Monday, January 30, 2006

p-Adic length scale hypothesis and the weakness of the gravitational constant

In the posting Reduction of long length scale real physics to short length scale p-adic physics and vice versa I discussed the idea that long range p-adically fractal physics can be reduced to local p-adic physics with p-adic continuity and smoothness alone implying the universal characteristics of long scale physics. Real field equations would determine local real physics and their p-adic counterparts the global real physics.

I mentioned also how multi-p-fractality and the pairing p≈2k, k prime, in p-adic length scale hypothesis can be understood in this scenario. There is however a problem involved with the understanding of the origin of the p-adic length scale hypothesis if the correspondence via common rationals is assumed.

1. How p-adic length scale hypothesis can be understood?

Here the problem and its resolution is discussed (I have discussed this point already earlier but from different view point).

  1. The mass calculations based on p-adic thermodynamics for Virasoro generator L0 predict that mass squared is proportional to 1/p and Uncertainty Principle implies that Lp is proportional to p1/2 rather than p, which looks more natural if common rationals define the correspondence between real and p-adic physics.

  2. It would seem that length dp≈ pR, R or order CP2 length, in the induced space-time metric must correspond to a length Lp≈ p1/2R in M4. This could be understood if space-like geodesic lines at real space-time sheet obeying effective p-adic topology are like orbits of a particle performing Brownian motion so that the space-like geodesic connecting points with M4 distance rM has a length rX propto rM2. Geodesic random walk with randomness associated with the motion in CP2 degrees of freedom could be in question. The effective p-adic topology indeed induces a strong local wiggling in CP2 degrees of freedom so that rX increases and can depend non-linearly on rM.

  3. If the size of the space-time sheet associated with the particle has size dp≈ pR in the induced metric, the corresponding M4 size would be about Lp propto p1/2R and p-adic length scale hypothesis results.

  4. The strongly non-perturbative and chaotic behavior rX propto rM2 is assumed to continue only up to Lp. At longer length scales the space-time distance dp associated with Lp becomes the unit of space-time distance and geodesic distance rX is in a good approximation given by

    rX= (rM/Lp)dp propto p1/2× rM ,

    and is thus linear in M4 distance rM.

2. How to understand the smallness of gravitational constant?

The proposed explanation of the p-adic length scale hypothesis allows also to understand the weakness of the gravitational constant as being due to the fact that the space-time distance rX appearing in gravitational force as given by Newtonian approximation is by a factor p1/2 times longer than rM so that the strong gravitational force proportional to Lp2/rX2 scales down by a factor p as rX is expressed in terms of rM. M4 distance rM is indeed the natural variable since distances are measured using space-time sheets as units and their sizes are always measured in M4 metric or almost flat X4 metric.

A more precise argument goes as follows.

  1. Assume first that the space-time sheet is characterized by single prime p: also multi-p-fractality is possible. The strong gravitational constant Gs characterizes the interactions involving exchanges of string like objects of size scale measured naturally using Lp as a unit. In this case the force is mediated in M4 as an exchange of a particle. By dimensional estimate Gs is proportional to Lp2 and string model picture gives a precise estimate for the numerical factor n in Gs=nLp2.

  2. The classical gravitational force is mediated via induced metric inside the space-time sheets and in long length scales is proportional to Gs/rX2 propto Lp2/rX2 propto R2/rM2, where R≈ 104G1/2 is CP2 length. Hence the effective gravitational constant is reduced by a factor 1/p and is same for all values of p.

  3. The value of the gravitational constant is still by a factor of order R2/G≈ 108 too high. A correct value is obtained if multi-p-fractality prevails in such a manner that p1/2 is replaced by n1/2 with n=2× 3× 5...× 23× p. One can visualize the situation as hierarchy of wavelets: to p-adic wavelets very small q=23-adic wawelets are superposed to which in turn q=19-adic ... The earlier estimates for the gravitational constant are consistent with this result and fix the numerical details.

  4. This approach predicts a p-adic hierarchy of strong gravitons and unstable spin 2 hadrons are excellent candidates for them. It is however not clear whether Newtonian graviton is predicted at all: in other words could the gravitation inside space-time sheets be a purely classical phenomenon? One can certainly imagine the exchange of topologically condensed Newtonian gravitons moving along light-like geodesics along space-time sheets and the lengths of spatial projections of these geodesics would be indeed scaled up by p1/2 factor.

For more details see the chapter TGD as a Generalized Number Theory I: p-Adicization Program of TGD.

Matti Pitkanen

Sunday, January 29, 2006

Reduction of long length scale real physics to short length scale p-adic physics and vice versa

The number theoretic vision about physics (this, this, and this) relies on the idea that physics or, rather what we can know about it, is basically rational number based. Also a generalization of the notion of number is involved. Very roughly, real numbers and various algebraic extensions of p-adic number fields are glued together along common rationals to form a book like structures.

