Tuesday, September 30, 2014

New experimental information about chiral selection

Chirality selection is fundamental problem in biology. It means large parity breaking since only second molecular handedness appears in living matter. This is not the case in inanimate matter. This distinction must be somehow fundamental for what it is to be living. The problem with large parity breaking is however that although it is caused by weak interactions it is extremely small effect and it is difficult to imagine how it could emerge. Even more difficult it is to understand why it would emerge only for the in vivo variants of bio-molecules.

One promising idea is that the original parity asymmetry would not be biological but would transferred to biology. In 1967 biohemist Frederic Vester and environmental scientist Tilo Ulbricht proposed that some physical phenomenon could have changed the balance between left and right handed molecule concentrations during earlier stages of evolution. Beta decays are certainly the first candidate to come in mind since in beta decays the breaking of parity symmetry manifests itself as the appearance of only second helicity for electrons. One says that the electrons from beta decays of nuclear neutron to proton are polarized with spin directing to direction opposite from the momentum of electron. For high energies electron is an eigenstate of parity operator and can be said to be left or right-handed. At low energies both chiralities are present and the spin projection to the direction of motion an have both signs. For instance, one could imagine that cosmic rays decaying in the atmosphere producing nuclei and muons suffering beta decay in atmosphere could produce the polarized electrons.

This asymmetry would manifest itself as slightly different decay rates for molecule and its mirror image induced by the absorbtion of the polarized electron. This small difference could be however exponentially amplified by reaction kinetics and lead to chirality selection by say cosmic rays. The process would have taken place long time ago and led to the dominance of second molecular handedness.

The challenge would be to find a chemical process achieving this. A strong constraint is that this effect should be present only for the in vivo variants of biomolecules. It is difficult to imagine why recent physics as we find it in text books could distinguish between in vivo and in vitro.

The attempts to identify the chemical process involved have not been successful hitherto. Now however Nature published an interesting article about a possible chemical mechanism leading to chirality selection.

  1. Gay and Joan Dreiling working at the University of Nebraska-Lincoln irradiated a organic compound bromocamphor with low energy spin-polarized electrons and achieved a success. The rates of decays induced by absorption of polarized electron differ by about .6 per cent for the two possible polarizations. This is large difference. Note that the chemical reaction is not expected to involve parity breaking. The parity breaking would be inherited from electrons. There are however some problems involved.

  2. The asymmetry occurs only for electron energies below electronvolt. Electrons from cosmic rays have much higher energies but one could argue that there should exist a slowing down mechanism of electrons or there is some other natural source of very low energy polarized electrons.

  3. Second problem is that for low energies one cannot anymore have a well-defined electron chirality but one can speak about spin component in the direction of momentum - actually any direction can be chosen for the quantization axis. Does the result mean that it is the sign of spin projection rather than handedness of electron which matters? This would suggest that at the low energy limit the mirror reflection leaves electron invariant and the parity invariance of physical chemistry would imply that there is no distinction between the decay rates! To me this looks a serious problem: maybe I have misunderstood something.
TGD based view about dark matter suggests a scenario in which external parity breaking is not necessary. Parity breaking would be a feature of chemical reaction itself and involve "new chemistry". This of course makes no sense in the chemistry supported by the standard model. The basic elements are dark matter identified as a hierarchy of dark phases with effective value of Planck constant given by heff=n× h and the notion of magnetic body. Magnetic body would use biological body as sensory receptor and motor instrument and EEG and its possible scaled variants would make the communications with and control of biological body possible.
  1. In dark phase weak bosons would be effectively massless below the scaled up weak scale and weak interactions would be as strong as electromagnetic interaction. The scaling corresponds Lw→ (heff/h × Lw and the resulting dark weak scale can be even of cellular size scale. The otherwise extremely weak parity breaking effects would be large in dark phase. The large parity breaking of weak interaction for the weak decays of dark variants of molecules would directly imply different decay rates for dark magnetic/field bodies of left- and right-handed molecules.

  2. Parity breaking effects of weak interactions causing chiral selection would large due to the presence of dark effectively massless W bosons and Z boson whose interactions break parity. The description of parity breaking effects in nuclear physics (see this suggests that one parity breaking effect would be induced by the interaction s∇ VZ, where VZ is the scalar potential associated with the classical Z field.

  3. The additional bonus is that this mechanism would be possible only in vivo since living matter would be made living by large heff phases identifiable as dark matter at magnetic flux tubes!

