New findings challenging the notion of galactic dark matter halo and its identification as exotic particles

Very interesting popular article in Nature tells about very interesting new results found by Safti et al. The findings challenge the prevailing particle physics view about existence of galactic dark matter halo and consisting of some exotic new particles behaving like dark matter. These findings add to a long list of negative results related to the existence of dark matter halo and the attempts to find predicted dark matter particles.

There are two observed candidates for ford particles what would form the speculative galactic dark matter halo. They would have as decay products monochromatic gamma rays at energy of around .5 MeV and 3.5-keV X rays having no standard identification. The recent findings exclude the possibility that these particles reside in the conjectured galactic dark matter halo. They could however reside in galactic centers so that their existence is not challenged.

A. .5 MeV gamma ray signal

There is an old gamma ray signal from Milky Way at gamma ray energy of slightly more than electron mass. It has been proposed that it results as dark particle and antiparticle almost at res with respect to each other annihilate.
Now it seems that the interpretation as in the proposed sense seems to be excluded.

One can of course, why not a particle which has mass nearly twice the electron mass could not decay to two gamma rays. For some reason this option haven not been experienced as interesting.

1. Support from the existence of pseudo-scalar with this mass emerged already at seventies but because it did not fit witht he standard model picture it was forgotten. Later evidence for a particle with masses twice the mass of muon and tau lepton with similar interpretation emerged. For the same reason also these pieces of evidence were forgotten.
   
   
2. TGD led long time ago to what I call lepto-pion hypothesis (see this). In TGD color is not spin-like but angular momentum-like quantum number. Color correspond to the analog of angular momentum for the analog of rigid body rotation in CP_2 degrees freedom. In particular, TGD allows colored excitations of leptons: for instance, electron could appear in color octet state. Color excited electron and positron might form a pion-like color confined pion with mass very nearly 2 times electron mass. Same for muon and tau.
   
   
3. These states could be dark in the sense that they have non-standard value of effective Planck constant h_eff=n×h₀. This would explain why they are not produced in the decays of Z₀ boson and therefore do not affect its decay rate. Otherwise Z₀ and W decays widths exclude leptopions.
   
   
4. This darkness has however nothing to do with the darkness of galactic matter, which reside as energy and possibly dark matter at long very cosmic strings to which linear structures formed by galaxies can be assigned. These cosmic strings can locally thicken to flux tubes and liberate energy as particles forming galaxies. They generate radial gravitational force predicting the flat velocity spectrum of distant stars.
   
   

TGD picture would explain why these particles have not been observed outside galactic nucleus.

B. 3.5-keV X ray signal

Can one imagine any standard physics identification for the 3.5-keV line?. An interesting atomic physics based identification is as as X ray emitted in the capture of electron by sulphur ion with principal quantum number n≥9, which is rather high (see this and this ). This requires plasma at temperature of order 3 keV plus cold dense cloud moving at few hundred km/s .

3.5-keV X rays appearing as an un-identified mono-chromatic line in X ray spectrum have been proposed to result from the annihilation of dark particles having mass about 7 keV: annihilation of inert neutrinos is one proposal. The experimental findings exclude the possibility that these X rays are produced in the proposed galactic halo. TGD suggests two alternative explanations based on the notion of monopole flux tube.

1. In TGD framework also 3.5-keV X rays could result in a decay of pion-like state with mass of 7 keV. TGD indeed predicts new nuclear physics in keV scale.
   
   As a matter fact, TGD leads to a new vision about nuclear physics on basis of model of "cold fusion" (see this) . Magnetic flux carrying monopole flux serve as basic building bricks also now: TGD Universe is indeed fractal.
   
   
2. Nuclear string model relies on the assumption that nuclei are sequences of nucleons connected by pionlike bonds - loopy flux tubes much longer than the M⁴ distance between nucleons. These loopy flux tubes have length of order electron Compton length are essential for the TGD based model of nuclear reactions and also of "cold fusion".
   
   
3. This model allows to consider two options concerning the interpretation of 3.5-keV line.
   

   Option I:
   

   These flux tubes would be like pions with mass about 7 keV decaying to two X rays with energy 3.5-keV. They might be produced even in nuclear physics laboratory. Also now darkness in TGD sense (h_eff =n×h₀>h) is essential and one can talk about dark nuclei.
   

   In the annihilation of pion like bond to X ray pair, fission of the nucleus would take place. There is no dependence on environmental parameters like temperature.
   

   Option II:
   

   The 3.5-keV energy could correspond to a cyclotron transition of for a light quark with mass scale of E=7 MeV assignable to the flux tube having cyclotron energy of this order of magnitude. Recall that cyclotron frequency is determined by the radius of the monopole flux tube and from the quantization of magnetic flux assumed to be minimal plus the from the fact that B_end= .2 Gauss for electron is .6 MHz.
   

   In this case however the pion-like loopy flux tube bonds between nucleons would have mass about 2m_u, which would be of the order of nuclear binding energy of order E rather than being in keV range. The energy differences for subsequent states at nuclear IR Regge trajectories assignable to nucleons are predicted also to have energy of order E. Both the intra-nucleon bonds and inter-nucleon bonds would have the same mass scale. The model for nucleus constructed recently however assumed that the mass scale for the bond is keV. The masses of bonds ncreasing mass could be compensated by downwards shifts at IR Regge trajectories of nucleons.
   

   The cyclotron transitions would naturally correspond to the return to the ground state after thermal excitation. Temperature would correspond to thermal energy of order 3 keV. The line intensity depends on the temperature of environment.
   

   Remark: For Option I the cyclotron energies for quarks with masses in keV range would be of order eV, which is also predicted to be a nuclear energy scale in the proposal for TGD based nuclear physics.
   
   

4. The intensity of 3.5-keV lines depends on environment. This excludes Option I but saves Option II. For instance, it is known that 3.5-keV line is associated with galactic clusters and galactic nuclei but not with spheroidal dwarf galaxies with little or no star dust, no recent star formation, and low luminocity (see this). The presence of plasma at temperature of order 3 keV distinguishing between these options seems necessary. This temperature is possible for several astrophysical X-ray sources (see this). Also celestial sources such as the surfaces of stars with surface temperature of this order of magnitude are possible (for Sun the surface temperature is 3 orders of magnitude lower).
   

   The temperature of order 3.5-keV makes possible for hot fusion to start- in solar core the temperature is 1.5 keV) so that 3.5-keV line could serve as a signature for regions, where star formation is beginning. In TGD framework, where dark fusion explaining "cold fusion" serves as a "warm-up band" for hot fusion, this correlation is especially natural.
   
