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

*Fri, 10 Sep 1999 08:57:58 +0300 (EET DST)*

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Dear Matti,

Matti Pitkanen wrote:

[SPK]

*> John Baez explains well my problem with QFT and symmetries!
*

*>
*

*> In article <sNluueA1XM03Ewgw@upthorpe.demon.co.uk>,
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*> Oz <Oz@upthorpe.demon.co.uk> wrote:
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*> >In article <7qpnl4$78f@charity.ucr.edu>, John Baez
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*> ><baez@galaxy.ucr.edu> writes
*

*>
*

*> >>(Personally I suspect that the whole idea of spacetime as
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*> >>a manifold breaks down at this point, but we really know
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*> >>rather little about these things - though we calculate
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*> >>endlessly and publish lots of papers.)
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*>
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*> [MP] I express point of view immediately. What breaks down, according
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*> to my belief, is the approximate identity of psychological and
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*> geometric
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*> time in time scale of order 10^4 Planck lenghts. Psychological time
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*> is discrete (the center of mass temporal coordinate of cognitive
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*> spacetime sheet increases the average amount by about 10^4 Planck times
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*> in quantum jump). No revolutions in understanding of geometric time:
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*> Riemann did something rather final!
*

[SPK]

I see that you could what I has thinking right away! :-) But, you

are a minority in not seeing a problem with the concept of "geometric

time"! One problem I have is how do you model the communication between

two observers, do you propose wormholes connecting their "cognitive

space-time sheets". I am having trouble translating your fixed geometry

ideas over to my "every thing is process" way of thinking...

[MP] Spacetime is not fixed: every 10^4 Planck times it is

replaced with a quantum superposition of new ones!

Information transfer occurs certainly via wormholes since

they mean physical contact. "Ontogeny recapitulates.." suggests

the following that the following rules are OK.

a) Cognitive spacetime sheetsglued to material spacetime sheet

or larger cognitive spacetime sheet by *wormhole contacts*

is the geometric counter part for subself of self: my mental image

psychologically. Ideas in my head are cognitive spacetime sheets

and ideas might float around everywhere as Sheldrake and

meme theoreticians suggest. Very good ideas (from my

point of view) might be enlightened Buddhas providing good vibes

for a patient thinker.

b) Cognitive spacetime sheets can also get glued to other

cognitive spacetime sheets by join along boundaries contacts.

Join along boundaries contacts make possible *entanglement*: formation

of larger wholes, associations.

Formation of JABs is topological synonym for direct touch. Join along

boundariers contacts can also be long: the axons from sensory organ to

brain could give rise to occasional formation of join along boundaries

contacts between cognitive spacetime sheets in sensory organ and brain

representing objects of perceptive field.

I am now working with the model of brain. The strategy has been

to invent all possible objections against *sensory organs as primary

sensory experiencers* hypothesis. The strategy has been very successful.

It has led to understanding of how TGD:eish brain computes part of

sensory experiences and provided connection with hologram brain idea,

which reduces to its bare essentials in TGD: neurons have neuronal windows

to external world provided by axons where microtubules serve

as wave guides making coherent light from sensory organs to propage

to brain. Small piece of hologram <---> small window.

The picture looks at this moment rather nice. In particular,

axonal join along boundaries contacts between brain and sensory

organs make possible occasional communication and entanglement between

brain and sensory organs. For instance, brain communicates data required

for stereo vision and eye receives it and takes care of experiencing.

There is beautiful hierarchy: sensory organs experience, midbrain is

mostly emotional, cortex calculates.

*> >Wouldn't this be a stressful break to how we view spacetime and
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*> >possibly (certainly?) make GR just an approximation?
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*>
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*> About the only thing that everyone working on quantum gravity
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*> agrees upon is that general relativity is just an approximation.
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*> It must be, because it doesn't take quantum mechanics into account,
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*> and the world is quantum-mechanical.
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*>
*

*> So the big question is: how radically must we break from the picture
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*> of spacetime provided by general relativity?
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*>
*

*> It makes sense to try the most conservative things first, then
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*> if those don't work, more radical things, and so on. People have
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*> been working on this for about 50 or 60 years, so by now they are
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*> getting desperate and trying some fairly radical things. In the
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*> conferences on quantum gravity that I went to earlier this spring,
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*> I noticed a surprising unanimity of opinion about one thing. People
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*> from string theory, loop quantum gravity, noncommutative geometry
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*> and so on disagreed about almost everything, but they almost all
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*> seemed to agree that we need to move away from the picture of
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*> spacetime as a manifold.
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*>
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*> [MP] I am really happy to see that things develop. Colleagues are slow
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*> minded but it is pleasure to find that they are thinking hardly(;-).
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*>Even
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*> string people are beginning to admit that there is something wrong and
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*> this is great. Perhaps time is soon ripe for TGD(;-).
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*> ********
*

I hope so! :-)

*> But you're right, this is very stressful. This is especially true
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*> because general relativity and quantum field theory - our two best
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*> theories of physics - both assume that spacetime IS a manifold.
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*> People have been assuming something like this at least since Descartes,
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*> so most of our mathematical tools are suited to dealing with situations
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*> where spacetime is a manifold. If we want to switch to something new,
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*> it's not easy or quick. It's very hard to build up the necessary new
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*> tools to replace all the old ones.
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*>
*

*> >Has anyone any
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*> >sensible idea as to what structure might replace manifolds in this
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*> >situation let alone how to manipulate objects in it?
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*>
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*> Various people have different ideas: spin networks, spin foams, the
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*> Regge calculus, matrix models, dynamical triangulations, noncommutative
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*> geometry, and so on. I talk about them a lot here on
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*> sci.physics.research, because this is my main interest: figuring out
*

what

*> spacetime is really
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*> like. As you probably know, I'm a fan of using spin networks to
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describe