  4. Also the observations about bromocamphor could have explanation in terms of dark matter at flux tubes relevant for the observed decays. This would allow to circumvent the problem that the electrons in the experiments involving bromocamphor have so low energy that they do not have well-defined chirality and the difference between the decay rates should be very small.

Another analogous idea is based on polarisation of photons in atmosphere, which in turn induces faster decay for the second molecular chirality: see this. Now the polarisation would be due to the scattering of originally unpolarised photons with atmosphere. This would not involve parity breaking but just Raileygh scattering. Now the polarization is however linear rather than circular and I must confess that I failed to understand how this could lead to breaking of parity which would correspond dominance of either circular polarization. If some reader understands this, I would be happy for explanation.

Sunday, September 28, 2014

A new twist in the inflationary story

There is a highly interesting article about the possible impact of BICEP2 results for inflation (see this). For my earlier comments on BICPE2 see this, this, and this.

The original belief after BICEP2 was that inflation finds strong support from the unexpectedly strong dependence of CMB temperature on the polarization of CMB photons claimed by BICEP2. This would have been caused by primordial gravitational waves. Most bloggers were however silent about a serious problem. If the finding is real, the large polarization implies that QFT approximation fails. Inflationary scenario is indeed essentially QFT based with inflaton field playing the role of Higgs field such that the energy of inflation field decays to particles during inflationary period before the radiation dominated phase.

As already mentioned, now another serious objection has emerged. Inflation predicts a spectrum of gravitatonal waves with amplitudes proportional to mass density fluctuations. The longer the scale, the larger the amplitude should be. The spectrum claimed by BICEP2 shows however exactly the opposite behavior as was found by the authors of the article.

Situation has turned around! The highest desire of inflation theorists is now that BICEP2 results are wrong and due to dust or some other effect! This might well be the case. Paul Steinhardt - one of the developers of inflationary model - has turned into skeptic, and says that unfortunately this is not the only severe problem of inflation. For instance, basic prediction is that we should observe multiverse realized as space-time regions obeying different physics laws (different values of basic parameters of say standard model). We do not! I have been myself wondering why this wrong prediction does not seem to bother multiverse enthusiasts. Is just this corner of Universe with its own physics laws so large that we cannot observer other regions? Strange indeed!

BICEP2 finding forced me to develop TGD view about the TGD counterpart of inflation. The physical interpretation in TGD is totally different from that of inflationary model.

  1. The rapid expansion is a quantum critical period during which the curvature scalar of 3-space vanishes (no scales during criticality) and the induced 3-metric is flat. A phase transition from a phase dominated by a gas of cosmic strings in the future light-cone of Minkowski space (imbedding space is M4×CP2) to radiation dominated cosmology would be in question.
    In the string gas phase GRT description does not apply. Lorentz invariance of the gas phase implies that the universe is isotropic and homogenous and therefore one should avoid the multiverse. It is important to realize tht Lorentz invariance is not present as global symmetry in GRT based cosmology and inflation was hoped to solve the resulting problems.

  2. The phase transition means the emergence of many-sheeted space-time. GRT space-time emerges as its simplification obtained by lumping together the sheets of many-sheeted space-time to a region of Minkowski space provided with a naturally defined effective metric. GRT space-time is assumed to be modellable using single sheeted space-time identifiable as vacuum extremal of Kähler action. This assumption is natural but can be criticized.

  3. Not too surprisingly, the cosmic expansion during critical phase is rapidly accelerating and the energy density of the critical cosmology which is unique apart from it duration would become infinite without transition to radiation dominated cosmology (the gas of cosmic strings has finite mass density). A transition to radiation dominated cosmology must happen before this. CMB temperature fluctuations emerge from the variations of the value of cosmic time at which the transition to radiation dominated cosmology takes place. The magnetic energy of cosmic strings decays to particles so that inflation field is replaced with Kähler magnetic field which also explains the
    appearance of magnetic fields in cosmic scales elegantly.

What one can say about the amplitude of the gravitational waves as a function of scale? Does it increase with the scale as it should do in inflationary models predicting that the amplitude is proportional the amplitude of density fluctuations? Does the amplitude of density fluctuations increase with scale or does Lorentz invariance or properties of string gas phase prevent this? And what density fluctuations are? And what defines the scale?

