String Theory and its derivatives:

[beecee]

Is string theory, or one of its derivatives  still our best chance for a TOE?

Is the verification or validating of string theory, hindered by our lack of technical know how and limitations in being able to observe at such infinitesamally small scales?

Is the acceptance of multiple dimensions a barrier?

Will the LHC or any similar experiment be able to shed more light onto the string regime story?

My interest in string theory was first awaken after reading a book called "Hyperspace" by Michio Kaku, many years ago, but in the intervening years I have heard other scientists poo-pooing the idea simply because after so many years, it is still only hypothetical. Is this fair?

[MigL]

Don't ask me.
I'm a Loopy Quantum Gravity guy. 

[beecee]

14 minutes ago, MigL said:

Don't ask me.
I'm a Loopy Quantum Gravity guy. 

Knowing even less about LQG, I checked out https://en.wikipedia.org/wiki/Loop_quantum_gravity                                                                extract: "LQG begins with relativity and tries to add quantum features, while string theory, conversely, begins with quantum field theory and tries to add gravity".

So as per my second point in the OP,"Is the verification or validating of string theory, hindered by our lack of technical know how and limitations in being able to observe at such infinitesamally small scales?"

Reading in that link, certainly LQG, appears to be a more logical path as it is based on the geometry of spacetime itself...which according to Einstein, is all gravity is.

[Mordred]

LQG is a good solid modelling system, Myself I prefer QFT under quantum geometrodynamics.

Here is an intro from arxiv.

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1108.3269&ved=0ahUKEwjdtJmq7s3VAhXl1IMKHQZUB20QFghBMAk&usg=AFQjCNG0UYMuDcmyD_f900Ksskv7b1ei8Q

Either method String, QFT or LQG stand an equal chance in my opinion. They are all equally capable of describing any  dynamic from the quantum scale to individual interactions to spacetime fields There are full treatments of SO(10) both MSM a(minimal standard model) and MSSM ( minimal supersymmetric model) in either methodology of the above. Under particle interactions or under field treatments. 

 

Edited August 11, 2017 by Mordred

[Mordred]

For string theory itself I feel twistor  theories has a strong potential.

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://conservancy.umn.edu/bitstream/handle/11299/130081/spradlin.pdf%3Fsequence%3D1&ved=0ahUKEwji3Z7g8M3VAhUT24MKHSqDCSAQFggoMAI&usg=AFQjCNGgWPZJMvC0M8LxeTX2RTtu_bCesA

Twistor theory link above. You can replicate spinfoam via twistor, just an fyi

Edited August 11, 2017 by Mordred

[beecee]

24 minutes ago, Mordred said:

Either method String, QFT or LQG stand an equal chance in my opinion. They are all equally capable of describing any  dynamic from the quantum scale to individual interactions to spacetime fields There are full treatments of SO(10) both MSM a(minimal standard model) and MSSM ( minimal supersymmetric model) in either methodology of the above. Under particle interactions or under field treatments. 

Other then the technological know how and advancements of observing at those scales, what other indication then would see one as a stand out, or at least some other equal valid point to see at least some acceptance of a bonefide TOE with any of them. 

[Mordred]

 As you have already mentioned the extreme difficulty measuring gravity at the quantum scale, about the best we can do is set the upper and lower constraints based upon numerous studies and methodologies based upon indirect and multi particle studies that we can measure. Much like what happened with the Higgs field. Prior to being discovered. The studies pointed to where to look by numerous constraints being gradually tightened.  The data to set those bounds would comprise of years of research and various model comparisons to fine tune the bounds.

One solid example of applicable datasets is the GW wave data being collected. You get a ton of details that are applicable to quantizing gravity. Amplitude, strength and spin statistics (quadupole data). 

A solid range of samples will provide incredibly useful data to tighten our constraints.

 

Edited August 11, 2017 by Mordred

[beecee]

19 hours ago, Mordred said:

 One solid example of applicable datasets is the GW wave data being collected. You get a ton of details that are applicable to quantizing gravity. Amplitude, strength and spin statistics (quadupole data). 

A solid range of samples will provide incredibly useful data to tighten our constraints.

 

Gravitational radiation from the BB itself?

[Mordred]

Gravity waves arise from anistropies of spacetime. The BB from 10^-43 sec forward is considered homogeneous and isotropic so you wouldn't have GW production from the rapid expansion due to BB

[Solenodon Paradoxus]

On 8/11/2017 at 10:01 AM, Mordred said:

LQG is a good solid modelling system, Myself I prefer QFT under quantum geometrodynamics.

