Could this unified theory be correct?

[carl_sebastian]

First they got the higgs mass wrong (according to 2 independent measurements) but later they found a way to get the correct mass (after the mass already had been determined via LHC).

https://arxiv.org/abs/hep-th/0610241
https://arxiv.org/abs/1208.1030

The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.

a main advantage of the model is that it gives a geometric interpretation for all the parameters in the standard model. In particular, this leaves room for predictions about the Yukawa couplings, through the geometry of the Dirac operator.

This looks too good to be true to me.

 

[MathematicalPhysicist]

As you said first they got it wrong then they fixed it, sounds dubious to me.

 

[carl_sebastian]

As you said first they got it wrong then they fixed it, sounds dubious to me.

It looks very bad.

But if it is the case that their theory predicts the correct higgs mass and the theory was published before the LHC discovery (assuming they didn't make a mistake at cern) it would still be very impressive assuming they havn't changed the underlying theory.

But of course we would look into if their theory actually gives the details of the standard model as they claim.

We should also see if their theory could explain the following
-apparent dark matter.
-accelerated expansion of our universe.
-the collapse of the wave-function.

I didn't see them go into these things in the paper.

 

[Auto-Didact]

[hep-th/0610241] Gravity and the standard model with neutrino mixing
[1208.1030] Resilience of the Spectral Standard Model

These papers are on Alain Connes' infamous non-commutative geometry. More specifically, they are on non-commutative geometry applied to the Standard Model of particle physics together with gravitation: the particular model presented in these papers is called the Spectral (Standard) Model.

The equations of the original paper and the final paper are identical: the difference is that the original paper incorrectly makes an assumption - purely for mathematical simplification purposes - that one of the scalar fields coupled to the Higgs field could be integrated out. This, while several others already had shown before that due to nontrivial interactions between these two fields that making such a simplification is impossible i.e. that the original assumption of Connes et al. to integrate out the scalar field is incorrect.

The latter paper then removes this assumption and recalculates this nontrivial coupling between the fields based on how it was already calculated by several others: when Connes et al. do this they predict the correct Higgs mass within known experimental accuracy; this achievement in itself is nothing short of a miracle. It should be noted that this unique model predicts specifically the existence of three scalar fields: the Higgs field, the singlet field and the dilaton field.

If string theory or any other BtSM theory could do anything like what non-commutative geometry has achieved here, we would read about it in the headlines of all newspapers on Earth and Nobel prizes would be flying left and right to string theorists.

 

[carl_sebastian]

These papers are on Alain Connes' infamous non-commutative geometry. More specifically, they are on non-commutative geometry applied to the Standard Model of particle physics together with gravitation: the particular model presented in these papers is called the Spectral (Standard) Model.

The equations of the original paper and the final paper are identical: the difference is that the original paper incorrectly makes an assumption - purely for mathematical simplification purposes - that one of the scalar fields coupled to the Higgs field could be integrated out. This, while several others already had shown before that due to nontrivial interactions between these two fields that making such a simplification is impossible i.e. that the original assumption of Connes et al. to integrate out the scalar field is incorrect.

The latter paper then removes this assumption and recalculates this nontrivial coupling between the fields based on how it was already calculated by several others: when Connes et al. do this they predict the correct Higgs mass within known experimental accuracy; this achievement in itself is nothing short of a miracle. It should be noted that this unique model predicts specifically the existence of three scalar fields: the Higgs field, the singlet field and the dilaton field.

If string theory or any other BtSM theory could do anything like what non-commutative geometry has achieved here, we would read about it in the headlines of all newspapers on Earth and Nobel prizes would be flying left and right to string theorists.

It's a bit strange i didn't hear about this theory earlier, looks very promising.

There are a lot of details in the standard model you have to get right and if you are using a proper approach for a fundamental theory and get all details correct it's actually very likely your theory correct.

in Comparison there are 10^172000 versions of string theory and they haven't found a single one that actually gives us all the details of the standard model.

 

[nrqed]

These papers are on Alain Connes' infamous non-commutative geometry. More specifically, they are on non-commutative geometry applied to the Standard Model of particle physics together with gravitation: the particular model presented in these papers is called the Spectral (Standard) Model.

The equations of the original paper and the final paper are identical: the difference is that the original paper incorrectly makes an assumption - purely for mathematical simplification purposes - that one of the scalar fields coupled to the Higgs field could be integrated out. This, while several others already had shown before that due to nontrivial interactions between these two fields that making such a simplification is impossible i.e. that the original assumption of Connes et al. to integrate out the scalar field is incorrect.

