How dark matter and visible matter interact?

How dark matter and visible matter interact is the question that I have pondered for a few weeks in light of results achieved in understanding the role of von Neumann algebras in quantum TGD. I have posted two variants of the model for this interaction but found better to delete the postings. I hope that the third version is already nearer to the final one. The basic hypothesis that the value of hbar is dynamical, quantized and becomes large at the verge of a transition to a non-perturbative phase in the ordinary sense of the word has fascinating implications. In particular, dark matter, would correspond to a large value of hbar and could be responsible for the properties of the living matter. In order to test the idea experimentally, a more concrete model for the interaction of ordinary matter and dark matter must be developed and here of course experimental input and the consistency with the earlier quantum model of living matter is of considerable help.

1. Basic implications from the scaling of hbar

It is relatively easy to deduce the basic implications of the scaling of hbar.

• If the rate for the process is non-vanishing classically, it is not affected in the lowest order. For instance, scattering cross sections for say electron-electron scattering and e^+e^-annihilation are not affected in the lowest order since the increase of Compton length compensates for the reduction of alpha_{em}. Photon-photon scattering cross section, which vanishes classically and is proportional to alpha_{em}^4*hbar^2/E^2, scales down as 1/hbar^2.
• Higher order corrections coming as powers of the gauge coupling strength alpha are reduced since alpha= g^2/4*pi*hbar is reduced. Since one has hbar_s/hbar= alpha*Q_1*Q_2/v_0, alpha*Q_1*Q_2 is effectively replaced with a universal coupling strength v_0=about 4.6*10^{-4}. In the case of QCD the paradoxical sounding implication is that alpha_s becomes very small in non-perturbative phase.

2. Simple model for dark atoms

The model for dark atoms requires model for dark nuclei and dark electrons.

• The simplest model for dark nuclei is as blobs of N_{cr} dark nuclei surrounded by dark electrons at distance which is scaled by a factor k^2, k=hbar_s/hbar from that for ordinary atom. Thus the dark nucleus looks point-like from the point of view of the electron cloud. As far as electrons are considered there are two options. a) Dark electrons could behave as independent particles with the interaction strength with the dark nucleus given by N*Z*alpha. The critical value N_{cr} of N is determined from the condition of criticality for single electron dark nucleus interaction: [X]=1, X=N_{cr}*Z*alpha. Here [X] denotes the largest integer smaller than X. Criticality implies hbar_s/hbar=X/v_0=about 1/v_0. Note that the condition 1 <=X< 2 implying that hbar_s/hbar is in the range [1/v_0, 2/v_0). b) Dark electrons are in the same state apart from the values of super-canonical conformal weights making possible to satisfy fermionic statistics. They behave like a single super-electron with mass N_{cr}*m_e and em charge N_{cr}*e. In this case the criticality condition reads [X]=1, X= N_{cr}^2*Z*alpha. The criticality implies hbar_s/hbar=X/v_0=about 1/v_0.
• The binding energy scale E propto Z^2*alpha_{em}^2*m_e of atoms scales as 1/hbar^2 so that a partially dark matter for which protons have large value of hbar does not interact appreciably with the visible light. Scaled down spectrum of atomic binding energies would be the experimental signature of dark atoms. The resulting binding energy spectrum is independent of the atom in the approximation X=1. The binding energy scale defined by the ionization energy E_0=Z^2*alpha^2*m_e/4 as given by Bohr model is replaced with E_0=v_0^2*m_e/4*X^2 =about 26.5/X^2 meV. Different values of X allow to distinguish between different atoms since the energy scale differ by a factor 1/4 from the maximal one. It should be noticed that the resting potential of neuron is around .64 meV (the value varies in considerable limits up to 80 meV).
• The ionization wavelength for ordinary hbar would be =about 46.5*X^2 microm, which for X=1 below the maximal size of neuron about 100 microm. For hbar_s= hbar/v_0 the wavelength is given by factor 46.5*X^3/v_0 and =about 9.4*X^3 cm, which happens to be the size scale of brain hemisphere for X=1.
• The Bohr radius of dark atom scales as hbar^2 and is given by a_d=(X/v_0)^2*a_0 =about .2*X^2<.8 mm, (a_0=hbar/alpha_{em}m_e). The size of basic multi-neuron modules in cortex is about 1 mm. These intriguing observations give hints about the possible role of dark atoms in the functioning of living matter and brain.

