Does the Lorentz invariance for p-adic mass calculations require the p-adic mass squared values to be Teichmüller elements?

p-Adic mass calculations involve canonical identification I: x= ∑_nx_npⁿ ∑ x_np^-n mapping the p-adic values of mass squared to real numbers. The momenta p_i at the p-adic side are mapped to real momenta I(p_i) at the real side. Lorenz invariance requires I(p_i· p_j)= I(p_i)· I(p_j). The predictions for mass squared values should be Lorentz invariant. The problem is that without additional assumptions the canonical identification I does not commute with arithmetics operations.

Sums are mapped to sums and products to products only at the limit of large p-adic primes p and mass squared values, which correspond to x_n≤≤ p. The p-adic primes are indeed large: for the electron one has p= M₁₂₇=2¹²⁷-1∼ 10³⁸. In this approximation, the Lorentz invariant inner products p_i· p_j for the momenta at the p-adic side are indeed mapped to the inner products of the real images: I(p_i· p_j)= I(p_i)· I(p_j). This is however not generally true.

1. Should this failure of Lorentz invariance be accepted as being due to the approximate nature of the p-adic physics or could it be possible to modify the canonical identification? It should be also noticed that in zero energy ontology (see this), the finite size of the causal diamond (CD) (see this) reduces Lorent symmetries so that they apply only to Lorenz group leaving invariant either vertex of the CD.
2. Or could one consider something more elegant and ask under what additional conditions Lorentz invariance is respected in the sense that inner products for momenta on the p-dic side are mapped to inner products of momenta on the real side.

The so called Teichmüller elements of the p-adic number field could allow to realize exact Lorentz invariance.

1. Teichmüller elements T(x) associated with the elements of a p-adic number field satisfy x^p=x, and define therefore a finite field G_p, which is not the same as that given by p-adic integers modulo p. Teichmüller element T(x) is the same for all p-adic numbers congruent modulo p and involves an infinite series in powers of p.

   The map x→ T(x) respects arithmetics. Teichmüller elements of for the product and sum of two p-adic integers are products and sums of their Teichmüller elements: T(x₁+x₂)= T(x₁)+T(x₂) and T(x₁x₂)= T(x₁)T(x₂).

2. If the thermal mass squared is Teichmüller element, it is possible to have Lorentz invariance in the sense that the p-adic mass squared m²_p= p^kp_k defined in terms of p-adic momenta p_k is mapped to m²_R=I(m²_p) satisfying I(m²_p)= I(p^k)I(p_k). Also the inner product p₁· p₂ of p-adic momenta mapped to I(p₁· p₂)=I(p₁)· I(p₂) if the momenta are Teichmüller elements.
3. Should the mass squared value coming as a series in powers of p mapped to Teichmüller element or should it be equal to Teichmüller element?
   1. If the mass squared value is mapped to the Teichmüller element, the lowest order contribution to mass squared from p-adic thermodynamics fixes the mass squared completely. Therefore the Teichmüller element does not differ much from the p-adic mass squared predicted by p-adic thermodynamics. For the large p-adic primes assignable to elementary particles this is true.

   2. The radical option is that p-adic thermodynamics and momentum spectrum is such that it predicts that thermal mass squared values are Teichmüller elements. This would fix the p-adic thermodynamics apart from the choice of p-adic number field or its extension. Mass squared spectrum would be universal and determined by number theory. Note that the p-adic mass calculations predict that mass squared is of order O(p): this is however not a problem since one can consider the m²/p.

This would have rather dramatic physical implications.

1. If the allowed p-adic momenta are Teichmüller elements and therefore elements of G_p then also the mass squared values are Teichmüller elements. This would mean theoretical momentum quantization. This would imply Teichmüller property also for the thermal mass squared since p-adic thermodynamics in the approximation that very higher powers of p give a negligible contribution give a finite sum over Teichm\"muller elements. Number theory would predict both momentum and mass spectra and also thermal mass squared spectrum.

   What does it mean that the product of Teichmüller elements is Teichmüller element? The product xy can be written as ∑_k (xy)_k p^k, (xy)_k=∑_l x_k-ly_l. For Teichmüller elements (xy)_k has no overflow digits. This is true also for I(xy) so that I(xy)= I(x)I(y). Similar argument applies to the sum.

2. The number of possible mass squared values in p-adic thermodynamics would be equal to the p-adic prime p and the mass squared values would be determined purely number theoretically as Teichmüller representatives defining the elements of finite field G_p. The p-adic temperature (see this), which is quantized as 1/T_p=n, can have only p values 0,1,...p-1 and 1/T_p=0 corresponds to high temperature limit for which p-adic Boltzman weights are equal to 1 and the p-adic mass squared is proportional to m²= ∑ g(m) m/∑g(m), where g(m) is the degeneracy of the state with conformal weight h=m. T_p=1/(p-1) corresponds to the low temperature limit for which Boltzman weights approach rapidly zero.

See the article Could the precursors of perfectoids emerge in TGD? or the chapter Does M⁸-H duality reduce classical TGD to octonionic algebraic geometry?: Part III

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

3 kielimallin avulla tehtyä videota TGD:stä ja TGD:n inspiroimasta tietoisuuden teoriasta.

Marko Manninen ja Tuomas Sorakivi tekivät kielimallia käyttänen videon TGD inspired theory of consciousness TGD:n insproimasta tietoisuuden teoriasta.

Tuomas Sorakivi teki kielimallin avulla videon Topologinen Geometrodynamiikka ja Tietoisuus liittyen TGD:n inspiroimaan tietoisuuden teoriaan ja videon Todellisuus yhtälönä liittyen holografia = holomorfia periaatteeseen.

Vaikka mukana on hypeä niin videot antavat mielestäni hyvän kokonaiskuvan siitä mistä on kyse.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Periodic table of topological insulators and topological superconductors and discrete symmetries at the space-time level

At the level of the embedding space H=M⁴× CP₂, the TGD view about discrete symmetries T, P, and C is essentially the same as in the standard model except that C has a geometric interpretation as a complex conjugation in CP₂ and has therefore a geometric meaning (see this). At the space-time level holography = holomorphy principle (see this, this, and this) forces us to reconsider the TGD based view of discrete symmetries. They would relate naturally to transformations relating different holomorphic structures differing by a conjugation of some in some complex coordinates of H or of a hypercomplex coordinate of M⁴.