One interpretation would be that space-time surfaces, the induced spinors at space-time surfaces, configuration space spinor fields, S-matrix, etc..., can be obtained by algebraically continuing their values in a discrete subset of rational variant of the geometric structure considered to appropriate completion of rationals (real or p-adic). The existence of the algebraic continuation poses very strong additional constraints on physics but has not provided any practical means to solve quantum TGD.

This view leads to a very powerful iterative method of constructing global solutions of classical field equations from local data and at the same time gives justification for the notion of p-adic fractality, which has provided very successful approach not only to elementary particle physics but also physics at longer scales. The basic idea is that mere p-adic continuity and smoothness imply fractal long range correlations between rational points which are very close p-adically but far from each other in the real sense and vice versa.

1. The emergence of a rational cutoff

For a given p-adic continuation only a subset of rational points is acceptable since the simultaneous requirements of real and p-adic continuity can be satisfied only if one introduces ultraviolet cutoff length scale. This means that the distances between subset of rational points fixing the dynamics of the quantities involved are above some cutoff length scale, which is expected to depend on the p-adic number field Rp as well as a particular solution of field equations. The continued quantities coincide only in this subset of rationals but not in shorter length scales.

The presence of the rational cutoff implies that the dynamics at short scales becomes effectively discrete. Reality is however not discrete: discreteness and rationality only characterize the inherent limitations of our knowledge about reality. This conforms with the fact that our numerical calculations are always discrete and involve finite set of points.

The intersection points of various p-adic continuations with real space-time surface should code for all actual information that a particular p-adic physics can give about real physics in classical sense. There are reasons to believe that real space-time sheets are in the general case characterized by integers n decomposing into products of powers of primes pi. One can expect that for pi-adic continuations the sets of intersection points are especially large and that these p-adic space-time surfaces can be said to provide a good discrete cognitive mimicry of the real space-time surface.

Adelic formula represents real number as product of inverse of its p-adic norms. This raises the hope that taken together these intersections could allow to determine the real surface and thus classical physics to a high degree. This idea generalizes to quantum context too.

The actual construction of the algebraic continuation from a subset of rational points is of course something which cannot be done in practice and this is not even necessary since much more elegant approach is possible.

2. Hierarchy of algebraic physics

One of the basic hypothesis of quantum TGD is that it is possible to define exponent of Kähler action in terms of fermionic determinants associated with the modified Dirac operator derivable from a Dirac action related super-symmetrically to the Kähler action.

If this is true, a very elegant manner to define hierarchy of physics in various algebraic extensions of rational numbers and p-adic numbers becomes possible. The observation is that the continuation to various p-adic numbers fields and their extensions for the fermionic determinant can be simply done by allowing only the eigenvalues which belong to the extension of rationals involved and solve field equations for the resulting Kähler function. Hence a hierarchy of fermionic determinants results. The value of the dynamical Planck constant characterizes in this approach the scale factor of the M4 metric in various number theoretical variants of the imbedding space H=M4× CP2 glued together along subsets of rational points of H. The values of hbar are determined from the requirement of quantum criticality meaning that Kähler coupling strength is analogous to critical temperature.

In this approach there is no need to restrict the imbedding space points to the algebraic extension of rationals and to try to formulate the counterparts of field equations in these discrete imbedding spaces.

3. p-Adic short range physics codes for long range real physics and vice versa

One should be able to construct global solutions of field equations numerically or by engineering them from the large repertoire of known exact solutions. This challenge looks formidable since the field equations are extremely non-linear and the failure of the strict non-determinism seems to make even in principle the construction of global solutions impossible as a boundary value problem or initial value problem.

The hope is that short distance physics might somehow code for long distance physics. If this kind of coding is possible at all, p-adicity should be crucial for achieving it. This suggests that one must articulate the question more precisely by characterizing what we mean with the phrases "short distance" and "long distance". The notion of short distance in p-adic physics is completely different from that in real physics, where rationals very close to each other can be arbitrary far away in the real sense, and vice versa. Could it be that in the statement "Short length scale physics codes for long length scale physics" the attribute "short"/"long" could refer to p-adic/real norm, real/p-adic norm, or both depending on the situation?

The point is that rational imbedding space points very near to each other in the real sense are in general at arbitrarily large distances in p-adic sense and vice versa. This observation leads to an elegant method of constructing solutions of field equations.

  1. Select a rational point of the imbedding space and solve field equations in the real sense in an arbitrary small neighborhood U of this point. This can be done with an arbitrary accuracy by choosing U to be sufficiently small. It is possible to solve the linearized field equations or use a piece of an exact solution going through the point in question.