   

5. One should be able to predict correct value of the cyclotron energy with natural assumptions. The loopy flux tube would correspond to k=127 for electron. The endogenous magnetic field carrying monopole flux corresponds
   to B_end= .2 Gauss assignable to k=167 flux tube. The cyclotron of f_e= B_end/m_e of is electron f_J=6× 10⁵ Hz for h_eff=h . f_e is scaled up by a factor 2⁴⁰≈ 10¹² in the replacement k=167→ 127.
   

   Proton cyclotron frequency is scaled f_p=(m_e/m_p)f_e. For proton cyclotron energy one obtains (h_eff/h) × (m_e/m_p)× (g_p/2)× f_J. Proton has magnetic oment μ_p= 2.79 e/2m_p . For h_eff/h=2¹¹ this gives E_c,p) ≈ 3.78 keV, which is sligthly higher than 3.5 keV. If one has h_eff/h≈ m_p/m_e≈ 1876 one obtains 3.46 keV quite near to 3.5 keV! For h_eff=h one have in this case 1.8 eV so that eV scale emerges and would correspond to the cyclotron energy of single sheet of covering. Therefore proton's cyclotron energy for h_eff/h≈ m_p/m_e or electron's cyclotron frequency for h_eff=h could be in question in B_end scaled up from k=167 to k=127.
   

   For neutron the dipole momenta is μ_n=-1.91× e/2m_p and cyclotron energy would be E_c,n=2.46 keV, which might be a testable prediction. Cyclotron energy per single sheet would be E_c,n=1.31 eV.
   
   

C. Questions raised by the interpretation of 3.5-keV signal

These interpretation of 3.5-keV signal raises several questions.

1. The earlier proposal has been that nuclear neutrons could correspond to pairs of proton and pion-like flux tube carrying negative charge. The observation above forces to ask whether the intra-nucleon flux tubes carry electrons and have h_eff=h. Could nuclear proton transform effectively to neutron by the presence of flux tube carrying electron so that the idea about neutrons as pairs of proton and electron-neutrino pair could make sense inside nuclei.
   
   
2. Could also interpret the bonds as scaled down analogs of weak bosons? I have actually considered the possibility of scaled down variants of electroweak gauge bosons earlier in the model (see this) for the so called X boson anomaly. The inspiration for this came from CVC resp. PCAC hypothesis relates the conserved vectorial resp. partially conserved axial electroweak currents to strong interactions. This hypothesis is encouraged also by M⁸-H duality strongly suggesting that QCD type description provides the quark-gluon description at high energies at the level of H=M⁴× CP₂ and M⁸= M⁴ × E⁴ description provides the description of hadron physics in terms of O(4)= SU(2)× SO(3) symmetry group acting as isometries of E⁴ of old-fashioned hadron physics appearing in CVC and PCAC.
   

   What is important is that weak bosons would be effectively massless below the scaled up weak scale L(127), and depending on the situation also to some other scales as p-adic length scale hypothesis suggests, and being as strong as electromagnetic interactions below this scale. Could one interpret strong interactions in hadronic and nuclear scales as scaled-down weak interactions?
   
   

This hypothesis combined with p-adic length scale hypothesis is very powerful and can be tested.

1. Higgs boson with mass 125 GeV would correspond to k=89. Higgs mass would be minimal possible if p-adic mass squared is of order O(p) so that real mass squared is m²_R= 1/p. Contrary to the long-held expectations W and Z bosons with standard values of Weinberg angle naturally correspond to k=90 if pure U(1) boson would have Higgs mass.
   

   
   TGD predicts also pseudo-scalar variant of Higgs. For k=90 the minimal mass would be 88 GeV. LHC has observed a bump at about 96 GeV (see this), and this could correspond to pseudo-scalar Higgs, call it P, and assume its mass is indeed 96 GeV. The masses of weak bosons would be therefore (m(H),m(P),m(W),m(Z))= (125 ,96, 80.4, 91.2) GeV and masses for other p-adic length scales follow by simple scaling.
   
   

   
   

2. The masses of Higgs and W and Z bosons with same Weinberg angle for k=127 would be obtained by scaling
   with a factor 2^(-127+k)/2, k= 89 for Higgs and k=90 for P, W and Z. This would give (m(H),m(P),m(W),m(Z))= (.238 ,.129 , .11, .12) MeV. What is nice is that these scales are considerably below the nuclear binding energy scale about 7-8 MeV per nucleon for heavier and 1.1 MeV for D so that one could indeed assign nuclear binding and excitation energies to the nucleon flux tubes as proposed.
   
   

This raises questions.

1. Could also the intra-nuclear flux tube bonds have scaled-down weak boson masses but with different p-adic length scale? Can one regard the electrons in these bonds effectively as free electrons as far as cyclotron energies are considered? Could the old-fashioned hadron physics at least partially reduce to weak interaction physics below electron Compton length and possible other p-adic length scales assignable to the flux tubes involved?
   
   
2. Intra-nucleon flux tubes have been assumed to have intra-nucleon binding energy scale about 7-8 MeV (1.1 MeV for neutron-proton pair)? The proposal is that binding energy scale corresponds to the energy scale of IR Regge trajectories for nucleons and is thus single nucleon property (or that of the MB of nucleon). Nuclear strings would be strings formed from ⁴He strings a units, possible D type string, and lonely nucleons (protons or neutrons depending on the sign of Z-N.
   

   Nuclear binding energy scale 7-8 MeV would be assignable to the MB of nucleons of ⁴He and of heavier nuclei and 1 MeV energy scale to the MBs of p and n in D. The binding energy scale and energy scale of excitations would be determined by the p-adic length scale assignable to the intra-nucleon flux tubes and depending on environment via the value of k defining the p-adic lengths scale.
   
   

3. What would this mean p-adically? The scaling of weak boson masses with mass scale .1 MeV to larger mass scale should correspond to that for the binding energy scale and give binding energy scale 1 MeV for D and 8 MeV for ⁴He.
   
   
   1. Consider first 1 MeV scale assignable to intra-nucleon flux tubes in D. k=127-6=121 would give (m_H,m_P,m_W,m_Z)=(1.90,1.06,.877, .8) MeV. The mass of P is quite near the the D binding energy 1.11 MeV.
      

      A connection with lepto-hadron hypothesis suggests itself. For k= 121=11² the mass of P would be 1.06 MeV and very nearly twice the electron mass 1.022 MeV. The mass of the electro-pion proposed to explain the pseudo-scalar resonance observed in heavy ion collisions is very very near to 2m_e. Could electro-pion identified as a pair of color octet leptons correspond scaled down P? Also evidence for muon-pion and tau-pion exists. Could these correspond to higher generations of weak bosons predicted by TGD?
      