How do these discrete symmetries relate to those of condensed matter physics? According to Wikipedia (see this), the periodic table of topological insulators and topological superconductors, also called tenfold classification of topological insulators and superconductors, is an application of topology to condensed matter physics. It indicates the mathematical group for the topological invariant of the topological insulators and topological superconductors, given a dimension and discrete symmetry class. The ten possible discrete symmetry families are classified according to three main symmetries: particle-hole symmetry, time-reversal symmetry and chiral symmetry. The table was developed between 2008 2010 by the collaboration of Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig; and independently by Alexei Kitaev. The table applies to topological insulators and topological superconductors with an energy gap, when particle-particle interactions are excluded. The table is no longer valid when interactions are included. The table applies in dimensions D=1, 2, 3. The table also gives the value set of the topological invariant with the associated symmetry, which can be Z₂, Z or 2Z in these dimensions.

Three basic symmetries appear in the 10-fold periodic table for topological insulators and superconductors and various cases are classified by the symmetries T, C, and S for which the squares of these symmetries are well-defined and by the broken symmetries. T acts as time reversal, C is the analog of charge conjugation, which transforms particles and holes to each other, and chiral transformation S transforms left-and right-handed chiralities to each other. C and T are antiunitary operators involving hermitian conjugation at the level of the Hilbert space and expressible as products of a unitary operator with a complex conjugation operator K. CPT is therefore unitary and it is possible to have CPT=1. These transformations are idempotent: T²=Id, C²=Id, S²=Id. In quantum theory, one can consider the possibility that their representations are projective so that one can have T²=-Id and C²=-Id. S²=1 holds always true.

In the table of the Wikipedia article, the violation of these symmetries is expressed using the symbol X. My understanding is that for instance, the charge conjugate need not belong to the space of allowed states. The TGD counterparts of T, S, and C at the space-time level would be naturally realized in terms of various conjugations of the complex coordinates and hypercomplex coordinate of H.

1. In the TGD framework, holography = holomorphy vision involves the notion of Hamilton-Jacobi structure for M⁴ ⊂ M⁴× CP₂ (see this) as a combination of longitudinal hypercomplex structure and transversal complex structure. The hypercomplex coordinate u has coordinate lines with light-like tangent vectors and the hypercomplex conjugation transforms u to its conjugate v (both coordinates are real).

   The complex coordinate w is transversal to (u and v). The coordinate lines define local polarization direction and light-like direction and characterize massless extremals as analogs of modes of massless fields. To simplify the situation, it is convenient to consider the simplex possible hypercomplex structure with (u= t-z,v= t+z) and w identifiable as the transversal planar complex coordinate w=x+iy.

2. There are two complex CP₂ coordinates ξⁱ but the conjugation as a symmetry applies simultaneously to both of them. CP₂ complex conjugation is naturally related to C, or at least its particle physics counterpart mapping fermions with antifermions and vice versa. In condensed physics C maps creation and annihilation operators of fermions (electrons and holes) to each other and one expects that CP₂ complex conjugation is involved.

   The complex conjugation in M⁴ cannot be involved with C. Does C involve HC? Geometric picture does not favor this. CPT =1 at the space-time level does not allow the presence of HC in C since HC is involved with both P and T realized at the space-time level assuming holography= holomorphy principle.

3. Chiral transformation S changed the chirality of say DNA strand and actd as reflection P. S would therefore naturally correspond to the HC: u→ v combined with w→ -w? Also no hypercomplex structure goes to its conjugate. This definition of S and the relation S=TC which by S²=1, is assumed in the 10-fold periodic table, corresponds to CPT=1. Together with S²=1, which is always true in the periodic table, it guarantees CST=1 as a counterpart of CPT=1. Note that neither C nor P are symmetries at the level of the Dirac equation at the embedding space level while CP is.
4. For the simplest option (u,v)=(t-z,t+z), HC combined with T corresponds to u→ -u and changes the functional form of f. This does not affect the generalized complex structure but affects the space-time spacetime surface. T corresponds to HC followed but u→ -u and conjugation of the HC structure and change of the analytic form. For P the presence of HC conjugation changes the hypercomplex structure.
5. w→ -w and (u,v)→ -(u,v) as analog of PT does not affect the generalized complex structure but affect the space-time surface since the functional form of the functions (f₁,f₂) obeying generalized holomorphy is changes. P, T, and CP affect the generalized complex structure and are always accompanied by HC. These symmetries cannot leave space-time surfaces invariant unless they consist of regions with different generalized complex structures glued together.
6. The minus sign in T² and C² could be also due an additional multiplication of the complex coordinate of H with an imaginary unit. In the case of T, -1 sign cannot appear in this way but would come from the unitary operator.

A possible interpretation of these symmetries is as space-time analogs of the basic symmetries of H representable in terms of complex and hypercomplex conjugations allowing to transform space-time surfaces satisfying holography= holomorphy principle to new such surfaces.

1. If all 3 basic conjugations are performed one obtains a new preferred extremal if longitudinal and transversal M⁴ degrees are independent. Same is true if one performs either both M⁴ conjugations or both CP₂ conjugations.
2. What is new is that the holomorphy violates these symmetries locally at the level of a single space-time surface. For instance, matter and matter could correspond to space-time regions with holomorphic structures related by CP₂ conjugation C and the formation of large space-time regions with a given holomorphic structure could correspond to matter antimatter asymmetry. This globalization of C and CP could relate the mystery of antimatter symmetry. These regions could correspond to the field bodies with large size induced antimatter asymmetry at the smaller space-time sheets associated with them. Quantum coherence in astrophysical and even cosmic scales with a quantum coherence scale characterizing the space-time surface, would be essential (see this).
3. The model for elementary particles (see this) involves in an essential manner a pair of parallel Minkoskian space-time sheets connected by wormhole contacts. How could the complex structures of the Minkowskian space-time sheets relate to each other?

   Ordinary complex surfaces are invariant under complex conjugation although the complex structure changes in the conjugation. Also the space-time surface can remain invariant under the complex conjugation although it is holomorphic with respect to the complex coordinates. What about the hypercomplex conjugation? Could the parallel space-time sheets be related by a hypercomplex conjugation HC and possibly also by the conjugation w→ w and C? If they are related by charge conjugation C (see this), fermions and antifermion lines would reside at the wormhole throats of opposite space-time sheets, which has been assumed.

4. One can also consider quantum superpositions of the space-time surfaces with different complex and hypercomplex structures. The expectation is that fermion and antifermion lines reside at the opposite wormhole throats of the space-time sheets connected by wormhole contacts. Do the space-time sheets have conjugate complex structures in both CP₂ and M⁴? Interesting questions relate to the CP breaking of K⁰ and B⁰ mesons. CP involves HC conjugating the hypercomplex structure and affecting the space-time surface: at the level H and Dirac equation this kind CP violation does not occur. Could the presence of HC explain the CP violation?

See the article TGD and Condensed matter or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

How large heff states are stabilized?