  2. Select a subset of rational points in U and interpret them as points of p-adic imbedding space and space-time surface. In the p-adic sense these points are in general at arbitrary large distances from each and real continuity and smoothness alone imply p-adic long range correlations. Solve now p-adic field equations in p-adically small neighborhoods of these points. Again the accuracy can be arbitrarily high if the neighborhoods are choose small enough. The use of exact solutions of course allows to overcome the numerical restrictions.

  3. Restrict the solutions in these small p-adic neighborhoods to rational points and interpret these points as real points having arbitrarily large distances. p-Adic smoothness and continuity alone imply fractal long range correlations between rational points which are arbitrary distant in the real sense. Return to the first step and continue the loop indefinitely.

In this manner one obtains even in numerical approach more and more small neighborhoods representing almost exact p-adic and real solutions and the process can be continued indefinitely.

Some comments about the construction are in order.

  1. Essentially two different field equations are in question: real field equations fix the local behavior of the real solutions and p-adic field equations fix the long range behavior of real solutions. Real/p-adic global behavior is transformed to local p-adic/real behavior. This might be the deepest reason why for the hierarchy of p-adic physics.

  2. The failure of the strict determinism for the dynamics dictated by Kähler action and p-adic non-determinism due to the existence of p-adic pseudo constants give good hopes that the construction indeed makes it possible to glue together the (not necessarily) small pieces of space-time surfaces inside which solutions are very precise or exact.

  3. Although the full solution might be impossible to achieve, the predicted long range correlations implied by the p-adic fractality at the real space-time surface are a testable prediction for which p-adic mass calculations and applications of TGD to biology provide support.

  4. It is also possible to generalize the procedure by changing the value of p at some rational points and in this manner construct real space-time sheets characterized by different p-adic primes.

  5. One can consider also the possibility that several p-adic solutions are constructed at given rational point and the rational points associated with p-adic space-time sheets labelled by p1,....,pn belong to the real surface. This would mean that real surface would be multi-p p-adic fractal.

    I have earlier suggested that even elementary particles are indeed characterized by integers and that only particles for which the integers have common prime factors interact by exchanging particles characterized by common prime factors. In particular, the primes p=2,3,.....,23 would be common to the known elementary particles and appear in the expression of the gravitational constant. Multi-p p-fractality leads also to an explanation for the weakness of the gravitational constant. The construction recipe for the solutions would give a concrete meaning for these heuristic proposals.

This approach is not restricted to space-time dynamics but is expected to apply also at the level of say S-matrix and all mathematical object having physical relevance. For instance, p-adic four-momenta appear as parameters of S-matrix elements. p-Adic four-momenta very near to each other p-adically restricted to rational momenta define real momenta which are not close to each other and the mere p-adic continuity and smoothness imply fractal long range correlations in the real momentum space and vice versa.

4. p-Adic length scale hypothesis

Approximate p1-adicity implies also approximate p2-adicity of the space-time surface for primes p≈ p1k. p-Adic length scale hypothesis indeed states that primes p≈ 2k are favored and this might be due to simultaneous p≈ 2k- and 2-adicity. The long range fractal correlations in real space-time implied by 2-adicity would indeed resemble those implied by p≈ 2k and both p≈ 2k-adic and 2-adic space-time sheets have larger number of common points with the real space-time sheet.

If the scaling factor λ of hbar appearing in the dark matter hierarchy is in good approximation λ=211 also dark matter hierarchy comes into play in a resonant manner and dark space-time sheets at various levels of the hierarchy tend to have many intersection points with each other.

5. Does cognition automatically solve real field equations in long length scales?

In TGD inspired theory of consciousness p-adic space-time sheets are identified as space-time correlates of cognition. Therefore our thoughts would have literally infinite size in the real topology if p-adics and reals correspond to each other via common rationals.

The cognitive solution of field equations in very small p-adic region would solve field equations in real sense in a discrete point set in very long real length scales. This would allow to understand why the notions of Universe and infinity are a natural part of our conscious experience although our sensory input is about an infinitesimally small region in the scale of universe.

The idea about Universe performing mimicry at all possible levels is one of the basic ideas of TGD inspired theory of consciousness. Universe could indeed understand and represent the long length scale real dynamics using local p-adic physics. The challenge would be to make quantum jumps generating p-adic surfaces having large number of common points with the real space-time surface. We are used to call this activity theorizing and the progress of science towards smaller real length scales means progress towards longer length scales in p-adic sense. Also real physics can represent p-adic physics: written language and computer represent examples of this mimicry.

For more details see the chapter TGD as a Generalized Number Theory I: p-Adicization Program of TGD.