  1. In inflationary models density fluctuations are generated by gravitational perburbations in existing space-time.
    In TGD Universe many-sheeted space-time is just emerging during inflationary period and QFT starts to make sense
    during radiation dominated phase. Density fluctuations should correspond to the density fluctuations for the gas of cosmic strings topologically condensed to the emerging space-time sheets during the phase transition analogous to a condensation of vapour to 2-D surface.

  2. This would suggest that density fluctuation at space-time sheet corresponds to a maximum amount of string energy in the volume in question. The energy density of cosmic string gas is proportional to T/a2 - here a is the light-cone proper time characterizing the scale and T is string tension. This predicts that density fluctuations decrease with length scale. TGD prediction would be consistent with BICEP2 finding even if it is correct. Otherwise the situation remains unsettled.

  3. Note that as the Minkowski space projections of cosmic strings gradually thicken, they become Kähler magnetic flux tubes carrying monopole flux: this explains the presence of cosmic magnetic fields since no current is needed to generatate monopole fields. The mass density per unit length of cosmic string is given by string tension essentially as the density of the magnetic energy which decays partially to matter. As the string thickens, the energy density of string decreases as the inverse of its transversal area. The total mass of string however remains proportional to its length.

Thursday, September 25, 2014

No blackholes?

I received an interesting link from Ulla about blackholes. The claim of physics professor Laura Mersini-Houghton is that black holes cannot be created in star collapse. The collapse of star would involve at endphases a "swelling" which evaporates the blackhole candidate as Hawking radiation so that no blackhole would be formed!

One positive consequence would be that this would put an end to the endless prattling about blackhole entropy, firewalls, etc.. which to my opinion are just gnawing of an old bone. Even better: no-one would waste time to a desperate attempt to reduce QCD, nuclear physics, or condensed matter physics to the physics of blackholes in 10 dimensions!

Personally I take blackholes only as a singularity of GRT. For some reason colleagues seem to be unable to admit that GRT space-time is not enough. String theories do not bring anything new since strings as such have too low dimension to tell anything about space-time physics and their long length scale limit is (or is hand-waved to be) just Einstein-YM type theory. In the theory next to GRT blackholes must be replaced with something more well-defined.

This sounds extremely blasphemous, but after 37 years or hard work I can safely state that TGD is one of the very few real candidates for the theory next to GRT.

  1. In TGD framework one can imbed Schwarschild solution down to some critical radius. Something happens at the horizon of blackhole. Scwartchild-Nordström solution suggests what. By an arbitrary small deformation of the radial component grr=1/(1-2GM/r) so that it becomes finite at horizon r=rS=2GM the determinant of 4-metric becomes vanishing. CP2 is one of the extremals of Einstein-Maxwell action with cosmological constant.

    This observation suggests that horizon in improved theory is the 3-surface at which the signature of the metric transforms from Minkowskian to Euclidian. Euclidian space-times are used in the quantization of GRT as a mathematical trick in an attempt to make some sense about path integral by transforming it to functional integral but are not taken seriously physically.

  2. In TGD space-time surfaces indeed consist of both Minkowskian and Euclidian regions and Euclidian regions correspond to the 4-D lines of generalized Feynman diagrams. A good model is as deformations of CP2 type vacuum extremal which are locally just CP2 but whose imbedding to M4× CP2 is non-standard having light-like random curve as M4 projection giving rise to conformal invariance and Virasoro conditions. Blackhole would be replaced with particle like object identifiable as line of generalized Feynman diagram. All material objects would have space-time sheet which has Euclidian signature of induced metric and represents the object as particle like object.

It must be emphasized that GRT space-time is indeed only an approximate concept in TGD framework.
  1. Einstein-Yang-Mills space-time is obtained from the many-sheeted space-time of TGD by lumping together the sheets and describing it as a region of Minkowski space endowed with an effective metric which is sum of flat Minkowski metric and deviations of the metrics of sheets from Minkowski metric. Same procedure is applied to gauge potentials to get standard model.

  2. The motivation is that test particle topologically condenses at all space-time sheets present in given region of M4 and and the effects of the classical fields at these sheets superpose. Thus superposition of fields is replaced with superposition of their effects and linear superposition with set theoretic union of space-time sheets. TGD inspired cosmology assumes that the effective metric obtained in this manner allows imbedding as vacuum extremal of Kähler action. The justification of this assumption is that it solves several key problems of GRT based cosmology. One can also represent a subset of solutions of Einstein's equations as vacuum extremals but in the generic case the many-sheeted space-time cannot be approximated by single space-time sheet.