3. How dark photons transform to ordinary photons?

The transitions of dark atoms naturally correspond to coherent transitions of the entire dark electron BE condensate and thus generate N_{cr} dark photons which have complex conformal weights and are conformally confined and behave thus like laser beams. Dark photons do not interact directly with the visible matter. The simplest guess is that the transformation of dark photon BE condensates to ordinary photons corresponds to a loss of coherence by conformal liberation in which conformal weights of photons become real. An open question is whether even ordinary laser beams could be identified as beams of dark photons. Note that the transition from dark to ordinary photons implies the reduction of wave length and thus also of coherence length by a factor v_0. Dark-visible transition should have also a space-time correlate. The so called topological light rays or MEs ("massless extremals") represent a crucial deviation of TGD from Maxwell's ED and have all the properties characterizing macroscopic classical coherence. Therefore MEs are excellent candidates for the space-time correlate of BE condensate of dark photons. MEs carry in general a superposition of harmonics of some basic frequency determined by the length of ME. A natural expectation is that the frequency of classical field corresponds to the generalized de Broglie frequency of dark photon and is thus hbar/hbar_s *lower than for ordinary photons. In completely analogous manner de Broglie wave length is scaled up by k=hbar_s/hbar. Classically the decay of dark photons to visible photons would mean that an oscillation with frequency f inside topological light ray transforms to an oscillation of frequency f/k such that the intensity of the oscillation is scaled up by a factor k. Furthermore, the ME in question could naturally decompose into 1< N_{cr}=< 137 ordinary photons in case that dark atoms are in question. Of course also MEs could decay to lower level MEs and this has an interpretation in terms of hierarchy of dark matters to be discussed next.

4. Hierarchy of dark matters and hierarchy of minds

The notion of dark matter is only relative concept in the sense that dark matter is invisible from the point of view of the ordinary matter. One can imagine an entire hierarchy of dark matter structures corresponding to the hierarchy of space-time sheets for which p-adic length scales differ by a factor 1/v_0=about 2^{11}. The BE condensates of N_{cr} ordinary matter particles would serve as dynamical units for "dark dark matter" invisible to the dark matter. The above discussed criticality criterion can be applied at all levels of the hierarchy to determine the value of the dynamical interaction strength for which BE condensates of BE condensates are formed. This hierarchy would give rise to a hierarchy of the values of hbar_n/hbar coming as powers of v_0^{-n} as well as a hierarchy of wavelengths with same energy coming as powers or v_0^{n}. For zero point kinetic energies proportional to hbar^2 this hierarchy would come in powers of v_0^{-2n}, for magnetic interaction energies proportional to hbar the hierarchy would come in powers v_0^{-n} whereas for atomics energy levels the hierarchy would come in powers of v_0^{2n} (assuming that this hierarchy makes sense). The most interesting new physics would emerge from the interaction between length scales differing by powers of v_0 made possible by the decay of BE condensates of dark photons to ordinary photons having wavelength shorter by a factor =about v_0. This interaction could provide the royal road to the quantitative understanding how living matter manages to build up extremely complex coherent interactions between different length and time scales. In the time domain dark matter hierarchy could allow to understand how moments of consciousness organize to a hierarchy with respect to the time scales of moment of consciousness coming as 2^{11k} multiples of CP_2 time scale. Even human life span could be seen as single moment of consciousness at k=14^{th} level of the dark matter hierarchy whereas single day in human life would correspond to k=12.