Matti Pitkanen

Sunday, January 22, 2006

Hydrogen bond and dark matter

The notion of dark N-H atoms leads to a new view about hydrogen bond. For the necessary context see background ideas see this, this, and this. Indeed, the little discovery of this morning was that the hydrogen atoms associated with hydrogen bonds could be actually λk-H atoms. This hypothesis has interesting implications and predicts the formula H1.5O for water in atto-second time scales suggested by neutron diffraction and electron scattering.

  1. The formation of hydrogen bond would correspond to a fusion of name and conjugate name between N-H-O-H atom and its conjugate Nc-H-O-H atom (the shorthand notation Nc= λk-N will be used. This process would drop one proton to a larger space-time sheet and could transform it to a dark proton. In the original situation water would be chemically like H2O expect that the water molecules would have fractional positive charges N/λk and 1- N/λk meaning that water without hydrogen bonds would be positively charged.

  2. H-O-(λk-H)-O-H pairs obey the chemical formula H3-O2. Hence the darkening of protons in the formation of hydrogen bonds would predict the H1.5O formula suggested by neutron diffraction and electron scattering in atto-second time scale.

  3. The mass of (N-H)-O-H molecule would be by N-1 electron masses higher than ordinary water molecule and it would behave like fractionally charged object. The λk-hydrogen associated with hydrogen bond would in turn have mass mpkme. For λ≈ 211≈ mp/me and k=1, this would mean that the mass would be approximately 2mp instead of mp.

    On the other hand, the hydrogen bonding in TGD framework yields pairs H-O-(λk-H)-O-HH3O2== 2H1.5O rather than pairs H2O-H...OH2== 2H2O. For the favored value λ=211≈ mp/me of λ and k=1 the mass of a pair of hydrogen bonded molecules in TGD Universe would be nearly the same as the mass for ordinary hydrogen bonded H2O molecules in the Universe of standard model. This could explain why chemists would have failed to discover that water is not quite what we believe it to be. Be as it may, these are testable predictions and in principle could allow to check whether the model makes sense and if so, also determine the value of λ and k.

  4. It is quite possible that most of water is ordinary and an interesting question is whether pH could measure the amount of pairs of (N-H)-O-H atom and its conjugate (Nc-H)-O-H. If pH measures the number of pairs of this kind of molecules, the mass density of water would depend slightly on pH.

  5. As discussed in previous posting, the stability of negatively charged DNA strand is poorly understood. The presence of fractionally charged (N-H)-O-H water molecules in the vicinity of DNA would have a stabilizing effect.

  6. The energy needed to cut hydrogen bond is expected to depend on N-Nc pair characterizing the final state and on the molecular environment where the pair exists and would not thus be a property of hydrogen bond. It is not clear whether this energy can be identified as the energy of hydrogen bond (the value of which varies in water). The letters appearing in the names of molecules would be characterized by the energies needed to produce them, and the N-Nc pair with the minimum energy would dominate in a given environment which could be also macromolecule so that name of the molecule would be dictated by the properties of molecule.

  7. Genetic code would reduce at deeper level to the names of DNA nucleotides. It is quite possible that the splitting of DNA double strand gives rise to quantum superposition of N-Nc pairs. This would make possible quantal mechanism of mutations. McFadden has suggested this kind of mechanism but assuming that different DNAs would superpose which to my opinion cannot be the case. Also quantum computations by RNA strands can be imagined if it is possible to achieve the situation that the probabilities of various pairs in superposition are essentially identical.

For more details see for instance the chapters Pre-biotic Evolution in Many-Sheeted Space-Time of "Genes, Memes, Qualia,...".

Friday, January 20, 2006

Universal mechanism of catalytic action and stability of charged polymers

I have explained in two earlier postings (this and this) the idea that dark N-H-atoms could naturally serve as names of bio-molecules, and that molecules labelled by conjugate names could play the role of lock and key in catalytic action. This would mean that the emergence of symbolic representations and "molecular sex" between conjugate named molecules distinguishes bio-chemistry from the ordinary chemistry. Below some further remarks related to this idea.

1. Basic observations

The basic observations are following.

  1. Since fine structure constant for the interactions of dark electrons with proton (and any other charge) is scaled down by 1/hbar factor the effective charge of proton plus dark N-electron system is 1-N/λk and positive except for full shell of electrons with N=λk.

  2. The fusion of N-H-atom and its conjugate must liberate proton and decay of λk-atom requires that proton is feeded to the system.

2. A universal model for a catalytic action

The previous observations lead to a detailed model for bio-catalytic action.

  1. N-hydrogen atoms have effective charge 1-N/λk for N< λkso that the binding regions of catalysts and reacting molecules should carry effective fractional surface charge which is always positive: this is a testable prediction.