      

   2. What about 7-8 MeV scale? k=113 is basic candidate for nuclear scale and the corresponding masses would be scaled by factor 2⁷=128 giving (m_H,m_P,m_W,m_Z)=(30.5,16.5,14.1,15.4) MeV. These scales are too large by a factor of order 2 that k=111 looks more appropriate.
      
      
4. There exists evidence for what is called X boson with mass of 17 MeV. One interpretation would be in terms of pion like state which could corresponds to the electroweak pseudo-scalar predicted by TGD. The mass of k=113 P-boson would be 16.5 MeV and quite near to X boson mass. This would suggest that several p-adic length scales are indeed possible. This interpretation can be tested by checking whether other exotic bosons in this range exist.
   
   

To sum up, the TGD inspired model for nucleus predicts correctly the 3.5-eV X ray energy as cyclotron energy with using the earlier assumptions of the model. Also other predictions and tests follow. For instance, the model could be tested by irradiating nuclei in laboratory using 3.5 eV X rays and looking whether this has effects. For instance, nuclear decay rates could be affected.

What M⁸-H duality together with CVC and PCAC suggests and the above observations quantitatively support is that p-adic length scale hierarchy could allow a description of hadronic and nuclear physics in terms of p-adically scaled down variants of weak interactions such that the value of k for weak bosons would depend on the energy scale of the strong interactions.

See the article The implications of .5 MeV and 3.5 keV monochromatic lines for TGD based nuclear model.

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

Articles and other material related to TGD.

Could TGD provide new solutions to the energy problem?

The city of Helsinki has posed an ambitious goal to be carbon neutral before year 2035. The role of Helsinki could be therefore decisive in the fight agains climate crisis. More than half of the population of the world lives in towns and more than 2/3 of the energy is consumed by cities and are responsible for more than 70 per cent of the carbon oxide emission of the world. About 56 per cent of the carbon oxide emissions of Helsinki are due to the heating. Finding of a sustainable heating method has a decisive effect on the total amount of carbon oxide emissions of Helsinki.

Concerning heat production Helsinki is searching for new kind of thinking and internal collaboration. The goal is to search for the solutions to energy problems even in the world scale. Therefore Helsinki city as challenged innovators and the specialist of the field to sustained solutions to the production of energy in a competition. The competition "Helsinki Energy Challenge" opened February 27 2020 is international.

The requirement of carbon neutrality leaves allows renewable energy sources, energy efficiency, and concentration of pure low carbon technologies (see this). The understanding of photosynthesis could make possible to mimic it technologically and is is a promising approach. Nuclear energy is another alternative despite its problems.

Could artificial photosynthesis or nuclear energy be a solution to the energy problem?

1. The options related to nuclear energy

There are three options related to nuclear power.

1. At this moment the power plants use fission of heavy nuclei, which liberates energy because the nuclear binding energy per nucleon decreases as the mass number of the nucleus increases.
   

   The problem is that one obtains as a waste long-lived isotopes which are unstable against decay and produce radiation, which is dangerous for health. The storage of the waste is a problem. Furthermore, the temperature needed in fission reactors is of the same order of magnitude as in the solar core and causes serious problems in the control of fission as also the Fukushima accident demonstrated.
   

   Small scale fission power planets are not so dangers and work is done to develop applications in which nuclear power would be produced in small scale.
   
   

2. Second option is fusion of light nuclei, which liberates energy for nuclei lighter than iron (Fe). Also the temperature prevailing in the solar core is needed. Now the problem is plasma confinement. Magnetic bottle is the basic solution but it has instabilities: for instance magnetic bottle tends to develop a pinch. Fusion plants still do not exist despite the research which has lasted more than seven decades (see this).
   
   
3. The third option is non-orthodox and would be based on "cold fusion" (CF), which was reported already 1920 and 1989 by Pons ja Fleischman. Mainstream physics has had a hostile attitude to cold fusion as becomes clear from the ultra-skeptic Wikipedia article see this) but gradually the attitude has changed and CF researchers are taken seriously.
   

   On basis of recent understanding one can say that CF is not a proper term. Ordinary fusion cannot be in question already because it is not possible at low temperatures and because the distributions of heavier isotopes do not correspond to those assignable to ordinary fusion. Low energy nuclear reactions (LENR) or nuclear transmutations are slightly better terms. In the sequel I will use the term CF keeping however in mind that the term is only a convention.
   

   The book about the history of CF written by Krivit and having 3 parts (see this , this, and this) provides a good overview about the situation.
   
   

To my opinion the basic problem of CF research is that theoretical understanding is missing so that the attempts to develop a technology are like searching a needle in haystack. Of course, the hostile attitude of the mainstream is second problem. The situation is not made easier by two optimistic promises in order to get funding and the underrating of theoretical understanding. Part of the problem is that the goal is to produce energy although at this stage the main emphasis should be on the understanding of the phenomenon.

2. Could TGD have something to give?

My own goal has been to develop theoretical understanding about CF and also about nuclear physics on basis of the new physics predicted by Topological Geometrodynamics (TGD) (see this and this), which can be can be regarded as my lifework hitherto. In the sequel I try to summarize this work in hope that it could help to invent the desired new technology.

The following gies a very brief summary about tGD.

1. TGD leads to an identification of dark matter as phases of ordinary matter with non-standard value h_eff= n× h₀ of effective Planck constant, which make possible quantum coherence in arbitrarily long length scales proportional to h_eff. The hypothesis follows from a generalization of physics to describe correlates of cognition: number theory becomes an essental part of quantum physics (this).
   
   
2. This leads to a model of quantum biology (see this). The coherence of living matter is the basic problem of biology: biochemistry cannot explain it. The basic problem of standard quantum biology is in turn the smallness of the ordinary Planck constant h - it is very difficult to understand the coherence of living matter as macroscopic quantum coherence. TGD would solve this problem: dark matter with genuine quantum coherence in long scales would induce coherence of ordinary matter (not quantum coherence anymore).
   

   Dark matter in TGD sense would provide also a starting point for the attempts to understand photosynthesis, which is now believed to involve quantum physics in an essential manner. The mimicry of the photosynthesis at the level of technology would be an alternative new energy technology.
   
   

3. Dark nuclei would be in central rol int he proposed model of CF (see this), which would reduce to the production of dark nuclei by feeding to the system energy increasing the value of h_eff. Dark nuclei for which the binding energies of basic build blocks would be very small, would decay to ordinary nuclei and liberate energy as in ordinary nuclear fusion.
   

