Wednesday, October 29, 2014

Geometric theory of harmony

For some time ago I introduced the notion of Hamiltonian cycle as a mathematical model for musical harmony and also proposed a connection with biology: motivations came from two observations (see this). The number of icosahedral vertices is 12 and corresponds to the number of notes in 12-note system and the number of triangular faces of icosahedron is 20, the number of aminoacids and the number of basic chords for the proposed notion of harmony. This led to a group theoretical model of genetic code and replacement of icosahedron with tetraicosahedron to explain also the 21st and 22nd amino-acid and solve the problem of simplest model due to the fact that the required Hamilton's cycle does not exist.

This led also to the notion of bioharmony. This article is a continuation to the mentioned article providing a proposal for a theory of harmony and detailed calculations.

  1. 3-adicity and also 2-adicity are essential concepts allowing to understand the basic facts about harmony. The notion of harmony at the level of chords is suggested to reduce to the notion of closeness in the 3-adic metric using as distance the distance between notes measures as the minimal number of quints allowing to connect them along the Hamilton's cycle. In ideal case, harmonic progressions correspond to paths connecting vertex or edge neighbors of the triangular faces of icosahedron.

  2. An extension of icosahedral harmony to tetraicosahedral harmony was proposed as an extension of harmony allowing to solve some issues of icosahedral harmony relying on quint identified as rational frequency scaling by factor 3/2.

  3. The idea that the rules of bioharmony realized on amino-acid sequences interpreted as sequences of basic 3-chords leads to highly non-trivial and testable predictions about amino-acid sequences.
If one can find various icosahedral Hamilton's cycles one can immediately deduce corresponding harmonies. This would require computer program and a considerable amount of anlysis. My luck was that the all this has been done. One can find material about icosahedral Hamilton's cycles in web, in particular the list of all 1024 Hamilton's cycles with one edge fixed (see ) (this has no relevance since only shape matters). If one identifies cycles with opposite internal orientations, there are only 512 cycles. If the cycle is identified as a representation of quint cycle giving representation of 12 note scale, one cannot make this identication since quint is mapped to fourth when orientation is reversed. The earlier article about icosahedral Hamiltonian cycles as representations of different notions of harmony is helpful.

The tables listing the 20 3-chords of associated with a given Hamilton's cycle make it possible for anyone with needed computer facilities and music generator to test whether the proposed rules produce aesthetically appealing harmonies for the icosahedral Hamiltonian cycles.

For details see the chapter Quantum model of hearing of "TGD and EEG" or the article Geometric theory of harmony.

Sunday, October 26, 2014

p-Adic length scales hypothesis for twin primes

A theorem of Yitang Zhang about distribution of distances of twin primes (see this) has caught the attention of media. The theorem states that there exists number of order 107 such that the number of twin prime pairs with mutual distance smaller than this number is infinite. The naive expectation is that minimum distance between twins increases and becomes infinite at the limit as also the average distance does.

In TGD framework the result is not so counter-intuitive.

  1. p-Adic length scale hypothesis implies that elementary particles correspond to p-adic primes characterizing the effective p-adic topology assignable to them. If cognition is accepted to be part of world order then one must generalize physics by gluing together real and various p-adic physics and p-adic space-time sheets are correlates for cognition. The basic hypothesis emerging from the comparison of the results of p-adic mass calculations with experimental numbers is that physically preferred p-adic primes correspond to primes p≈ 2k, k positive integer. has as preferred values primes and Mersenne primes. Also Gaussian Mersennes assignable to Gaussian (complex) integers appear an define important p-adic length relevant to living matter (scales between cell membrane thickness and cell nucleus size. One can also consider twin pairs for $k$ and these will be indeed discussed below.