  3. The number of field patterns in TGD Universe is extremely small - given by preferred extremals - and the relationship of TGD to GRT and YM theories is like that of atomic physics to condensed matter physics. In the transition to GRT-Yang-Mills picture one gets rid of enormous topological complexity but the extreme simplicity at the level of fields is lost. Only four CP2 coordinates appear in the role of fields in TGD framework and at GRT Yang-Mills limit they are replaced with a large number of classical fields.

Many-sheeted space-time makes itself therefore visible only via anomalies.
  1. We indeed see everywhere outer boundaries: they could be identifiable as effective or genuine boundaries of space-time sheets in TGD framework: this depends on whether one adds to Kähler action a boundary term allowing the presence of boundaries or not. If not, the space-time sheets are pairs of sheets glued together along would-be boundaries. Seeing is however not believing. We must somehow measure the presence of space-time sheets before we can take them seriously!

  2. In many-sheeted space-time signal from say supernova can arrive along several space-time sheets simultaneously and the arrival time depends on the sheet. In case of SN1987A this effect was observed for neutrinos and photons as one can learn from Wikipedia article).

  3. The "dropping" of particles from smaller to larger space-time sheet at the boundary of smaller one provides a possible mechanism of metabolism since the zero point kinetic energy decreases.

Addition: Lubos has been highly emotional about Laura Mersini's paper. It is a pity that Lubos experiences all questioning of cherished assumptions as an organized attempt to destroy quantum mechanics, general relativity, or superstring theory and reacts accordingly. Also this posting is full of adjectives such as "nutty", "idiotic", "stupid", "silly","lunatic","crank","super-idiotic", to list few of the evergreens of Lubos. Everyone can decide whether to take seriously a person whose arguments are full of this kind of ad hominem attacks.

These bursts of anger do not change the fact that black hole represents a mathematical singularity of an otherwise highly successful theory. There is no doubt that GRT describes the physics outside the exterior of blackhole. The challenge is to find a theory which allows to understand what really happens in the interior. Essentially microscopic view about space-time replacing the GRT view, which is essentially "astroscopic" . Superstrings tried this but did not bring in nothing new since all predictions emerge from ad hoc hypothesis known as spontaneous compactification. Someone has correctly said that superstring theory predicts 10-dimensional Einsteinian gravity, the rest is an inflation of ad hoc hypothesis. Also Big bang cosmology is very successful but "What is the real physics behind and before what we identify as inflation?" is the question which we should approach with an open mind.

Monday, September 22, 2014

Why I keep my mind open concerning BICEP2 findings?

Some time ago BICEP2 published an eprint, which became the scientific news of year. They claimed that cosmic microwave background (CMB) exhibits co called B modes with a local polarization, which is rotational ("whirly"), and would be caused by primordial gravitational waves during the inflationary period. I discussed the finding from TGD point of view here.

Inflation theorists interpreted this as a support for inflation although the size of the effect was so large that quantum field theoretic modelling in terms of inflaton concept (analogous to Higgs) becomes highly questionable mathematically. Soon the finding of BICEP2 was challenged (I wrote about this here) . Later BICEP2 published an article in which they admitted that the effect could be due to the dust. Planck collaboration published now an eprint supporting the view that the signal observed by BICEP2 is probably due to dust.

The effect forced to develop in more detail the TGD view about the transition from primordial cosmic string dominated cosmology (gas of cosmic strings) to radiation dominated cosmology. TGD view forces to leave the world as quantum field theories (QFTs) general relativity see it. Primordial cosmology would correspond to tring gas dominated phase in which standard view about space-time does not make sense. The counterpart of inflationary period would correspond to a transition to radiation dominated phase in which the space-time sheets - slightly curved pieces of Minkowski space - make sense and GRT limit of TGD obtained by replacing the space-time sheets of many-sheeted space-time with single slightly curved piece of M4 is practical and many-sheetedness makes it manifest only via anomalies. In GRT framework the gas of cosmic strings does not make sense and inflationary period in which space-time sheets already appear is a bridge to the world, where GRT space-time is a useful concept.

This transition is phase transition and quantum criticality fixes the cosmology during this period completely apart from the duration of the period. The curvature scalar of 3-space vanishes (no scales at quantum criticality) as it does also in inflationary cosmology. Hence it should not be surprising (it was!) that the outcome were very similar to that in inflationary cosmology: accelerated expansion. This period must have finite duration as it has because otherwise the mass density would become literally infinite, which is not possible since the density of cosmic strings in "vapour phase" is finite.