  2. Catalyst in general has several names: one for each reactant molecule. Catalytic action involving the formation of reactants-catalyst complex by fusion of N-H-atoms and their conjugates necessarily involves a temporary liberation of protons, one for each letter of each name of the catalyst.
  3. The generation of λk-H-atom in the fusion of letter and conjugate letter should correlate with the formation of hydrogen bonds between catalyst and substrate.
  4. The liberated protons could drop to a larger space-time sheet and liberate metabolic energy quanta kicking the complex formed by the reacting molecules over the potential wall separating it from the outcome of the reaction. In the transition to the final state the surplus energy would be liberated and kick a protons back to the original space-time sheet and λk-atom would decay to N-atom and its conjugate. Also metabolism could kick the dropped protons back to the system so that the catalyst would not be stuck to the product of the reaction.

3. How to understand the stability of charged bio-polymers?

The fact that the names of bio-molecules carry positive effective charge relates in an interesting manner to the problem of how charged bio-polymers can be stable (I am grateful for Dale Trenary for pointing me the problem and for interesting discussions). For instance, DNA carries a charge of -2 units per nucleotide due to the phosphate backbone. The models trying to explain the stability involve effective binding of counter ions to the polyelectrolyte so that the resulting system has a lower charge density.

The simulations of DNA condensation by Stevens however predict that counter ion charge should satisfy z> 2 in the case of DNA. The problem is of course that protons with z=1 are the natural counter ions. The positive surface charge defined by the dark N-H-atoms attached to the nucleotides of DNA strand could explain the stability. In the case of DNA double strand the combination of names and conjugate names liberates one proton per nucleotide and stability could be guaranteed by these, possibly dark, protons residing at a larger space-time sheet.

For more details see the chapter Crop circles and life at parallel space-time sheets: part I of "Genes, Memes, Qualia,...", where a brief overview about living systems as ordinary matter quantum controlled by dark matter is given. If you are too afraid that you neighbor spots you in the middle of act of reading something about crop circles, you might prefer the end of the chapter Many-Sheeted DNA.

Matti Pitkanen

More precise definition of N-atom and dark matter as a matter in wrong place

In the earlier posting I speculated with the notion of dark N-particle (-atom or -molecule) and the possible significance of N-particles for the deeper understanding of lock and key mechanism of bio-catalysis and DNA replication.

Dark N-particles associated with DNA, possibly hydrogen bonds, could serve as names for nucleotides so that the emergence of symbols would distinguish between molecules in vitro and vivo. Dark fermionic N-particle and λk-N, particle a would serve as names for DNA nucleotide and its conjugate and their composite would be λk-atom analogous to a full electronic shell and therefore highly stable. Quite generally, molecules with conjugate names would be like opposite sexes: sex, symbolic representations, and meaning would emerge already at the molecular level.

1. Objection

There is an obvious objection against dark N-hydrogen atoms as names of DNA nucleotides. λ is in general integer valued and λ ≈ 211 seems to be favored. This value of λ would however make the mass of N-hydrogen atom or its conjugate quite too high to be physically acceptable.

Somehow it seems that N-hydrogen atom involves only single ordinary proton. In this case however the total electronic charge of the system would be N units of dark electronic charge and one protonic charge, which seems strange. The resolution of the problem is that dark electron-electron Coulomb interaction energy is reduced by 1/λk by the scaling down of the dark fine structure constant (proportional to 1/hbar). Hence effectively electronic and protonic charges would compensate each other for λk atom whereas for N-atoms the charge would be effectively fractional and 1-N/λk units.

2. How to observe N-atoms?

The most elegant definition of dirt is as a matter in wrong place. It would seem that also dark matter is matter in wrong place, but only effectively.

The question is how to observe N-atoms and N-molecules. The key observation is that the transition energies of N-molecules are N times large than corresponding ordinary molecules. This makes them thermally stable under much higher temperatures. The transitions of these molecules give rise to dark N-photons, which can decay to N ordinary photons with same energies as emitted in the transitions of ordinary molecules.

The presence of spectral lines of transitions of atoms or molecules which are not be stable at the temperature of environment, would serve as a signature of dark N-particles. Interestingly, spectral analysis demonstrates the presence water inside sunspots, where the temperature varies in the range 3000-4500 K. The decay of N-photons to ordinary photons emitted by thermally stable N-water molecules with N> 10 would explain the finding. Also the quite recent evidence discovered by M. Moshina that Sun has a solid surface consisting mostly of calcium-ferrite is inconsistent with the fact that photosphere has temperature 5800 K. The explanation of the puzzle would be in terms of dark N-iron and other dark N-elements.

Without exaggerating one can say that the systematic search for the presence of molecules and condensed matter structures in places where it is thermally stable could revolutionize our world view.

3.Plasmoids as life forms?