  2. If one accepts the idea that elementary particles correspond to primes, one can turn the wheel around and ask whether physics might help in understanding the distribution of primes. Elementary particles form bound states. These bound states would correspond to twin pairs or larger clusters of primes near to each other. If this is the case then one can make number theoretical conjectures based on approximate scale invariance. Twin prime pairs are analogous to bound stats of particles and have some minimal size and the number of pairs with this size is infinite just like the number of twin primes. Same applies to bound states of arbitrary many twin primes. Besides twin primes there are, triple primes, etc. and also they form bound states. Same conjecture applies to the number of them having minimal size.
As such the idea that twin primes might be important in physics does not look interesting. One can however consider p-adic length scale hypothesis restricted so that one considers only primes p≈ 2k, k prime (another such restriction considered earlier is that the second scale of twin scale pair corresponds to Gaussian Mersenne). What does one obtain if one considers only pairs of twin primes (k,k+2)? The twins form pairs of p-adic length scales L(k) and L(k+2) differ by scaling of 2 and already during the first years of p-adic physics I noticed that this kind of pairs might be relevant in biomatter and also in particle physics. Twins appear as basic scale pairs also in solar system as following considerations show. A reasonable conjecture is that twin pairs define an important set of fundamental length scales allowing to get a glimpse about entire physics from CP<sub>2</sub> scale up to longest cosmological scales.

First some background about twins and p-adic length scales hypothesis.

  1. From Wolfram Mathworld ) one finds the following list of twin pairs. The first few twin primes are of form n± 1 for n=4, 6, 12, 18, 30, 42, 60, 72, 102, 108, 138, 150, 180, 192, 198, 228, 240, 270, 282, .... Explicitly, these are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ... . All twin primes except (3, 5) are of the form $6n± 1$.

  2. From this one can calculate p-adic length scales L(k), k=n± 1 and mass scales assuming p≈ 2k. It is convenient to use electrons Compton length in the scale involved rather than p-adic length scales proper (as a matter fact, I confused for a long time these two scales). By Lp=L(k)∝ p1/2≈ 2k/2 one has Le(k)= 2(k-151)/2Le(151), where scaled up electron Compton length Le(151)= 2(151-127)/2=12)Le(127) can be also written as Le(151) ≈ L(151)/(5+x)1/2, where x<1 (most naturally very near to zero) is a parameter left free by uncertainties of the model behind p-adic mass calculations.

    The reference scale can be taken as Le(k=151)≈ 10 nm, which is cell membrane thickness. Note that this suggests that Cooper pairs of electrons and perhaps even their light and dark variants are important. Macroscopic quantum phases of dark electrons are highly suggestive. The Gaussian integer (1+i)kG=151-1 defines Gaussian Mersenne as also kG= 157,163,167. Such a large number Gaussian Mersennes in so small an integer interval can be regarded as a number theoretical miracle and must relate to the very special physics of living matter systems. The natural guess is that both p-adically scaled up and dark variants of strong interaction physics, weak physics, and electromagnetism appear in these scales varying up to the size of cell nucleus.

  3. p-Adic mass scales are obtained from electron mass me= .5 MeV by the scaling m(k)= 2(127-k)/2 × me/(5+x)1/2. It seems physically more natural to use as the mass scale also the mass me(k) of electron if it were be characterized by k.
Consider first the twin length scales assignable to elementary particle and atomic physics.
  1. n=102 defines pair (101,103). I have earlier assigned these p-adic prime to to b and c quark. One has me(101)= 4 GeV and me(103)= 2 GeV.

  2. n=108 defines pair (107,109). k=107 is assigned with hadronic space-time sheets and with proton. The mass scales are mk(107)=512 MeV and mk(109)=256 MeV. k=109 could be assigned with deuteron. An interesting question is twin pair is relevant for the understanding of also QCD. The current masses of u and d quark (with the mass assignable to the magnetic body not included) are rather light - in the range 5-20 MeV. This means that their Compton lengths are much longer than those of hadron itself! The interpretation is that they are associated with the magnetic body of the hadron, say proton. This could explain the anomalous finding that the charge radius of proton seems to be slightly larger than it should be.