*> space and spin foams to describe spacetime. Thus it's my job to cook up
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*> lots of nice tools to work with these objects.
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*>
*

*> [MP] Why not try something more simpler and less radical: already
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*> Riemann tried this but too early when he proposed that 3-space
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*> is curved surface in 4-space. Start from the
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*> age old problem of General Relativity. How to define energy and momentum
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*> when spacetime is not curved anymore and does not possess Poincare group
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*> as its isometries? What about spacetime as surface in M^4_+xS?
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*> You get Poincare! Plus isometries of S, color group perhaps! And You
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*> get generalization of string model too! This should make bell ringing
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*> in every head thinking about theoretical physics! But it does
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*> not. I am frustrated(;-).
*

[SPK] I really would like to see this mental picture you have. I am just

not bisimulating your thinking at all, I see too many contradictions, but

that is, more than likely, due to my way of thinking... :-)

[MP] I see also contradictions and this is why I am updating all the time.

This is the only way to keep this big thing in control. I however dare

say that contradictions are at the level of models and of

interpretation now.

I want to emphasize one important thing. My approach have been

problem motivated: not an attempt to explain universe starting from some

existing philosophical or mathematical paradigm: the

mathematics and philosophy around TGD has developed painfully

during 20 years.

The difficulties related to time concept are numerous and TGD solves

them.

a) The existence of reversible and irreversible worlds.

b) Nondeterminism of quantum jump contra determinism of Schrodinger

equation.

c) Loss of time in General Relativity

d) The difficulties related to the definition of energy concept in General

Relativity

e) Difficulties in understanding the irreversibility of psychological

time contra reversibility of geometric time of physicists: why

we remember only past experiences.

Typically colleagues do not start from these problems but see

the problem as a highly technical one, which can be circumvented

if sufficiently clever formalism is invented. Smolin's approach is

typical example of this. He suggests a flaw on arguments showing

that time is lost in GRT rather than starting from these big problems

obvious to every graduate year student in theoretical physics.

In string models situation is degenerated also to this kind of

game.

*> >Presumably a whole new category of things would have to replace the
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*> >manifold approach.
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*>
*

*> Right! Or maybe even an n-category!
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*>
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*> [MP] I looked the definition of category in separate
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*> posting: objects and morphisms between
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*> them. Is this all? I think it makes sense one speaks about
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*> category of, say, Riemann spaces. Morphisms would be isometries.
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*> Or groups, morphims would preserve group multiplication.
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*> I am however sceptic about the idea that category theory could
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*> describe physics. The space of 3-surfaces, infinite-dimensional
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*> Riemann geometry, should be, and as I believe is, essentially unique.
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*> Category of infinite-dimensional geometries (with some natural
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*> restrictions) would contain only single member!
*

[SPK]

The primitive quantities in Category theory are objects and

morphisms, yes. This gives us an easy way of, literally, graphing out the

situations, since we can consider objects as nodes in a graph and

morphisms as edges... :-) I am VERY interested in what the "natural

restrictions" would be such that InfDimGeo (the category of infinite

dimensional geometries) would be a monoid! See Baez definition of such

in: http://math.ucr.edu/home/baez/week74.html

[MP] Well, I am also. I hope I could have the required infinite

time and infinite mental capacities. I would not be surprised if

mathematicians could say something about all possible infinite dimensional

geometries allowing Riemann connection and finite curvature tensor.

One could also require that they correspond to symmetric

spaces or unions of them: in this case *finiteness* of the curvature

scalar alone implies that *Einstein's vacuum equations* are satisfied.

[R_ab= Lambda g_ab: R= N*Lambda, N--> infty: therefore Lambda =0

and G_ab=0 so that vacuum Einstein's equations are true.]

{SPK] The way that Pratt discusses how CABAs "collapse the whole algebra

into a singlet" when a "new equation" is added, seems to me to relate to

what you are saying! The difficulty that I see is that the "classification

of 3-surfaces" is NP-Complete computationally! We can not just assume

non-constructive arguments! I am thinking that each particular

"experience" is a particular "classification" (a morphism from a subset

of MEM to a subset of InfDimGeo, see below...) of a 3-surface. We can

just assume that the 3-surfaces are "out there" already sorted for us.

This thought is equivalent to the idea that there exist a single

absolute space-time and all events are like bubbles frozen in the 4-cube

and the subjective flow of time is an illusion! (See [time 623])

[MP] I cannot say anything about about classification of

3-surfaces. What is however clear that NP completeness is based

on a model of mind which relies on classical computationalism.

And I am sceptic about this model of mind.

TGD mind corresponds to infinite quantum computer perfoming quantum

computation of infinite duration during every 10^4 Planck times. The

entire universe has infinitely long memory about its

experiences: the number of quantum jumps occurred can quite well

have cardinality much larger than that of integers of reals.

Consider what this means when one introduces lexicons and generalizations

of them! We should not assume that we are the master minds of the universe

when trying to understand universe(;-)!

*> It could be interesting to find whether morphism idea could
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*> somehow make sense in case of selves. Sensory experience
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*> provides representation for other selves and a lot of else
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*> as subself. Could the map of self in external world to subself
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*> be regarded as a morphism in some sense? Sensory experience
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*> as morphism?
*

[SPK] Yes! the map of "self in external world to subself" is, I believe,

best described as a morphism! Pattern recognition, of sense data, would be

defined as a functor between the Category MEM (of memories of PAST) and

some subcategory of InfDimGeo, maybe! :-)

Best,

MP

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