5. Realization of intentional action and hierarchy of dark matters

How long length scales are able to control the dynamics in short length scales so that the extremely complex process extending down to atomic length scales realizing my intention to write this word is possible. This question has remained without a convincing answer in the recent day biology and there strong objections against the idea that this process is planned and initiated at neuronal level. I have proposed a concrete mechanism for the realization of intentional action in terms of time mirror mechanism involving the emission of negative energy photons and proceeding as a cascade in a reversed direction of geometric time from long to short length scales. This cascade would induce as a reaction analogous processes proceeding in the normal direction of geometric time as a response and would correspond to the neural correlates of intentional action in very general sense of the word. The counterparts for the negative energy signals propagating to the geometric past would be phase conjugate (negative energy) laser beams identifiable as Bose-Einstein condensates of dark photons. In the time reflection these beams would transform to positive energy dark matter photons eventually decaying to ordinary photons. The space-time correlate would be MEs decaying into MEs and eventually to CP_2 type extremals representing ordinary photons. The realization of intentional action as desires of boss expressed to lower level boss would naturally represented the decay of the phase conjugate dark laser beam to lower level laser beams decaying to lower level laser beams decaying to... . This would represent the desire for action whereas the time reflection at some level would represent the realization desire as stepwise decay to lower level laser beams and eventually to ordinary photons. The strong quantitative prediction would be that these levels correspond to a length and time scale hierarchies coming in powers of 1/v_0sim 2^{11}.

6. Wave-length hierarchy, coherent metabolism, and proton-electron mass ratio

The fact that a given wavelength length corresponds to energies related to each other by a scaling with powers of v_0 provides a mechanism allowing to transfer energy from long to short long scales by a de-coherence occurring either in the standard or reversed direction of geometric time. De-coherence in the reversed direction of time would be associated with mysterious looking processes like self-assembly allowing thus an interpretation as a normal decay process in reversed time direction. It is perhaps not an accident that the value of v_0=about 4.6*10^{-4} is not too far from the ratio of m_e/m_p=about 5.3*10^{-4} giving the ratio of zero point kinetic energies of proton and electron for a given space-time sheet. This co-incidence could in principle make possible a metabolic mechanism in which dark protons and ordinary electrons co-operate in the sense that dark protons generate dark photon BE condensates with wave length lambda transforming to ordinary photons with wavelength v_0*lambda absorbed by ordinary electrons. Some examples are in order to illustrate these ideas.

• As already found, in the case of dark atoms the scaling of binding energies as 1/hbar^2 allows the coupling of about 9 cm scale of brain hemisphere with the length scale about 50 mum of large neuron. N_{cr}<= 137 ordinary IR photons would be emitted in single burst and interacting with neuron.
• For a non-relativistic particle in a box of size L the energy scale is given by E_1=hbar^2*pi^2/2*m*L^2 so that the visible photons emitted would have energy scaled up by a factor (hbar_s/hbar)^2=about 4*10^6. The collective dropping of N_{cr} dark protons to larger space-time sheet would liberate a laser beam of dark photons with energy equal to the liberated zero point kinetic energy. For instance, for the p-adic length scale L(k=159=3*53)=about .63 microm this process would generate laser beam of IR dark photons with energy about. 5 eV also generated by the dropping of ordinary protons from k=137 atomic space-time sheet. There would thus be an interaction between dark protons in cell length scale and ordinary protons in atomic length scale. For instance, the dropping of dark protons in cell length scale could induce driving of protons back to the atomic space-time sheet essential for the metabolism. Similar argument applies to electrons with the scale of the zero point kinetic energy about 1 keV.
• If the energy spectrum associated with the conformational degrees of freedom of proteins, which corresponds roughly to a frequency scale of 10 GHz remains also invariant in the phase transition to dark protein state, coherent emissions of dark photons with microwave wave lengths would generate ordinary infrared photons. For instance, metabolic energy quanta of=about.5 eV could result from macroscopic Bose-Einstein condensates of 58 GHz dark photons resulting from the oscillations in the conformational degrees of freedom of dark proteins. A second option is that the conformal energies are scaled by hbar_s/hbar (omega would remain invariant). In this case these coherent excitations would generate ordinary photons with energy of about 1 keV able to drive electrons back to the atomic k=137 space-time sheet.
• Since magnetic flux tubes have a profound role in TGD inspired theory of consciousness, it is interesting to look also for the behavior of effective magnetic transition energies in the phase transition to the dark matter phase. This transition increases the scale of the magnetic interaction energy so that anomalously large magnetic spin splitting hbar_seB/m in the external magnetic field could serve as a signature of dark atoms. The dark transition energies relate by a factor hbar_s/hbar to the ordinary magnetic transition energies. For instance, in the magnetic field of Earth with a nominal value .5*10^{-4} Tesla dark electron cyclotron frequency is 6*10^5 Hz and corresponds to ordinary microwave photon with frequency =about1.2 GHz and wavelength lambda=about 25 cm. For proton the cyclotron frequency of 300 Hz would correspond to energy of ordinary photon with frequency of 6*10^5 Hz and could induce electronic cyclotron transitions and spin flips in turn generating for instance magneto-static waves. It is easy to imagine a few step dark matter hierarchy connecting EEG frequencies of dark matter with frequencies of visible light for ordinary photons. This kind of hierarchy would give considerable concreteness for the notion of magnetic body having size scale of Earth.