  3. n=138 gives rise to pair (137,139). The pair defines atomic length scales possibly highly relevant for the condensed matter and molecular physics. The length scale pair is (Le(137)=.79 Angstroms and Le(139)=1.57 Angstroms. A new physics in these length scales is strongly suggestive if p-adic length scale hypothesis is accepted.

The next group of twin length scales can be assigned to living matter.
  1. n=150 gives rise to the pair (149,151) corresponding to the thicknesses of lipid layer of cell membrane and cell membrane itself. The scales are Le(149)=5 nm and Le(151)=10 nm. Especially the scale of 10 nm appears very often in bio-systems as a basic scale: for instance, the thickness of DNA coil is of this order of magnitude.

  2. n=180 defines pair (179,181) differing by a scaling by 215≈ .512× 106 from the pair defined by cell membrane. The scales are Le(179)=2.5 mm and Le(179)=5 mm and might relate to binary columnar structures appearing in the cortex (orientation and ocular dominance columns). The thickness of cortex is of order 2-3 mm.

  3. n=192 defines pair (191,193) related by scaling with 2×106 to lipid-cell membrane pair. The scales are Le(191)=1 cm and Le(179).

The last two scales in the length scale range considered could relate to the physics of solar system.
  1. n=270 defines pair (269,271) related by scaling by scaling 1018 to cell membrane system. One has Le(269)=5 Mkm and Le(271)=10 Mkm. These scales are larger than the size scale .7 Mkm defined by solar radius but smaller than astronomical unit AU defined size scales for planetary orbital radii. In the model of solar system based on the notion of gravitational Planck constant Earth corresponds to n=5 Bohr orbit with radii proportional to n2. The radius of n=1 orbit would correspond to the length scale AU/52≈ 5.98 Mkm rather near to Le(169) so that the size scale of gravitational atom would be in question. The pair of atomic length scales (137,139) would be replaced with its gravitational variant (269,271). The interpretation proposed earlier is that the invisible gravitational orbitals correspond to dark matter around which no visible matter has condensed (yet).

  2. n=282 defines pair (281,283) related by scaling 32 to the previous pair. The scales are 160 Mkm and 320 Mk. The radius of the orbit of Earth defines astronomical unit AU=149.60 Mkm and again the order of magnitude is same.

It is remarkable that electron Compton scales in various p-adic length scales are in question which suggests that dark electrons are involved in an essential manner. To my opinion these findings are so remarkable that p-adic length scale hypothesis deserves serious consideration since it also leads to excellent predictions for elementary particle masses.

There is also an exceptional twin pair not considered above. It is formed by primes 2 and 3. Recently I have been developing a model of music harmony based among other things on the interplay of these primes. Octaves in music correspond to powers of 2 and under octave equivalence the notes of 12-note scale constructed by using quint rotation correspond to powers of 3/2 of equivalently of 3. One has both 2-padic and p-adic aspects. The natural distance for notes corresponds to the number of quints related the notes in quint rotation. This hypothesis allows to understand basic facts about harmony. Some time ago I commented about an article that I received from Jose Diez Faixat (see this) claiming what in TGD framework translates to the statement that 3-adicity is realized at the level of biological time scales. This conforms with the TGD based icosahedral model for biosystems suggesting a close relationship between twelve note scale and aminoacids and also leads to a proposal for icosahedral realization of genetic code (see this).

Thursday, October 16, 2014

Has dark matter particle been observed?

Lubos tells about claim that axions coming from Sun and transformed in Earth's magnetic field to X rays in keV range have been observed. The mass of the axion - to be distinguished from its much higher energy - would be few microeVs, which is rather small and corresponds to a p-adic length scale L(k=207) of about .5 meters. The next prime k=211 would give p-adic scale of 2 meters.

