Marko Manninen sent me a highly interesting link to the work of Prof. Anca Tureanu (see this), who challenges the prevailing standard physics view of neutrinos (see this).

Why the neutrino physics goes wrong?

Also in my opinion, the theoretical physics picture of neutrinos is wrong.

  1. Both neutrinos and quarks mix: we talk about CKM mixing. Neutrinos are no different from d-quarks in this respect. The mixing model for neutrinos coming from the Sun is in serious trouble. It assumes resonant mixing inside Sun and this is a completely ad hoc feature. This, along with many other anomalies, calls into question the entire view of the Sun's nuclear physics, on which the repeated failed attempts to build hot fusion reactors are based (see this). Strictly speaking, both U and D quarks as well as charged leptons and neutrinos mix: the difference in mixing corresponds to CKM mixing. What mixing is, is a complete mystery in the Standard Model.

    In TGD, mixing is reduced to topological mixing between different topologies of 2-dimensional parton surfaces (see for instance this). A sphere, a torus, and a sphere with 2 handles define the relevant parton topologies. For example, a torus collapses into a sphere in a mixing and a quantum state is a superposition of different topologies. TGD explains why there are 3 generations (why there couldn't be 3 handles, for example) and p-adic thermodynamics correctly predicts masses for different generations. Higher generations would be many particle systems of handles with continuum mass spectrum.

  2. One problem is whether neutrinos are massless or not. There is strong evidence for their massivation and in TGD the masses can be predicted by p-adic thermodynamics (see this, this, this, this and this).

    However, a right-handed neutrino has one exactly massless mode (see this) and this), which is color singlet but also an infinite number of colored modes like other fermions which are associated with color singlet physical states. Color confinement therefore applies also to leptons. The new view of color leads to the prediction of a hierarchy of copies of Standard Model physics (see this). There is already support for this prediction.

    The problem with masses is more general: also quarks are effectively massless in quark-gluon plasma but massive in initial and final states. The concept of quark-gluon plasma seems to be a much more general notion than believed. The proper understanding of this notion could allow us to get out from the confines of QCD and the standard model. TGD indeed leads to a new view of what happens in particle reactions and generalizes the quark-gluon-plasma state to all particles (see this).

  3. There is also the problem of the inert neutrino. It begins to be clear that there is no such thing as an inert neutrino. But the observations require something new to explain the observations. The observations are explained if neutrinos can be in a "dark" heff> h states (see this). Similar darkstate for protons, playhing a key role in TGD based quantum biology, explains the anomalous finding that the life-tme of a neutron depends on the way it is measured (see this).

The claims of Anca Tureanu

I looked at Anca Tureanu's article (see this). In the article, Tureanu claims that there is a logical contradiction in neutrino physics.

  1. The reaction rates are calculated by considering incoming and outgoing neutrinos as mass eigenstates. In contrast, in neutrino mixing observed in laboratory experiments, quantum coherent superpositions of neutrino generations of different masses are assumed in the model of mixing. The model can be tested in laboratory experiments.

    The mixing model is applied to the solar neutrinos inside the Sun. One has to make a very ad hoc assumption about a resonance arising in the interaction with the environment (low energy neutrinos interact extremely weakly). Quarks are also mixed in incoming and outgoing states, but they are assumed to be eigenstates of mass. Note that we cannot study the possible dynamic mixing of quarks in the laboratory.

  2. Can neutrino states with different masses be in quantum superposition? Or do they have to be massless for this to be possible? In what sense would they be massive? Tureanu proposes that neutrinos are massless but that in some sense also massive.

    The proposal is that the phenomenon is analogous to birefringence, which occurs in an insulator, where the dielectric constant for photons coming in perpendicular directions is different. The velocity of propagation is light speed c#< c as in the case of a massive particle. The different polarizations of the incoming light are refracted differently because the speeds of light are different. The light beam splits into two beams travelling in different directions. In birefringence, the polarizations move at speeds v1<c and v2<c. In this sense there is a superposition of photons with different masses.

    What about neutrinos? Instead of two polarizations for neutrinos, there would be 3 different generations moving at different speeds v1, v2, v3 <c in a substance that would be analogous to a birefringent substance. This would give them an effective mass. The polarization direction would be replaced by mass. Now there would be no refraction.

The basic claim of Anca Tureanu and the notion of warping

How does this relate to TGD?