Here is an intro from arxiv.

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1108.3269&ved=0ahUKEwjdtJmq7s3VAhXl1IMKHQZUB20QFghBMAk&usg=AFQjCNG0UYMuDcmyD_f900Ksskv7b1ei8Q

Either method String, QFT or LQG stand an equal chance in my opinion. They are all equally capable of describing any  dynamic from the quantum scale to individual interactions to spacetime fields There are full treatments of SO(10) both MSM a(minimal standard model) and MSSM ( minimal supersymmetric model) in either methodology of the above. Under particle interactions or under field treatments. 

 

Please kindly provide a link to the full treatment of SO(10) GUT in Loop Gravity.

[Mordred]

Simply replace the SO(1.3) Lorentz group under SO(10) with the Loop quantum gravity SU(2) groups. The remaining groups under SO(10) remain unchanged. LQG deals primarily with the SO(1.3) subgroup for its modifications.

SU(2) and U(1) still remain unchanged for charged fields, as well as the SU(3) group for the color charges and flavor charges.

Edited August 22, 2017 by Mordred

[Solenodon Paradoxus]

19 hours ago, Mordred said:

Simply replace the SO(1.3) Lorentz group under SO(10) with the Loop quantum gravity SU(2) groups. The remaining groups under SO(10) remain unchanged. LQG deals primarily with the SO(1.3) subgroup for its modifications.

SU(2) and U(1) still remain unchanged for charged fields, as well as the SU(3) group for the color charges and flavor charges.

Could you be more specific?

1. Afaik, there's two different (equivalence hasn't been proven so far) approaches to LQG The one due to Thiemann is based on the Hamiltonian constraint operator acting on the node, and the one due to Rovelli is based on the projection operator approximated by a series of (renormalized) EPRL spinfoams. Which one are we talking about here (or does it matter at all)?

2. SO(10) GUT *does not* include gravity. In fact, there's a famous no-go theorem due to Coleman and Mandula, which forbids any but trivial unification of gravitational SO(3,1) and internal symmetries in a larger Lie group. I agree that it is hardly valid in the background independent context (that is, prior to "breaking" of background independence and emergence of classical spacetime and matter QFT on it). But this at least deserves a detailed explanation.

3. Strictly speaking, even the "SO(3,1) part of SO(10)" in your post doesn't make sense, since a noncompact Lie group SO(3,1) cannot be a subgroup of a compact SO(10).

[Mordred]

 

No it doesn't matter if you use Rovelli or Theiman we are only affecting the SO(3) group

 

Look specifically at how LQC handles the SU(2) homomorphic mappings unto SO(3).

Here is an article showing the mappings I just referred to

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://indico.cern.ch/event/243629/material/slides/0.pdf&ved=0ahUKEwiOmu-KqO3VAhXj1IMKHboCA9cQFggrMAU&usg=AFQjCNFE6xIi4bnwku7sfLNQkcXBBfwpWw

 

if you follow then you should see that SO(3) can be represented by the double cover SU(2)

[latex] SO(1.3) =SU(2)\times SU(2) [/latex] 

Here this shows the Poincare and Lorentz group with the SU(2) correlations

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://www.physics.uci.edu/~tanedo/files/notes/FlipSUSY.pdf&ved=0ahUKEwiTgs2zq-3VAhVD6mMKHVO8AsMQFgglMAM&usg=AFQjCNG5dHCxvtyhAM5wLW3R0yUCYF7vIA 

in essence the SO(3) isomorphism is [latex] SO(3)\simeq SU(2)/\mathbb{Z}_2[/latex]

Think of it this way, SO(3) is the non relativistic vector representations.

SU(2) is the  spinor representations 

SO(1.3) is the relativistic vector representations.

[latex] SL(2,\mathbb{C})[/latex] is the double covering of SO(1,3)

SO(3) is compact all orthogonal groups are.

[latex]SO(n\mathbb{R})[/latex] is a closed group as is [latex]\mathbb{R}[/latex]

Edited August 24, 2017 by Mordred

[Solenodon Paradoxus]

21 hours ago, Mordred said:

 

No it doesn't matter if you use Rovelli or Theiman we are only affecting the SO(3) group

 

Look specifically at how LQC handles the SU(2) homomorphic mappings unto SO(3).

