Exploring the Complexity of String Theory

[wolram]

Its an open question, To my little brain LQG is the only contender, even
though it is still an ongoing work.
I have read lots about ST, but as someone pointed out, you can not
understand it without understanding the maths, but why is it so complex?
Surly beautiful theories are easy to explain, while ST just keeps going
on and on in compexity, and this is the reason why most of the population only
have a vague idea, or any comprehension on the subject.

 

[selfAdjoint]

All you do is assume that the fundamental thing in the universe is not zero-dimension particles but 1-dimensional, zero-thickness strings, and all the higher mathematics just comes out of that assumption. That's one of the things that has made string physics so attractive.

 

[Tom McCurdy]

Alright I know I am stuck in the old way of thinking here... but how can something one dimensional be a loop... that's the most common question I get when I tell people what I know about string theory and I never have a good response.

 

[Stingray]

Alright I know I am stuck in the old way of thinking here... but how can something one dimensional be a loop... that's the most common question I get when I tell people what I know about string theory and I never have a good response.

Set up a coordinate system that covers that loop. You only need one parameter to do this, so it is one-dimensional. Whether or not an object is embedded in a higher dimensional space is irrelevant.

Similarly, a hollow sphere is two dimensional since two numbers are needed to give any point on it.

I don't think that the complexity of string theory should really be a mark against it. Historically, most ideas looked very jumbled until they were finally understood in a coherent way. It usually takes a wider view to realize how everything can fit together in a nice textbook-ready form. And, as SelfAdjoint said, the fundamental concept is very simple.

Also, LQG is certainly not easy. It is a much smaller set of ideas than string theory, which makes it look more coherent, but the math is not at all simple. I also don't think it can't be explained adequately without the formalism. I actually don't think that there is really much at all in any field of physics that can be explained well without math. There are so many subtle connections between things even in classical physics that popular treatments are necessarily going to be very superficial.

 

[marcus]

Alright I know I am stuck in the old way of thinking here... but how can something one dimensional be a loop... that's the most common question I get when I tell people what I know about string theory and I never have a good response.

this one-dimensionality of a basic element is something shared by LQG as well as string theory.
In LQG it is the loops themselves or the somewhat more complicated networks ("spin networks") used to describe quantum states of the gravitational field.

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Tom M maybe one way to explain it to them is to say
Imagine you were living on a loop of string (with zero thickness)
you don't care how that string is ARRANGED in the ordinary 3D world because you can't see that surrounding world. You are a one-D creature living in that one-D loop of string and all you see is your world.
It doesn't matter to you how your world is embedded in some higher-D surroundings.

So in that sense the loop of zero thickness string is one dimensional.

Maybe you already tried this with them? And they said something like "but how do you bring it around and connect it, so it makes a loop, if you don't have at least 2D?"

It's two notions of dimension. there is the thing's own intrinsic dimensionality, which would be experienced by a critter living in it,
and there is the dimensionality you and I need to embed the thing in our familiar standard space like R² or R³

Maybe that will keep them quiet for a while and maybe it wont.

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I still think there is a wide difference between LQG and string. but
it certainly is true that they both deal extensively in one-D objects.

 

[wolram]

By Stigray
Set up a coordinate system that covers that loop. You only need one parameter to do this, so it is one-dimensional. Whether or not an object is embedded in a higher dimensional space is irrelevant.
I can understand, with difficulty, one dimensional objects, its the last part
"higher dimensional space", 1,2,3,4 is ok but beyond that i am lost.

 

[Stingray]

.
I can understand, with difficulty, one dimensional objects, its the last part
"higher dimensional space", 1,2,3,4 is ok but beyond that i am lost.

By that, I just meant a dimension higher than than the one of the object you're talking about. In this case, we normally visualize (1D) loops as existing in a 3-dimensional space, although it isn't necessary to their mathematical description.

 

[marcus]

Its an open question, To my [modest but quite adequate] brain LQG is the only contender, even
though it is still an ongoing work...

I should say that to my [also hopefully adequate] mind CDT is an equal contender with LQG. Both are background independent approaches
that manage to reproduce some standard big bang cosmology.

the CDT effort is tiny. Only 3 papers this year.
but then it hardly existed at all last year.

but before mentally narrowing down the field and maybe betting everything on one horse, I have to say that CDT (causal dynamical triangulations) approach to quantum gravity does NOT
rely on a basic one-D element. It is slightly different.

it uses 4-simplices-----4D solids analogous to tetrahedra and triangles----naturally these do have edges, which constitute one-D parts in the picture. Not as if one-D pieces are completely absent!

the basic kit for CDT is a lot of little 4D solids
plus there are rules for how you fasten them together.