The latter paper then removes this assumption and recalculates this nontrivial coupling between the fields based on how it was already calculated by several others: when Connes et al. do this they predict the correct Higgs mass within known experimental accuracy; this achievement in itself is nothing short of a miracle. It should be noted that this unique model predicts specifically the existence of three scalar fields: the Higgs field, the singlet field and the dilaton field.

If string theory or any other BtSM theory could do anything like what non-commutative geometry has achieved here, we would read about it in the headlines of all newspapers on Earth and Nobel prizes would be flying left and right to string theorists.

Is it possible to briefly summarize here what are the numerical inputs they use to calculate the Higgs mass?

 

[arivero]

If string theory or any other BtSM theory could do anything like what non-commutative geometry has achieved here, we would read about it in the headlines of all newspapers on Earth and Nobel prizes would be flying left and right to string theorists.

Ah, but NCG theory fails to predict supersymmetry

 

[phyzguy]

Ah, but NCG theory fails to predict supersymmetry

You say this as though it were a negative. Since there is no evidence for supersymmetry, despite years of looking, this could be viewed as a positive aspect of the theory. It doesn't predict something that doesn't exist.

 

[nrqed]

You say this as though it were a negative. Since there is no evidence for supersymmetry, despite years of looking, this could be viewed as a positive aspect of the theory. It doesn't predict something that doesn't exist.

I may be wrong but I took arivero's post as being tongue in cheek. With the implied meaning that this is actually a pro for NCG. But I may be completely wrong.

 

[Vanadium 50]

Since there is no evidence for supersymmetry

What do you mean there's no evidence? We've found half the particles!

 

[phyzguy]

I may be wrong but I took arivero's post as being tongue in cheek. With the implied meaning that this is actually a pro for NVG. But I may be completely wrong.

Ah. Perhaps I missed the sarcasm.

 

[arivero]

Ambiguous sarcasm, intentionally. On one hand, it is positive that the theory does not find supersymmetry. On the other hand, I think we should understand how and why does it fail to produce SUSY.

Note that the spectral triple is, (mod 8), ten dimensional, so one could think that it has guessed the string theory extra dimensions. So it could be just as the non-susy superstring theories.

My -personal and opinionated- guess is that it is related to other problem of NCG as a final theory: the prediction of the number of generations. Some models of NCG were able to force n > 1, to produce consistent not trivial spectral triples. But there is no reason for n=3.

 

[mfb]

Where is an experimentally testable prediction with a clear error bar (that was not discovered after a measurement with more precision has been made)? Something that deviates from the SM or cannot be predicted by the SM, of course - reproducing SM predictions is necessary anyway.

 

[mitchell porter]

when Connes et al. do this they predict the correct Higgs mass within known experimental accuracy

They do not predict, or even retrodict, the correct mass. They only show that it lies within their parameter space, see figure 2. The only noncommutative model that directly gives the right mass, is one by Marcolli and a student, which uses the mechanism of asymptotic safety (as in Shaposhnikov & Wetterich 2009).

 

[carl_sebastian]

Review of this model:
https://www.physicsforums.com/insights/spectral-standard-model-string-compactifications/
Newer model that claims to get dark matter particles and the correct higgs mass:
https://iopscience.iop.org/article/10.1088/1367-2630/17/2/023021/meta

 

[Auto-Didact]

They do not predict, or even retrodict, the correct mass. They only show that it lies within their parameter space, see figure 2.

Indeed. Just by eyeballing figure 2 though, 125.5 GeV does pretty much lie on the 'mean value' line within the parameter space, which a posteriori naturally suggests a conjecture that some stationarity principle might come into play as a selection mechanism; the correct enlargement of the parameter space should enable a bifurcation analysis to validate or falsify this conjecture, but I'm assuming this has already been done and falsified.

Review of this model:
https://www.physicsforums.com/insights/spectral-standard-model-string-compactifications/

Urs' review is pretty enlightening; it shows again a reoccurring trend in mathematical physics, namely that by honestly following applied methodology based on pure mathematics from extremely different starting points - beginning in seemingly completely separate areas of mathematics - to their logical end, the answers can suddenly spontaneously begin to converge in a very unique and exact manner.

I suspect most mathematicians of course know this feeling quite well and have an aesthetic appreciation for it: the sense of the unity of mathematics. Penrose calls such unexpected successful unifications in mathematics 'miracles' and has written on the psychological effect that they clearly have on mathematical researchers, even after a generalization showing the miracle to be purely coincidental; it goes without saying that such miracles of course also seem to be what drives the unerring faith among string theorists.