One of my first speculative applications of the evolving TGD view of dark matter (roughly 15 years ago) and of the TGD based interpretation of the Nottale's formula for the gravitational Planck constant, was the proposal that could be interpreted as a TGD counterpart for a Bohr orbit, not as an orbit but a spherical layer (see this and this.
At that time I had no ideas about number theoretic interpretation of the dark matter hierarchy nor a general view of the formation of astrophysical objects in terms of a transformation of dark energy of cosmic strings to dark matter at monopole flux tubes in turn transforming to the ordinary matter (see this).
The recent view of the formation of planets and their moons and rings indeed allows spherical layers having as representative Oort clouds; torus-like flux tubes having as representative the rings of Jupiter; and ordinary planets.
- They would be formed in a phase transition in which the gravitationally dark matter associated with a bubble formed by monopole flux tubes transforms to ordinary matter and can be also localized to lower dimensional structure. The analog of localization in state function reduction in astrophysical scale taking place in measurement would be in question. For instance, the formation of a planet would correspond to a measurement of a momentum direction and radial distance for a delocalized state described approximately by the analog of hydrogen atom wave-function.
- The Nottale model predicts that the inner planets Mercury, Venus and Earth correspond to Bohr orbits with n=3,4,5 . What about n=1 and n=2 orbits? For Earth one has n=5 and from the radius of Earth orbit, which is AU = 1.5× 108 km by definition, the radius of n=1 orbit given by gravitational Bohr radius agr and is agr=AU/25 ≈ 6.0× 106 km. The radius of the photosphere is R= 6.96× 106 km giving agr/R≈ .87. n=1 Bohr orbit or Bohr shell with radius R1= agr would be just below the photosphere. n=2 Bohr orbit would correspond to the radius R2= 2.4× 107 km. Is there any evidence for a spherical layer or a a ring, at this distance?
- If the mass of the layer of thickness Δ R is the same as that of Mercury (.055× ME) with radius RM= .38× RE and the density of the layer is the same as that of Earth, one obtains the estimate Δ R= (RM/R1)2 RM/3≈ 3.2 m. The layer would be extremely thin. If the mass is Earth's mass, Δ R increases by the factor .383, roughly by two orders of magnitude.
- There was already 17 years ago evidence that there is a solid surface with radius of n=1 Bohr orbit. Recently new satellites have begun to provide information about what lurks beneath the photosphere. The pictures produced by Lockheed Martin's Trace Satellite and YOHKOH, TRACE and SOHO satellite programs are publicly available on the web. SERTS program for the spectral analysis suggests a new picture challenging the simple gas sphere picture \cite{bcast/Moshina}.
The visual inspection of the pictures combined with spectral analysis has led Michael Moshina to suggests that Sun has a solid, conductive spherical surface layer consisting of calcium ferrite. The article of Moshin provides impressive pictures, which in my humble non-specialist opinion support this view. Of course, I have not worked personally with the analysis of these pictures so that I do not have the competence to decide how compelling the conclusions of Moshina are. In any case, I think that his web article (this) deserves a summary.
- Before SERTS people were familiar with hydrogen, helium, and calcium emissions from the Sun. The careful analysis of SERTS spectrum however suggest the presence of a layer or layers containing ferrite and other heavy metals. Besides ferrite SERTS found silicon, magnesium, manganese, chromium, aluminum, and neon in solar emissions. Also elevated levels of sulphur and nickel were observed during more active cycles of the Sun. In the gas sphere model these elements are expected to be present only in minor amounts. As many as 57 different types of emissions from 10 different kinds of elements had to be considered to construct a picture about the surface of the Sun.
- Moshina has visually analyzed the pictures constructed from the surface of the Sun using light at wavelengths corresponding to three lines of ferrite ions (171, 195, 284 Angstroms). On the basis of his analysis he concludes that the spectrum originates from rigid and fixed surface structures, which can survive for days. A further analysis shows that these rigid structures rotate uniformly.
The existence of a rigid structure idealizable as spherical shell in the first approximation could by previous observation be interpreted as a spherical shell corresponding to n=1 Bohr orbit of a planet not yet formed. This structure would already contain the germs of iron core and of crust containing Silicon, Ca and other elements.
- Ordinary iron and also ordinary iron topologically condensed at dark space-time sheets, becomes liquid at temperature 1811 K at atmospheric pressure. Using for the photospheric pressure pph , the ideal gas approximation pph = nph Tph , the values of photospheric temperature Tph ≈ 5800 K and density ρph ≈ 10-2 ρatm , and idealizing photosphere as a plasma of hydrogen ions and atmosphere as a gas of O2 molecules, one obtains nph ≈.32natm giving pph ≈ 6.4patm .
This suggests that calcium ferrite cannot be solid at temperatures of order 5800 K prevailing in the photosphere (the material with highest known melting temperature is graphite with melting temperature of 3984 K at atmospheric pressure). Thus it would seem that dark calcium ferrite at the surface of the Sun cannot be just ordinary calcium ferrite at dark space-time sheets. A more reasonable option is that there is new physics allowing to have a low temperature at the layer.
- There is also a problem with the existence of water in the photosphere. The bond energy is 4.4 eV per bond so that the total bond energy is 8.8 eV. The peak energy of blackbody radiation is given by Epeak= 2.4× 10-4T/K eV and 8.8 eV is below the thermal energy of order 12.1 eV associated with the photospheric temperature T=5,500 K so that water molecules are not be stable at these temperatures.
- In the model of the solar cycle in terms of monopole flux tubes, the flux loops at the surface have inner and outer parts. The inner parts are always parallel to the solar surface and reside below it. Outer parts form flux loops extending outside the photosphere. With a 11 year cycle, the long monopole loops return to thin parallelepiped configuration, which splits to short monopole flux loops by reconnections, which then reorganize to flux tubes with opposite polarity. Could these monopole flux loops be accompanied by a solid surface of ordinary matter with the radius of n=1 Bohr orbit.
The interior portion of the gravitational monopole flux loops would carry dark matter with ℏgr= GMm/β0, β0≈ 2-11 and corresponding gravitational Compton length Λgr= GM/β0≈ 6× 103 km, which happens to be in a good approximation the radius of Earth.
- Could the monopole flux tubes shield the ordinary matter at the layer from the effects of the radiation arriving from the solar interior in the same way as they would shield the biosphere from the cosmic radiation and solar wind? Could the radiation from the solar interior be caught by monopole flux tubes and leave the Sun as a solar wind.
- If there are stable water molecules in this layer, its temperature should be rather low. If the water is in liquid or solid phase, the temperature must be of the order of the temperature at Earth. Could the monopole flux tubes carrying gravitational dark matter allow even chemical life inside this layer \cite{btart{precns,penrose? How low the temperature of dark matter at the flux tubes can be and is it possible to estimate it using the existing data?
- The cyclotron energies of dark particles are proportional to ℏeff=ℏgr. Could this allow us to transform the arriving high temperature radiation from the solar interior to a low temperature radiation at the monopole flux tubes from which it could leak out as solar wind? Could even the radiation from the solar interior arrive along radial gravitational U-shaped monopole flux loops and have a low temperature? If so, the magnetic body of the solar interior would be an astrophysically quantum coherent system and very different from what we believe it to be.
For a summary of earlier postings see Latest progress in TGD.
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