Here is an article showing the mappings I just referred to

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://indico.cern.ch/event/243629/material/slides/0.pdf&ved=0ahUKEwiOmu-KqO3VAhXj1IMKHboCA9cQFggrMAU&usg=AFQjCNFE6xIi4bnwku7sfLNQkcXBBfwpWw

 

if you follow then you should see that SO(3) can be represented by the double cover SU(2)

SO(1.3)=SU(2)×SU(2)  

Here this shows the Poincare and Lorentz group with the SU(2) correlations

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://www.physics.uci.edu/~tanedo/files/notes/FlipSUSY.pdf&ved=0ahUKEwiTgs2zq-3VAhVD6mMKHVO8AsMQFgglMAM&usg=AFQjCNG5dHCxvtyhAM5wLW3R0yUCYF7vIA 

in essence the SO(3) isomorphism is SO(3)≃SU(2)/Z2

Think of it this way, SO(3) is the non relativistic vector representations.

SU(2) is the  spinor representations 

SO(1.3) is the relativistic vector representations.

SL(2,C) is the double covering of SO(1,3)

SO(3) is compact all orthogonal groups are.

SO(nR) is a closed group as is R

Thank you for this, but it wasn't the original question. Let me repeat the question here so that there's no misunderstanding: I am interested in your claim that "there's a full treatment of SO(10) GUT in LQG" (or did I misunderstand the claim?).

Please follow up on your previous post where you proposed replacing SU(2) with SO(10), which I don't understand because it is a rough sketch with not enough details to make things clear.

Specifically, I want to understand which group and how the usual SU(2) of spin networks extends to, and which group does the SL(2,C) of spinfoams extend to and how.

In fact, let me ask this same question in an even more unambiguous way. Say we go with the spinfoam formulation. Then there's a mapping from SU(2) representation theory to the SL(2,C) unitary (principal series) representation theory called the upsilon-gamma map, which determines the amplitude of the spinfoam vertex. This completely defines the projection operator as a limit of spinfoam amplitudes.

Now how would you modify this to include SO(10) GUT gauge&matter fields? Do you simply add another labels to the spinfoam faces (= spin network links), or do you consider a gauge-gravity unifying group (which one?). How does the spinfoam amplitude change? Please provide all these details or just a reference, because this is what "full treatment of SO(10) GUT in LQG" means in my opinion. And it happens to be a subject I am currently extremely interested in.

Note that:

1. You can't extend SU(2) to SO(10) because SO(10) GUT *does not* include gravity, and you are making the gravitational SU(2) a part of it which means that you no longer model the GUT theory. You could, however, extend SU(2) to something encompassing both SU(2) and SO(10) and say that in the regime where a classical spacetime emerges this splits into a semidirect product (this is demanded by Coleman-Mandula theorem). Is this what you mean?

2. You can't extend SL(2,C) to SO(10) or its double-cover because of the same reason, and in addition, because noncompact groups (SL(2,C)) can't be subgroups of compact groups (SO(10)).

 

Update: no, it is not true that $SO(3,1) = SU(2) \times SU(2)$. It is true for the complexified Lie algebras that $so(3,1) = d_2 = su(2) + su(2)$, but not true for the Lie groups. And I am not just being nitpicky, this is actually significant to LQG.

Edited August 24, 2017 by Solenodon Paradoxus

[Mordred]

 

The first link shows the double cover did you think I made this up? There is quite frankly 100's of papers showing the double cover.  Though I should have typed SO(3) and not SO(1,3).

read the first link. Its expicitly shown there.

What do you think LQC is doing with its SO(3) modifications its literally in every paper on the topic? In particular the tetrahedron example used here?

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf&ved=0ahUKEwjegdaV6e_VAhVLx2MKHezFCEEQFggdMAA&usg=AFQjCNF439-LNY6kKP0LG0RCUaK3SELZlQ

 

Surely you are aware that under clifford algebra a plane can be described by a bivector?

 

 

Edited August 24, 2017 by Mordred

[Solenodon Paradoxus]

30 minutes ago, Mordred said:

 

The first link shows the double cover did you think I made this up? There is quite frankly 100's of papers showing the double cover.  Though I should have typed SO(3) and not SO(1,3).

read the first link. Its expicitly shown there.

What do you think LQC is doing with its SO(3) modifications its literally in every paper on the topic? In particular the tetrahedron example used here?

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf&ved=0ahUKEwjegdaV6e_VAhVLx2MKHezFCEEQFggdMAA&usg=AFQjCNF439-LNY6kKP0LG0RCUaK3SELZlQ

 

I'm gonna try to reach out to you for the last time.

I have no doubt that what you said about the double cover is correct. In fact, I couldn't agree more!

I am interested in generalizing this construction to include the SO(10) GUT. Can you or can you not provide any arguments/links to support *this* claim of yours (and not any other)?

