Haven't come across anyone here who understands any of the approaches to QG

[jana]

Hi,

 

Is there anyone here who understands any of the approaches to QG?

[[Tycho?]]

I sure as hell don't.

 

My guess would be Martin, but I believe you have already talked to him...

[jana]

']I sure as hell don't.

 

My guess would be Martin' date=' but I believe you have already talked to him...[/quote']

 

No, martin doesn't really understand this stuff either. Oh well.

[Severian]

What do you mean by QG as such? String theory is an attempt to explain gravity quantum mechnically - is this what you mean?

 

Although I don't know much string theory, I more or less understand supergravity, in which gravity is a consequence of local supersymmetry. Would you like to know something about this?

[Martin]

What do you mean by QG as such?

 

Suggest you look at Lee Smolin's essay "Invitation to Loop Quantum Gravity"

http://arxiv.org/hep-th/0408048

 

the acknowledgements thank John Schwarz (a string founder)

for suggesting to Smolin that he write it

it is being submitted to "Reviews of Modern Physics"

(you are probably familiar with this series of survey articles)

 

If you would glance at this review article it would be easier

to discuss Quantum Gravity since you would know the status

of one other approach beside String------then talking would not

be so abstract.

[Dave]

To me (at least) it seems like there are a heck of a lot of interpretations of Quantum Theory and a lot of different Quantum Gravity theories. My concern is similar to what happened to a lot of mathematics some time ago; a lot of theories were written without being properly reviewed first. People naturally assumed these theories in their calculations, and as a result they broke rather spectacularly. It was only noticed when different theories that should give the same results, didn't.

 

I'm not particularly well informed in this area of Physics, but is this opinion shared by anyone else?

[Martin]

To me (at least) it seems like there are a heck of a lot of interpretations of Quantum Theory and a lot of different Quantum Gravity theories.

 

About different interpretations of Quantum Theory itself I can't help---that discussion seems to have been going on since 1925 or since QT began.

In one sense it is a "meta-theory" and a good bit of the discussion concerns "How should one quantize a classical (i.e. non-quantum) theory?"

 

Ulimately one probably has to be pragmatic and say one quantizes the classical (Gen Rel) theory of gravity however will make good testable predictions.

 

You are right to be concerned with mathematical rigor! Concern for rigorous development has been a specialty of Abhay Ashtekar. He and his co-worker Jerzy Lewandowski have been helpful in the rigor department. Clear definitions and derivations are especially important where experimental results are not coming in to give guidance.

 

There is a recent survey paper: "Background Independent Quantum Gravity: A Status Report" by Ashtekar and Lewandowski----it's heavy mathematical going.

http://arxiv.org/gr-qc/0404018

 

Of course there is some rivalry between the two main lines of research:

stringy and non-stringy QG. what A and L mean by Background Independent QG is essentially non-stringy QG-----well they might not like my interpretation but that is how i see it.

 

On the non-stringy side, Loop is the main approach.

So when they say Background Indep QG that boils down to just another name for Loop Gravity. I am not sure where you get the idea that there are a lot of different approaches. Maybe you are thinking of all the different stringy concepts. But in non-string QG research the situation (statistically anyhow:-)) is fairly simple.

 

There used to be more different approaches, say in 1998, but there has been something of a shakedown and a consolidation (again on the non-stringy approaches).

 

A lot of bridging has been done, showing equivalences. So if something comes up in some other (nonstring) line of research it can be related to Loop. this my impression from what I've seen going on.

 

what other non-stringy QG approaches have you heard of?

that might be one way to proceed. Tell me something besides Loop and I will tell you how I think it fits in the picture and whether AFAIK people are still working on it.

[Severian]

At 51 pages, I may be some time reading this....

 

As for other non-string QC approaches, as I mentioned above the foremost seems to be 'supergravity'. The other 3 forces in nature seem to be well described by the Standard Model: one imposes a symmetry on the universe (eg SU(3)) and then when one insists that the symmetry is 'local' (so causally disconnected observers can make different choices with respect to the symmetry) one is forced to introduce new paricles; these new particles are the guage bosons, the force carriers of the three forces. So that the gluon is a consequence of local SU(3) for example.

 

This works amazingly well, so it makes sense to use it for gravity too.

 

Now, the Standard Model has certain problems associated with it which are serious but generally aesthetic. The most famous one is the 'hierarchy problem'. When one calculates quantum corrections to the mass of one of the particles, the Higgs boson, one finds that it is naturally very very heavy (the Planck mass) unless one fine tunes the parameters very carefully. (This is actually a consequence of it being spinless.) The Higgs boson cannot be this heavy if it is to break elecroweak symmetry as in the Standard Model. But if one introduces a new symmetry - supersymmetry - one also introduces new contributions to the quantum corrections which exactly cancel the old ones, stabilising the Higgs mass.

 

But this is not the most interesting thing about supersymmetry. In the 1970s Coleman and Mandula proved a theorem which says that the Poincare Algebra (the symmetry group of GR) is the largest possible symmetry group that space-time has - it cannot be extended. But in the 80s Sohnius et al showed that they had a flaw in one of their steps and you could extend space-time by adding 'fermionic' directions. So a field is then not just [math]\phi (x)[/math] but is [math]\phi (x,\theta, \bar \theta)[/math] where [math]\theta[/math] and [math]\bar \theta[/math] are new fermionic 'directions'.

 

This of course is an alteration to space-time, so one might assume that it has something to do with gravity. In fact it is supersymmetry which provides the 'super' to superstrings. But even more amazingly, when one insists that supersymmetry transformations be local (just like we did for SU(3), SU(2) and U(1)) then we find that we generate a new force with a new force mediating particle. This is gravity and the mediator is a spin 2 particle known as the graviton.

 

This is supergravity. Unfortunately it has a problem: while the leading order works fine, when one calculates quantum corrections to observables, infinities start appearing all over the place. My feeling is that supergravity is a low energy effective theory limit of a string theory at high energies. Just as the Fermi theory has infinities in it, once it is incorporated into a higher theory, the infinities will go away.

[jana]

Hi severian,

 

You’ll be happy to know that the known low-energy effective field theories of string theory are in fact various supergravity theories. However, supergravity doesn’t on it’s own make sense as a QG theory.

 

Hi martin,

 

Progress in physics doesn’t pivot on dotting and crossing every mathematical ‘i’ and ‘t’. Concentration on mathematical rigor indicates we’re stuck.

[Martin]

...

Hi martin' date='

 

Progress in physics doesn’t pivot on dotting and crossing every mathematical ‘i’ and ‘t’. Concentration on mathematical rigor indicates we’re stuck.[/quote']

 

concentration on rigor sometimes indicates stuck

 

what you said here is a widely shared perception in physics and it has worked very well for much of 20th century especially in cases where there was experimental data coming in to guide intuition so one could extend ideas without rigorous basis---take the sum of infinite series by guess and gosh and so on. No reasonable person could find this objectionable!

 

However I personally would not want to make a categorical claim about the uselessness of rigor in all physics situations. There may be cases where there is insufficient or spotty data where requiring mathematical clarity can actually provide intuition and play an important role.

 

I dont want to argue about this. Simply it may have a value.

Classical General Relativity, in 20th century, has been developed with unusually much rigor (there being, until the 1990s, not so much interesting observational data about the shape of the universe and such).

this long period of rigorously making sure of the mathematics may not after all have been bad in that case

 

even tho very different from more free-wheeling unrigorous progress in field theory and particle physics.

 

Maybe. Maybe not. probably it is not useful for me to discuss the role of mathematical clarity and carefulness in this situation.