This brings in mind TGD explanation (see this) of and old anomaly - the production of electron positron pairs in collisions of heavy nuclei just above the Coulomb wall - in terms of production of axion-like states in the strong non-orthogonal electric and magnetic fields of colliding giving rise to non-vanishing "instanton density" E•B which generates coherent states of electropions which are bound states of color octet excitations of electron and positrons. Electropions would decay to electron positron pairs and gamma pairs. Later also other leptopion candidates have been detected. Unfortunately they do not represent dark matter in the sense of the prevailing dogmatics so that they have b den forgotten.

Color excited electrons should not be produced in the decays of weak bosons so that they must be either very heavy as free particle or dark in TGD sense and thus having non-standard value of Planck constant given as multiple heff=n× h. Same "instanton" coupling would cause the transformations of solar axions to X rays and the change of the orientation of the Earth's magnetic field with respect to Sun would imply the characteristic variation allowing to detect the small signal from large background.

p-Adic length scale hypothesis predicts the possibility of several copies of QCD like and weak physics. This copy could correspond prime p∼ 2211 and color excitations of corresponding electrons could be in question. Mass of scaled up electropion would be about 4 micro eV. Also scaled down quarks and thus scaled down analogs of ordinary pion can be considered.

Perhaps the simplest production mechanism would be the time reversal of the mechanism assumed to produce the ob served anomalous X rays. X rays from Sun could transform to axions in the magnetic fields of the sunspots. This would predict correlation with sunspot activity.

There have been also earlier reports about axion candidates at rather low masses and p-adic length scale hierarchy and dark matter hierarchy realized in terms of heff would provide a generic explanation. In biology both hierarchies of QCD type and weak physics could play a central role. Big Science is often experienced as a reductionistic invasion proceeding towards shorter and short length scales and this view still dominates physics although the construction of new accelerators is becoming more and more expensive. Big things have big inertia and it takes a long time for Big Science to be able to turn its direction and return to the regions which it has considered to be already conquered.

Wednesday, October 15, 2014

Easiest and cheapest manner to kill TGD

One of the cheapest and fastest manners to end up with a claim that TGD a crackpot theory is to notice that H=M4×CP2 does not allow imbedding of an arbitrary solution of Einstein's equations. The dimension of Minkowskian space allowing this is counted in hundreds. This requires however the failure to realize that the whole point of TGD is just the fact that imbedding really matters! With sufficient amount of academic arrogance one can however become unaware of this basic fact and even argue that Einstein's theory is the final word in this respect. The basic academic gift needed is listening without listening and reading without reading - as Wheeler might have formulated it.

In the belief system of General Relativity imbedding space of course has absolutely no relevance. In TGD framework it is of utmost significance. This is why TGD is revolutionary! Imbedding space defines the "shape" of space-time surface as "seen" by 8-D observer, its symmetries define quantum number spectrum, its spinor connection defines weak gauge fields classically, it brings in many-sheeted space-time, etc. Surface property extends the theory of gravitation to a unified theory of known interactions. The irony is that you get also non-gravitational nteractions by reducing the number of local field degrees of freedom (to four!) rather than introducing a lot of new ones!

Imbeddability to 8-D space-time implies that space-time dynamics is extremely constrained as compared to that in GRT. This has been of course basic worry shadowing the amazing predictions such as understanding of standard model symmetries and quantum numbers and solution of basic problems of cosmology (why mass density is below critical, absence of horizons,…). The ultimate solution of the problem was that the transition to GRT space-time involves in long length scales replacement of many-sheeted - this is the key-word- space-time regions with regions of Minkowski space whose metric is sum of M4 metric and deviations of the metrics of sheets from M4 metric. Similar description applies to gauge potentials and gives standard model gauge fields. In simple situations one can assume that this effective GRT space-time is representable as 4-surface in H and I do this with successful predictions in cosmology.

Imbedding of 2-D string world sheet of course mattered also in the original string model. Unfortunately our space-time is not 2-dimensional but a trick called spontaneous compactification was invented and imbedding space as something given and possibly fixed by the consistency and existence of the theory was replaced with dynamical one. This was a desperate attempt to obtain 4-D space time at least in certain approximation.

