Survey on Theories of Everything

[Mr. James]

Hey all,

I'm a senior in high school doing a research report on all the various Theories of Everything in physics. I'm familiar with most of them and have a basic understanding of the concepts behind them. I'm starting this thread to get a better understanding on people's general opinions on these Theories of Everything. Which theory (string theory, loop quantum gravity, etc.) do you think is the most promising in accomplishing the goals of the final theory, such as explaining space and time or unifying the four fundamental forces? What are the downfalls of some theories? What are their merits?

If anyone has any other relevant information that would be helpful to my research feel free to post that also.

Thanks,

James

 

[humanino]

Loop quantum gravity is not a "TOE". Good luck.

 

[atyy]

http://books.google.com/books?id=2V...&resnum=1&ved=0CAsQ6AEwAA#v=onepage&q&f=false

 

[Fra]

Hey all,

I'm a senior in high school doing a research report on all the various Theories of Everything in physics. I'm familiar with most of them and have a basic understanding of the concepts behind them. I'm starting this thread to get a better understanding on people's general opinions on these Theories of Everything. Which theory (string theory, loop quantum gravity, etc.) do you think is the most promising in accomplishing the goals of the final theory, such as explaining space and time or unifying the four fundamental forces? What are the downfalls of some theories? What are their merits?

If anyone has any other relevant information that would be helpful to my research feel free to post that also.

Thanks,

James

Since there are _no_ what I would call mature or well defined TOE-theories theories yet, I think it's more accurate to say that there are various research programs, whose ambition is to find one.

As I see it, there simply aren't any set of competing well defined theories to compare, there are more like a set of research programs who each have their own choice of perspective, and different way of thinking what the right questions are.

So what I would personally do, is to make a survey of, and try to classify the different logic and startings points in the different research programs and try to evalute from your perspective which strategy is more likely to bear fruit. The "string theory logic" contains some problems, such as the landspace problem. ie. their framework generates only a lot of options, but no method of selection. Probably each strategy implies unique "problems" to be solved.

String theory is a certain framework, with certain starting points and logic, with a somewhat grand ambition. But so far there is not yet one unique TOE. So the quesion isn't wether some particular theory is right or wrong, all you can evaluate is the soundness and rationality of the starting points and methodology and I think so far that's going to be very subjective.

Where would you start, when looing for a TOE? What are the immutable structures or principles that it "must" be based on? Here there are a set of opinions. Some lead to string theory, some don't. I doubt there is such a thing as an objective assessment of which choice is right.

/Fredrik

 

[marcus]

The book that Atyy offered is called "Approaches to Fundamental Physics" and it has chapters on various approaches to fundamental physics.

The book has a chapter on Loop Quantum Gravity written by Hermann Nicolai, a string theorist who has shown interest in LQG and knows a lot about it, at least the basics as of 4 years ago. The Nicolai chapter is available free here

http://arxiv.org/pdf/hep-th/0601129
Loop and spin foam quantum gravity: a brief guide for beginners
Hermann Nicolai, Kasper Peeters
20 pages, 11 figures; Contributed article to "Approaches to Fundamental Physics: an Assessment of Current Theoretical Ideas", ed. I. Stamatescu, Springer
(Submitted on 18 Jan 2006)
AUTHORS' SUMMARY: "We review aspects of loop quantum gravity and spin foam models at an introductory level, with special attention to questions frequently asked by non-specialists."

My comment: it is not bad as an overview for beginners, which is all it pretends to be. Nicolai gives a fair balanced outsider perspective. IMO.

The book that Atyy gave you a googlebooks link to is this:
https://www.amazon.com/dp/3540711155/?tag=pfamazon01-20
It's edited by two guys, Seiler and Stamatescu, who gathered chapters together written by various experts. they have a section on String Theory, and a section on Loop, and one on an approach you probably haven't heard of called Asymptotic Safety which tries to overcome the difficulties of the two theories we already have (General Rel and Quantum Field Theory) and get them to work together without anything radically new. And so on. The editors beat the bushes and got chapters on a variety of approaches. The amazon link will let you look at the Table of Contents and do some browsing free.

I wouldn't buy the book because it is expensive ($80) and already out of date. But if I was at a college or university library that had it on the shelf I sure would grab it and have a look! Atyy often comes up with interesting sources.

It hasnt been settled what a "TOE" is supposed to look like. It might, in fact, treat gravity differently. There are different research programs approaching fundamental physics. Different paths, approaches. One (like LQG) involves developing a quantum theory of spacetime geometry (i.e. gravity as geometry) and then putting matter into that quantum spacetime setting. Another approach could well be to treat gravity as just another force, like the strong or weak nuclear force----and assume that everything is just forces operating in some fixed pre-established rigid geometry. Other strategies are theoretically possible as well, I imagine. Not every approach would conform to a naive "unification of the four forces" concept. We just don't know the future course of research.

So we have various approaches to discovering the fundamental physics underlying today's kind of patchwork approximate effective picture.

 

[tom.stoer]

Loop quantum gravity is not a "TOE" ...

... as it is restricted to quantum gravity; one can add certain matter couplings but w/o any attempt of "unification".

An intersting approach could be to apply the LQG quantization to SUGRAs.

 

[petergreat]

An intersting approach could be to apply the LQG quantization to SUGRAs.

Is this your own new idea? Can you elaborate?

 

[ensabah6]

what about non-commutative geometry?

 

[tom.stoer]

Yes and no.

I was thinking about the combination of LQG and SUGRA for some time. Then I found some papers in arxiv presenting something in that direction, e.g.
http://arxiv.org/abs/0906.4978

The basic idea is the following:

SUGRA uses an approach via a local symmetry (local SUSY) which requires to incorporate a graviton (spin 2) and a gravitino (spin 3/2 super partner).
SUGRA is formulated as a standard quantum gauge theory and is typically quantized perturbatively; there's the hope that certain SUGRA models are renormalizable or even finite due to on-shell symmetries; a hidden symmetry is already present in pure Einstein gravity w/o matter: by power counting Einstein gravity is divergent at one loop level, but explicit calculation shows that it is finite.

LQG on the other does not ask where the gravitational field comes from; neither does it ask where matter degrees of freedom come from. You can add it to your theory but there is no attempt of unification.
LQG simply uses the classically equivalent Ashtekar formulation of Einstein gravity, but together with the loop approach it becomes inequivalent at the quantum level (it must be inequivalent because otherwise it could not solve the problems of perturbatively quantized Einstein gravity).

One observes that LQG should be enlarged by the so-called Nieh-Yan topological invariant which is comparable to the topological term introducing the theta-parameter into the QCD action. On can try to turn this parameter into a dynamical field which leads to certain structures similar to SUGRA.

On the other hand the one can think about a non-perturbative quantization of SUGRA. As SUGRA contains gravity it makes sense to try to use the loop approach. This approach is not restricted to gravity - you can use it with any gauge theory - but it makes more sense if the theory is diffeomorphism invariant. Because a non-perturbative approach is rather interesting for any quantum field theory one can bring SUGRA quite close to a LQG-like formulation.

So there is no contradistinction between SUGRA and LQG, just the opposite way round:

LQG:
- it misses the explanation "why gravity?" and "why certain matter fields?"
+ it provides a non-perturbative formulation to (consistently) quantize gravity

SUGRA:
+ it may provide an answer to "why gravity?" and "why certain matter fields?"
- it lacks a non-perturbative quantization approach - and it is still unclear if it is really finite (or renormalizable perturbatively)

So why not try to combine the strengths of both approaches?

(remark: here SUGRA is seen as a theory on its own, not as low-energy limit of a string theory)