Unlike the purely phenomenological QFT mode involving inflaton type fields, TGD provides a detailed geometric mechanism for the generation of the CMB polarization in terms of magnetic flux tubes. I cannot however calculate the size of the effect, and one can also imagine effect caused by the presence of the magnetic flux tubes and it could contribute also at later times.

Lubos has a very interesting posting emphasizing the David-Goliath setting: big and arrogant Planck against tiny Bicep2! On basis of my own frustrating experiences as tiny David I am forced to take this sociological interpretation seriously.

Lubos argues that the whirling pattern observed for the polarisation direction vector is regular and exhibits a definite scale. One can argue that dust - if it it is dust - would produce a random pattern. Personally I do not have any strong attitudes pro or con: TGD predicts primordial gravitational waves but I am unable to calculate the magnitude of the effect. TGD also suggests aan alternative mechanism producing the whirling: it could be due to rotational magnetic fields at magnetic flux tubes (having cosmic strings as predecessors) - that is vectorial rather than tensorial effect. This effect could be present also at later times and produce regular whirling pattern.

Magnetic fields are indeed known to exist in arbitrary long astrophysical and cosmological scales. This is one of the big challenges of cosmology since their presence requires currents but in cosmology thermodynamical equilibrium does not allow this kind of currents in long length scales. In TGD framework (due to the topology of CP2) the flux tubes carry monopole fluxes requiring no currents, and in the first approximation these fields can be locally irrotational although they have closed flux lines. A flow around an annulus in plane illustrates this: the flow can ge locally irrotational everywhere but obviously there is a global rotation. Does local irrotational character of these magnetic fields imply that local polarization of CMB cannot be generated by closed flux tubes? Or does the whirling pattern make the web of flux tubes directly visible?

Average blogger is quite too hasty in putting BICEP2 findings to the same category as the "discovery" that neutrinos travel with a speed slightly higher than photons (doing this with emotional rhetorics is an easy manner to increase the number of visitors!). Ironically, supernova SN1987 demonstrated for 27 years that neutrinos indeed seem to move faster than photons! The neutrinos from SN1987 came in two groups and both neutrino bursts came earlier than the gamma ray burst. TGD explanation is that the the neutrinos bursts and potons arrived along different space-time sheets with slightly different arrival times meaning Δc/c ∼ 10-9. The effect claimed by the OPERA collaboration would have been much larger, something like Δc/c ∼ 10-5.

Thursday, September 18, 2014

Is cosmic expansion a mere coordinate effect?

There is a very interesting article about cosmic expansion or rather a claim about the absence of cosmic expansion.

The argument based on the experimental findings of a team of astrophysicists led by Eric Lerner goes as follows. In non-expanding cosmology and also in the space around us (Earth, Solar system, Milky Way), as similar objects go further away, they look fainter and smaller. Their surface brightness remains constant. In Big Bang theory objects actually should appear fainter but bigger. Therefore the surface brightness- total luminosity per area - should decrease with distance. Besides this cosmic redshift would be dimming the light.

Therefore in expanding Universe the most distant galaxies should have hundreds of times dimmer surface brightness since the surface are is larger and total intensity of light emitted more or less the same. Unless of course, the total luminosity increases to compensate this: this would be of course total adhoc connection between dynamics of stars and cosmic expansion rate.

This is not what observations tell. Therefore one could conclude that Universe does not expand and Big Bang theory is wrong.

The conclusion is of course wrong. Big Bang theory certainly explains a log of things. I try to summarize what goes wrong.

  1. It is essential to make clear what time coordinate one is using. When analyzing motions in Solar System and Milky Way, one uses flat Minkowski coordinates of Special Relativity. In this framework one observes no expansion.

  2. In cosmology one uses Robertson-Walker coordinates (a,r, θ,φ). a and r a the relevant ones. In TGD inspired cosmology R-W coordinates relate to the spherical variant (t,rM,θ,φ) of Minkowski coordinates by formulas

    a2= t2-rM2, rM= a×r.

    The line element of metric is

    ds2= gaada2 -a2[dr2/(1+r2)+r22]

    and at the limit of empty cosmology one has gaa=1.

    In these coordinates the light-cone of empty Minkowski space looks like expanding albeit empty cosmology! a is just the light-cone proper time. The reason is that cosmic time coordinate labels the a=constant hyperboloids (hyperbolic spaces) rather than M4 time=constant snapshots. This totally trivial observation is extremely important concerning the interpretation of cosmic expansion. Often however trivial observations are the most difficult ones to make.

