Space and state, spacetime and process

[john baez]

Peter May and I are about to run a workshop on n-categories at the Institute for Mathematics and its Applications:

http://www.ima.umn.edu/categories/

We'll mainly be trying to compare different definitions of n-categories, but there will be an afternoon about applications of n-categories to mathematical physics, especially topological quantum field theory. Since most of the audience won't be experts on physics, I'm giving an introductory talk which may be of interest to some people here too:

http://math.ucr.edu/home/baez/n_categories/index.html#spacetime_and_process

This includes some of the math I deliberately left out of my paper "Quantum Quandaries: A Category-Theoretic Perspective":

http://math.ucr.edu/home/baez/quantum/

Check it out! You can also see transparencies of two of my n-category talks.


John Baez

 

[Olias]

Peter May and I are about to run a workshop on n-categories at the Institute for Mathematics and its Applications:

http://www.ima.umn.edu/categories/

We'll mainly be trying to compare different definitions of n-categories, but there will be an afternoon about applications of n-categories to mathematical physics, especially topological quantum field theory. Since most of the audience won't be experts on physics, I'm giving an introductory talk which may be of interest to some people here too:

http://math.ucr.edu/home/baez/n_categories/index.html#spacetime_and_process

This includes some of the math I deliberately left out of my paper "Quantum Quandaries: A Category-Theoretic Perspective":

http://math.ucr.edu/home/baez/quantum/

Check it out! You can also see transparencies of two of my n-category talks.


John Baez

Is there any PDF format for these papers?..I tried the links, but could not get any info, may be a problem with my computer though?

 

[marcus]

Is there any PDF format for these papers?..I tried the links, but could not get any info, may be a problem with my computer though?

One has the memorable arxiv number of



quant-ph/0404040


but, Olias, I think you have seen that one already. In any case it
is available from arxiv in PDF

http://arxiv.org/quant-ph/0404040

since you are in UK you will probably be using the UK mirror

others may be inPDF also, I will let you know if and as I find them

 

[john baez]

Peter May and I are about to run a workshop on n-categories at the Institute for Mathematics and its Applications:

http://www.ima.umn.edu/categories/

You can get a lot of papers and transparencies of talks here now.

Since most of the audience won't be experts on physics, I'm giving an introductory talk which may be of interest to some people here too:

http://math.ucr.edu/home/baez/n_categories/index.html#spacetime_and_process

This and my other two talks are available in PDF now, not just Postscript. Thanks for asking, Olias.

 

[rick1138]

Wow, great files.

 

[jeff]

Peter May and I are about to run a workshop on n-categories at the Institute for Mathematics and its Applications:

http://www.ima.umn.edu/categories/

We'll mainly be trying to compare different definitions of n-categories, but there will be an afternoon about applications of n-categories to mathematical physics, especially topological quantum field theory. Since most of the audience won't be experts on physics, I'm giving an introductory talk which may be of interest to some people here too:

http://math.ucr.edu/home/baez/n_categories/index.html#spacetime_and_process

This includes some of the math I deliberately left out of my paper "Quantum Quandaries: A Category-Theoretic Perspective":

http://math.ucr.edu/home/baez/quantum/

Check it out! You can also see transparencies of two of my n-category talks.


John Baez

This is the wrong forum for this stuff. Move it to the math forums.

 

[sol2]

We expect that the divergences of quantum gravity would similarly be resolved by introducing the correct short-distance description that captures the new physics. Although years of effort have been devoted to finding such a description, only one candidate has emerged to describe the new short-distance physics: superstrings.
Vibrational
modes

This theory requires radically new thinking. In superstring theory, the graviton (the carrier of the force of gravity) and all other elementary particles are vibrational modes of a string (figure 1). The typical string size is the Planck length, which means that, at the length scales probed by current experiments, the string appears point-like.
The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory!

http://cerncourier.com/main/article/39/3/11

http://cerncourier.com/objects/thumb/1999/quantum1_4-99.gif

I appreciate seeing the difference between strings and LQG in terms of describing quantum gravity. We can see this, in terms of continuity in strings...

http://math.ucr.edu/home/baez/quantum/img8.gif

and discreteness in LQG...

http://simscience.org/membranes/advanced/essay/images/fold.gif

Is this not the fundamental difference between the two?