   This leads also to a proposal for a theory of nuclear physics, which could replace the nuclear models, which typically explain only some aspects of nuclear physics. The birth of dark nuclei in the collisions of nuclei would replace the tunnelling phenomenon, which reduces the value of energy above which the nuclear reactions can take place from its classical estimate by factor of order 1/100. Because the energy of dark states increases with h_eff, this would require high collision energy and high temperature in hot fusion.
   
   

4. In CF the production of dark nuclei would require only a relatively because the building bricks of dark nuclei would be free protons, deuterons, perhaps even heavier nuclei for which one would not do anything. They would form dark nuclei as string like entities assignable to flux tubes and the binding energy for the interaction between basic building bricks would be much smaller than that in ordinary nuclei and assignable to flux tube bonds between them. The increase of h_eff to produce dark nuclei from - say - deuterons would require only a small energy because the binding energy of dark nucleus would reduce the needed energy. For instance, laser beam could be enough as the researchers like Holmlid indeed claim this).
   After this the dark nuclei could transform spontaneously to ordinary nuclei in the transition h_eff→ h=6h₀ and liberate energy which is of the same order of magnitude as the binding energy of ordinary nuclei. Dark nuclei can also react - as in ordinary hot fusion - before the transformation to ordinary nuclei.
   

   One can say, that in CF one goes to the edge of the energy cliff and jumps down. In hot fusion one jumps from the bottom to te edge and then jumps down.
   
   

5. The basic mechanism of CF and also ordinary fusion would be rely on quantum coherence provided by large h_eff; the notion of magnetic flux tube; quantum criticality (QC) of TGD Universe making possible flux tube contacts of small energy between reactants with various lengths as analog of long range fluctuations (this would break the limitation due to the short range of nuclear forces and Coulomb wall); the breaking of QC induced by increase of length scale dependent cosmological constant Λ for flux tubes predicted by twistor lift of TGD increasing their string tension so that the resulting force attracts reactants together and allows to overcome the Coulomb wall so that reaction can proceed: the shortening of flux tube would however involved temporary reduction of h_eff.
   

   The energy to increase Λ and string tension for the flux tube energy would come from reactant: essentially analog of metabolic energy provided by reactants would be in question. The mechanism is basically the same as in bio-catalysis, where the energy wall hindering the reactions corresponds to Coulomb wall.
   
   
   

Energy production would not be the only application of CF. Modern technology needs various elements such as metals and there is a shortage of these. CF might allow to produce these elements in industrial scale. Also in quantum biology dark matter and dark nuclei -albeit in different scale as compared to CF - are in central role (see this), and might provide a theoretical basis for developing artificial photosynthesis.

See the article Could TGD provide new solutions to the energy problem? or a chapter with the same title .

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

Articles and other material related to TGD.

New pseudoscalar particle having no explanation in standard model detected?

Thanks for Wilhelmus de Wilde for a link to a popular article in Schitechdaily telling about completely unexpected finding by by a team led by professors Tacemichi Okui and Kohsaku Tobioka. The decay of longlived kaon K_L suggests the existence of new longlived particle with quantum numbers of axion - or equivalently pion. The finding is published in Physical Review Letters (see this). Standard model cannot explain this kind of particle.

A rough estimate for mass is not far from pion mass. There exists earlier evidence that pion has mass spectrum. Could an excitation of pion be involved?

This is actually not new. The experimental claim of Tatischeff and Tomasi-Gustafsson (see this ) is that pion is accompanied by pion like states organized on Regge trajectory and having mass 60, 80, 100, 140, 181, 198, 215, 227.5, and 235 MeV means that besides pion also other pion like states should be there. Similar satellites have been observed for nucleons with ground state mass 934 MeV: the masses of the satellites are 1004, 1044, 1094 MeV. Also the signal cross sections for Higgs to gamma pairs at LHC suggest the existence of several pion and spion like states, and this was the reason why I decided to again the search for data about this kind of states. Their possible interpretation in TGD framework is discussed in here.

One explanation could be that the states correspond to "infrared Regge trajectories" of pion related to the structure of its magnetic body. Genuine Regge trajectories would have slope of about GeV. IR trajectories could be associated with the electromagnetic body and ordinary Regge trajectories with the color magnetic body. One can also consider p-adically scaled down variant of color interactions.

It is interesting to look the situation quantitatively.

1. It is clear that the masses in question do not fit to a single Regge trajectory. One can however restrict the consideration to Regge trajectory M²=M₀² + nT(π), where T(π) denotes string tension. Since the masses obey approximately linear formula one can assume linear approximation Δ M²= 2MΔM at pion mass M₁= m(π)= .140 GeV and consider the mass squared difference for pion and its predecessor with M₀=.100 GeV so that one has Δ M=.040 GeV.
   

   One obtains Δ M²= M₁²-M⁰²= T(π). This would give for the string tension T(π)= 0.96×10^-2 T_H≃ .96× 10^-2 GeV², where T_H≈ GeV² is hadronic string tension assignable to color interactions.
   
   

2. What about the value of M₀²? In string models it tends to be negative but one can assume that the values of mass squared for physical states are negative. Also in TGD the value is negative in p-adic mass calculations. One must require that several values for pion mass below m(π) are possible. The formula m(π)² =M₀²+nT(π) gives formula M₀²=
   m(π)²-nT(π). For n(π)=2, which looks rather reasonable guess, one has M₀²=.04 GeV², which corresponds to M₀= 20 MeV.
   
   

There is actually a lot of confusion about the value of hadronic string tension.

1. In early models hadronic string tension was taken to be 1 GeV. Much smaller values for the string tension smaller by a factor or order x×10^-2 GeV², x in the range 2-11.1 for mesons and in the range 2.2-4.55 for baryons are however suggested by the study of hadronic spectrum (see this). Intriguingly, the lower bounds is twice the above estimate T(π)≃ .01 GeV² obtained above. Does this mean that the p-adic prime involved is about 2 times smaller or is this factor due to a numerical factor 1/2 related to the difference between N-S and Ramond type representations of Super-Virasoro algebra.
   
   
2. The reason for the confusion about string tension could be simple: besides the string tension 1 GeV assignable to color flux tubes there are string tensions assignable to possible scaled down color flux tubes and possible elecromagnetic and even weak flux tubes. Several p-adic length scales could be associated coming in powers of 2 by p-adic length scales hypothesis are involved.
   
   

This picture led to an unexpected development in the nuclear string model that I constructed more than 2 decades ago (see this). The key assumption - very natural in TGD, where monopole flux tubes prevail in all scales - is that nucleons form nuclear strings. Nuclear radius satisfies R ∝ A^1/3, A mass number, so that nuclei have constant density in good approximation (see this) so that the flux tube would will the entire volume. I have proposed that also blackholes and other final states of stars are flux tube spaghettis of this kind (see this) .