There is evidence that plasmoids satisfy the basic criteria for primitive living systems (E. Lozneanu and M. Sanduloviciu (2003), Minimal-cell system created in laboratory by self-organization, Chaos, Solitons and Fractals, Volume 18, Issue 2, October, p. 335. See also Plasma blobs hint at new form of life, New Scientist vol. 179 issue 2413 - 20 September 2003, page 16.)

One of the basic ideas of TGD based quantum model of living systems is that plasmoids identified as rotating magnetic systems analogous to Searl device are primitive life forms and predecessors of the molecular life. Rotation generates radial electric field having non-vanishing divergence whose sign depends on the direction of rotation (difficult to understand in Maxwellian ED), which in turn generates radial ohmic current charging the system. The dropping of electrons of this current to larger space-time sheets at the boundaries of rotating system liberates zero point kinetic energy as a usable metabolic energy. This mechanism would define fundamental metabolic energy currencies also in ordinary living matter.

4. Is molecular high-T life possible?

Life based on dark N-molecules could in principle survive at high temperatures.I have already earlier considered half seriously the possibility that Earth interior (say mantle-core boundary) and even solar photosphere could serve as seats of high-T life developed from plasmoids and that the Earth interior would be like the womb of Mother Gaia, where life evolved from simple plasmoids. The basic inspiration came from the evidence that crop circles cannot be fraud. See the chapters Crop circles and life at parallel space-time sheets: part I and II of "Genes, Memes, Qualia,...", where a brief overview about living systems as ordinary matter quantum controlled by dark matter is given.

Matti Pitkanen

Wednesday, January 11, 2006

Empirical evidence for the p-adic evolution of cosmological constant?

The evolution of the cosmological constant Λ is different at each space-time sheet, and the value of Λ is determined by the p-adic length scale size of the space-time sheet according to the formula Λ (k)= Λ (2)× (L(2)/L(k))2, where L(k)=2kL0, k integer, is the p-adic length scale associated with prime p≈ 2k. L0 is apart from a numerical constant CP2 geodesic length. Prime values of k are especially interesting.

The formula is derived in the chapter TGD and Cosmology of TGD from the requirement that gravitational energy identfied as the difference of inertial energies and matter and antimatter (or vice versa) is non-negative. This means discrete evolution of cosmological constant with jumps in which cosmological constant is reduced by a power of 2.

In standard physics context piecewise constant cosmological constant would be naturally replaced by a cosmological constant behaving like 1/a2 as a function of cosmic time. p-Adic prediction is consistent with the study of Wang and Tegmark according to which cosmological constant has not changed during the last 8 billion years: the conclusion comes from the reshifts of supernovae of type Ia. If p-adic length scales L(k)= p ≈ 2k, k any positive integer, are allowed, the finding gives the lower bound TM > 21/2/( 21/2-1))× 8= 27.3 billion years for the recent age of the universe.

Now Brad Shaefer from Lousiana University has studied the red shifts of gamma ray bursters up to a red shift z=6.3, which corresponds to a distance of 13 billion light years, and claims that the fit to the data is not consistent with the time independence of the cosmological constant. In TGD framework this would mean that a phase transition scaling down the value of the cosmological constant by a power of 2 can be located in cosmological past at a temporal distance in the range 8--13 billion years.

For more details see the chapter Cosmic Strings of TGD.

Matti Pitkanen

What if....

In some New Scientist towards the end of 2005 there were interesting articles speculating with what would have happened if Newton for some reason had not published his Principia or if Einstein's 1905 papers had been rejected and Einstein had remained an unknown crackpot or .... I shall continue the speculation but first it is good to briefly summarize what happened during the last two Golden Decades of Physics we have been enjoying. Since this is not a scientific article I summarize only the discoveries without mentioning the names of those who have already visited Stockholm.

A. The real course of events

We all of course remember quite well that the revolution that began around 1983 as TGD made its breakthrough. Although the work was a mere thesis worked out during four years containing no hightech calculations, it stimulated a fantastically rapid development of ideas. In the perspective provided by these two decades it is easy to understand that the identification of space-time as a four-surface in certain higher dimensional space-time fixed completely by the standard model symmetries, happened to be a bottleneck idea which opened flood gates for cascades of new profound ideas which revolutionized the world view just like quantum mechanics had did for almost century before.

1. Physics as spinor geometry of the world of classical worlds

After a couple of years of unsuccessful attempts to quantize the theory using functional integral approach the idea about physics as the spinor geometry of the world of classical worlds was proposed. Apart from quantum jump the construction of quantum states of the Universe reduced to the construction of the modes of classical spinor fields in the "world of classical worlds" as representations of certain super-conformal algebras. Could one imagine anything simpler conceptually! Soon popped up the idea that this infinite-dimensional space could determined completely by its mere mathematical existence. The generalization of Einstein's geometrization program to infinite-dimensional context might allow only single physics! It is easy to imagine what explosive enthusiasm this raised in the brilliant minds of my brilliant colleagues.