The quantum critical state is unstable by definition because the h_eff> h states are more energetic than the h_eff=h states and spontaneously decay into these.

One way to avoid this would be for the h_eff> h molecule to form a bound state, for example with a molecule or a larger structure. The electric field of the larger charged structure and that in turn a state where h_eff would be stabilized. However, I do not understand the details of the mechanism. How to build a state in which h_eff> h dark protons are possible in the minimum energy state. Is this possible if only the electromagnetic interaction is involved?

This is a fundamental question. So let's start from a clean table.

1. In the case of DNA and cell membranes, h_eff stabilization is related to the presence of electric fields, but do they produce the stabilization or are they a consequence of it?

   A h_eff> h state and a state bound with another state are created so that the h_eff> h state stabilizes because the dissociation is no longer energetically favorable. It should be noted that due to their large negative charge DNA and the cell membrane are biologically completely unique. Charge separation does also occur at the level of the brain and the whole body and its sign correlates with the level of consciousness: the sign of the voltage changes during sleep. The Earth itself also has an electric field, which suggests that the biosphere is conscious.

2. In the case of DNA, the bound state would be between phosphate and deoxyribose. Would the large h_eff=h_em somehow be made possible by the longitudinal and radial electric fields of DNA or is it a consequence of a stabilization mechanism? Maintaining the electric field requires energy, so metabolic energy input is still necessary but at the level of classical fields. But do electric fields maintain dark protons at the monopole flux tubes or vice versa?

   The problem: In the case of DNA, the repulsive energy of the negative charges of the phosphates destabilizes the state. In addition, there is repulsion between the dark protons in the flux tubes. Charge separation, where the dark protons and the phosphate ions are far apart, requires energy because the neutral ground state is of minimum energy.

   The solution of the problem: Some interaction energy must compensate for the increase in interaction energy. Could strong interactions of the dark protons in the flux tubes, proposed to form dark nuclei with a scale down nuclear binding energy, be involved? The strong interaction would stabilize the repulsive energy of the negative charge of the phosphates, the same would happen for the dark protons. Long range electric field would be a consequence, not the cause.

   1. The TGD-based model of cold fusion this, this, this, and this) indeed assumes that the dark protons in the magnetic flux tubes form an analogy of the atomic nucleus and the scaled binding energy of the nucleus would produce the binding energy. Strong interactions in the TGD sense would play a key role in biology and also in electrolysis. This would be new and revolutionary.
   2. Of course, one could try to cope with just electromagnetic interactions.

      i) The negative electrostatic energy would be between the dark protons and the negative charge of the phosphates. One would expect this energy to be small, but is it for flux tubes?
      ii) What about the role of water? It can become positively charged (and for example Mg²⁺ ions do), which can produce a Coulomb bound state. Mg²⁺ ions are naturally present in monopole flux tubes, but is the contribution large enough?
      iii) The binding energy is related to the bound state between negatively charged phosphates and riboses. The problem is that ribose molecules are not permanently positively charged. This doesn't seem promising.
      

   3. In the case of the cell membrane, the electric field associated with the membrane potential should accompany large values of h_eff. A decrease in the field strength below a critical value would lead to a decrease in the value of h_em, perhaps down to h_eff=h because h_em is proportional to the field value and quantized as an integer. The scale of quantum coherence would be reduced and a nerve impulse would be generated.

      The naive Maxwellian assumption would be that a nerve impulse is generated when the voltage is too high: there would be a di-electric breakdown, just as is supposed to happen in a Tesla coil. The fact that exactly the opposite happens is a central mystery of biology. A decrease in h_em would explain the mystery. One can pose an interesting and somewhat nosy question: has it really been tested that breakdown is the correct mechanism in Tesla coils?

      Also now the strong interactions with monopole flux tubes would stabilize the state.

   4. The negative charge on the surface of the Earth's electric field and the protons and ions in the gravitational flux tubes and electric flux tubes and their strong interaction would stabilize the biosphere as a conscious system.

See the article How the genetic code is realized at the level of the magnetic body of DNA double strand? or the About honeycombs of hyperbolic 3-space and their relation to the genetic code.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

The findings of RHIC about quark gluon plasma from the TGD point of view

The study of quark gluon pasma (QGP) at RHIC has revealed many surprises.

1. Jet quenching means that jets predicted by QCD lose energy much faster than expected. This would be due to the strong interactions with quark gluon plasma implying dissipation. In QCD, this interaction is modelled in terms of collisions of quarks with the quark gluon plasma formed by quarks and gluons.
2. The almost ideal perfect fluid behavior was totally unexpected. This hydrodynamic flow is known as elliptic flow. A further surprise was that heavy quarks also participate in the elliptic flow. This is like boulders flowing in a river.
3. Also light ions create the quark-gluon plasma. QGP, or whatever it is, is created even in the collisions of photons and heavy ions.
4. The basic questions concern the critical temperature and critical collision energy per nucleon at which the transition to QGP occurs. There is no consensus but the proposal is that 19.6 GeV collision energy could be a critical point. There is however a bumpy structure also below this critical point.

What can be said about these findings in the TGD framework?

1. The counterpart of quenching would be conformal dissipation or equivalently p-adic occurring for mass squared scale identifiable as conformal weight rather than energy. p-Adic temperature T_p which depends logarithmically on the p-adic mass scale has a discrete spectrum and would decrease in a stepwise manner in the p-adic cooling. T_p is naturally identifiable as the temperature of the counterpart of QGP and has also an interpretation as Hagedorn temperature.
2. p-Adic length scales hypothesis suggests that there is an entire discrete hierarchy of critical temperatures rather than only a single critical temperature. These temperatures would come as logarithms of p-adic mass squared scales proportional to 2^k.
3. In the TGD framework, the large values of h_eff associated with the quantum criticality and implying long scale quantum coherence could explain the perfect liquid behavior in terms of long term correlations, which are typical for hydrodynamics. Recall that at the classical level TGD is essentially a hydrodynamical theory since field equations reduce to conservation laws for the charges associated with the isometries of H.
4. The TGD based explanation for the boulders flowing in the river would be that for the TGD analog of QGP, the induced Dirac equation in X⁴ implies that both leptons and quarks behave like massless particles. Masses emerge only in the hadronic initial and final states constructed as modes of the H Dirac equation.

See the article The findings of RHIC about quark gluon plasma from the TGD point of view and the chapter Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD .

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Gemini assisted discussion about microtubules and Carbon Nanotubes

We had with Tuomas Sorakivi a Google assisted discussion about Carbon nanotubes (CNTs) (see this) and microtubules (MTs) (see this). Both are cylindrical structures, albeit the MTs are much more complex. Google's language model demonstrated convincingly its power as a tool allowing us to get the information needed to test new ideas. Of course, the language models make mistakes so that they cannot be used as authorities.