Cosmic expansion would to high extend a coordinate effect but why should one then use R-W coordinates in cosmic scales? Why not Minkowski coordinates?
  1. In Zero Energy Ontology (ZEO) - something very specific to TGD - the use of these coordinates is natural since zero energy states are pairs of positive and negative energy states localized about boundaries of causal diamonds (CD), which are intersections of future and past directed light-cones having pieces of light-cone boundary as their boundaries. The geometry of CD suggests strongly the use of R-W coordinates associated with either boundary of CD. The question "Which boundary?" would lead to digression to TGD inspired theory of consciousness. I have talked about this in earlier postings.

  2. Thus the correct conclusion is that local objects such as stars and galaxies and even large objects do not participate in the expansion when one looks the situation in local Minkowski coordinates - which by the way are uniquely defined in TGD framework since space-time sheets are surfaces in M4×CP2. In General Relavity the identification of the local Minkowski coordinates could be highly non-trivial challenge.

    In TGD framework local systems correspond to their own space-time sheets and Minkowski coordinates are natural for the description of the local physic since space-time sheet is by definition a space-time region allowing a representation as a graph of a map from M4 to CP2. The effects caused by the CD inside which the space-time surfaces in question belong to the local physics are negligible. Cosmic expansion is therefore not a mere coordinate effect but directly reflects the underlying ZEO.

  3. In General Relativity one cannot assume imbeddability of the generic solution of Einstein's equations to M4 × CP2 and this argument does not work. The absence of local expansion have been known for a long time and Swiss Cheese cosmology has been proposed as a solution. Non-expanding local objects of constant size would be the holes of Swiss Cheese and the cheese around them would expand. The holes of cheese would correspond to space-time sheets in TGD framework. All space-time sheets can be in principle non-expanding and they have suffered topological condensation to large space-time sheets.

One should also make clear GRT space-time is only an approximate concept in TGD framework.
  1. Einstein-Yang-Mills space-time is obtained from the many-sheeted space-time of TGD by lumping together the sheets and describing it as a region of Minkowski space endowed with an effective metric which is sum of flat Minkowski metric and deviations of the metrics of sheets from Minkowski metric. Same procedure is applied to gauge potentials.

  2. The motivation is that test particle topologically condenses at all space-time sheets present in given region of M4 and and the effects of the classical fields at these sheets superpose. Thus superposition of fields is replaced with superposition of their effects and linear superposition with set theoretic union of space-time sheets. TGD inspired cosmology assumes that the effective metric obtained in this manner allows imbedding as vacuum extremal of Kähler action. The justification of this assumption is that it solves several key problems of
    GRT based cosmology.

  3. The number of field patterns in TGD Universe is extremely small - given by preferred extremals - and the relationship of TGD to GRT and YM theories is like that of atomic physics to condensed matter physics. In the transition to GRT-Yang-Mills picture one gets rid of enormous topological complexity but the extreme simplicity at the level of fields is lost. Only four CP2 coordinates appear in the role of fields in TGD framework and at GRT Yang-Mills limit they are replaced with a large number of classical fields.

Is evolution 3-adic?

I received an interesting email from Jose Diez Faixat giving a link to his blog. The title of the blog is "Bye-bye Darwin" and tells something about his proposal. The sub-title "The Hidden rhythm of evolution" tells more. Darwinian view is that evolution is random and evolutionary pressures select the randomly produced mutations. Rhythm does
not fit with this picture.

The observation challenging Darwinian dogma is that the moments for evolutionary breakthroughs - according to Faixat's observation - seems to come in powers of 3 for some fundamental time scale. There would be precise 3-fractality and accompanying cyclicity - something totally different from Darwinian expectations.

By looking at the diagrams demonstrating the appearance of powers of 3 as time scales, it became clear that the interpretation int terms of underlying 3-adicity could make sense. I have speculated with the possibility of small-p p-adicity. In particular, p-adic length scale hypothesis stating that primes near powers of 2 are especially important physically could reflect underlying 2-adicity. One can indeed have for each p entire hierarchy of p-adic length scales coming as powers of p1/2. p=2 would give p-adic length scale hypothesis. The observations of Faixat suggest that also powers p=3 are important - at least in evolutionary time scales.