The basic objection against the model is that the harmonic oscillator model for nuclear works surprisingly well. The justification for this model is that one can reasonably well describe nucleus as motion of nucleons in an effective nuclear potential, which in linearization becomes harmonic. Nucleons themselves have no mutual interactions in this approximation.

Could nuclear string model allow to understand harmonic oscillator model of nuclei as an approximation?

1. It is best to start from the problems of the harmonic oscillator model. The first problem is that the description of nuclear binding energies is poorly understood. For instance, nuclear binding energies have scale measured in MeVs. The scale is much smaller than energy scale of hadronic strong interactions for which pion mass is a natural scale. Rather remarkably, the ratio of the scales is roughly the ratio of fine structure constant to color coupling strength. Could one imagine that electromagnetic interactions somehow determine the energy scale of nuclear binding energies and excitations?
   
   
2. As noticed, also nucleons are reported to have IR Regge trajectories. The first guess is that the trajectories have same string tension as in the case of pion. TGD suggests a model of nuclei as three nucleons connected by color flux tubes characterized by hadronic string tension T_H≈ 1 GeV². Besides color flux tubes hadrons are expected to have also electromagnetic and perhaps also weak flux tubes with a smaller value of string tension. Em flux tubes should give a contribution to the energy, which is of the order of Coulomb energy of nucleon about α/L^c(p) ≈ 7.5 MeV. Intriguingly, this is of same order of magnitude as nuclear binding energy: could IR Regge trajectories correspond to em interaction so that the spectrum of nuclear binding energies and excitation energies would be determined by electromagnetic interactions?
   
   
3. If the value of p-adic prime p ≃ 2^k corresponds to k=113 assumed to characterize nuclei in nuclear string model, hadronic string tension would be scaled down by factor 2^107-113= 1/64 to T_H/64, which corresponds to a mass of 125 MeV, which is somewhat larger than the value about 96 MeV obtained from the above estimate. For Δ M² ≃ 2MΔ M = T(π) this gives ΔM ≈ 7.8 MeV for Δ n=1, which corresponds to the maximal nuclear binding energy per nucleon. This string tension is naturally assignable to em flux tubes assignable nuclei as 3 -quark states. Color flux tubes would be responsible for the hadronic string tension T_H.
   

   Remark: Flux tubes carry all classical gauge fields, which are induced from the spinor connection of CP₂ but it seems that one can assign to given flux tube quanta of particular interaction.
   
   

4. In the case of baryons one would have 3 color flux tubes and and 3 em flux tubes. For large mass excitations one would have in linear approximation for M² harmonic oscillator spectrum! Could linearization of mass squared formula replace linearization of effective potential function leading to harmonic oscillator model? The dimension D=3 for the nuclear harmonic oscillators would correspond to the fact that nucleons consist of 3 quarks. The free nucleon approximation would have simple justification: in good approximation one can treat the nucleons of nuclear strings as independent particles!
   
   
5. Could the nuclear binding energy per nucleon correspond to a reduction of the value of n for the IR Regge trajectory of free nucleon? The mass squared formula for IR trajectory would be M²= M₀²(N)+ nT(π). This mechanism requires that the one has M₀≤ m(N) so that one has n>0 for nucleons. For Δ n=-1 one has Δ M =Δ nT(π)/2m(N) ≃ 7.8 MeV.
   

Could one understand the qualitative features of the nuclear binding energy specrum on basis of this picture?

1. Binding energy per nucleon is below 3 MeV for nuclei lighter than ⁴He and has tendency to increase up to Fe. For the most abundant stable isotope of Fe with (Z,A)=(26,56) it is 8.78 MeV. For heavier nuclei neutron number N increases and binding energy per nucleon starts to decrease.
   
   
2. For D one must have Δ n=0 and p-n pairing would be somehow responsible for the binding. For T the total binding energy is 8.478 MeV and could involve Δ n =-1 for one nucleon. ³He has total binding energy 7.715 MeV and also now one nucleon could have Δ n=-1. ⁴He has binding energy per nucleon equal to 7.07420 eV. This suggests that p-n pairing causes the reduction Δ n=-1 for all nucleons in ⁴He units proposed to be building bricks of nuclei.
   

   For nuclei with odd Z and nuclei there are would be also deuteron sub-unit present and also |A-Z| unpaired neutrons. This would reduce the binding energy. The prediction is that for nuclei with N=Z with even Z the binding energy exceeds that for ⁴He. For heavier nuclei this can happen also for odd Z and also for N different from Z.
   
   

3. The pairing of to D subunits should be rise to binding energy 2.223 MeV per deuteron unit. Why the value is so small? Could deuteron unit correspond to a smaller string tension: perhaps corresponding to k=9 as the ratio of ⁴He and D binding energies per nucleon would suggest. The ratio of the maximal binding energy 8.7892 MeV per nucleon to deuteron binding energy is rather precisely 8, which supports the interpretation.
   
   
4. What causes the increase of the binding energy per nucleon e_B up to Fe? Attractive potential energy is not an attractive interpretation in TGD framework. Some repulsive interaction should reduce the binding energy per nucleon for lighter nuclei than Fe from the value 8.8 MeV. The increase from ⁴He to Fe is about 1 MeV. Why does this repulsive contribution decrease up to Fe? Does it start to increase after that or is the presence of surplus neutrons the reason for the reduction? Or are both mechanisms involved?
   

   The IR Regge trajectories considered are not the only ones as already the findings of Tatischeff and Tomasi-Gustafsson suggest and there might be trajectories with smaller string tension. The value of k=9 with string tension T(π)/8 assignable to D, which corresponds to a e_B of about 1 MeV and this is roughly the total variation of the e_B from ⁴He to Fe. Could both k=6 and k=9 flux tubes be present for given nucleon. Could the reduction of n for k=9 flux tubes take place also for ⁴He units as nuclei become heavier. What happens in nuclei heavier than Fe? Could the increase of neutron surplus reduce e_B?
   
   

To sum up, nuclear string model would reduce nuclear physics that for the magnetic body of the nucleon - obviously an enormous simplification.

See the article Exotic pion like states as "infra-red" Regge Trajectories and new view about nuclear physics or the chapter New particle physics predicted by TGD: Part I.

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

Articles and other material related to TGD.

Comparing Penrose-Hameroff theory with TGD inspired theory of consciousness

Robert Paster made a question about the relationship between the Penrose-Hameroff and TGD approaches to consciousness. In the following I try to give a short explanation.