Microtubules (MTs) from the TGD point of view

1. MT consists of tubulins with 2 basic conformations, which Hameroff proposed to define a classical bit. This is quite possible. The energy difference between the conformations is .043 eV which corresponds to the typical energy of membrane potential around .05 eV.
2. Around the turn of the millennium, I proposed that the TGD view of space-time allows us to consider the possibility that MTs could act as quantum antennas and receive and send signals (see this). Later the findings of Blackman and others (see this) led to the notion that the hierarchy of effective Planck constants h_eff allow long scale quantum coherence at the field body of the system. For instance, communications from a MT to its magnetic body (MB) using large h_eff photons, which behave like dark photons, can be considered. The MB could also control the MT.
3. Some MTs could be quantum-critical systems in long, even astrophysical, scales. In some cases (for example, for MTs associated with cilia at the cell surface) MT length varies all the time and they are accompanied by a longitudinal electric field which in TGD framework is a signature of large h_eff phases which can be generated by Pollack effect.

   Since the increase of h_eff requires energy, quantum criticality requires metabolic energy input and GTP molecules at the surface of MT as a counterpart ATP counterparts would provide the metabolic energy. The fundamental frequency of the transmitted radiation thus varies and frequency-modulated signals are produced as the fundamental frequency of the sent signal is varied. Frequency modulation is the basic representation of information in the TGD model for biology and central in the TGD based view of number pulse and EEG (see this).

   Also the cell membrane would produce frequency-modulated Josephson radiation. The variation of the membrane potential would induce the frequency modulation. The MB of the cell would receive sensory information in this way as Josephson radiation would transform to a sequence of cyclotron resonance pulses.

4. The length of MT varies from 20 nm to 25 micrometers: this makes 3 orders of magnitude. The energies for the antenna photons would be in the range 62.5 eV -.05 eV. The lower limit of .05 eV corresponds to the typical Josephson energy associated with the cell membrane voltage (see this). Communication from and control of cell (axonal) membranes is suggestive. This could be essential for the cell motility based on ciliar dynamics.

   At the upper wavelength limit, the energies could correspond to the energy difference between X-OH and X-O^- + dark protons at the monopole flux tube defining the two states of a topological qubit. Could MT produce photons that, instead of solar light as in the ordinary Pollack effect, would produce the Pollack effect and kick the protons of -OH to a magnetic body and change the value of the topological bit? The energy range covers the frequency range of light up from infrared to the upper limit of UV. The lower limit of X-ray frequencies is 100 eV. These energies could induce molecular transitions. As found, the lower limit also corresponds to the energy difference between the 2 tubulin conformations.

5. After the discussion, the following question popped up. How do the in vivo and in vitro states for biomatter differ? Metabolism is of course the answer. In vivo, a part of the biosystem receives metabolic energy that is needed to maintain the h_eff distribution because h_eff tends to decrease all the time. This is not the case in vitro. This explains the differences. In the case of DNA and RNA, the permanent negative charge means in the TGD framework that dark protons reside at the monopole flux tubes stably. However, metabolic energy is needed to preserve the charge separation making possible the electric field. Same applies in the case of the cell membrane. The TGD based view of the basic information molecules and genetic code is discussed in detail in the article (see this).

Carbon nanotubes (CNTs) in the electromagnetic field of a Tesla coil as a candidate for a living computer?

CNTs are hexagonal lattices with a helical structure stable at room temperature. The hexagons form a helix and the pitch angle of the helix characterizes the helical structure. The notion of chirality makes sense and there is an analogy with DNA.

First some background.

1. TGD allows us to consider the possibility of hybrids of classical computers and quantum computers transforming them to genuinely intelligent living and conscious entities (see this and this). In the proposed model, the states of a topological qubit are realized as two states defined by the -OH side group and -O^- + dark protons (large h_eff on a magnetic body of the system.

   This dynamical topological qubit would accompany the ordinary bit. There are also more general identifications of topological qubits and cold plasmas are excellent candidates for the realization of dark qubits (see this). Dark protons could be replaced with dark metal ions and the findings of Blackman indeed support that dark Ca^{2+ ions are possible and led to the hypothesis about large h_eff hierarchy as phases of the ordinary matter behaving like dark matter.}

2. The basic prediction of TGD is that the dynamics of the space-time surfaces as analogs of Bohr orbits for particles identified as 3-surfaces ise slightly-non-deterministic: this leads to what I call zero energy ontology (ZEO) (see this). This is true also for the topological qubits: so that the temporal bit sequences defined by them are non-deterministic without a violation of the classical field equations. Temporal bit sequences are represented as Bohr orbit-like space-time surfaces and bits would correspond to the 3-D loci of non-determinism. The superpositions of these Bohr orbits as analogs of computer programs are possible and would accompany the classical program. Similar situation would prevail at the level of DNA and RNA (see thisand this).

Could the -OH side groups be added to a CNT somehow to build a topological quantum computer and could CNT also give rise to a counterpart of ordinary bit as a transistor? This would give rise to a conscious computer (see this). Here Google Gemini came to the rescue.

1. In the CNT lattice, 3 valence bonds emanate from each C. The remaining electron is delocalized to a hexagon forming an aromatic ring. sp² hybridization, where s and p characterize electron orbitals, occurs. The energy spectrum of the π electron is in the range 1 meV - few eV.
2. The problem is that there are only C atoms present in CNT: -OH side groups must be created. Google informed us that this is possible. If the π electron is localized, the -OH can be placed at the resulting defect.
3. This cannot yet give a hybrid of quantum - and classical computers. How to get ordinary bits as partners for these topological qubits? A transistor provides the standard realization of a classical bit. Are CNT transistors possible? And again Google helped us: CNT transistors (CNFETs) represent a possible future technology and they define a basic research area in electronics!

The discussion led to the idea that CNTs could give rise to conscious computers along lines discussed in (see this). A week later I realized that the phenomenon of Teslaphoresis that I discussed above 9 years earlier from the TGD point of view (see this) is highly encouraging in this respect.

For about 9 years ago I learned about mysterious looking self-organization of CNTs in the electromagnetic fields of Tesla coils (see this) and proposed a TGD based model for it (see this). This self-organization, occurring in unexpectedly long length scales of order 30 cm and involving their alignment, brings to mind microtubules.

Teslaphoresis means that CNTs self-organize in the oscillating electromagnetic field of a Tesla coil in length scale of order 30 cm, which is much longer than expected on basis of standard physics. CNSs tend to align in parallel. This unexpected self-organization of the CNTs brings to mind microtubules.

