The original model for inherently dark atom relies on the scaling of hbar by λ^{k} at the k^{th} level of the dark matter hierarchy. Here λ is integer and λ ≈ 2^{11} defines a preferred value of λ. Also the harmonics and integer valued sub-harmonics of λ might be possible. In the case of hydrogen atom the model predicts that the energies of hydrogen atom proportional to 1/hbar^{2} are scaled down by 1/λ^{2k} so that dark atoms would not be thermally stable at room temperature. In practice this would exclude dark atoms and molecules as biologically interesting inherently dark systems.

The topological condensation of ordinary atoms and molecules at λ^{k}-sheeted (now in the sense of "Riemann surfaces" over M^{4}) dark magnetic flux quanta is however possible and means scaling up of the cyclotron energy by λ^{k} making possible cyclotron Bose-Einstein condensates at high temperatures identifiable as dark quantum plasmas. The same scaling occurs to the energy of dark plasma oscillations so that their energies can be above thermal threshold. Dark plasmoids and plasma oscillations are indeed fundamental in the TGD based model of quantum control in living matter.

This leads to a very restrictive model for living matter. This model is very successful but has some features which suggest that it is not the whole story. For instance, the conformal and rotational spectra of bio-molecules correspond to microwave frequencies and would be below thermal threshold and thus should be of minor importance in contrast with experimental facts. This would also reduce the importance of liquid crystals known to be of crucial for the functioning of living matter. There is also a feeling that the role of fermionic bio-ions such as Na^{+}, K^{+}, and Cl^{-} should be more important than this picture allows.

In the sequel a modification of the notion of inherently dark atom in which the dark energy spectra are essentially the same as the ordinary ones, will be discussed.

** 1. Inherently dark atoms as radial anyons?**

The model of inherently dark atoms as radial anyons predicts that the energy spectra of dark atoms and molecules are nearly the same as their ordinary counterparts.

- Dark atoms having ordinary size and ordinary energy spectrum could be possible if the principal quantum number n is fractionized to n→n/λ
^{k}. The fractionization could make sense if the atomic space-time sheet is λ^{k}-folded and atoms become radial anyons. The corresponding Bohr orbits would close in the radial direction only after λ^{k}turns. The formation of dark atoms could be interpreted as a transition to chaos by period λ^{k}-folding in radial and angular degrees of freedom. This option would differ from the original model in that radial scaling in M^{4}by a factor λ^{2k}is replaced by a radial λ^{k}-folding so that the M^{4}projection of dark atom has the same size as in the case of ordinary atom. - Since dark atom would define a λ
^{k}-fold covering of M^{4}, one expects a degeneracy of states corresponding to the phase factors exp(ikn2π/λ^{k}), k=0,...,λ^{k}-1, where n labels the sheets of the λ^{k}-fold covering of M^{4}. The nuclei and electrons of N≤ λ^{k}dark atom could form many-particle states separately and fermionic statistics becomes effectively para-statistics for the resulting N-atoms. Note that the N electrons and nuclei would be in identical states in ordinary sense of the word since Bohr orbits must be identical: kind of fermionic Bose-Einstein condensates become thus possible. - The quantum transitions of N-atoms for N=λ
^{k}would give rise to dark counterparts of the photons emitted in the ordinary atomic transitions. For N ≤ λ^{k}the energies of dark photons would be N times higher than the energies liberated in the ordinary transitions. The claims of Randell Mills about the scaling up of the binding energy of the hydrogen ground state by a square k^{2}of an integer in plasma state might be understood as being due to the formation of dark N=k^{2}-atoms emitting dark photons with k^{2}-fold energies de-cohering to ordinary photons. Also nore general states are however predicted now. A fraction of plasma phase in Mills experiments would be in dark plasma state. The chemistry of bio-molecules identified as N-molecules would definitely differ from the ordinary chemistry. - The fractionization n→n/λ
^{k}of the integer n labelling vibrational modes and cyclotron states would be unavoidable. Single particle cyclotron states having E= hbar (k)ω of the earlier picture would in this framework correspond to single particle states having n=λ^{k}or to N=λ^{k}-ion states. Fermionic N=λ^{k}-states are expected to have a special role since these configurations are analogous to noble gas atoms with full shells of electrons and to magic nuclei with full cells of nucleons. Most biologically important ions are fermions and N=λ^{k}states would give rise to what might be regarded as fermionic analogs of Bose-Einstein condensates. For bosonic ions there is no restriction to the occupation numbers of λ^{k}single particle states involved.

**2. Connection with quantum groups?**

The phase q= exp(i2π/λ^{k}) brings unavoidably in mind the phases defining quantum groups and playing also a key role in the model of topological quantum computation tqc}. Quantum groups indeed emerge from the spinor structure in the "world of classical worlds" realized as the space of 3-surfaces in M^{4}× CP_{2} and being closely related to von Neumann algebras known as hyper-finite factors of type II_{1} vNeumann}. Unfortunately, the integer n characterizing the phase cannot be identified as λ. This allows to ask whether quantum groups could emerge in two different manners in TGD framework.

If so, living matter could perhaps be understood in terms of quantum deformations of the ordinary matter, which would be characterized by the quantum phases q= exp(i2π/λ^{k}). Hence quantum groups, which have for long time suspected to have significance in elementary particle physics, might explain the mystery of living matter and predict an entire hierarchy of new forms of matter.

**3. Are both options for dark matter realized?**

For N=λ^{k} molecules which dark photons emitted in the rotational and conformational transitions would be above thermal threshold. It is of course quite possible that both options are realized. The fact that also fermionic ions (such as Na^{+}, K^{+}, Cl^{-}) are important for living system suggests that this is the case. This would also provide a justification for the hypothesis that microtubular conformations represent bits and allow protein conformational dynamics to serve as metabolic controller by providing microwave dark photons with energies above thermal threshold.

**4. How to distinguish between N-molecules and ordinary molecules?**

The unavoidable question is whether bio-molecules in vivo could be actually N-molecules or whether they could involve some component which is N-molecule. This raises a series of related questions.

- Could it be that we can observe only the decay products of dark N-fold molecules to ordinary molecules? Is matter in vivo dark matter and matter in vitro ordinary matter? Could just the act of observing the matter in vivo in the sense of existing science make it ordinary dead matter?
- How can one distinguish between N-fold and ordinary molecules? Electromagnetic interactions, and more generally gauge forces, do not allow to distinguish classically between these molecules since there are no direct quantum interactions between them. The gravitational forces generated by N-molecules are too weak to allow to distinguish from N molecules.
- The decay of N-molecule via decay to N ordinary molecules in principle allows to conclude that N-molecule was present. But could this process mean just the replacement of DNA in vivo with DNA in vitro?
- The emission of dark N-photons decaying via decay to N photons can serve as a signature of N-molecules. If the molecules are fermions this would in principle allow to exclude the interpretation in terms of coherent emission of photons from Bose-Einstein condensate of N ordinary molecules. Bio-photons indeed represent this kind of radiation having no obvious explanation in standard physics context.

For more detailed views see the chapter Many-Sheeted DNA of "Genes, Memes, Qualia,...".

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