New Scientist: Knowing the mind of God: Seven theories of everything

[rhody]

From a very very brief http://www.newscientist.com/article...god-seven-theories-of-everything.html?page=1"of seven competing theories for a Theory of Everything:
from New Scientist: 15:33 04 March 2010 by Michael Marshall

1. String theory
2. Loop quantum gravity
3. Causal dynamical triangulations (CDT)
4. Quantum Einstein gravity
5. Quantum graphity
6. Internal relativity
7. E8

Doing a search on numbers 3 - 6 on PF Forum does not result in a great number of hits.

Could those "in the know" about CDT, Quantum Einstein gravity, Quantum graphity, and Internal relativity list a bit more detailed summary of the major strengths, weaknesses of each of these theories ?

Thanks in advance...

Rhody...

Edit: Thanks Justin/Tom I should have known better, than to qualify the heading in my post, and that 2 - 6 were quantum theories of gravity and in fact NOT a theory of everything. I wanted to see if PF members who work in any of items 3 - 6 above have any insight or opinions on them. I may send a link to this thread to the editorial staff at: New Scientist as to their choice of words for their article.

Rhody...

 

[JustinLevy]

Just because it is a quantum theory of gravity, doesn't mean it is a theory of everything.
In your list
2. Loop quantum gravity
3. Causal dynamical triangulations (CDT)
4. Quantum Einstein gravity

are just quantum theories of gravity. They still need to postulate matter separately, and some can't even handle matter yet.

7. E8
isn't really a theory yet (someone just had an idea for how the group structure could be used in a theory, but it turned out not to work as originally hoped).

A few comments on the remaining:
1. String theory
It has been commented in this forum that there are papers showing string theory seems to have real problems with an expanding universe and curled dimensions.

5. Quantum graphity
6. Internal relativity
I haven't heard much about these.

 

[tom.stoer]

I pretty much agree with JustinLevy.

I always hated to blindly list "theories of everything" w/o knowing what the scope of these theories really is - or w/o discussing what a "theories of everything" could be.

Looking at the list

1. String theory
2. Loop quantum gravity
3. Causal dynamical triangulations (CDT)
4. Quantum Einstein gravity
5. Quantum graphity
6. Internal relativity
7. E8

it seems that one compares apples and oranges.

(1) was aiming for something like a ToE, but in the meantime many researchers are rather disappointed as it (seems) to lack predictiveness (at least in the current stage of research).
(2) is a rather advance theorie of quantum gravity - not more, not less. One canm add matter degrees of freedom, but this has neither been fully investigated nor is there much progress to exüplain matter instead of just adding it.
(3) is more or less a computer physics approach to triangulate spacetime; it has some very interesting features and shows some structures like "fractal dimension" which can be derived in other models; but as for LQG, it is a theory of quantum gravity - not more, not less.
Regarding (8) the article states that "some physicists heavily criticised the paper, while others gave it a cautious welcome." As far as I can see there are good reasons to believe that E8 is not able ro produce all known symmetry structures of the standard model + gravity.

All models are interesting, should be discussed in some detail, but to present them as if they were of the same value is rather dangerous.

 

[ensabah6]

What about Group field theories, noncommutative geometries, emergent models like Volovik and Wen-Levin?

 

[tom.stoer]

What about Group field theories, noncommutative geometries, ...

Non-commutative geometry is certainly missing in this list; it belongs more to the "ToE approaches" than to the "QG-only approaches".

 

[ensabah6]

Non-commutative geometry is certainly missing in this list; it belongs more to the "ToE approaches" than to the "QG-only approaches".

2) is a rather advance theorie of quantum gravity - not more, not less.

LQG you really think is advance QG? I thought it's still works in progress (i.e semiclassical limit, couplings to QFT, physical inner product, etc)

 

[tom.stoer]

LQG you really think is advance QG? I thought it's still works in progress (i.e semiclassical limit, couplings to QFT, physical inner product, etc)

I agree that it is still work in progress; you list current research topics, but some of them are already rather well understood.

to be investigated
A physical inner product has been constructed in the physical Hilbert space.

Couplings to QFT have been investigated (but they have to be put in be hand); especially spinor matter has been investigated and it has been found that LQG should be completed by the so-called Nieh-Yan topological invariant (which explains to some extend the Immirzi parameter similar to the QCD theta angle). A full RG analysis of SM gauge theories is missing.

The low-energy limit should produce Einstein-Cartan spacetime. Striking progress on graviton propagators (as effective degrees of freedom) has been made in the last couple of years. As far as I know a good low-energy state (like a coherent state) is still missing.

