Quantum hydrodynamics in nuclear physics and hadron physics

The field equations of TGD defining the space-time surfaces have interpretation as conservation laws for isometry charges and therefore have a hydrodynamics character. The hydrodynamic character is actually characterized in quite concrete ways (see this, this, and this).

Also nuclear and hadron physics suggest applications for Quantum Hydrodynamics (QHD). The basic vision about what happens in high energy nuclear and hadron collisions is that two BSFRs take place. The first BSFR creates the intermediate state with h_eff>h: the entire system formed by colliding systems need not be in this state. In nuclear physics this state corresponds to a dark nucleus which decays in the next BSFR to ordinary nuclei.

The basic notions are the notion of dark matter at MB and ZEO, in particular the change of the arrow of time in BSFR.

1. Cold fusion, nuclear tunnelling, ℏ_eff, and BSFRs

This model allows us to understand "cold fusion" in an elegant manner (see this, this, and this). The dark protons at flux tubes associated with water and created by the Pollack effect have much smaller nuclear binding energy than ordinary nucleons. This energy is compensated to a high degree by the positive Coulomb binding energy which corresponds roughly to distance given by electron Compton length.

Dark nuclear reactions between these kinds of objects do not require large collision energy to increase the value of h_eff and can take place at room temperature. After the reaction the dark nuclei can transform to ordinary nuclei and liberate the ordinary nuclear binding energy. One can say that in ordinary nuclear reactions one must get to the top of the energy hill and in "cold fusion" one already is at the top of the hill.

Quite generally, the mechanism creating intermediate dark regions in the system of colliding nuclei in BSFR, would be the TGD counterpart of quantum tunnelling in the description of nuclear reactions based on Schrödinger equation. This mechanism could be involved with all tunnelling phenomena.

2. QHD and hadron physics

Hadron physics suggests applications of QHD.

2.1 Quark gluon plasma and QHD

In hadron physics quark gluon plasma (see this) has turned out to be what it was thought to be originally. Instead of being like a gas of quarks and gluons with a relatively large dissipation, it has turned out to behave like almost perfect fluid. This means that the ratio η/s of viscosity and entropy is near to its minimal value proposed by string model based arguments to be η/s=ℏ/m.

To be a fluid means that the system has long range correlations whereas in gas the particles move randomly and one cannot assign to the system any velocity field or more general currents. In the TGD framework, the existence of a velocity field means at the level of the space-time geometry generalized Beltrami flow allowing to define a global coordinate varying along the flow lines (see this and this). This would be a geometric property of space-time surfaces and the finite size of the space-time surface would serve as a limitation.

In the TGD framework the replacement ℏ→ ℏ_eff requires that s increases in the same proportion. If the fluid flow is realized in terms of vortices controlled by pairs of monopole flux tubes defining their cores and Lagrangian flux tubes with gradient flow defining the exteriors of the cores, this situation is achieved.

In this picture entropy could but need not be associated with the monopole flux tubes with non-Beltrami flow and with non-vanishing entropy since the number of the geometric degrees of freedom is infinite which implies limiting temperature known has Hagedorn temperature T_H which is about 175 MeV for hadrons, and slightly higher than pion mass. In fact, the Beltrami property holds for the flux tubes with 2-D CP₂ projection, which is a complex manifold for monopole flux tubes. The fluid flow associated with (controlled by) the monopole flux tubes would have non-vanishing vorticity for monopole fluxes and could dissipate.

The monopole flux tube at the core of the vortex could therefore serve as the source of entropy. One expects that η/s as minimal value is not affected by h→ h_eff. One expects that s → (ℏ_eff/ℏ)s= ns since the dimension of the extension of rationals multiplies the Galois degrees of freedom by n.

Almost perfect fluids are known to allow almost non-interacting vortices. For a perfect fluid, the creation of vortices is impossible due to the absence of friction at the walls. This suggests that the ordinary viscosity is not the reason for the creation of vortices, and in the TGD picture the situation is indeed this. The striking prediction is that the masses of Sun and Earth appear as basic parameters in the gravitational Compton lengths Λ_gr determining ν_gr= Λ_grc.

2.2 The phase transition creating quark gluon plasma

The phase transition creating what has been called quark gluon plasma is now what it was expected to be. That the outcome behaves like almost perfect fluid was the first example. TGD leads however to a proposal that since quantum criticality is involved, phases with ℏ_eff>h must be present.

p-Adic length scale hypothesis led to the proposal (see this and this) that this transition could allow production of so called M₈₉ hadrons characterized by Mersenne prime M₈₉=2⁸⁹-1 whereas ordinary hadrons would correspond to M₁₀₇. The mass scale of M⁸⁹ hadrons would be by a factor 512 higher than that of ordinary hadrons and there are indications for the existence of scaled versions of mesons.

