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

*Thu, 9 Sep 1999 08:22:50 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 723] Projecting internal world to external world"**Previous message:**Stephen P. King: "[time 721] Re: [time 720] "... What the universe looks like from the Inside"!"**Next in thread:**Stephen P. King: "[time 731] Re: [time 722] John Baez and the problem of time"

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!

*>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(;-).

********

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(;-).

*>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!

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?

Best,

MP

**********************************

**Next message:**Matti Pitkanen: "[time 723] Projecting internal world to external world"**Previous message:**Stephen P. King: "[time 721] Re: [time 720] "... What the universe looks like from the Inside"!"**Next in thread:**Stephen P. King: "[time 731] Re: [time 722] John Baez and the problem of time"

*
This archive was generated by hypermail 2.0b3
on Sat Oct 16 1999 - 00:36:40 JST
*