1. For a believer in standard physics, Tesla coils (see this) are a mere entertainment tool. From the TGD point of view they might be much more, a primitive life form. Google Gemini informs that Tesla coil is a resonant transformer circuit producing extremely high-voltage, high-frequency alternating current that creates spectacular lightning-like electrical arcs and demonstrates wireless energy transfer and high-frequency phenomena like X-rays and phosphorescence. It works by using coupled coils, capacitors, and spark gaps to amplify voltage dramatically, often exceeding a million volts, which corresponds to the mass scale of the electron.

   The electricity generated by the Tesla coil travels over the skin without harm, and lights up bulbs wirelessly. Standard physics explains this in terms of high frequency. In the TGD framework, the frequency would be very low but the energy E= h_emf would be high and could cause the exotic looking remote effects by energy resonance with ordinary matter with standard value of h_eff.

2. Tesla coils carry both classical magnetic fields and electric fields. In the TGD framework, the self-organization suggests a long range quantum coherence in length scales of order 30 cm. In TGD, one can speak of the electric body of the system characterized by a large value of electric Planck constant h_em and plasma phase (see this). Therefore the Tesla coil could be an essential element in making the system a macroscopically quantum coherent system.
3. In the TGD framework, this suggests that a large value of h_eff=h_em proportional to the electric field strength (see this) characterizes the electrons and makes possible for electrons to have long wavelength. Also dark protons at the magnetic body of the system would be present and could be characterized by the gravitational Planck constant ℏ_gr of the Earth. Pollack effect would transform protons to dark protons and generate a negative charge. This would make Tesla coils analogous to charged biological systems like DNA, microtubules and cells carrying strong electric fields.

   In the absence of a metabolic energy feed, the values of h_eff for particles tend to decrease. The electric fields require a charge separation and a permanent negative charge is a direct signature for the presence of condensate of dark protons at the magnetic body. Metabolic energy feed is required but would be used to preserve the electric field rather than to kick the protons back to the magnetic body. This mechanism would make DNA and RNA with constant linear charge density completely unique information molecules (see this). Something analogous would happen in the case of Tesla coil at its field bodies.

The consideration of the Tesla coil from the perspective of TGD could stimulate some ideas about how one might build living computer like systems using Tesla coils and CNTs.

1. The large charges in the capacitors C₁ and C₂ generate so strong electric fields that di-electric breakdown occurs in both of them. In the TGD framework (see this), the strong electric field is accompanied by dark electrons with a very large value h_eff =h_em proportional to the electric at the surface of the capacitor. Also dark protons at the magnetic body of the Earth could be generated. The long range of quantum coherence could explain the strange effects observed in length scales much longer than the size scale of the system and also the energy transfer by radiation over long distances.
2. Could the capacitor pair act as Josephson junction and generate oscillating non-dissipative Josephson currents generating Josephson radiation? This would mean an analogy with the cell membrane as it is modelled in TGD (see this).

   In the TGD based model of EEG, the Josepson radiation mediates information to the magnetic body of the system and cyclotron frequencies for dark ions in the "endogenous" magnetic field B_end∼ 2B_E/5, where B_E= .5 Gauss, assignable to monopole flux tube loops mediating the Earth's gravitational field, are favoured. These frequencies are in EEG range and correspond to resonance frequencies. The AC frequency, which for Tesla coils is typically 50 Hz, corresponds to the cyclotron frequency of a Lithium ion.

   One can ask whether the di-electric breakdowns could be analogs of nerve pulses. Note however that the nerve pulse is generated when the membrane potential is below a threshold rather than above it.

3. Radio waves with frequencies typically between 40 kHz and MHz are generated and energy and information are transferred wirelessly. An interesting possibility is that the photons with AC frequency are dark and have the same energy as the photons of ordinary radio wave photons. This requires h_em= ω₁/ω_AC. Already the wavelength λ_AC is rather long: for f= 1 MHz the wavelength would be λ₁=300 m. The presence of the gravitational magnetic body of the Earth suggests the presence of dark photons with energies which can be even in the visible range.

   The scaled up wavelength for f_AC=50 Hz would be λ_AC=6000 km to be compared with the Earth's radius R_E=6,371 km. Dark photons with wavelength of order Earth radius energy of radio wave photons might realize the dream of Tesla about effective energy transfer in the size scale of the Earth. The energy of these photons would be about 10^{-8 eV and rather small. For dark photons producing biophotons the energy would be in visible and UV range.}

4. The lighting of the bulbs is believed to be caused by strong electric fields associated with the Tesla coil. In fluorescent bulbs (ionization), the strong radio frequency electric fields generated by the Tesla coil accelerate electrons which collide with gas atoms and ionize them and create a plasma. The photons from the decays of excited electrons generate light. In the case of incandescent bulbs (induced current), the changing electric and magnetic induce currents directly to the bulb's tungsten filament.

   Could the large value of h_eff possibly associated with the "massless" extremals (see this) associated with the radiation could make possible dissipationless acceleration scaled up length scale, increasing the energies achieved in the acceleration. Also in the case of electrolytes the problem of how the relatively weak electric fields can induce ionization is encountered and the TGD proposal for the mechanism is the same as in the recent case.

5. In the TGD inspired biology, dark EEG photons transfer information. Could the Tesla coils plus CNTs give some day raise to conscious computers forming networks using dark AC photons to communicate. Could the biosphere be doing this already?

To sum up, this discussion also demonstrated that the language models can be extremely useful tools allowing us to get instantly information impossible to find by the usual means. It is a pity that they can be also used to produce massive amounts of pseudoscience.

See the article Tesla phoresis and TGD or the chapter About Concrete Realization of Remote Metabolism.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

How the genetic code is realized at the level of the magnetic body of DNA double strand?

Suppose that the proposed view of the ITT realized at the level of the magnetic body (MB) of DNA is correct that dark genetic codons as induction of ITT from the MB of DNA have as a chemical counterpart of DNA or RNA double strand. How the more precise view of ITT affects the earlier model discussed in (see this).

First a couple of facts.

1. The numbers of (T,I,O) per vertex should be (20,12,10) if the T-I interface always involves O. Therefore also DNA codons correspond to faces of O:s and DNA sequences can be identified as a sequence of faces of O:s.
2. 10 DNA codons define the shortests DNA sequence for which the twist is a full multiple of 2π. One should have a sequence of triangles representing genetic codons and each codon should correspond to a face of I and to a 3-chord of a fixed Hamiltonian cycle defining a bioharmony.

This raises the following questions.