The notion of gravitational holography emerged as a basic implication of the general coordinate invariance which implied that given 3-surface corresponds to a unique 4-surface having identification as a generalized Bohr orbit.

The microlocality at space-time level was replaced in TGD framework with purely classical locality in the world of classical worlds having 3-surfaces as its points. The basic mathematical implication was that the theory was free of those divergences of quantum field theories which were due to the space-time-local interactions. Space-time non-locality implied also the breakdown of age-old reductionistic dogma implying that theory has highly non-trivial implications in all length scales, perhaps the most interesting ones in biology. Within few years became clear that the reductionistic dogma had been perhaps the most colossal self deception that human kind had ever managed to perform.

The construction of configuration space spinors led to deep connections with von Neumann's algebras. The so called hyper-finite factors of type II1 were discovered to correspond directly to Clifford algebras for configuration space spinors. Direct connections with minimal conformal theories, quantum groups, braid groups, topological quantum computation,... emerged: these fields were developing in parallel with TGD. The most fascinating implication was a possible elimination of infinities based on the replacement of the extremely singular von Neumann algebras of quantum field theories known as factors of type III of quantum field theories with the mentioned hyper-finite factors of type II1.

At the same time came the realization that four-dimensional space-time is completely unique in the sense that light-like causal horizons at which induced metric becomes degenerate allow generalized conformal invariance. Partons could be identified as 2-dimensional sections of the causal horizons and a very close connection with conformal field theories emerged since in certain well defined sense parton physics was effectively 2-dimensional.

2. New view about space-time

Even classical theory, which had become an exact part of quantum theory, experienced a conceptual revolution. The notion of many-sheeted space-time, topological quantization of classical fields implying the notion of magnetic body which became the basic notion of TGD inspired quantum biology, the new views about the relationship between geometric and subjectively experienced time and gravitational and inertial energy, are only few items in the list of discoveries. The new views implied intense theoretical speculations about new communication technologies based on signals propagating backwards in geometric time whereas non-local energy usage was made possible by emission of negative energy signals: these mechanisms became conceptual corner stones of TGD inspired quantum biology.

Despite intense collective efforts, it took rather long time to discover the correct interpretation for the predicted classical long ranged color and weak fields seemingly in complete contradiction with experimental reality. The resolution of mystery came with the realization that the theory predicts entire fractal hierarchy of standard model physics at various sheets of many-sheeted space-time. p-Adic length scale hierarchy and hierarchy of dark matters labelled by values of Planck constant provided quantitative content for this picture. This discovery would have not been taken seriously unless already the anomalies of physics of water would have provided direct experimental support for this picture. Just as people suddenly began to see solitons and fractals everywhere for few decades earlier, subtle signatures of dark matter suddenly popped up everywhere.

3. From quantum measurement theory to a quantum theory of consciousness

The interpretational problems of quantum TGD did not leave any other possibility than extending the existing quantum measurement theory to a theory of consciousness. This in turn forced to generalize quantum theory itself: dynamical quantized Planck constant having arbitrarily large values meaning the possibility of macroscopic quantum phases even in astroscopic length scales was one the most powerful implications, and led to a rapidly growing understanding of dark matter as a hierarchy of macroscopic quantum phases characterized the value of Planck constant. Simultaneously came the realization that it is dark matter which makes living matter alive, and this launched a vigorous evolution of ideas in a new branch of science christened quantum biology.

4. Physics as a generalized number theory

A further thread in the evolution of ideas were number theoretical vision about physics which emerged gradually from an observation that elementary particle mass spectrum could be understood in terms of p-adic thermodynamics for super-conformal invariant system with Hamiltonian replaced by the generator of scaling. This approach assigned to each particle a prime characterizing its mass scale.

Later emerged the vision about physics as a generalized number theory obtained by algebraically continuing rational physics to various number fields with p-adic space-time sheets interpreted as space-time correlates of intentionality. The concept of number field was generalized by fusing real numbers and various p-adic number fields along common rationals to a larger book like structure. The notion of infinite primes emerged and the construction of infinite primes turned out to be very much analogous to a repeated quantization of an arithmetic quantum field theory. Number theoretical approach led also to a new number theoretic notion of information, with genetic code as one application of this concept.

B. Why "What if..."?

I know that most readers think that things could not have gone differently. I am however not so sure about this. After all, there was very strong opposition in my own country against TGD. There were very determined attempts to silence me completely: even after the publication of thesis I had to continue working as an unemployed, and only the breakthrough changed the situation completely. What if Witten had not read the thesis that I had sent to him? After all, Witten must have received tons of preprints and it was sheer luck that he happened to look whether this particular randomly picked up paper might contain something interesting. Of course, I had sent the work to many other well-known physicists but I still stubbornly insist that my work might have gone un-noticed. And what if Witten had not had time to read the paper carefully enough to realize the implications and intuitively realize how fascinating mathematics and physics it could lead to?