The correct manner to proceed would have been as an answer to the question how to generalize string model by replacing string world sheets with 4-D surfaces. Even worse, for "technical reasons" also the idea about string world sheet as sub-manifold with induced metric was given up and dynamical metric at it was induced (there was also the failure to realize that also spinor connection and spinor structure could be induced: this would have immediately led to the geometrization of known interactions and quantum numbers).

As a result, one obtained 2 gravities: stringy 2-D gravity and 10-D gravity to become later 11-D gravity in M-theory context. This from the attempt to quantize 4-D gravity! I must say that I felt deep co-shame and pity since I could only passively inspect as the catastrophe took place without being able to help. This was like seeing helpless victims of a traffic accident to suffer without being able to do anything except to wait for ambulance.

Now a common realization of the horrible mistake has emerged. For reasons easy to understand, this is not a reason for hypeing and the community has wisely chosen to be silent. There are however still some very loudy and very aggressive advocates of the dead science program, who obviously have failed to realize what went wrong (rather amazing but possible if one has a "true fan" attitude).

Perhaps not surprisingly, these individuals are not doing active research on strings themselves (one of the advocates sees everyone disagreeing with him as an evil communist and explains that the reason is that doing research without salary would be communism!). They are trying desperately to gain some scientific respectability using besides ultra-aggressive rhetorics a classical trick: make a lot of noise about pseudoscience since this gives you unearned scientific status. Cold fusion, water memory and anything challenging text book wisdom are excellent targets in this respect. In Finland, people calling for some reason themselves skeptics - most of them actually academic dropouts desperately wanting to appear in the role of wise scientist - are using the same simple trick.

Recipe is simple and conforms with the ultraconservative attitudes of these people explaining also why they are not able to do real research, which always requires challenging of own beliefs. Direct the negative emotions against a researcher, who has found something which does not conform with the text book wisdom. Emotional brain begins to dominate and logical thinking ceases. You indeed get the praise of those who do not have the needed background to decide themselves and are too naive to realize that they are cheated.

Rossi's E-cat used by Lubos for the propagandistic purposes is a perfect target in this respect. I am just wondering how Lubos can see Rossi's E-cat as a failure because it is not commercialized during 4 years and at same time sees no reason to worry about hot fusion program, which has lasted at least 60 years and the outcome is only a bet from Lockheed Martin that fusion plants will be here around 2024. Needless to say, cold fusion plants were here after decade already at seventies and probably already before this!;-)


Saturday, October 11, 2014

Rossi's E-cat spoils again the day of standard physicist!

The battle about reality of cold fusion is approaching its unavoidable end. Third party researchers have now verified cold fusion in a version of Andrea Rossi's E-cat (see this).

Tommaso Dorigo comments the latest finding and admits that the methodology looks very sound. Tommaso is not able to find any other explanation than fraud for the unpleasant fact that cold fusion occurs contrary to what text books tell us.

Lubos, who he is ready to accept that we live in the landscape of 11-dimensional M-theory at some brane without able to predict anything as physicists and test this belief in any manner, has attacked vigorously against new nuclear physics using instead of facts all his rhetoric skills to convince the readers that the people involved with cold fusion are swindlers, idiots, etc... - only "communist" and "criminal" seem to be missing from the the list.

I have commented cold fusion several times in my blog discussing also the TGD based views about cold fusion involving dark phases of matter realized as phases with non-standard value of Planck constant. I have also developed alternative variants of the model in my books (see this and this).