1. Does the sequence of 10 O:s correspond to a single ITT vertex and does DNA correspond to a sequence of ITT vertices such that each vertex corresponds to an O and associated 20 T:s and 12 I:s?
2. Do the two DNA strands correspond to separate dark strands or does a single dark strand correspond to both of them as the fact that the DNA strands are conjugates of each other as the latest proposal assumes. Assume this. Single O has 3+3 faces and has two disjoint triangular faces. Could these two faces correspond to DNA codon and its conjugate?
3. This sequence of 10 O:s corresponds to a sequence of 12 I:s. 2 I:s would be "empty" and would not correspond to dark proton triplet: what does this mean? Does this mean that all vertices of the I and T carry ordinary protons and the activation of the codon transforms the ordinary protons of the face to dark proton triplet. I have considered a possible interpretation of this. In the state in which DNA is opened (transcription) the 2 codons would become active and correspond to dark proton triplets.
4. What distinguishes between I and T type active codons? When the dark proton triplet is of T type and when it is of I type? Could the presence of the Hamilton cycle, the assignment of 3-chords to the faces, and resonance interaction allow us to understand this? Does the 3-chord assigned to the face determine whether the dark proton triplet belongs to the T or I type Hamiltonian cycle? Is there some symmetry breaking mechanism selecting from the T type conds the one while the remaining ones act as stop codons. Could the presence of I or T type Hamiltonian cycle in given I or T determine whether it can define an active codon and whether an associated ordinary proton triplet can be transformed to a dark one?

   The cyclotron frequencies assignable to T type codons are different from those assignable to I type codons if the frequency ratio for two subsequent vertices of the cycle is 3/2 for the Hamilton cycle at I in the Pythagorean model.

   Note that the basic problem of the Pythagorean model of harmony (known already by Pythagoras) is that the full Hamiltonian cycle, involving 12 frequency scalings by factor 3/2, does not give quite precisely a full multiple of octaves. One must allow irrational frequency scaling of 21/12 on a well-tempered 12-note scale to get rid of the problem. This might relate to the symmetry breaking.

   For a tetrahedron with 4 vertices the frequency ratio should be also such that the cycle spans a multiple of octaves. This is not possible for rational scalings. In any case, I and T options are not consistent and this suggests that the 3-chords select between I and O options. The chords dictated by the character of the Hamilton's cycle select whether the face is of type I or O. The presence of the Hamiltonian cycle would be necessary for the transformation of the ordinary proton triplets to dark proton triplets and only the I or T type cycle can be realized.

   In the standard realization of the code there are 3 stop codons, which are transcribed to mRNA but are not translated to amino-acids. There are 4 codons of type T. There should be a symmetry breaking in the sense that 3 of them are not translated. This could be due to the failure of 3-chord resonance conditions so that there would be no tRNAs with the required resonance frequency triplest. Only a single tetrahedral codon would be translated for the standard realization of the code. This model also allows deviations from the standard realization of the code.

Pollack effect and ATP→ ADP+P_i transformation

The molecules XP, where X ∈ {A,T,C,G} denotes DNA nucleotide, are basic building blocks of DNA. The molecules XP are stable unlikes the more complex molecules. The molecules ATP, ADP and GTP, GDP involving 2 or 3 phosphates ions. The latter molecules are essential for the metabolism and appear as carries of metabolic energy assigned in the TGD view to the dark protons at the magnetic body associated with the molecule. What distinguishes them from the mononucleotides appearing in DNA and RNA?

We talked with Ville-Einari Saari (a member of our Zoom group) about whether it might be possible to build stable negentropic systems with a large Planck constant h_eff. Without any stabilizing mechanism, large h_eff systems are unstable against the decrease in h_eff because their energies increase with h_eff, so as free systems they require a continuous energy input and only flow equilibrium is possible. This is the case in the case of XDP and XTP and this make for ADP and GTP to transfer metabolic energy.

In water, the Pollack effect is a fundamental process and produces dark protons that transform into ordinary ones in an attosecond time scale. This expectation comes from the observation of exotic phases of water with effective stoichiometry H_1.5O having attosecond life time. The explanation is that a phase transition in which every fourth proton becomes a dark proton at monopole flux tubes takes place under external energy feed. The negatively charged exclusion zone (EZ) created in Pollack effect by radiation is an example of this effect. The essential prerequisite for the Pollack effect is external energy feed and TGD has led to various generalizations of the Pollack effect. In particular formation of biomolecules generates binding energy and this could stabilize dark phase \cite{btar/penrose,hem,QCs} and cold plasmas are excellent candidates for the carriers of stable dark phases.

An illustrative example is provided by transformation of chemical energy to a usable energy as a transition ATP→ ADP +P_i, where P_i is inorganic phosphorus. This process occurs spontaneously. The reverse process requires metabolic energy input and mitochondria are specialized to produce ATP from ADP. The process ADP→ ATP→ ... can be seen as a kind of a karmic cycle.

1. The phosphorus P appearing in ATP and ADP ions is organic. It is not clear what this really means and biologists argue about a mysterious high energy phosphate bond which would carry the metabolic energy to the final uses as ATP transforms back to ADP + P_i. In the TGD framework, the interpretation is that ATP and also ADP involves a dark proton at the MB that neutralizes the negatively charged system and is generated by the generalization of the Pollack effect in the formation of ATP or ADP.
2. The conversion of the chemical energy into a usable form occurs in the mitochondria in a biochemical machine that resembles a rotating turbine of a power plant. 3 ATP are produced in one revolution of the turbine from three ADP. This would strongly suggest that a precursor of dark genetic codon as dark proton triplet is involved.

   Google informs that the lifespan of the ATP varies enormously: when the environment needs energy, its lifespan is shortened. In vivo it varies from a few seconds to about 100 seconds whereas in vitro ATP can be almost stable.

What about DNA and RNA?

1. DNA and RNA have a stable negative charge (as Google informs): there are a negative charge of 3 units per codon. A natural guess is that it corresponds to the exclusion zone (EZ) of the Pollack effect. This suggests that that there must be a stable positive charge in the form of dark proton triplets at the magnetic body associated with the DNA and the proposal is that these triplets define dark codons. What stabilizes the negative charge of DNA and therefore also the dark protons and makes the negentropic state stable
2. Bound states are formed between phosphates and DNA nucleotides. If their chemical binding energy is so high that the total binding energy, which is reduced by the energy of the dark proton, remains positive, the state is stable. I have suggested earlier (see this) that the formation of biomolecules as bound states can stabilize the dark protons, so the creation of biomolecules would also produce negentropy at the magnetic body. In fact, the formation of biomolecules as bound states during the biological evolution would have generated the dark protons at the monopole flux tubes of their magnetic bodies.