[Mordred]

"It is almost 15 years [2] since it became well-established that ordinary Minkowski space-
time might have to be replaced with its noncommutative counterpart as one probes shorter
distances."

https://arxiv.org/abs/1311.2826

 

You mean like this example though I still have to read the paper on my way to work.

You can get the noncommutative SO(10) and how the action is broken down with the IR/UV cutoffs applied.

Here is one describing De-Sitter space

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://cds.cern.ch/record/298607/files/9603063.pdf&ved=0ahUKEwjjr_mL7e_VAhVR8mMKHSEUD3gQFggkMAE&usg=AFQjCNGA9n07atFa9NbXAnIy6gtJBWszsQ

 

Surely your aware that the Levi Cevita connection is holomorphic.

Anyways hers is LQC in regards to noncommutative spacetimes.

http://www.sciencedirect.com/science/article/pii/S0370269303007615

 

Edited August 24, 2017 by Mordred

[Solenodon Paradoxus]

48 minutes ago, Mordred said:

"It is almost 15 years [2] since it became well-established that ordinary Minkowski space-
time might have to be replaced with its noncommutative counterpart as one probes shorter
distances."

https://arxiv.org/abs/1311.2826

 

Ok, that's something new, finally. Thank you.

But in the paper it is not mentioned how this relates to LQG. That is the point I would like clarified.

[Mordred]

You have to look at how LQG uses the SU(2) Hilbert spaces though they go further into triads etc. In particular the spin matrixes under SU(2) 

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf&ved=0ahUKEwjim472_O_VAhVY7WMKHb2bDqgQFggdMAA&usg=AFQjCNF439-LNY6kKP0LG0RCUaK3SELZlQ

 

Of particular note beyond the quantization of space procedures with the cutoffs is also the holonomy relgations which in essence describes your departures from parallel transport ie levi Cevitta connection is holomorphic

 

page 24 gives the SU(2) relations under LQG.  Anyways the 224 pages of the last link goes into extensive details on how to apply it to 3d and 4d spacetimes 

LQC can be a bit tricky as it replaces the Wilson loops with spinfoam so one has to be careful between the two treatments with regards to the unitary groups

For spin networks the edges are irreducible to SU(2)

Edited August 24, 2017 by Mordred

[Solenodon Paradoxus]

9 hours ago, Mordred said:

You have to look at how LQG uses the SU(2) Hilbert spaces though they go further into triads etc. In particular the spin matrixes under SU(2) 

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf&ved=0ahUKEwjim472_O_VAhVY7WMKHb2bDqgQFggdMAA&usg=AFQjCNF439-LNY6kKP0LG0RCUaK3SELZlQ

 

Of particular note beyond the quantization of space procedures with the cutoffs is also the holonomy relgations which in essence describes your departures from parallel transport ie levi Cevitta connection is holomorphic

 

page 24 gives the SU(2) relations under LQG.  Anyways the 224 pages of the last link goes into extensive details on how to apply it to 3d and 4d spacetimes 

LQC can be a bit tricky as it replaces the Wilson loops with spinfoam so one has to be careful between the two treatments with regards to the unitary groups

For spin networks the edges are irreducible to SU(2)

Dear Mordred,

I am aware of the way LQG is constructed and how the SU(2) group enters this construction.

I still don't see though how replacing SU(2) with SO(10) would describe anything useful and you still haven't answered how you propose to modify the spinfoam amplitude, which is, and I couldn't emphasize this any harder, dependent on the structure of unitary representations of SU(2) and SL(2,C). You can find this on page 141 of that "Covariant Quantum Gravity" textbook.

LQC does not consider spinfoams (do you mean spinfoam cosmology?), it has always been a polymer quantization of symmetry-reduced cosmological models of spacetime.

Edited August 24, 2017 by Solenodon Paradoxus

[Mordred]

I have been referring to LQG and the phase space relations described by the Ashtekar-Barbero-Immirzi parameter. Which is the GR reductions to SU(2) using the Hamiltonian Yang Mills phase space. Your already familiar with it as you are with SO(10).

 So quite frankly I'm not sure where were on the wrong page here You already know how to compactify space time via

[latex]A^a_j [/latex] and [latex] E^a_j[/latex] where a,b,c are the spatial indices and j,k,l are the SU(2) indices.