The most recent model (see the article) starts from the model of Widom and Larsen reported to explain the observed isotope ratios, and assuming that the basic step of the reaction involves the transformation of proton to neutron by absorption of orbital electron. Contrary to naive intuitions, weak interactions would be involved in an essential manner in the process! To my opinion this is however one of the weak points of the model at quantitative level although I believe that weak interactions are involved. Second weak point is the assumption that neutron approaches the target with extremely low velocity thus making the interaction cross section very large (proportional to inverse of the relative velocity). Here the new dark physics predicted by TGD would come in rescue: as dark variant of weak interaction physics with weak boson Compton scale scaled up to atomic length scale would make impossible possible. Below the scaled-up scale weak bosons would behave like massless particles and weak interactions would get as strong as electromagnetic ones. Also the de-Broglie wavelength of neutron would be scaled up since it is proportional to heff: this is equivalent with having very low relative velocity.

My sincere hope is that hard empirical facts could eventually force the main stream colleagues to admit that something in our standard view about physics is badly wrong as also the failed attempts to understand dark matter and dark physics have repeatedly demonstrated. I do not however expect any fast changes. The natural dynamical time scale for the phychology of face keeping is of the order of human lifetime!

Addition: In his blog posting about latest developments in cold fusion Lubos demonstrates that he has become a parody of himself, kind of a living joke. Lubos talks about scientific method and would certainly agree that objectivity free of non-emotional attitude is one of its basic signatures. Lubos is however exploding of anger and his arguments rely on personal insults instead of contents. The basic tragedy and paradox of Lubos is that he always reacts instead of acting. Instead of realizing that all ideologies are dangerous because they do not allow freedom of thought, he sees communism as the Devil. The irony is that he behaves just like an ideal communist respecting authorities more than anything else and experiencing those who think differently as enemies. Lubos even sees conspiracy against quantum mechanics and blackholes! Lubos has become age-fan of the dying M-theory and - in amusing contrast - extremely conservative believer on the most hardnosed reductionism. Hence for Lubos the physics below TeV energies is fully done and any-one who considers that cold fusion might be something real and that biology might involve some interesting new physics is swindler, criminal, crackpot, communist,.... - there is long menu of options and you can choose whatever you like!

I want to make absolutely clear that I am not a fan of cold fusion. My attitude is different because TGD predicts new physics in all scales and allows to consider models for how cold fusion would happen. TGD is a genuine theory rather than some random model cooked up to explain some anomaly or unexpected observation (say dark matter or dark energy or why supersymmetry is not seen at LHC). If I would still live in the old ontology, I would certainly have a temptation to accept conspiracy theories as an easy way out of cognitive dissonance. Cognitive dissonance is what scientist should be able to tolerate and here the problem of Lubos and many others is.

Wednesday, October 08, 2014

What EEG sounds like?

TGD view about living matter and brain suggests a possible connection with dark photons and sound. Dark cyclotron photons are central in TGD inspired mnodel of living matter (see this). I have asked whether also the notion of dark sound could make sense: dark sounds would correspond to oscillations of dark matter and magnetic flux tubes.

A rather stringent variant of dark photon idea is that dark cyclotron photons have universal cyclotron energy spectrum (see this). This follows from the proportionality of heff to the mass of the charged particle. This in turn follows from the condition heff =hgr= GMm/v0 (v0 has dimensions of velocity) having the interpretation that electromagnetic Planck constant equals to gravitational Planck constant so that same flux tubes can mediate gravitational and electromagnetic interactions (dark photons and gravitons). Note that both gravitational and em Compton lengths would be independent of mass of the particle: something essential for macroscopic quantum coherence of different particles. Some experimental input obtained by taking seriously the claim that the observed slightly too large mass of electron Cooper pair in measurements involving magnetic field (see this) is due to a gigantic gravimagnetic London moment proportional to h2 is due to to the replacement h→ heff. Dark cyclotron photons would have energies in biophoton range (visible and UV energies corresponding to energy range for excitations of biomolecules) and would thus having biological effects and optimal for biocontrol by magnetic body and communication of sensory input to magnetic body.

