is our main question, as

we consider the model of QGR from your perspective. So, I believe that,

understanding the logic of consciousness is equivalent to the logic of

mapping the features of these surfaces to each other!

[MP]

*> With the risk of repeating myself: there is no observer in the sense
*

*> of continuous stream of consciousness residing in some corner
*

*> of spacetime or floating above the Hilbert space.
*

*> Observer exists only in the quantum jumps, moments of consciousness.
*

*> Therefore one cannot say that there is any observer subject to these
*

*> transformations: the problem disappears.
*

I agree completely! :) But, how one "quantum jumps" can

encode/decode

information that is bisimilar to that of another is, IMHO, the key to

consciousness.

[Matti]

Interesting question! What is communication basically? Or what is

conscious communication basically? Is it basically fusing

of communicators to single larger conscious subsystem for

few moments of consciousness? I must say that I have not

pondered what 'communication' or 'information transfer' would

mean in my conceptual framework.

*> > Of course, in practice one must almost always solve field equations in
*

*> > some frame of reference typically fixed to high degree by symmetry
*

*> > considerations. This does not mean breaking of GCI but only finding
*

*> > the coordinates in which things look simple.
*

*> > For Robertson-Walker cosmology standard coordinates (t,r, theta, phi)
*

*> > are special in the sense that t= constant snapshots
*

*> > correspond to the orbits of Lorentz group SO(3,1)
*

*> > acting as isometries of this cosmology. t= constant snapshots
*

*> > are coset spaces SO(3,1)/SO(3) originally
*

*> > discovered by Lobatchewski and identical
*

*> > with proper time constant hyperboloids of future lightcone of
*

*> > Minkowski space.
*

[SPK]

*> I must confess that I do not fully understand the meaning of the
*

*> group symbols, but I am beginning to! :) Thank you Matti! ;)
*

[MP]

*> > RW coordinates are *NOT UNIQUE*. For subcritical cosmology,
*

*> > any Lorentz transformation generates new equally good
*

*> > RW coordinates with different origin interpretable as position of
*

*> > comoving observed! The cosmic time t is Lorentz invariant under
*

Lorentz

*> > transformations and is not changed.
*

[SPK]

*> I think that Hitoshi's use of the RW metric to talk about the
*

*> expansion of an observer's space-time applies here! We must remember
*

that

*> each observer, at each moment, is using a time origin unique to the
*

*> individual LS, which is the observer. Thus, when we think of modeling
*

*> the observations of co-moving observers, we are inferring from our own
*

*> time origin point.
*

*> [MP]
*

*> You can interpret different Lorentz transformation related frames
*

*> as associated with various comoving 'observers', yes. There however
*

still

*> remains rotational degeneracy of the frame (rotation group SO(3)): this
*

*> is the problem from my point of view in the sequel.
*

A friend of mine (mentioned below) is working on this! From what I

can

remember of our discussions, the problem results from the mutual

observations of motions given more that 2 observers. In the 2 observer

case, we have a nice reflection like symmetry, e.g. I see you move XOR

you see me move. (This is an example of my thought on subject object

symmetry, HItoshi)

But when we introduce a third observer, we break the symmetry,

since it

may be synchronously co-moving with either of the original pair and the

possible observations of the 4-vectors are different! I am strongly

encouraging him to write this up for us, but he is very busy with his

family. He, like me, is not working in a university.

[Matti]

Interesting ideas and might have some relationship with what I am

trying here. BTW, I am also outlaw(;-).

*> [Stephen]
*

*> A local friend and I have been exploring the implications of
*

*> Lorentz
*

*> transformations, and have arrived at the conclusion that such are
*

*> restricted to the possible inferences of a single observer and can not
*

*> be assumed to well-model the actual observations of other LSs. In other
*

*> words, the Lorentz invariance of possible observations is a group that
*

*> each observer has, and there is no necessary isomorphism between the
*

*> SO(3,1) of one LS's observations and another's. All that is required for
*

*> consistency is that there is the possibility of mutual entropy in the
*

*> information that can be encoded in the SO(3,1) of each.
*

*>
*

*> [MP]
*

*> This would be very nearly equivalent with the viewpoint of General
*

*> Relativity. SO(3,1) is only the group of tangent space rotations
*

*> preserving tangent space inner product and physically corresponds to
*

*> approximate Lorentz invariance of the spacetime locally. This symmetry
*

*> is however gauge symmetry and does not give rise to conserved charges
*

such

*> as angular momentum and is hence problematic.
*

*>
*

*> In TGD the big idea is that Lorentz invariance is actual global symmetry
*

*> of the imbedding spaceH=M^4_+xCP_2, rather than spacetime itself.
*

*> Poincare invariance is broken only by the presence of lightcone
*

*> boundaries. Immediate prediction is standard subcritical RW cosmology.
*

*>
*

*> I realize that we have quite different view about observer concept. You
*

*> assume that observer is modellable mathematically at fundamental level
*

*> whereas I throw the observer out and leave only conscious observations
*

*> associated with quantum jumps replacing physical time evolution
*

*> with a new one so that also the hypothesis about single objective
*

*> reality is thrown out. With so much thrown out also many problems
*

*> disappear(;-). I hope that this what I am doing is not like solving
*

*> the problem of consciousness by saying that there is no consciousness.
*

In Hitoshi's model, we say that there is not Time! :) These model

are

complementary! We can use either the idea of consciousness XOR time as a

primitive. I think I am saying this right, please correct me other wise.

:)

[Matti] Whereas I say that there are two times, subjective and

geometric(;-).

There is no end for theorizing! In any case, I am only saying

that there is no consciousNESS (consciousness as a property of physical

state): there are only moments of 'consciousness'. In Finnish there

is nice word 'tajunta', which does not contain the the idea about

consciousness as a property. Sad that English has no such word.

*> [Stephen]
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*> Thus we say that that rock is at such and such a position iff each
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*> observer involved has information encoded is a similar enough manner. I
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*> hope to have some more quantitative formulation of this soon! :)
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*>
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[Matti]

I stop here and represent remaining comments in separate mail.

MP

**Next message:**Matti Pitkanen: "[time 311] Re: [time 297] Mapping p-adic spacetime to its real counterpart"**Previous message:**Stephen P. King: "[time 309] Rethinking relativity part IV"

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