Theoretician friendly character of Nature implies holography

I have been developing a model of hadrons based on the idea that hadrons involve both ordinary quarks and their dark counterparts (see this).

The basic idea is that Nature is theoretician friendly: when the perturbation series fails to converge, a phase transition increasing the value of h_eff=nh₀ takes place and reduces the value of gauge coupling strength proportional to 1/ℏ_eff. The color of the ordinary quarks q_o ("o" for "ordinary") must be neutralized by color entangling them with corresponding dark antiquarks q_d^c ("d" for "dark") at color magnetic body (MB) to form a color singlet (color for them is screened) . After that one adds to color MB dark variants q_d of quarks. This mechanism would actually apply quite generally to all elementary particles.

It came as a surprise that this principle actually realizes holography, which is a basic principle of TGD and implied by general coordinate invariance. The good news is that there is actually experimental evidence for this holography.

Theoretician friendly character of Nature implies holography

The two key ideas behind the proposal deserve restating.

1. Nature is theoretician friendly and guarantees the convergence of perturbation theory by h→ h_eff phase transition. The simple and perturbatively convergent dynamics at the level of MBs for the dark images X_d of the particles induces the dynamic of particles X_o by stable color quantum entanglement. The MB of the dark particle would be the boss and the dynamics of the ordinary particle would be shadow dynamics in accordance with the general vision about induction as the basic dynamical principle of TGD.

   One open question is whether the ordinary matter follows the dynamics of dark particles instantaneously or whether the time scales of the dynamics of dark matter and ordinary matter can be different in which case only the asymptotic states would realize the proposed correspondence between X_d and X_o.

2. It took some time to realize that the map of X_o to X_d based on colored entanglement is nothing but a concrete actualization of the quantal version of the TGD based holography. In the classical realization of this holography, the 3-D boundary of the space-time surface determines the space-time surface (tangent space data are not needed). In quantum realization, the states X_o are analogous to states at the 3-D boundary of space-time surface and states X_d to those in its interior. Instead of strings in the interior AdS₅ as in AdS/CFT correspondence, one has monopole flux tubes, indeed string like objects) in the interior of space-time carrying state X_d and X_o^c determine the dark state.
3. In the classical holography, 3-D surfaces carry holographic data fixing the 4-D complement of 4-surface (see this and this). Also 2-D string world sheets are involved and 1-D surfaces as orbits of boundaries of string world sheets at the light-like orbits of partonic 2-surfaces fix the interiors of string world sheets. An additional condition could be that the string world sheets are surfaces in H³ ⊂ M⁴⊂ M⁸. The pair of dark sea quarks and leptons would be delocalized at string worlds sheets associated with the color magnetic flux tubes. This is in accordance with the hadronic string model, which was one of the original motivations for TGD.

Theoretician friendly Nature would realize the quantum variant of the holography. An information theoretic view of elementary particles and of the relationship between ordinary and dark matter is suggestive. There is also an analogy with blackholes. States X_d are analogous to states in blackhole interior and states X_o to those at horizon.

Experimental support for the holography and for proton as an analog of blackhole

There is experimental evidence for the analogy of protons with a blackhole (see this) found from deep inelastic electron-proton scattering (DIS). The report (see this) of the research group led by theorists Krzysztof Kutak and Martin Hentschinski, published in European Physical Journal C, provides evidence for the claim that portions of proton's interior exhibit maximal quantum entanglement between constituents of photon.

The following statement of the report gives a rough idea of what is claimed.

"If a photon is 'short' enough to fit inside a proton, it begins to 'resolve' features of its internal structure. The proton may decay into particles as a result of colliding with this type of photon. We've demonstrated that the two scenarios are intertwined. The number of particles originating from the unobserved section of the proton is determined by the number of particles seen in the observed part of the proton if the photon observes the interior part of the proton and it decays into a number of particles, say three."

The abstract of (see this) gives a technical summary of the article.

"We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low x and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low x, which we obtain from an unintegrated gluon distribution subject to next-to-leading order Balitsky–Fadin–Kuraev–Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both next-to-next-to-leading order and next-to-next-to-leading with small x resummation, where the latter provides an acceptable description of data."

The following is my rough view of what the article says.

1. Deep inelastic scattering (DIS) is described in terms of photon exchange with momentum q a large value of q²=Q². The parton distribution functions at the low x limit, where x= X²/2p• q, (p denotes proton momentum). This limit corresponds to the perturbative high energy limit at which α_s<< 1 is true. The theoretical proposal is that DIS would only probe the parts of the proton wave function, which give rise to entanglement entropy. This entanglement characterizes correlation between the two parts of the system.
2. By theoretical arguments authors end up with a proposal that DIS at low x limit probes a maximally entangled state and a relation between parton number and final state hadron multiplicity. A more precise statement is that the partonic entropy S(x,Q²) coincides with the entropy S(h) of the final state hadrons in DIS. This means that parton and hadron pictures are dual. Mathematically this corresponds to the simple fact that entanglement entropies obtained by tracing over either entangled system are identical.
3. More concretely, the partonic entropy is given by S(x,Q²)=ln(≤n(ln(1/x,Q²)≥), where ≤n(ln(1/x,Q²)≥ is the average number of partons with longitudinal momentum fraction x. S(x,Q²) is deducible from the measured parton distribution functions. Also S(h) is deducible from experimental data.

With my amateurish understanding, I try to translate the proposed parton-hadron duality to the TGD framework.

1. The unseen parts of the proton are probed by virtual photons inducing a large enough momentum transfer Q². In standard quantum theory this corresponds by Uncertainty Principle to short distances. In TGD, large h_eff means that the size of the color MB of protons is scaled up by h_eff/h so that distances can be rather large as in the case of EMC effect.
2. Low x large Q² limit would more or less correspond to the dark part of proton for which h_eff is larger and α_s ∝ 1/ℏ_eff small. This suggests that the situation would be described in terms of dark scattering. This might hold true quite generally if the dynamics of the color magnetic MB dictates the dynamics of ordinary quarks.
3. The portions of proton would correspond to ordinary and dark parts of the proton. The maximal entanglement would correspond to the color entanglement between ordinary and dark quarks/partons. The counterpart of the blackhole entropy would be the entanglement entropy obtained when one integrates over the invisible dark degrees of freedom, which might, but need not, correspond to the parton sea. The integration over the dark degrees of freedom justifies the statistical approach of QCD used to describe hadrons.
4. The equality of partonic and hadronic entropies states simply the fact that the integration over partonic degrees of freedom (ordinary quarks) gives the same density matrix as the integration over hadronic degrees of freedom. Dark degrees of freedom would correspond to hadronic ones and ordinary degrees of freedom to partonic ones.
   See the article What it means if a Higgs-like particle decaying to eμ pairs exists? or the chapter with the same title.

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