Piezoelectric effect suggests a transformation of to ordinary sound waves with low frequencies (see this). A bunch of ordinary phonons (h_eff= n×h) with low energy could be created from single dark photon. Could this transformation be involved with a transformation of visual percepts to auditory percepts in association areas of brain and with a production of virtual sensory input as feedback from auditory areas to ears using dark photons from brain or magnetic body through brain propagating to ear and transformed to bunches of phonons with the same low frequency.

Then comes the question. Has anyone tested what EEG sounds like!? Phase information is lost in EEG power spectrum so that testing requires additional information -probably crucial for the information content - but one could try to get some idea about this. What is remarkable that the part of EEG present during wake-up state corresponds to the sound frequencies is above 10 Hz and we aso hear consciously frequencies above 10-20 Hz! The scientific contents bill of century: EEG in sounds sounds like internal speech!;-)

A little notice: Science Daily reports about experimental search of XMASS collaboration excluding the possibility that super-weakly interacting particles constitute all dark matter. This is also a further blow against standard SUSY. Maybe time is ripe for a serious reconsideration of the simplistic idea about dark matter as some exotic particle. And maybe the ideas about the nature of SUSY might need some updating.

Monday, October 06, 2014

More precise view about remote replication

Both Luc Montagnier and Peter Gariaev have found strong evidence for what might be called remote replication of DNA. I have developed a TGD inspired model for remote replication using the data from Peter Gariaev, who has developed the notion of wave DNA waveDNA supported by Montagnier's findings.

Polymer chain reaction (PCR) provides a manner to buildcopies of piece of DNA serving as template. Once single copy is produced, it serves as a template for a further copy so that exponential amplification is achieved. Montagnier's and Gariaev's works suggest however that the synthesis of DNA could also occur without a real matrix DNA as remote replication. According to the proposal of Gariaev DNA template would be remotely represented as what he calls wave DNA. Montagnier uses 7 Hz ELF radiation to obtain the effect whereas Gariaev uses scattering of laser light into large interval of frequencies to achieve the effect.

In TGD approach magnetic body containing dark matter with large Planck constant, the associated cyclotron radiation for which energy scale is proportional to effective Planck constant heff=n× h having large values implying conjectured macroscopic quantum coherence of living matter, dark analog of DNA represented as dark proton sequences at magnetic flux tubes and accompanying ordinary DNA, plus reconnection of U-shaped magnetic flux tubes assignable to the magnetic bodies of bio-molecules and allowing them to recognize each other, are the basic elements. The model has evolved from the attempts to understand water memory and homeopathy in TGD framework (see this).

Both 7 Hz ELF radiation and scattering of laser light would both generate dark photon (large Planck constant) spectrum with a wide spectrum of frequencies but with the same energy which in Gariaev's experiments would naturally be the energy of scatter laser light. The dark photons would provide representation for DNA codons. If 7 Hz frequency radiation involves dark photons with energies of visible photons transforming to ordinary photons before scattering from DNA the outcome would be same as in Gariaev's experiments.

The updated model involves same elements as the model discussed in (see this) but there are also new elements due to the developments in the model of dark DNA allowing to imagine a detailed mechanism for how water can represent DNA and how DNA could be transcribed to dark DNA. The transcription/association represents a rule and rules are represented in terms of negentropic entanglement in TGD framework with pairs of states in superposition representing the instances of the rule. Transition energy serves as a characterizer of a molecule - say DNA codon - and the entangled state is a superposition of pairs in which either molecule is excited or dark DNA codon is excited to higher cyclotron state with same energy: this requires tuning of the magnetic field and sufficiently large value of heff at the flux tube. Negentropic entanglement is due to the exchange of dark photons: this corresponds to wave DNA aspect. Dark cyclotron photons also generate negatively charged exclusion zones (EZs) discovered by Pollack and in this process transform part of protons to dark ones residing at the magnetic flux tubes associated with EZs and forming dark proton sequencies.

For details see the chapter Quantum gravity, dark matter, and prebiotic evolution or the article More Precise View about Remote DNA Replication .