As far as I know we do not have anyone at PF who can help us out with CDT. There is a risk that, simply because some of us have learned about String on the one hand and Loop on the other hand, we could get narrowed down too much.

BTW perhaps I shouldn't have suggested that Loop and String were cousins on account they both involve one-D elements (call them loops or spin networks or strings). I forgot to mention extensions of the idea of string to higher dimensions to make "branes". Extending mathematical ideas to more dimensions opens up endless possibilities (a common theme in all 20th century mathematics, not just in stringy business.)

At any rate the initial idea of string was the one-D string----and in that sense it has something in common with LQG. Which CDT doesn't.

So that by itself makes CDT a little different. It also extends an enterprise that hawking and his friends worked on in the 1980s and which (I thought) got bogged down and abandoned.

it is frustrating that we don't have someone here at PF who has taken an interest in Causal Dynamical Triangulations and read up some on it.
One essential keyword is Regge. Regge managed to translate the einstein equation into something discrete and combinatorial involving 4-simplices. he was able to translate curvature into a COUNT of vertices and volumes.
This was, like 1960, I think. Now over 40 years later Ambjorn and Loll are using Regge formulas. I better find out more about Regge. someone should anyway.

 

[marcus]

unless there is objection, let's include Regge

Wolram this thread you started says "LQG or String"

I can start a separate CDT, or Regge thread, if you would prefer not to have this one expanded to include that.
If you are at all uncomfortable with having a third alternative, just indicate same and I will depart forthwith!

Unless there is objection I would like to include Causal Dynam. Triang. in consideration.

First here is about Tullio Regge. he was born in 1931 in Torino...:
http://www.millennium.xnet.it/authors/c_regge.html

Around 1960 he was at the Munich Max Planck Institute and got to work with Heisenberg. After that, in the early Sixties, he was at the Princeton Institute of Advanced Studies and got to work with John Wheeler.
That was when he invented discrete gravity.

It is the business of implementing the eistein equation , which is a differential equation (and therefore depends on infinitesimals or limits as things go to zero), with a scheme where you measure spacetime curvature by counting vertices and faces and volumes of little blocks. The smooth differential equation was made into a discrete jumpy combinatorial thing, doing masses of arithmetic at very small scale.

He must be a very original man, if not outright eccentric. Or have been at that time. maybe he toned down later. Sometimes you have to have people with a great deal of mental independence----who just don't do things en masse----and other times such people can be problematical.

At some point Tullio Regge left the Institute of Advanced Study at Princeton and went home to Italy.

The biographical article that I gave the link to ends this way:
"In 1989 he was elected Member of the European Parliament. For years he has been involved in a difficult campaign against New Year Celebrations."

 

[wolram]

By MARCUS
BTW perhaps I shouldn't have suggested that Loop and String were cousins on account they both involve one-D elements (call them loops or spin networks or strings). I forgot to mention extensions of the idea of string to higher dimensions to make "branes". Extending mathematical ideas to more dimensions opens up endless possibilities (a common theme in all 20th century mathematics, not just in stringy business.)
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This is where i struggle ST "seems ,"to have some conection with LQG but
the connection is far in the future, if at all, the word "branes", makes me
nervous, as every theory must have some limits.

 

[wolram]

I can start a separate CDT, or Regge thread, if you would prefer not to have this one expanded to include that.
If you are at all uncomfortable with having a third alternative, just indicate same and I will depart forthwith!
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Please do, although i am quite comfortable with some derivative of
LQG, Mix and match is also ok.

 

[marcus]

Please do [start a separate]...

I shall be happy to do so!
Or maybe i can find an old thread that will do. I any case
I will avoid mixing CDT in here as it really isnt
an offshoot of LQG

 

[selfAdjoint]

He must be a very original man, if not outright eccentric. Or have been at that time. maybe he toned down later. Sometimes you have to have people with a great deal of mental independence----who just don't do things en masse----and other times such people can be problematical.

At some point Tullio Regge left the Institute of Advanced Study at Princeton and went home to Italy.

You left out that he studied with Heisenberg. Tullio Regge is also the author of the Regge trajectories that are important for the spectrum of the quantized string. So he spans a lot of the field you have been discussing on this thread.