How M₈₉ hadrons could be created. The temperature T_H= 175 MeV is by a factor 1/512 lower than the mass scale of M₈₉ pion. Somehow the colliding nuclei or hadrons must provide the needed energy from their kinetic energy. What certainly happens is that this energy is materialized in the ordinary nuclear reaction to ordinary pions and other mesons. The mesons should correspond to closed flux tubes assignable to circular vortices of the highly turbulent hydrodynamics flow created in the collision.

Could roughly 512 mesonic flux tubes reconnect to circular but flattened long flux tubes having length of M₈₉ meson, which is 512 times that of ordinary pions? I have proposed this kind of process, analogous to BEC, to be fundamental in both biology (see this, this, and this) and also to explain the strange findings of Eric Reiter challenging some basic assumptions of nuclear physics if taken at face value (see this).

The process generating an analog of BEC would create in the first BSFR M₈₉ mesons having ℏ_eff/ℏ=512. In the second BSFR the transition ℏ_eff→ ℏ would take place and yield M⁸⁹ mesons. It would seem that part of the matter of the composite system ends up to n M₈₉ hadronic phase with 512 times higher T_H. In the number theoretic picture, these BEC like states would be Galois confined states (see this and this).

2.3 Can the size of a quark be larger than the size of a hadron?

The Compton wavelength Λ_c= ℏ/m is inversely proportional to mass. This implies that the Compton length of the quark as part of the hadron is longer than the Compton length of the hadron. If one assigns to Compton length a geometric interpretation as one does in M⁸-H duality mapping mass shell to CD with radius given by Compton length, this sounds paradoxical. How can a part be larger than the whole? One can think of many approaches to what might look like a paradox.

One could of course argue that being a part in the sense of tensor product has nothing to with being a part in geometric sense. However, if one requires quantum classical correspondence (QCC), one could argue that a hadron is a small region to which much larger quark 3-surfaces are attached.

One could also say that Compton length characterizes the size of the MB assignable to a particle which itself has size of order CP₂ length scale. In this case the strange looking situation would appear only at the level of MBs and the magnetic bodies could have sizes which increase when the particle mass decreases.

What if one takes QCC completely seriously? One can look at the situation in ZEO.

1. The size of the CD corresponds to Compton length and CDs for different particle masses have a common center and form a Russian doll-like hierarchy. One can continue the geodesic line defining point of CD associated with the hadron mass so that it intersects the CDs associated with quarks, in particular that for the lightest quark.
2. The distances between the quarks would define the size scale of the system in this largest CD and in the case of light hadrons containing U and D quarks it would be of the order of the Compton length of the lightest quark involved having mass about 5 MeV: this makes about .2 × 10^-13 m. There are indeed indications that the MB of proton has this size scale.

One could also require that there must be a common CD based on such an identification of h_eff for each particle that its size does not depend on the mass of the particles.

1. Here ℏ_gr= GMm/β₀ provides a possible solution. The size of the CD would correspond to Λ_gr =GM/v₀ for all particles involved. One could call this size the quantum gravitational size of the particle.

2. There is an intriguing observation related to this. To be in gravitational interaction could mean ℏ_eff=ℏ_gr=GMm/v₀ so that the size of the common CD would be given by Λ_gr= GMm/v₀. The minimum mass M given ℏ_gr>ℏ would be M=β₀ M_Pl²/m. For protons this gives M ≥ 1.5 × 10³⁸ m_p. Assuming density ρ ≈ 10³⁰A/m³, A the atomic number, the length L for the side cube with minimal mass M is L×β₀× 10²/A^1/3. For β₀= 2^-11 assignable to the Sun-Earth system, this gives L∼ 5/A^1/3 mm. The value of Λ_gr for Earth is 4.35 mm for β₀=1. The orders of magnitude are the same. Is this a mere accident?

One solution to the problem is that the ratio ℏ_eff(H)/ℏ_eff(q) is so large that the problem disappears.

1. If ℏ_eff(1)=ℏ, the value of ℏ_eff for hadron should be so large that the geometric intuitions are respected: this would require h_eff/h;≥ m_H/m_q. The hadrons containing u, d, and c quarks are very special.
2. Second option is that the value of h_eff for quarks is smaller than h to guarantee that the Compton length is not larger than ℏ. The perturbation theory for states consisting of free quarks would not converge since Kähler coupling strength α_K ∝ 1/ℏ_eff would be too large. This would conform with the QCD view and provide a reason for color confinement. Quarks would be dark matter in a well-defined sense.
3. The condition would be ℏ_eff(H)/ℏ_eff(q)≥ m(H)/m_q, where q is the lightest quark in the hadron. For heavy hadrons containing heavy quarks this condition would be rather mild. For light hadrons containing u,d, and c quarks it would be non-trivial. Ξ gives the condition ℏ/ℏ_eff≥ 262. The condition could not be satisfied for too small masses of the value of ℏ= 7!ℏ₀=5040ℏ₀ identifiable as the ratio of dark CP₂ deduced from p-adic mass calculations and Planck length.

See the article TGD and Quantum Hydrodynamics or the chapter chapter with the same title.

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

Articles and other material related to TGD.