   To sum up, negentropic states can be stabilized in this way and do not require a constant input of metabolic energy to maintain dark h_eff in the sense of flow equilibrium. DNA and RNA would be completely exceptional bio-molecules in this respect and would fully deserve the name information molecule.

Does the presence of ITT at the MB reveal itself in the structure of DNA the surrounding water

Does the presence of ITT at the MB of DNA reveal itself in the structure of DNA and the surrounding water. How does the presence of O:s, T:s and I:s at the MB reflect itself in the properties of chemical DNA and possibly of water? Could the structure of water around DNa reflect the projection of hyperbolic tessellation at 3-D Euclidean space E³.

Do the octahedrons of the field body have any counterpart in the nearby environment of DNA.

1. Here Google tells that the water around DNA indeed involves octahedral structures besides tetrahedral structures which generally present. They occur in the form of hexahydrated metal cations, such as Mg[H₂O]₆]²⁺ with positive charge of 2 units. Mg⁺² ions are bosons and could form Bose-Einstein condensate like states? The 6 water molecules reside at the 6 vertices of O and whether its two opposite disjoint faces could correspond to dark codons. Mg⁺² ions giving rise to Bose-Einstein condensate could give rise to quantum coherence at the level of ordinary DNA and make possible the simultaneous generation of 2 dark proton triplets by Pollack effect.
2. These octahedral complexes are commonly found in the major groove or the phosphate backbone region of the DNA, where they are thought to shield the negative charges and stabilize the overall structure. This assumption is natural also in the TGD based view. Only 15 percent of Mg⁺² ions is estimated to touch phosphate oxygens directly. They would form a kind of cloud, which conforms with the idea that they serve as stabilizers. That they accompany the vertices of octahedron conforms with the idea that the vertices involve negative charges created as protons are transformed to dark protons.
3. Mg⁺² ions screen 88-89 percent of the negative DNA charge. If one can assign this kind of octahedron with a net charge of +2 units with each genetic codon, one unit of negative charge remains unscreened for both strands. Fraction 2/3 of total charge would be screened. This is considerably less than 88-89 percent so that not all Mg⁺² ions would be associated with the vertices of the octahedra.

Could one understand the correspondence between ITT and DNA double strand more concretely? The natural guess is that the vertex figure of ITT relates to the structure of DNA double strand.

1. Could the pentagon associated with the deoxyribose (or ribose in the case of RNA) serve as a counterpart for the pentagon appearing in the vertex figure of ITT? The vertex figure has 12 pentagons, which could correspond to 12 DNA codons defining a cycle in the sense that the total twist angle of the double helix is 3× 2π in the open configuration of the DNA double strand.

   For a non-open double strand 10 DNA codons define a full cycle. One could say that there are 2 missing DNA codons and 2 empty IIT pentagons without dark protons triplets defining a gap separating the dark codons. If the corresponding Mg[H₂O]₆]²⁺ complexes, whose opposite triangles would represent DNA codon and its conjugate, are present at all, they should not give rise to dark protons. Mg⁺² ions giving rise to Bose-Einstein condensate could give rise to quantum coherence at the level of ordinary DNA and make possible the simultaneous generation of 2 dark proton triplets by Pollack effect.

2. Could also Mg⁺² ions be dark? The findings of Blackman (see this) can be explained in terms of bosonic Ca²⁺ ions which have cyclotron frequency 15 Hz in the endogenous magnetic field B_end∼ .2 Gauss consisting of gravitational monopole flux tubes. They are dark in the sense that they have a very large gravitational Planck constant ℏ_eff=ℏ_gr ∼ 10¹⁵ℏ (see this) implying that the cyclotron photons can have energies in the range of visible photons.

   Mg⁺² has cyclotron frequency 12.5 Hz for B_end∼ .2 Gauss. The crucial assumption is that besides protons, also other metallic ions can be dark in the sense of having large h_eff. This suggests that also Mg⁺² associated with a single codon as a face of ITT is dark in the sense it resides at the MB. The interpretation could be that its wave function is delocalized at the gravitational flux tube of the Earth's surface. When Mg⁺² is observed its wave function would localize to the surface of Earth, meaning "dropping" from the gravitational flux tube. The effects of electromagnetic radiation with this frequency on DNA could be tested.

   In fact, all metal ions M form M[H₂O]₆]²⁺ complexes (see this). The number of water molecules involved is known as the solvation number and is 6 for the third and fourth period of the periodic table containing Mg and Ca. The bosonic Mg and Ca ions are also involved with microtubules and cell membrane (see this). This gives support for the proposed 2-D realization of the genetic code in terms of dark proton triplets.

3. The ordinary codon should correspond to the dark codon as a triangle at the MB with dark protons at its vertices. At the level of DNA there is no triangle. Could the 1-D quasiperiodic lattice formed by the DNA codons correspond to periodic boundary conditions at the MB so that the linear codon as a unit cell of the lattice has a triangle as a counterpart at the level of ITT? 3 chemically identical pentagons associated with the codon should correspond to a single pentagon at ITT. A single Mg[H₂O]₆]²⁺ octahedron associated with the major groove should correspond to a single O of ITT? Whether there is indeed only a single O per pair of codon and its conjugate could be perhaps tested. One could argue that symmetry requires that both strands involve Mg[H₂O]₆]²⁺ octahedron. However, only the other strand is active. This could mean that only its codons contain the Mg[H₂O]₆]²⁺ octahedron.
4. What about the tetrahedral structures, which also characterize water, around DNA? Here Google informs that in the hydration shell of DNA tetrahedral ordering is present and is essential for the stability of DNA. The presence of tetrahedral ordering could reflect the presence of ITT at the magnetic body associated with DNA and also a region of water environment. There is an enhanced tetrahedral ordering in the DNA minor (not major as for octahedrons!) grooves (see this). The DNA molecule imprints its helical structure to the tetrahedral structure of water. The TGD interpretation is that the faces of tetrahedra also correspond to the faces of the Mg[H₂O]₆]²⁺ octahedron. This could be the analog for the I-T faces of ITT identifiable also as octahedral faces? An interesting question is whether the ribose pentagon could somehow correspond to a vertex figure of icosahedron also at the level of DNA.

Hen-egg questions related to the genetic code

Biology involves a long list of hen-egg questions (see this and this). What came first: metabolism, basic information molecules, bio-catalysis, or genetic code? Which biomolecules emerged first: RNA, DNA, or amino acids? TGD provides tentative general answers to these questions in terms of the dark genetic code, whose realization in terms of ITT was present from the beginning. It is instructive to consider these questions in the framework provided by the recent views about the realization of the genetic code in terms of ITT about the emergence of dark matter via the generalization of the Pollack effect. One can also try to develop an overall view.