  1. One of the fundamental differences between TGD and GRT are warped 4-surfaces, which are gravitationally and electroweak vacuums but for which the speed of light c# is less than c (see this). The surfaces are analogous to a thin metal plate that is unstable and vibrates, but does not stretch. This means that the light signals along the surface propagate more slowly because the distance between two points is longer.
  2. The simplest example of a warped (and therefore flat) space-time surface is obtained by considering a geodesic circle of CP2 with radius R and angle coordinate Φ. Denote the Minkowski coordinates of M4 with mk and the coordinates of space-time surface X4 by xα. The 4-surface is defined as a map X4 → H=M4× CP2 given by (mk= δkαxα, Φ= ω x0), where k=(ω,0,0,0) is time-like vector. The time-like geodesic of M4 is mapped to a light-like geodesic of H. The induced metric is gαβ ↔ (1-R2ω2,-1,-1,-1) =((c#/c)2,-1,-1,-1). The light velocity is reduced to c#/c=(gtt)1/2= (1-R2ω2)1/2. Note that Lorentz transformations produce additional solutions.

    The square of M4 projection of the 4-velocity dmk/dx0 equals constant R2ω2 just as for a massive particle. Therefore warping has two interpretations. Particles are massless in the induced metric of X4. They are also massless in the metric of H but massive in the metric of M4.

    This generalizes from the level of flat space-time surfaces to the level of Hamilton-Jacobi structures (see this) and does not need to be limited to flat 4-surfaces.

  3. There is actually empirical evidence for the warping from neutrino physics. In the case of SN1987A, the neutrinos arrived in two pulses (see this). I explained this using different warpings of the space-time sheets along which the neutrinos of pulses arrived. Quite recently, it turned out that warping also provides an elegant model for the Allais effect.
  4. Ordinary refraction for electromagnetic waves would occur at the interface of two regions with different c#. The phenomenon would be completely general and also occur for fermions (in TGD all particles are composed of fundamental fermions). In particular, massless neutrinos.

    In birefringence, different spin directions would be associated with different c# values. Could there be substances, where this would happen for fermions as well. Polarizations would correspond to different helicities (M4 chiralities) correlating with CP2 chirality by fermion number conservation.

  5. It however seems that in some sense neutrinos are massless and in some sense massive. This is a paradox. In TGD this is true for all particles. Initial and final many particle states are 8-D and particle states in interaction volume are 4-D.

    In the interaction volume the system is a 4-D surface and fermions fulfill the analogy of the 4-D massless Dirac equation. From the initial and final states of scattering fermions fulfill the 8-D Dirac equation and are massless in the 8-D sense but massive in the 4-D sense. This would generalize the notions of hadron phase and quark-gluon plasma phase so that it applies to all particles. Hadrons appear in the 8-D initial and final states and quarks appear in the 4-D interacting states. Color confinement occurs for both quarks and leptons and there is an infinite hierarchy of standard model physics since there is infinite hierarchy of color partial waves in CP2 for both quarks and leptons.

  6. The 4-surfaces associated with fermions would be massless but characterized by the reduced speed of light c#. Like photons, they would have an effective mass in the interaction volume. Warping gives a precise formulation of the intuition that fermions, in particular neutrinos, are massless in both H and X4 but massive in M4. Different neutrinos in 4-D states would be associated with different values of c#: this would be the counterpart for M4 massivation. p-Adic thermodynamics allows us to calculate the M4 masses as thermodynamic expectation values (see this, this, this, this and this).

Particle massivation and warping

The light-like geodesics of H assigned with the fermion line at the partonic orbit provides a model for the M4 mass squared of particles given as m2= k2R2ω2. This does not require that the space-time surface is a warped flat 4-surface everywhere and thus conforms with the idea that warped Hamilton-Jacobi structures for which M4 and CP2 degrees of freedom are coupled. However, the information about the warping would be coded for the Bohr orbits of the particles by the light-like geodesics at partonic orbits.

  1. If ω is identified as a Compton frequency for particle with mass m so that one has k= ℏeff/R and m= ℏeffω giving c#2= 1-R2ω2= 1-R2m2/ℏeff2= 1-R2/λc2, where λc is the Compton length for heff. This predicts the value of c#== β0 once particle mass and heff are known.
  2. The signature of the metric remains Minkowskian for ℏeff/m>R. For heff=h this requires that the particle mass is below CP2 mass. The stringy mass squared spectrum predicted by generalized super conformal symmetry allows larger mass and for these masses the value of heff>h is required to avoid tachyonicity.
  3. One can consider the situation for the electric Planck constant ℏem= Qq/β0 and gravitational Planck constant ℏgr= rsm/2β0. In these cases the value of c# is completely fixed. In the electric case, one has c#2= 1-R2m2c#2/Q2q2 giving c#/c= (1/(1+R2m2/Q2q2))1/2 and c# depends on the particle mass. The gravitational case gives c#/c= (1/(1+4R2/rs2))1/2. There is no dependence on the mass m: this reflects the Equivalence Principle.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD or the chapter with the same title.

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.