[latex]{A^j_a(x),A^k_b(y)}={E^a_j(x),E^b_K(y)}=0,,,,,{E^a_j(x),A^k_b(y)}=-G\gamma\delta^a_b\delta^k_j\delta(x.y)[/latex] where [latex]\gamma[/latex] is the Immersi parameter.

https://arxiv.org/abs/1507.00851

you referred to the right section as it comes up in page 143,

just a side note any particle dynamic can be described via Hamiltons of action, just as spacetime can be quantized, under its corresponding Hamiltonians. That is the basis of the SM model groups.

 

 

Edited August 25, 2017 by Mordred

[Solenodon Paradoxus]

2 hours ago, Mordred said:

I have been referring to LQG and the phase space relations described by the Ashtekar-Barbero-Immirzi parameter. Which is the GR reductions to SU(2) using the Hamiltonian Yang Mills phase space. Your already familiar with it as you are with SO(10).

 So quite frankly I'm not sure where were on the wrong page here You already know how to compactify space time via

Aaj and Eaj where a,b,c are the spatial indices and j,k,l are the SU(2) indices.

Aja(x),Akb(y)=Eaj(x),EbK(y)=0,,,,,Eaj(x),Akb(y)=−Gγδabδkjδ(x.y) where γ is the Immersi parameter.

https://arxiv.org/abs/1507.00851

you referred to the right section as it comes up in page 143,

just a side note any particle dynamic can be described via Hamiltons of action, just as spacetime can be quantized, under its corresponding Hamiltonians. That is the basis of the SM model groups.

 

 

1. What do you mean by "compactify"? Do you propose to start with a higher-dimensional spacetime manifold?

2. Ashtekar connections and the densitized triad are a preliminary step which we do prior to doing LQG. The real LQG consists of (a) the kinematical Hilbert space of spin networks and (b) the projection operator on the physical states (given through the spinfoam vertex).

3. I still don't see how you propose to modify the existing projection operator given by the EPRL vertex to include SO(10) GUT since every time I bring this up you end up replying about something completely unrelated.

I am sorry, but I feel like this conversation is going nowhere, because you obviously don't know what you are talking about. I won't reply unless I see something to support your initial claim that SO(10) GUT can be incorporated in LQG.

[Mordred]

You know the definitions when you compactify a group.  ie closed and bound. Yeesh the papers posted literally show how. Quite frankly I really couldn't care if you wish to continue.

I didn't propose modifying anything, quite frankly I have no idea how you even got that impression. When I stated SO(10) MSSM I meant under the standard or supersymmetric model not the group SO(10) specifically.

https://en.m.wikipedia.org/wiki/Compact_group

Edited August 25, 2017 by Mordred

[Mordred]

On 8/24/2017 at 2:52 AM, Solenodon Paradoxus said:

Note that:

1. You can't extend SU(2) to SO(10) because SO(10) GUT *does not* include gravity, and you are making the gravitational SU(2) a part of it which means that you no longer model the GUT theory. You could, however, extend SU(2) to something encompassing both SU(2) and SO(10) and say that in the regime where a classical spacetime emerges this splits into a semidirect product (this is demanded by Coleman-Mandula theorem). Is this what you mean?

2. You can't extend SL(2,C) to SO(10) or its double-cover because of the same reason, and in addition, because noncompact groups (SL(2,C)) can't be subgroups of compact groups (SO(10)).

 

Update: no, it is not true that $SO(3,1) = SU(2) \times SU(2)$. It is true for the complexified Lie algebras that $so(3,1) = d_2 = su(2) + su(2)$, but not true for the Lie groups. And I am not just being nitpicky, this is actually significant to LQG.

 

Here I guess you never seen this work done by Theiman back in 1997

https://arxiv.org/abs/gr-qc/9705019

 

which is funny as I was discussing this all along...I had to remember where I had read all this... the last set of equations did relate to the SL(2,C) problem you mentioned.  The paper has two solutions for this one being the Wicks rotation on the Wilson loops.

 Anyways as you can see the use of Wilson loops under the Loop formulation has been proposed to the UV and IR cutofffs I mentioned previously. This is what I have been discussing all along but I couldn't immediately jump the gun to simply posting the math without having some idea of your knowledge set. (It is a forum and you are a new member after all). Also I'm rusty on the loop formalism

 

You can see from this paper that such extensions to the matter fields have indeed been proposed before. Anyways if you do decide to return to the conversation then we can discuss the pros and cons directly related to the methodolies porposed by Thiemann in the above paper.

I noticed your update just now, let me get back to you on that one (edit: the last link addresses this) via the Wilson loop treatment under Wicks.

I need to review the steps for the SU(3) sub algebra under this treatment.

Edited August 26, 2017 by Mordred