1. The dark variants of DNA, RNA, tRNA, amino acids were present from the beginning and realized in terms of dark proton triplets assigned with ITTs at MBs. Stable dark realizations of the DNA, RNA and dark protons at MB were stabilized by the formation of corresponding biomolecules as bound states with the binding energy of the state compensating for the larger energy of the dark proton (see this). Hence one cannot say which came first.
2. The lifetimes of the basic biomolecules serve as guidelines in the attempts to build an overall view about whether the dark protons at the magnetic body of a biomolecule are relevant for its functioning.
   1. DNA is extremely long-lived: 521 years in bone. Also the negative charge associated with its phosphates is stable. The TGD based conclusion is that the dark protons at the magnetic body of DNA are stable. There is however a metabolic cost also in this case. The classical long range electric along DNA are a crucial aspect of DNA and make possible large values of h_em assignable to the DNA. Also the nuclear membrane potentials are crucial for the survival of the DNA nucleus. Metabolic energy feed is needed to preserve the charge separations generating the classical electric fields.
   2. Also the negative charge of RNA is stable but the lifetimes of RNA molecules vary in a wide range. mRNA has a lifetime from minutes to ours and the average lifetime of 2-20 mins. The lifetime can however be much longer, even days and can persist an organism's lifetime. Special RNAs such as tRNA, rRNA, circular RNAs and nuclear RNAs are very stable and long-lived.

      The finite life-time of RNA could be due to the instability of the -OH bond associated with the ribose making possible the transition to the -OH → O^- + dark proton at its magnetic body. This would be essential for the ability of RNA to act as a catalyst and could explain the varying lifetime. The stable negative charge of RNA serves as a signature for the presence of dark protons. The dark protons triplets would make possible the communications of RNA with dark DNA and dark tRNA by 3N-resonance.

   3. Amino-acids (see this) do not possess a stable negative charge, which suggests that they do not have dark protons at their magnetic body stably. However, Google AI tells that, a C=O bond in a protein can be temporarily converted into a gem-diol structure C(OH)₂ intermediate in an enzyme's active site during catalytic action. This process is a form of nucleophilic addition of water across the carbonyl double bond, which is often a key step in reactions such as the hydrolysis of peptide bonds (catalyzed by peptidases/proteases) or other reactions involving carbonyl-containing substrates. The 6 water molecules could be assigned with the 6 vertices of O and whether its two opposite disjoint faces could correspond to dark codons.

      In the TGD framework this could mean that during the enzyme catalysis a proton from C-OH is transferred to the magnetic body of the protein and drops back later. ATP could quite generally provide the needed metabolic energy to achieve this.

3. The emergence of communications and control was a crucial step in evolution. Cyclotron frequency triplets as chords assignable to the ITT made possible resonant communications between field bodies by 3N-resonance involving both frequency and energy resonance. The communications between levels involving different values of h_eff (and different length scales) involved only energy resonance and very ×probably 3N-resonance was replaced by the ordinary resonance. This led to an automatic generation of communication and control networks between field bodies characterized by varying values of h_eff and biological bodies. Dark cyclotron radiation and frequency modulated dark Josephson radiation inducing a sequence of pulses at the receiver's end are basic mechanisms suggested by TGD (see this).

   Large h_eff stability possible for DNA and RNA led to a generation of intelligence based on algebraic complexity and to a control by MB. This led to an evolutionary explosion. The electric and gravitational field bodies assignable to the Earth and the Sun were in essential roles (see this).

4. The emergence of replication was a crucial step. At the chemical level replication reduces to the replication of DNA. A doubling of the DNA strand must occur. In the bio-chemistry approach replication is something which is just accepted.

   In the TGD framework, the analog of the replication problem is encountered already at the level of particle physics. Fermion fields are free fields in H=M⁴× CP₂ as also the induced spinor fields at the space-time surfaces defined by them: how is fermion pair creation possible at all? The solution is simple and possible only in 4-D space-time: fermion makes a V-turn in time direction generalized (see this). The vertex of V corresponds to a 3-D edge of the space-time surface (see this), this) and this) at which the standard smooth structure has a defect (see this, this, and this). The magnetic body assignable to the dark DNA as a 3-surface would make a V-turn and induce DNA replication by transcription of the dark DNA to ordinary DNA.

   What was the first replicator and when did it emerge? This classical question becomes obsolete in the proposed framework. The replication could be a general property of space-time surfaces and therefore of the 3-surfaces associated with the dark DNA molecules realizing ITT at the magnetic body of DNA. There are many interesting questions to be pondered. For instance, how to relate the usual view about the role of various catalysts involved with the replication and what is the role of "big" state function reductions (BSFRs) changing the arrow of time in the process. Could the BSFR have a V-turn as a classical counterpart?

5. What bio-catalysis is and how did it emerge?
   1. In biocatalysis the reactants must find each other in a dense molecular crowd. How can they recognize each other's presence? In the simplest picture the U-shaped monopole flux tubes emerging from the reactants reconnect to form flux tube pairs connecting them. The shortening of the flux tube pair would force the reactants together and could be induced by a reduction of h_eff shortening the flux tube lengths.
   2. The potential wall preventing the bio-chemical reaction must be overcome. The shortening of the monopole flux tubes could liberate metabolic energy while the reduction of h_eff could help to overcome the potential wall. The attachment of a biocatalyst carrying large h_eff protons to the reacting system could also provide energy allowing it to overcome the potential wall.
   3. How are biocatalysts generated? In general, biocatalysts are unstable. The instability can be inherent or their degradation can be programmed for metabolic reasons since they are needed only when used. If bio-catalysts provide energy to overcome potential walls, they must carry dark protons and their generation requires metabolic energy feed, which also raises the algebraic complexity, "IQ" of the catalysts so that it can take the role of a midwife. ATP is a universal way to provide metabolic energy and dark protons in a standardized way. An alternative option is creation of chemical binding energy making it possible to generate dark protons with large h_eff.
   4. The dark proton of the catalyst should transform to an ordinary one in the reaction and liberate the energy needed to overcome the potential wall. Catalysts could be either inherently h_eff unstable or the instability could be induced in the reaction and induce the decay of the catalyst. Often the catalyst indeed decays after the reaction. Catalysts often have ATPs attached to them and ATP--§iogt;ADP is a basic aspect of catalysis.

      Note that in the translation of mRNA to proteins mRNA serves as a template and degrades after the translation. This could be due to the catalysis of the translation requiring the reduction of h_eff inducing a chemical instability. The instability could relate to the -OH sidegroup of the ribose.

   See the article How the genetic code is realized at the level of the magnetic body of DNA double strand? or the About honeycombs of hyperbolic 3-space and their relation to the genetic code.

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

   For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.