Note: The p-adic primes characterizing elementary particles are gigantic. For instance, Mersenne prime M127 = 2127 -1 characterizes electron. This scale could relate to the 2-adic scale L2(127)= 2127/2× L2(1). The hierarchy of Planck constants coming as heff=n× h also predicts that the p-adic length scale hierarchy has scaled up versions obtained by scaling it by n.

The interpretation would be in terms of p-adic topology as an effective topology in some discretization defined by the scale of resolution. In short scales there would be chaos in the sense of real topology: this would correspond to Darwinian randomness. In long scales p-adic continuity would imply fractal periodicities in powers of p and possibly its square root. The reason is that in p-adic topology system's states at t and t+kpn, k=0,1,...p-1, would not differ much for large values of n.

The interpretation relies on p-adic fractality . p-Adic fractals are obtained by assigning to real function its p-adic counterpart by mapping real point by canonical identification

SUMn xn pn → SUM n xn p-n

to p-adic number, assigning to it the value of p-adic variant of real function with a similar analytic form and mapping the value of this function to a real number by the inverse of the canonical identification, the powers of p correspond to a fractal hierarchy of discontinuities.

A possible concrete interpretation is that the moments of evolutionary breakthroughs correspond to criticality and the critical state is universal and very similar for moments which are p-adically near each other.

The amusing co-incidence was that I have been working with a model for 12-note scale based on the observation that icosahedron is a Platonic solid containing 12 vertices. The scale is represented as a closed non-self-intersecting curve - Hamiltonian cycle - connecting all 12 vertices: octave equivalence is the motivation for closedness. The cycle consists of edges connecting two neighboring vertices identified as quints - scalings of fundamental by 3/2 in Platonic scale. What is amusing that scale is obtained essentially powers of 3 are in question scaled down (octave equivalence) to the basic octave by a suitable power of 2. The faces of icosahedron are triangles and define 3-chords. Triangle can contain either 0,1, 2 edges of the cycle meaning that the 3-chords defined by faces and defining the notion of harmonic contain 0,1, or 2 quints. One obtains large number of different harmonies partially characterized by the numbers of 0-, 1-, and 2-quint icosahedral triangles.

The connection with 3-adicity comes from the fact that Pythagorean quint cycle is nothing but scaling by powers of 3 followed by suitable downwards scaling by 2 bringing the frequency to the basic octave so that 3-adicity might be realized also at the level of music!

There is also another strange co-incidence. Icosahedron has 20 faces, which is the number of amino-acids. This suggests a connection between fundamental biology and 12-note scale. This leads to a concrete geometric model for amino-acids as 3-chords and for proteins as music consisting of sequences of 3-chords. Amino-acids can be classified into 3 classes using polarity and basic - acid/neutrality character of side chain as basic criteria. DNA codons would would define the notes of this music with 3-letter codons coding for 3-chords. One ends up also to a model of genetic code relying on symmetries of icosahedron from some intriguing observations about the symmetries of the code table.

At the level of details the icosahedral model is able to predict genetic code correctly for 60 codons only, and one must extend it by fusion it with a tetrahedral code. The fusion of the two codes corresponds geometrically to the fusion of icosahedron with tetrahedron along common face identified as "empty" amino-acid and coded by 2 stopping codons in icosahedral code and 1 stopping codon in tetrahedral code. Tetrahedral code brings in 2 additional amino-acids identified as so called 21st and 22nd amino-acid discovered for few years ago and coded by stopping codons. These stopping codons certainly differ somehow from the ordinary one - it is thought that context defines somehow the difference. In TGD framework magnetic body of DNA could define the context.

The addition of tetrahedron brings one additional vertex, which correlates with the fact that rational scale does not quite closed. 12 quints gives a little bit more than 7 octaves and this forces to introduce 13 note for instance, Ab and G# could differ slightly. Also micro-tubular geometry involves number 13 in an essential manner.

DNAs humble beginnings as nutrient carrier; humble - really?

I received from Ulla an interesting link about the indications that DNA may have had rather humble beginnings: it would have served as a nutrient carrier. Each nuclteotide in the phosphate-deoxiribose backbone corresponds to a phosphate and nutrient refers to phosphate assumed to carry metabolic energy in high energy phosphate bond.

In AXP, X=M,D,T the number of phosphates is 1,2,3. When ATP transforms to ADP it gives away one phosphate to the acceptor molecule which receives thus metabolic energy. For DNA there is one phosphate per nucleotide and besides A also T, G, and C are possible.