7. A connection with the scaling law of homeopathy

The value of the parameter 1/v_0(is essentially the ratio of CP_2 radius and Planck length scale (as also the ratio of Compton lengths of electron and proton) and rather near to 2^{11}. Interestingly, much larger number 2 *10^{11}=about 25*2^{33} appears in the simplest form for what I have christened the scaling law of homeopathy. This rule has been proposed on basis of experimental findings but has no convincing theoretical justification. The scaling law of homeopathy states that high frequency em radiation transforms to a low frequency radiation and vice versa preferably with the frequency ratio f_{high}/f_{low}=about 2*10^{11}. I have discussed some mechanisms for the transformation of high energy photons to low energy photons consistent with the rule and proposed a generalization of the rule based on p-adic length scale hypothesis. For instance, high energy visible photons of frequency f could induce an excitation of the receiving system having same frequency, propagating with velocity beta =v/c=about 10^{-11}/2, and having wave length equal lambda_0= f/v= lambda/beta. This excitation would in turn couple to photons of wavelength lambda_0 and frequency f_0=beta f. The proposed hierarchy of dark matter and ensuing hierarchy of dark laser beams decaying into lower level beams might provide a deeper explanation for the scaling law of homeopathy. First of all, the factor about 2*10^{11} is roughly equal to 3^3*v_0^{-3} which means that only three level hierarchy can be in question and that the sub-harmonic v_0/3 instead of v_0 must appears. Also the model of outer planetary orbits requires the third sub-harmonic v_0/3, and TGD provides a topological explanation for these harmonics in terms of the decay of magnetic flux tubes to three smaller flux tubes carrying each one third of the original magnetic flux. If v_0 is replaced with v_0/3, the predicted scaling factor is correct for v_0=5.13*10^{-4} corresponding exactly to 1/v_0=1950 (I cannot resist the temptation to mention that this happens to be my own birth year!: the world is filled with funny numerological accidents). For v_0=4.6*10^{-4} and n=3 sub-harmonic the scaling factor is 2.8*10^{11} and is definitely too large. It must be however noticed that hbar_s/hbar=1/v_0 holds true only only approximately: in reality hbar_s/hbar belongs to the interval [1/v_0,2/v_0). This allows to consider the possibility that the value of v_0 deduced from the quantization of the planetary orbits is quite not correct but equals to v_0(eff)=v_0/X, X \in [1,2). For X= 1.4 and v_0=5.13*10^{-4} one would indeed have v_0(eff)=4.8*10^{-4}. Even the value v_0= m_e/m_p=about 5.3*10^{-4} can be considered. Also the value v_0(eff)=2^{-11}, which is especially natural from the point of view of p-adic length scale hypothesis could be achieved as effective value of v_0. For more details see the chapter TGD and Astrophysics" of TGD and the chapter "Quantum Coherent Dark Matter and Bio-Systems as Macroscopic Quantum Systems" of "Genes, Memes, Qualia,...".