 

[marcus]

I appreciate seeing the difference between strings and LQG in terms of describing quantum gravity...

sol you have quoted Yaron Oz in your last post, or an article from march 1999 in CERN courier paraphrasing Oz.
It makes a striking contrast with the mood nowadays!
I appreciate seeing the difference----showing the optimism of 5 years ago.
(I hope I am reading your article correctly)

 

[marcus]

You can get a lot of papers and transparencies of talks here now.



This and my other two talks are available in PDF now, not just Postscript. Thanks for asking, Olias.

Thanks also to John Baez for following up on this!
Actually this discussion of how category theory is applied to quantum gravity----and other physics----got started some here at PF some months back with a post by arivero
(Lethe, selfAdjoint, myself, others participated)

or even earlier

Most recently I think, we were looking at Baez
quantum gravity paper
http://arxiv.org/quant-ph/0404040
"Quantum Quandaries"
which shows relevance of so-called "star-categories" to physics.
and led to some of us wanting to look into the June workshop
that Baez and somebody else organized

the workshop is on n-categories and their applications
one of the most interesting applications being to physics, at least
in my view

it strikes me as hard to comprehend but from a quantum gravity
perspective something one should know something about
(at least at the quant-ph/0404040 level)

there is some more discussion of this at the Fotini thread
https://www.physicsforums.com/showthread.php?t=21030

 

[sol2]

sol you have quoted Yaron Oz in your last post, or an article from march 1999 in CERN courier paraphrasing Oz.

yes of course.

It makes a striking contrast with the mood nowadays!
I appreciate seeing the difference----showing the optimism of 5 years ago.
(I hope I am reading your article correctly)

One of the pictures was taken from John's Baez' article made avaliable through John's links.

http://math.ucr.edu/home/baez/quantum/img8.gif

Using strings wrapped and dividing in the pant style[ topological considerations ](quoted article), in relation to todays conclusions, I wanted to draw attention to the way in which Quantum gravity is looked at with these two models. This hasn't change from 1999, in terms of continuity and discreteness. This is a foundational principal of how quantum gravity is looked at between these two camps.

Strings

http://universe-review.ca/I15-15-topology2.jpg

Topology becomes an important tool in superstring when it is treated as quantum mechanical object. This branch of mathematics is concerned with smooth, gradual, continuous change of geometric shape. For example, a square can be continuously deformed into a circle by pushing in the corners and rounding the sides. The essential rule is that no new hole can be created in the new form by tearing. Some topological equivalent objects are shown in Figure 15-17.

http://universe-review.ca/F15-particle.htm

LQG

One way to simulate a surface is to use a triangulation. Instead of keeping track of every spot on the surface, we can approximate a two dimensional surface with a mesh made of triangles. An example of a triangulation is shown at left. The points at the corners of the triangles are called nodes. The lines that join the nodes and form the sides of the triangles are called links. The triangles themselves are sometimes called simplexes, and this is why the science of studying quantum gravity this way is called simplicial quantum gravity.

In the simplest of all simplicial quantum gravity simulations, the computer must only keep track of how the nodes are connected to form triangles.

http://simscience.org/membranes/advanced/essay/gravity_simulation1.html

Simscience and Quantum Gravity

This http://wc0.worldcrossing.com/WebX?14@162.bkc9cvs7f1Y.6@.1ddf4a5f/17

I am open to corrections here.

 

[rick1138]

So is the quantization scheme mentioned above basic simplicial homology. If not, how does it differ?