For both approaches state function reduction is central notion but what is meant with state function reductions is something
quite different. Also gravitation is important for both approaches but in totally different manner.

Penrose and Hameroff could give a better view about Penrose-Hameroff theory but I try.

1. Orch OR is not postulated but there is no explicit proposal for what it really is since quantum theory of gravitation is not proposed. There seems to be an idea about reduction of state function reduction to deterministic time evolution and that the experience of free will somehow due to the loss of computability. There is a visualization for analog for quantum superposition of space-time geometries and selection of geometry from this virtual superposition, which I fail however to understand. It is not clear to me whether Orch OR is meant to correspond to ordinary state function reduction - maybe not.
   Also a duration is assigned to Orch-OR, maybe it could correspond to the duration of conscious experience.
   
   
2. Microtubule hypothesis represents the biological part of the conjecture. Somehow microtubules would be the seat of consciousness and gravitation would be important. There is also the idea that somehow Planck scale is important: here I however fail to understand.
   
   

Concerning TGD view about the situation one can also discuss the aspects related to consciousness and biology separately.

In the attempt to understand state function reduction and consciousness one starts from two problems. The problem of quantum measurement theory is that state function reduction and time evolution for Schrödinger equation - unitary evolution or counterpart for that for Dirac equation - are not consistent with each. Second problem is that free will - which we experience directly - is not consistent with classical physics nor with determinism of unitary time evolution. Physicalism is the basic obstacle here.

1. The solution of is zero energy ontology (ZEO): quantum states are deterministic time evolutions - preferred extremals of action analogous to Bohr orbits - connecting "initial" and "final" states. In standard ontology quantum states are 3-D snapshots of these time evolutions. In neuroscience/biology/computer science behavior/function/program as deterministic temporal pattern would be the counterpart of zero energy state. Mathematician could say that initial value problem is replaced with boundary value problem.
   
   
2. "Small" state function functions (SSFRs) ("weak" measurement in standard quantum theory) occur between zero energy states with initial state fixed but final state changing. In statistical sense the temporal distance between initial and final states defining clock time increases. Sequence of SSFRs defines the flow of subjective time correlating with the clock time. The two basic problems are solved since there are two causalities: the causality of free will as state function reduction=moment of consciousness and causality of field equations.
   
   
3. The roles of "initial" and "final" states can change. This "big" state function reduction (BSFR) corresponds to ordinary state function reduction. The arrow of time changes. One can say that self defined by the sequences of SSFRs dies and reincarnates with opposite arrow of time. The experiments of Minev et al last summer gave strong support for this. See this.
   
   
4. Consciousness is universal - not only associated with microtubules or reducing to gravitation. Cognition is taken as a central and universal aspect of consciousness and p-adic number fields and their fusion to adele is identified as correlates of cognition -even at elementary particle level. One generalizes the notion of space-time surface to p-adic space-time surfaces and adelic space-time surfaces as representations of "thought bubbles". The fact that p-adic field equations are not completely deterministic, means that they only partially correspond to real space-time space-time surface - are "realistic". One can say that one has intention realizable only partially as real action. Imagined sensory percepts and motor actions are indeed partially realized percepts and motor actions.
   
   
5. Each extension of rationals defined by roots of irreducible polynomial defines its own adele and one obtains evolutionary hierarchy since the dimension n of extension of rationals increases in the sequence of SSFRs and BSFRs in statistically sense and therefore the algebraic complexity - kind of IQ - increases. n has interpretation as effective Planck constant h_eff= n×h₀ so that evolution corresponds to the increase of quantum coherence lengths. The interpretation for these phases of ordinary matter is as dark matter.
   
   
6. Cognitive representation as a set of points consisting of points of H with H-coordinates belonging to an extension of rationals defines a unique discretization ofthe space-time surface, and provides a number theoretical representation of finite measurement resolution.
   

   The higher the dimension of extension, the large the number of points in the discretization. At the never achievable limit one would obtain algebraic numbers and cognitive representation which is dense at space-time surface. Quantum TGD in finite measurement resolution can be formulated using quantum superpositions of cognitive representations as states and the Galois group of representation becomes symmetry group.
   

   The first conjecture is that geometry and number theory provide complementary views about TGD so that all physical quantum states could have representations in terms of quantum states assignable to Galois groups of extensions. Spin and color represent two example of this. M⁸-H duality would be one aspect of this duality.
   

   Second conjecture is that the sequence of SSFRs reduces to a sequence of purely number theoretical state function reductions for the wave functions in Galois group forming a group algebra. This state space has decomposition to a tensor product of subspaces associated with the normal subgroups of Galois extensions which is extension of extension of ... of rationals. SSFR would be a cascade of reductions leading to a product of states assignable to groups with prime order. The primes defining decomposition of the dimension n of extension to prime factors. Conscious experience would represent a sequence decompositions of integers n to their prime factors! See this.
   
   

The biological part of the story relies two key ideas. The notion of magnetic body (MB) and dark matter consisting of phases of ordinary matter labelled by the value of h_eff residing at it and controlling as intentional agent biological body (BB).

1. Space-time as 4-D surfaces of H=M⁴xCP₂ provides TGD view about quantum gravitation allowing geometrization of classical fields of standard model and leading also to a geometrization of entire quantum theory. One ends up with the notion of many-sheeted space-time.
   

   In particular, the systems have space-time sheets carrying classical fields assignable to them and defining what one can call field identity/field body. This is new as compared to Maxwellian theory. Magnetic body (MB) is of special importance in TGD inspired quantum biology.
   

   MB would be the wise guy controlling ordinary matter: one would have master slave hierarchy consisting of layers of MB and ordinary matter at bottom.
   
   

2. TGD view about gravitation is very different from standard proposals for quantum gravitation. The dark matter hierarchy is crucial for explaining coherence of living systems. h_eff can be rather large and correlates with the scale in which interaction is important.
   

   Since gravitation is mediated by massless quanta and is not screened, h_eff is expected to be very large for the flux tubes mediating gravitational interaction, and gravitation should be crucial for understanding higher evolution levels of consciousness.
   

   h_eff= h_gr= GMm/v₀ for Mm => v₀m_Pl² was originally postulated by Nottale can be very large and central for quantum biology in TGD Universe. For water the condition can be satisfied in M=m case for water blocks with mass below Planck mass. Also h_em as its electromagnetic analog would be important in atomic and molecular physics. These values of h_eff would characterize dark matter at the flux tubes and sheets of MB mediating particular interaction.
   
