Could large language models be useful in theory development?

OpenAI’s flagship ChatGPT O3 model (GPT in the sequel, see this) used here through the standard ChatGPT web interface underpins the research presented in the article by Marko Manninen and me (see this) paper. All questions were prompted in a single continuous session by Marko Manminen (see this) so that the model’s internal chain-of-thought engine could preserve context and build upon earlier reasoning steps. Whenever its pre-training knowledge proved insufficient, GPT launched its integrated browser to retrieve citable sources and anchor each claim in publicly available data. The first goal was to see how realistic answers GPT can give nowadays compared to the answers we got two and half years ago, when ChatGPT 3.5 was released. At that time, there was not much to report since the language models were at their early age without grounding. The second goal was to see whether GPT could be useful from the point of view of TGD. Notably, the TGD view of physics as number theory was not considered in this investigation as we thought it would definitely be too hard for any meaningful inference. 7 prompts were used. The first 3 prompts were questions related to the basic mathematical notions of TGD (see this and this) in the physics as geometry vision.

1. Explain in detail how the M⁴ times CP₂ geometry is induced to the spacetime surface in TGD and how the field equations are solved?
2. What does the holography= holomorphy (H-H) hypothesis mean in TGD?
3. What do induced geometry and induced spinor structure mean? What does the Dirac equation mean in TGD (use the latest material)

There were also 2 prompts related to the relation of TGD to other theories.

1. How does TGD differ from general relativity? How do TGD-inspired cosmology and astrophysics differ from what GRT predicts?
2. How does the particle physics predicted by TGD differ from that predicted by the Standard Model?

The last 2 prompts asked for criticism and tests of TGD and whether this kind of tests have been already carried out.

1. How should we stress test and attack this concept, be sceptic about?
2. Which of those tests have been already carried out?

The general conclusion was that the lack of real understanding and the learned attitudes leads to hallucinatory behavior and one cannot take responses of GPT seriously. However, GPT allows a bird’s eye view of large theoretic structures like TGD, developed over a long period of time. Although the objections represented by GPT turned out to be wrong, they forced a detailed study of the related parts of TGD landscape. This led to a considerable sharpening of the recent view of TGD, which has developed very rapidly during recent years and one can even say that TGD is now able to give the counterparts of Feynman rules. One can say that GPT does not lead to new discoveries but makes it possible to fill in the details. This GPT session is discussed in the article (see this).

Questions inspired by the analysis of the GPT session

The analysis created three kinds of questions related to the interpretation of TGD.

1. The idea (see this) about the phase transition between phases described in terms of Dirac equation in H resp. X⁴ as a generalization of the notion of the deconfinement phase transition resp. hadronization replaces the QCD type description with a stringy description in which the intersection of the space-time surfaces of colliding particles consisting of 2-D string worlds sheets determines the scattering amplitudes. In ZEO, this phase transition would involve two “big” state function reductions reversing the arrow of time and the time.
2. From the beginning it has been clear that color SU(3) is isometry group rather than gauge group and that its subgroup U(2) identifiable as a holonomy group acting on H spinors corresponds to a gauge group. The very definition of CP₂ as coset space states this geometrically.
   1. Could this mean the reduction of color confinement at the level of spinor quantum numbers to SU(2)_L confinement (see this)? Photons would not be confined, or screened by the pairs of right- and left handed neutrinos screening also the color of leptonic color partial waves (see this).
   2. Gluons do not appear as couplings of H spinors. Do gluons exist at all and is the identification of classical gluons as projections of Killing vectors wrong? Or do gluons correspond to electroweak gauge potentials in CP₂ spin degrees of freedom and would therefore correspond to electroweak interactions? But is this consistent with the fact that strong interactions are indeed strong?
3. A further stimulus came from the claim of GPT that already the existing data excludes copies of hadron physics labelled by Mersenne primes and their Gaussian variants. Is this really the case and are the earlier indications about bumps (see this and this) wrong?
   1. Under what conditions does the phase transition between M₁₀₇ and M₈₉ hadron physics occur with a significant rate?
   2. Is quantum criticality, forcing the Compton scales of ordinary hadrons and dark M₈₉ hadrons to be identical, necessary? This is indeed assumed in the model for the bumps as M₈₉ mesons reported at LHC. If so, the transition from M₁₀₇ H phase to X⁴ phase would occur in the first BSFR and the transition from the X⁴ phases to X⁴ phase to M₈₉ H phase would take place in the second BSFR. Just as in TGD inspired biology, the increase of the h_eff by factor 512 would require “metabolic” energy feed increasing the quark energies proportional to h_efff by this factor. This energy would come from the collision energy of colliding heavy nuclei. The decay of M₈₉ hadrons to M₁₀₇ hadrons would occur spontaneously. This kind of decay at the surfaces of the Sun is proposed to be responsible for the generation of solar wind and solar energy (see this).
   3. Is the assumption about the labelling of scaled variants of hadron physics by nuclear p-adic length scales too restricted since hadrons (say pions) are labelled also by other p-adic length scales than that of nucleon?
   4. Could the hierarchy of hadron physics correspond to the hierarchy color representations for quarks and leptons in 1-1 correspondence and labelled by single integer k appearing in the solution spectrum of the Dirac equation in H. If so, hadrons and leptons for a given value of k could correspond to several p-adic primes?