The attribute "humble" reflects of course the recent view about the role of nutrients and metabolic energy. It is just ordered energy what they are carrying. TGD view about life suggest that "humble" is quite too humble an attribute.

  1. The basic notion is potentially conscious information. This is realized as negentropic entanglement for which entanglement probabilities must be rational numbers (or possibly also algebraic numbers in some algebraic extension of rationals) so that their p-adic norms make sense. The entanglement entropy associated with the density matrix characterizing entanglement is defined by a modification of Shannon formula by replacing the probabilities in the argument of the logarithm with their p-adic norms and finding the prime for which the entropy is smallest. The entanglement entropy defined in this manner can be and is negative unlike the usual Shannon entropy. The interpretation is as information associated with entanglement. Second law is not violated since the information is 2-particle property whereas as Shannon entropy is single particle property characterizing average particle.

    The interpretation of negentropic entanglement is as potentially conscious information: the superposition of pairs of states would represent abstraction or rule whose instances would be the pairs of states. The large the number of pairs, the higher the abstraction level.

  2. The consistency with standard quantum measurement theory gives strong constraints on the form of the negentropic entanglement. The key notion is that if density matrix is proportional to unit matrix, standard measurement theory says nothing about the outcome of measurement and entanglement can be preserved. Otherwise the reduction occurs to one of the states involved. This situation could correspond to negentropic 2-particle entanglement. For several subsystems each sub-system-complement pair would have similar density matrix. There is also a connection with dark matter identified as phases with non-standard value heff=n×h of Planck constant. n defines the dimension of the density matrix. Thus dark matter at magnetic flux quanta would make living matter living.

    In 2-particle case the entanglement coefficients form a unitary matrix typically involved with quantum computing systems. DNA-cell membrane system is indeed assumed to form a topological quantum computer in TGD framework. The braiding of magnetic flux tubes connecting nucleotides with lipids of the cell membrane defines topological quantum computer program and its time evolution is induced by the flow of lipids forming a 2-D liquid crystal. This flow can be induced by nearby events and also by nerve pulses.

    Sidestep: Actually pairs of flux tubes are involved to make high temperature super-conductivity possible with members of Cooper pairs at flux tubes with same or opposite directions of spins depending on the direction of magnetic field and thus in spin S=0 or S=1 state. For large value of Planck constant heff=n×h the spin-spin interaction energy is large and could correspond in living matter to energies of visible light.

  3. Negentropy Maximization Principle (NMP) is the basic variational principle of TGD inspired theory of consciousness. NMP states that the gain of negentropic entanglement is maximal in state function reduction so that negentropic entanglement can be stable.

  4. NMP guarantees that during evolution by quantum jumps recreating the Universe (and sub-Universes assignable to causal diamonds (CDs)) the information resources of Universe increase. Just to irritate skeptics I have spoken about "Akashic records". Akashic records would form books in a universal library and could be read by interaction free quantum measurement preserving entanglement but generating secondary generating state function reductions providing conscious information about Akashic records defining also a model of self.

    Sidestep: Self can be identified as a sequence of state function for which only first quantum is non-trivial at second boundary of CD whereas other quantum jumps induce change of superposition of CDs at the opposite boundary and states at them). Essentially a discretized counterpart of unitary time development would be in question. This allows to understand how the arrow of psychological time emerges and why the contents of sensory experience is about so narrow a time interval. Act of free will corresponds to the first state function reduction at opposite boundary and thus involves change of the arrow of psychological time at some level of self hierarchy: this prediction is consistent with the Libet's findings that conscious decision implies neural activity initiated before the decision ("before" with respect to geometric time, not subjective time).

In this framework the phosphates could be seen as ends of magnetic flux tubes connecting DNA to cell membrane and mediating negentropic entanglement with the cell membrane. DNA as topological quantum computer vision conforms with the interpretation DNA-cell membrane system as "Akaschic records". This role of DNA-cell membrane system would have emerged already before the metabolic machinery, whose function would be to transfer the entanglement of nutrient molecules with some bigger system X to that between biomolecules and X. Some intriguing numerical co-incidences suggest that X could be gravitational Mother Gaia and flux tubes mediating gravitational interaction with nutrient molecules and gravitational Mother Gaia could be in question. This brings in mind Penrose's proposal about the role of quantum gravity. TGD is indeed a theory of quantum gravity predicting that gravitation is quantal in astroscopic length scales.