   

3. The quantum coherence of MB would force coherence of ordinary bio-matter and one would overcome the basic objections against quantum coherence against quantum biology. In particular, the change of arrow of time for dark matter at MB in BSFRs would induce apparent change of the arrow at BB.
   

   Self-organization as generation of quantum coherence would require increase of h_eff requiring energy feed quite generally. In ZEO self-organization would reduce to dissipation in reversed arrow of time. The decay of structures in opposite arrow of time implied by generalized second law looks like their generation in the standard arrow of time. No separate theory of self-organization is needed. Metabolic energy feed would be just loss of energy by dissipation with opposite arrow of time. System extracts - or should one say steals - its energy from environment if it is available.
   
   

4. Microtubules are predicted to be important level in the evolutionary and p-adic length scale hierarchies but not the fundamental seats of consciousness. There would be hierarchy of conscious entities and we would be only one level in it. Even astrophysical objects would be also conscious entities and the hypothesis that Mother Gaia controls biosphere must be taken seriously.
   
   

See for instance the articles

Why TGD and what TGD is?,

Getting philosophic: On the problems in Physics, Neuroscience and Biology,

Some comments related to Zero Energy Ontology (ZEO) .

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

Articles and other material related to TGD.

Why diseases do not like alkaline environments?

I received from Wes Johnson a link telling about the twork of Otto Warburg. He received Nobel Prize in Physiology of Medicine in 1941 for his work related to both aerobic and anaerobic metabolism. In particular, he noticed that healthy cells use mostly oxygen based metabolism whereas cancer cells use more anaerobic metabolism meaning that they can split glucoses into lactic acid through the process of fermentation. Also ordinary cells can do this but much less effectively.

Warburg proposed that cancer cells “live in hypoxic, very low oxygen, and acidic conditions and derive energy from sugars by fermenting them the way yeast does”. As cancer progresses, the body becomes more and more acidic as its pH drops below 7.35. His discoveries were revolutionary for their time, and contributed greatly to what we know about cancer today.

Somewhat embarrassing, I have managed to not become aware of these findings. Alkaline environment means negatively charged ions neutralizing the positively charged ions due to the protons (small pH). One could think that this leads to healing of say cancer.

Before asking what the TGD inspired interpretation could be, consider the basic ideas of TGD inspired biology (see for instance this).

1. TGD inspired quantum biology relies on the notions of magnetic body (MB) having monopole flux tubes as "body parts" carrying dark particles as ordinary particles with effective value h_eff=n×h₀ of Plankc constant serving as a kind of IQ and a measure for algebraic complexity. n would be the dimension of extension of rationals characterizing the cognitive representation of the system in adelic physics). MB with hierarchical structure would be the "boss" receivig information from biological body (BB) as dark photons and controlling it by dark photon signals.
   
   
2. The model for Pollack effect - irradiation of water in presence of gel generates exclusion zones, which are negatively charged regions - leads to the proposal that dark protons reside at flux tubes and give even rie to a realization of the genetic code already in water. Chemical realization would have emerged later during the evolution as a kind of mimicry of the deeper quantum dynamics at the level of MB.
   
   
3. The explanation for the effects of ELF radiation on vertebrate led also to the proposal that the cyclotron frequencies of biologically important dark ions in endogenous magnetic field B_end= .2 Gauss are central for the communications between MB and BB. The interpretation is as monopole part of the Earth's magnetic field with nominal value B_E= .5 Gauss.
   
   
4. The communications of sensory data from cell membrane to MB are also central element of the model. Cell membrane would act as generalized Josephson junction. The generalized Josephson frequency would be difference of cyclotron frequencies of these ions (proton included) at the two sides of membrane + ordinary Josephson frequency- essentially membrane potential. The membrane potential would frequency modulate the Josephson frequency and in this manner coding information about electric environment to frequency modulation. MB would be at resonance and be resonance only occasionally: the communications from cell membrane would experienced by flux tube of MB as a sequence of ticks.
   
   

How could one understand that findings of Otto Warburg in this framework?

1. I am still not quite sure whether pH as a measure for proton charge density counts dark protons at the magnetic flux tubes or only ordinary protons. If pH counts only ordinary protons, one might argue the number of dark protons with large h_eff at magnetic flux tubes of magnetic body (MB) is reduced as pH decreases - dark protons would transform to ordinary protons.
   

   The generation of dark protons requires metabolic energy so that the lack of appropriate metabolic energy feed could be one reason for the situation since the energy of the particle increases with h_eff: hence disease could be seen as a metabolic problem.
   
   

2. Too low concentration of dark protons would also mean that overall "IQ" or complexity of the system measured by average value of h_eff for the spectrum of h_eff:s is reduced, and system can carry less conscious information. Hence disease could be seen as lower complexity and lower level of consciousness (TGD predicts hierarchy of conscious entities extending down to the level of elementary particles).
   
   
3. The lack of dark protons and dark ions in general at magnetic flux tubes would make also the communication by dark cyclotron protons with the higher levels of magnetic body difficult: hence the disease could be interpreted as a failure of communications and control by MB.
   
   
4. At the level of water dark magnetic flux tubes would serve as antennas receiving dark photons from higher layers of MB and also from exterior world. Water memory would rely on the ability of water to mimic the invade molecule by tuning the cyclotron frequencies flux tubes so that they are in resonance with the cyclotron frequencies of MB of the invader molecule.
   

   It is quite possible that MB and BB go out of tune: flux tubes associated with would have magnetic field with wrong strength and could not communicate to "big" part of MB. The refreshing of water memory by irradiation of water by the proper frequencies could restore the resonance frequencies.
   
   

What about the role of alkali ions? Alkali ions could ionize the surplus of ordinary protons but would not increase the two low concentration of dark protons. Maybe they have however a much deeper role.

1. Also alkali atoms are involved with dark photon communications. In particular, K⁺, Na⁺, and Ca⁺⁺, Mg⁺⁺. Their cyclotron frequencies in B_endwould be associated with the communications from cell membrane acting as generalized Josephson junction to MB.
   
   
2. Could alkaline environment perhaps increasing the densities of also dark alkaline ions faciliate these commucations to MB and lead to healing. MB would receive information about BB and could control it more effectively.
   
   
3. Also Schumann resonance frequencies could be important and be responsible for quantum coherence in long length scales. MB of water could tune its flux tubes to these frequencies. (see this).
   
   

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

Articles and other material related to TGD.

Could string theorists be finally approaching the discovery of number theoretical physics?