Progress in the understanding TGD view of the relation between electroweak and strong interactions

TGD view predicts at the fundamental level strong correlations between electroweak and strong interactions. But the precise understanding of these correlations has developed rather slowly. The writing of the comments to the GPT prompts was a rather exhaustive process but it was not a waste of time. It led to considerable progress in this respect. Gluon couplings do not appear in Dirac equations and in (see this) the possibility that there are no gluon vertices at the fundamental level was discussed so that somehow electroweak couplings also describe strong interactions. The recent general view of interactions allows to make these considerations much more detailed.

1. Also for X⁴ Dirac equation one obtains quark color and it would correspond to conformal modes proportional to (ξ₁,ξ₂,1) possible for the induced Dirac equation and perhaps having interpretation as reduction of color triplet to U(2) doublet plus singlet. The triplet corresponds to different coordinate patches of CP₂ to which the three Z₃ poles can be assigned. Therefore one obtains annihilation to quark pairs in this sense. Conformal invariance could make higher modes gauge degress of freedom.
2. As noticed, a long standing puzzle has been the fact that electroweak U(2) has a holonomy group of CP₂ is the maximal compact subgroup of SU(3). Could one see electroweak interactions as an aspect of color interactions or vice versa? Could one say that there is a symmetry breaking reducing isometry group SU(3) to its subgroup U(2) identifiable as holonomy group and an electroweak gauge group? Could CP₂= SU(3)/U(2) realize the gauge group nature of U(2) geometrically. Could electroweak confinement by the pairs of left and right-handed neutrinos screening the weak isospin correspond to SU(2)_L⊂ SU(3) confinement in spin degrees of freedom. There would be no color confinement for photons associated with U(1). Full color confinement would take place for the light states formed from the H spinor modes.
3. Why are strong interactions strong? The annihilation rate to quark pairs by the proposed vertices is sum of three pairs and the rate is 9 times higher than for the annihilation to leptons. The electroweak coupling strength is of order α_em=1/137 so that the rate for quark pair production corresponds to α_s= 9α_em∼ .1. This would give a correct order of magnitude estimate!
4. Old-fashioned hadron physics talked about conserved vector currents (CVC) and partially conserved axial currents (PCAC). These notions emerged from the observations that hadronic reaction rates can be expressed in terms of correlations of electroweak currents. This raises the question whether the strong interaction could reduce to electroweak interactions in some sense (see this).
5. What happens to the scaled up variants of hadron and electroweak physics if strong and electroweak physics fuse to whatever one might call it (unified physics?)? The only way to understand why the range of strong interactions is given by the hadronic length scale is that strong interactions would correspond to electroweak interactions in p-adic length scales, which correspond to hadrons and possibly also quarks. Weak bosons should correspond to a much longer Compton scale. Nucleons would correspond to the p-adic length scale L(107) and pions to M(113). The original view of weak bosons was that weak interactions correspond to the scale L(89) corresponding to Mersenne prime. Weak boson mass scales turned out to correspond to L(91) However, the original view is rather attractive and would fit with the view that M₈₉ hadron physics fuses with ordinary electroweak physics and several p-adic length scales are involved with a given copy. The copies of this unified physics in turn could correspond to color partial waves for Dirac equation in H. Electro-weak bosons would be special kinds of mesons in the sense that they are superpositions of both quark and lepton pairs. Photon would be even more special in that SU(2)⊂ SU(3) confinement would not apply to it because U(1) is abelian.

The scaling hypothesis, stating that the mass scales of mesons are scaled by a factor 512 in the transition M₁₀₇→ M₈₉, is probably too strong but gives testable predictions to start with.

1. One key question concerns the M₁₀₇ counterparts of weak bosons. They would correspond to genus g=0 (u and d quarks). A naive scaling of masses by factor 1/512 would give a mass scale near 500 MeV. There is no report about the observation of these bosons. For ρ meson the mass scale without QCD hyperfinite splitting induced by color magnetism is around 500 MeV. Are these weak bosons separate from ρ assumed to involve only quark pairs or do they correspond to ρ? For the latter option their decays to leptons should reveal this.
2. What about pseudoscalar π accompanying ρ? Standard model does not predict pseudoscalar electroweak boson. Its counterpart for M₈₉ should exist. Evidence is reported for the existence of a pseudoscalar at the intermediate boson mass scale. For k=113, assignable to the Mersenne prime of the nucleus, one obtains the mass estimate 6.3 MeV. There is strong evidence for Xboson with mass around 7 MeV and I have considered the interpretation as a weak boson.
3. What about M₁₀₇ counterpart of Higgs scalar with mass of 125 GeV? By a naive scaling, it should have mass about 250 MeV. The are many candidates candidates for scalar mesons (see this) but they have masses above the mass 500 MeV of sigma boson whose existence is still not confirmed. σ is a very broad Breit-Wigner type resonance, which does not support interpretation as a scaled down Higgs boson. For k=113 the mass should be around 31 MeV.

See the article Could large language models be useful in theory development? by Marko Manninen and m.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.