Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 10 Sep 1999 08:57:58 +0300 (EET DST)
Dear Matti,
Matti Pitkanen wrote:
[SPK]
> John Baez explains well my problem with QFT and symmetries!
>
> In article <sNluueA1XM03Ewgw@upthorpe.demon.co.uk>,
> Oz <Oz@upthorpe.demon.co.uk> wrote:
> >In article <7qpnl4$78f@charity.ucr.edu>, John Baez
> ><baez@galaxy.ucr.edu> writes
>
> >>(Personally I suspect that the whole idea of spacetime as
> >>a manifold breaks down at this point, but we really know
> >>rather little about these things - though we calculate
> >>endlessly and publish lots of papers.)
>
> [MP] I express point of view immediately. What breaks down, according
> to my belief, is the approximate identity of psychological and
> geometric
> time in time scale of order 10^4 Planck lenghts. Psychological time
> is discrete (the center of mass temporal coordinate of cognitive
> spacetime sheet increases the average amount by about 10^4 Planck times
> in quantum jump). No revolutions in understanding of geometric time:
> 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
> >possibly (certainly?) make GR just an approximation?
>
> About the only thing that everyone working on quantum gravity
> agrees upon is that general relativity is just an approximation.
> It must be, because it doesn't take quantum mechanics into account,
> and the world is quantum-mechanical.
>
> So the big question is: how radically must we break from the picture
> of spacetime provided by general relativity?
>
> It makes sense to try the most conservative things first, then
> if those don't work, more radical things, and so on. People have
> been working on this for about 50 or 60 years, so by now they are
> getting desperate and trying some fairly radical things. In the
> conferences on quantum gravity that I went to earlier this spring,
> I noticed a surprising unanimity of opinion about one thing. People
> from string theory, loop quantum gravity, noncommutative geometry
> and so on disagreed about almost everything, but they almost all
> seemed to agree that we need to move away from the picture of
> spacetime as a manifold.
>
> [MP] I am really happy to see that things develop. Colleagues are slow
> minded but it is pleasure to find that they are thinking hardly(;-).
>Even
> string people are beginning to admit that there is something wrong and
> this is great. Perhaps time is soon ripe for TGD(;-).
> ********
I hope so! :-)
> But you're right, this is very stressful. This is especially true
> because general relativity and quantum field theory - our two best
> theories of physics - both assume that spacetime IS a manifold.
> People have been assuming something like this at least since Descartes,
> so most of our mathematical tools are suited to dealing with situations
> where spacetime is a manifold. If we want to switch to something new,
> it's not easy or quick. It's very hard to build up the necessary new
> tools to replace all the old ones.
>
> >Has anyone any
> >sensible idea as to what structure might replace manifolds in this
> >situation let alone how to manipulate objects in it?
>
> Various people have different ideas: spin networks, spin foams, the
> Regge calculus, matrix models, dynamical triangulations, noncommutative
> geometry, and so on. I talk about them a lot here on
> sci.physics.research, because this is my main interest: figuring out
what
> spacetime is really
> like. As you probably know, I'm a fan of using spin networks to
describe
> space and spin foams to describe spacetime. Thus it's my job to cook up
> lots of nice tools to work with these objects.
>
> [MP] Why not try something more simpler and less radical: already
> Riemann tried this but too early when he proposed that 3-space
> is curved surface in 4-space. Start from the
> age old problem of General Relativity. How to define energy and momentum
> when spacetime is not curved anymore and does not possess Poincare group
> as its isometries? What about spacetime as surface in M^4_+xS?
> You get Poincare! Plus isometries of S, color group perhaps! And You
> get generalization of string model too! This should make bell ringing
> in every head thinking about theoretical physics! But it does
> 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
> >manifold approach.
>
> Right! Or maybe even an n-category!
>
> [MP] I looked the definition of category in separate
> posting: objects and morphisms between
> them. Is this all? I think it makes sense one speaks about
> category of, say, Riemann spaces. Morphisms would be isometries.
> Or groups, morphims would preserve group multiplication.
> I am however sceptic about the idea that category theory could
> describe physics. The space of 3-surfaces, infinite-dimensional
> Riemann geometry, should be, and as I believe is, essentially unique.
> Category of infinite-dimensional geometries (with some natural
> 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
> somehow make sense in case of selves. Sensory experience
> provides representation for other selves and a lot of else
> as subself. Could the map of self in external world to subself
> be regarded as a morphism in some sense? Sensory experience
> 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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