You should certainly list the construction of the Hamiltonian H and the proof of the non-anomalous constraint algebra (especially the part involving H). Most results of LQG are on the kinematical level, avoiding dynamical considerations as these would a) make use of H which is poorely understood or b) would rely on semi-classical states which still have some arbitrariness.

In addition there's the problem to define observables (which is already present at the classical level!) and to derive physical results (a problem common with any other QG approach)

results
On the other hand there are some well-understood results which are definately very promising
- physical Hilbert space as solution to the Gauss- and diffeomorphism-constraint
- non-perturbative formulation w/o (or minimal) reference to background structures
- finiteness
- good understanding of quantum black holes including their entropy

I think this is more than any other QG-only approach.

For an expert's view on these topics I recommend

http://relativity.livingreviews.org/Articles/lrr-2008-5/
Loop Quantum Gravity
Carlo Rovelli
Centre de Physique Théorique
Abstract:
The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein–Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

especially Chapter 8 - Main Open Problems and Main Current Lines of Investigation

 

[arivero]

What I am not happy about E8 is that it is too big. Counting components, the standard model has 96 fermions, 24 bosons and the Higgs, which adds 4 components. E8 is of dimension 248; sometimes it is presented as a sum 120+128, relates to SO(16) etc.

And then we have, in strings, SO(32) and E8xE8. That is bigger.

 

[tom.stoer]

What I am not happy about E8 is that it is too big. Counting components, the standard model has 96 fermions, 24 bosons and the Higgs, which adds 4 components. E8 is of dimension 248; sometimes it is presented as a sum 120+128, relates to SO(16) etc.

I am not an expert on this E8 stuff, so perhaps the follwoing questions sound stupid:
- how does one get the correct chirality, especially in the neutrino-sector?
- how does one overcome the Weinberg–Witten theorem?
- how does one introduce spacetime + internal gauge symmetries w/o SUSY = how does one overcome Coleman-Mandula no-go theorem?

 

[garrett]

Hello Tom,

I am not an expert on this E8 stuff, so perhaps the follwoing questions sound stupid:

Let me take a swing at answering these.

- how does one get the correct chirality, especially in the neutrino-sector?

Consider spin(7,1) acting on a spinor. The spin(4) subalgebra is equal to su(2)_L + su(2)_R, and that su(2)_L acts only on the left chiral fermions in the spin(7,1) spinor -- according to how the spin(3,1) subalgebra acts on it. This is a direct result of how spin(3,1) and spin(4) sit in spin(7,1) and act on spinors.

- how does one overcome the Weinberg–Witten theorem?

Gravity is treated as a gauge theory, so there are only bosons of spin one (and spin zero when you factor out the Higgs) and spin half fermions.

- how does one introduce spacetime + internal gauge symmetries w/o SUSY = how does one overcome Coleman-Mandula no-go theorem?

This is the most important part. The unified bosonic connection is
[tex]
H = \frac{1}{2} \omega + \frac{1}{4} e \phi + A
[/tex]
in which [tex]\omega[/tex] is the spin(3,1) gravitational spin connection 1-form, [tex]e[/tex] is the gravitational frame 1-form, [tex]\phi[/tex] is a Higgs multiplet, and [tex]A[/tex] is the gauge field 1-form. Spacetime only exists after the frame-Higgs get a nonzero vacuum expectation value. Before that symmetry breaking, the group is unified, but spacetime doesn't exist so the Coleman-Mandula theorem does not apply.


Garrett

 

[tom.stoer]

Consider spin(7,1) acting on a spinor. The spin(4) subalgebra is equal to su(2)_L + su(2)_R, and that su(2)_L acts only on the left chiral fermions in the spin(7,1) spinor -- according to how the spin(3,1) subalgebra acts on it. This is a direct result of how spin(3,1) and spin(4) sit in spin(7,1) and act on spinors.

I understand the spinor rep. stuff, but I don't get to the point where half of the neutrinos decouple or disappear.

Then I do not understand what you mean by

Gravity is treated as a gauge theory, so there are only bosons of spin one (and spin zero when you factor out the Higgs) and spin half fermions.

Of course you can traet gravity as a gauge theory but that does not mean that the graviton becomes a vector particle. All Poincare gauge gauge theories, Einstein-Cartan / Ashtekar formulation end up with "spin-two gravitons". Do you mean that using a connection / vierbein instead of a metric field is the key ingredient?