I have been shaking my head from despair caused by the incredible slowness - or rather inability - of superstring people to realize the importance of number theory for physics. The popular article String Theory and Number Theory Have More in Common Than You Think, Maaaaaan however
gives hopes that superstring people are finally beginning to approach the discovery of adelic physics in which both real and p-adic numbers fields whose extensions are labelled by the hierarchy of extensions of rationals is central, and discretization of space-time surfaces defined by them defines measurement resolution. They do not of course mention TGD as the source of inspiration, why should they?

For adelic physics the article "Philophy of adelic physics" or the article published in a book by Springer which has reached considerable attentions from mathematicians .

The invariance of the scattering of scattering amplitudes associated with the discretization of space-time under Galois group associated with the extension of rationals would be in TGD very important discrete number-theoretical symmetry besides other symmetries of TGD: the latter mean huge extension of conformal symmetries of superstring models.

The basic notion is cognitive representation providing discretization of space-time surfaces consisting of points of 8-D imbedding space with coordinates in the extension of rationals. The number of these points is in the generic case finite so that the construction of scattering amplitudes in finite measurement resolution becomes rather simple. Number theoretical functions like L functions invariant or transforming like irreducble representations under Galois group are expected to be important in the construction. This number theoretical discretization is completely unique unlike typical discretizations.

Number theory would have most important applications to TGD based quantum biology and dark matter could be understood as phases of ordinary matter with effective Planck constant h_eff=n×h₀ with n the dimension of extension of rationals. Galois groups could also provide a number theoretical representation for discrete subgroups of ordinary symmetries

The latest application of Galois symmetry is to TGD based quantum biology. One ends up to the analog of color confinement for Galois group and to the observation that self as sequence of "small" state function reductions (SSFRs) correspond to a a sequence of decompositions of the integer defined by the order n of Galois group (dimension for the extension of rationals) to its prime factors so that Universe would be doing number theory at the basic level!: see this.

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

Articles and other material related to TGD.

No continents before Cambrian Explosion

I learned about highly interesting finding by geobiologists Benjamin Johnson and Boswell Wing. There is a popular article with title " Earth Could Have Once Been a Waterworld Covered by a Global Ocean, Study Suggests". The research article with title "Limited Archaean continental emergence reflected in an early Archaean 18O-enriched ocean " is published in Nature Geoscience.

The finding is very interesting from the point of view of TGD based Expanding-Earth model allowing to understand Cambrian Explosion (CE) about .54 billion years ago leading to a sudden mysterious emergence of life in a rather short time scale (13-25 million years).

TGD inspired cosmology predicts that cosmic expansion occurs for various astrophysical objects as relatively rapid jerks rather than smoothly. This allows to understand the paradoxical finding that astrophysical objects participate in cosmic expansion but do not seem to expand themselves. The expansion occurs in jerks in which the value of scale dependent cosmological constant characterizing the system decreases.

1. The radius of Earth would have expanded by a factor 2 in relatively short time scale from a value near to the radius of recent Mars and led to the formation of continents as the Earth's crust ripped. Multi-celllar life would had evolved in underground oceans shielded from meteoric bombardment and cosmic rays and bursted to the newly formed oceans at the surface.
   
   
2. The basic prediction of the model is that before CE there were no continents. This also kills the so called Snowball Earth model for the climate before CE.
   
   

The findings give a direct support for the absence of continents before CE. What the researchers did was following.

1. The goal was to understand the temperature ancient Earth about 3.2 billion years ago, and the researchers studied what they believed to be a bottom of an ancient sea. The isotope ratio of O16 to O18 decreases with temperature. The researchers constructed the temperature profile of the ancient Earth, and the surprising finding was that there was 3.2 per cent more O18 than expected. This is 4 per cent more than in today's relatively ice-free oceans and much higher than the previous estimates.
   
   
2. The isotope ratio is sensitive to landmass. The conclusion of researchers is that the unexpectedly low ratio could be due to the lack of landmasses. The Earth's surface could have been wet but there is no need to assume oceans. TGD prediction does not exclude wet surface but just the existence of continents. The high wetness could have been due to the percolation of water from underground oceans preceding the great burst - note that 3.2 billion years is by factor about 6 longer time than .54 billion years.
   
   

This picture however poses difficult questions. When and how did the continents emerge? How did life emerge if there were no landmasses so that standard model must be given up?

As already explained, TGD based model for Expanding Earth solving basic mystery of standard cosmology provides an answer to these questions and also to the mystery of Cambrian Explosion.

See the article Expanding Earth Model and Pre-Cambrian Evolution of Continents, Climate, and Life 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.

Could solar system be modelled as a miniature version of spiral galaxy?

The fractality of the TGD Universe motivates a model for planetary systems as miniature version of the model of spiral galaxy discussed in (see this). The first two key elements are many-sheeted space-time, the notion of magnetic flux tubes - both monopole flux tubes and gravitational flux tubes without monopole flux - and the identification of dark matter as phases of ordinary matter labelled by effective Planck constant h_eff=n× h₀ (h=6h₀ is a good guess (see this, this and this). Also the TGD generalization of Nottale's model for planetary system as analog of Bohr atom characterized by large gravitational Planck constant h_gr identified as h_eff is in a key role (see this) and this).

A further key aspect is the prediction of twistor lift of TGD (see this) and this) that cosmological constant is length scale dependent and characterizes various systems in all scales. The phase transitions reducing the cosmological constant lead to expansion of space-time sheet and define a sequence of jerks replacing smooth cosmic expansion for astrophysical objects expected in standard cosmology but not observed.

TGD provides a model for "cold fusion" based on dark fusion (see this) and suggests the possibility of fusion outside stellar cores perhaps serving as "warm-up band" for hot fusion during pre-stellar evolution. Also a new view about nuclear fusion in stellar interiors is suggestive (see this).

I did not originally end up with the model to be discussed from general theoretical considerations.

1. The first empirical input were the problems related to the collision - and accretion models for the formation of planets - TGD allows to consider the replacement of these models with quantal model involving the dark nuclear fusion in planetary cores.
   
   
2. The discovery of "too" heavy blackholes and neutron stars by LIGO (see this) suggesting that TGD view about the formation of also planets could provide understanding about the role of angular momentum.
   
   
3. There are also problems related to the understanding of the entire planetary system: the dramatic difference between terrestrial and giant planets is not really understood.
   
   

The problematic aspects of the Bohr orbit model together with the poorly understood differences between terrestrial and giant planets lead to a proposal that phase transition increasing the ℏ_gr by factor 5 and accompanying a transition reducing the length scale dependent cosmological constant Λ could have scaled up the orbital radii of former inner planets. The transition could have also scaled up the radii of the former inner planets so that they became giant planet.

See the article Could solar system be modelled as a miniature version of spiral galaxy? or the chapter with the same title.

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

Articles and other material related to TGD.