 

[garrett]

Tom,
Half of the spin(7,1) spinor components will couple to su(2)_L, and the other half to su(2)_R. And yes, using a connection instead of a metric is key.
-Garrett

 

[MTd2]

Here's the old question:

Garrett, have you finally solved the SM generation issue?

 

[tom.stoer]

Hi Garrett,

nice to talk to you!

Half of the spin(7,1) spinor components will couple to su(2)_L, and the other half to su(2)_R.

Yes, that's clear for electrons and quark; but I do not understand how half of the neutrinos simply vanish! How does this work?

And yes, using a connection instead of a metric is key.

So it's not that the graviton is spin 1, but it's something like Ashtekar's formulation which is the better starting point for the quantization.

 

[garrett]

MTd2,
Not yet. I'm working on a couple of ideas about it now, mostly using couplings to axions in a larger Higgs multiplet.

Tom,
Ah, I think I see what you're asking. The su(2)_R remains coupled to neutrinos, but presumably the corresponding Z' and W' bosons have large masses. (These would be great to see at the LHC, for unification.) And yes on the connection.

-Garrett

 

[rhody]

I may send a link to this thread to the editorial staff at: New Scientist as to their choice of words for their article.

A New Scientist, editor, Paul-Choudhury sent a reply, below:

Thanks for your message.

We actually have a fair few physics experts here at New Scientist, and
we've had some back-and-forth about whether the way we presented the
story was sufficiently clear. It would seem that our conclusion doesn't
entirely tally with those expressed on Physics Forums; bearing that in
mind, we've modified the introduction in a way that should hopefully
help clarify matters.

Thanks for bringing this to my attention.

Sumit Paul-Choudhury

This was added in front of the article:

This story has been edited to clarify that it discusses different approaches being taken to develop a theory of everything

Rhody...

 

[tom.stoer]

Garrett,

I still do not see (in you paper) how the left-right symmetry in the fermion sectors becomes "broken". Can you give me a hint, e.g. an equation?

 

[arivero]

MTd2,
Not yet. I'm working on a couple of ideas about it now, mostly using couplings to axions in a larger Higgs multiplet.

Tom,
Ah, I think I see what you're asking. The su(2)_R remains coupled to neutrinos, but presumably the corresponding Z' and W' bosons have large masses. (These would be great to see at the LHC, for unification.) And yes on the connection.

In Kaluza Klein, SU(2)xSU(2) is in some way unnatural. If one considers the homotopy classes of S1 circle fiber bundles over the sphere S2, they have always symmetry group SU(2)xU(1), except the hopf bundle, which is the sphere S3 and then has the symmetry SU(2)xSU(2). Note that it is generical that any lie group G, when seen as a manifold M(G), has the symmetry GxG, given by left and right actions of G in the manifold. But S3 is peculiar because this manifold is also a hopf fibration and then it has a guide to squash it, breaking the symmetry.

What I would like to see in the KK case is a way to put SU(2)xSU(2) in the middle of a series of classes going from the trivial S2xS1 to the trivial S1xS2. Then given the duality between both extremes, SU(2)xSU(2) should be more a case of symmetry enhancement (in the extreme of a moduli space, as bosonic strings under T duality) than of symmetry breaking.

 

[yoda jedi]

From a very very brief http://www.newscientist.com/article...god-seven-theories-of-everything.html?page=1"of seven competing theories for a Theory of Everything:
from New Scientist: 15:33 04 March 2010 by Michael Marshall

1. String theory
2. Loop quantum gravity
3. Causal dynamical triangulations (CDT)
4. Quantum Einstein gravity
5. Quantum graphity
6. Internal relativity
7. E8

Doing a search on numbers 3 - 6 on PF Forum does not result in a great number of hits.

Could those "in the know" about CDT, Quantum Einstein gravity, Quantum graphity, and Internal relativity list a bit more detailed summary of the major strengths, weaknesses of each of these theories ?

Thanks in advance...

Rhody...

Edit: Thanks Justin/Tom I should have known better, than to qualify the heading in my post, and that 2 - 6 were quantum theories of gravity and in fact NOT a theory of everything. I wanted to see if PF members who work in any of items 3 - 6 above have any insight or opinions on them. I may send a link to this thread to the editorial staff at: New Scientist as to their choice of words for their article.

Rhody...

relativistic nonlinear quantum gravity.



or:

...there is no real time ordering behind quantum causality. This means that at
the fundamental level it is impossible to unify Quantum Mechanics and Relativity,...

unless:
the REALITY is poly-ordered or omni-ordered, can coexist (in principle or possibily) past, present and the future (multi-time existence)

nature establishes order without time (no determinism or a convoluted determinism, non chronological determinism).