Some of us probably remember that around 1983 there was also a competing theory at market known as super-string model. Who knows, in absence of anything better it might have catched the attention of the physics community. And who knows, if my influential colleagues had managed to silence me, only few years of super string dominance might have been enough to establish it as a theory of everything for purely psychological and sociological reasons. The work in theoretical physics is incredibly demanding and requires fanatic devotion: you must be a total believer and you can work only with single theory during single life time. Believe me, theorists are not those cold rational thinkers that they might pretend themselves to be.

I hope that these arguments are enough to justify my light hearted attempt to imagine what might have happened during the next two decades if something had went wrong in the golden year 1983.

C. What could have happened

The following is one possible imagined history, and I admit that it ends as too many scifi stories tend to end: in the last chapter the author loses his control completely and even the last bits of plausibility are lost as the supposed to be climax is approached. Forgive me, I am not a professional science fictionist.

1. First super string revolution

The pressures were very strong for something new after the frustration created by un-successful quantum gravity theories relying on Kaluza-Klein philosophy. The first super string revolution occurred around 1984 since something had to happen. Witten came the intellectual leader of the field. What made this approach so fascinating was the promise for finiteness of the theory suggested already by the fact that point particles were replaced with 1-dimensional entities and the singularities of Feynman diagrams were expected to be smoothed out. Indeed, finiteness arguments left only 5 super string models into consideration.

There was also a severe problem: the connection with the experimental reality was lacking. Spontaneous compactification, the legacy from un-successful Kaluza-Klein approach to quantum gravitation, was the obvious proposal for how to get at least a semi-realistic theory. In absence of anything better it become rapidly something regarded as an established fact. Using conformal invariance as a guide line people ended up with Calabi-Yau manifolds as a reasonable guess for the 6-dimensional internal space (assuming 4 un-compactified dimensions): also this guess became soon regarded as an established fact.

A lot of work trying to deduce standard model was done but with a meager success. Spontaneous compactification destroyed also the original belief on the uniqueness of the theory. Ten years later the situation began to be desperate and the time was ripe for

2. Second super string revolution

The work after the first superstring revolution had taught that Kaluza-Klein program might not be enough to understand particle spectrum. This had led to the idea that perhaps also higher-dimensional surfaces should be accepted as derived dynamical entities. Also the TGD based idea that space-time might correspond to four-surface began to look attractive. In-officially people of course knew about TGD but it was too late to turn around and they took the risk and hoped that harmful TGD would emerge as a special case of some more bigger theory.

Some new language was necessary. The expression "Super string models" was replaced with "M-theory": in practice this meant more or less a polygon with five super-string models at is vertices and M-theory in its interior. Higher-dimensional surfaces were re-christened as branes. Since strings were the basic objects, branes were not regarded as primary dynamical entities but thought to result as some vague non-perturbative effect. The dream was that 4-branes would turn out to be unique and standard model gauge group would emerge. The dualities discovered long time ago provided a rather impressive technical tool and a voluminous industry of dualities emerged: probably no one knows which fraction of these dualities are true. The slogan was that if you cannot prove duality to be wrong in five minutes, it must be true.

No one can deny that M-theory, whose most fascinating property was advertised to be its non-existence, was a perfect media success. Spontaneous compactification had already introduced huge amount of confusion but after the introduction of branes the control was lost completely. A after a decade of swet, blood, and tears the situation had not improved in any essential manner. Worse, the situation began to look really desperate. There was still no idea about why the observed space-time dimension is four. The landscape of Calabi-Yaus had turned out to be immense. The standard model was still patiently waiting to be reproduced. To make situation even worse, web was suddenly full of blogs full of nasty commentary about the situation. The time was ripe for

3. Third super string revolution

Referring freely to the words of one of its fathers, the manifesto of the third super string revolution was that since M-theory cannot predict anything, and since M-theory is decided to be the theory, we must adopt a new definition of what science is. What is left to physicist is to try to discover whether the huge landscape of non-physical solutions might contain in some distant corner a solution resembling to some degree the universe we happen to live in, and use our own existence as a condition to deduce the predictions of the theory. No more even hope of predicting proton to Planck mass ratio. Not a very inspiring future vision for a young student of theoretical physics.

Yes...I am now in the last chapter of not so good scifi book and every bit of plausibility has obviously evaporated. True, the third super string revolution was unforgivably reckless imagination and I hope that my literary hallucinations did not irritate the reader too much. In our right mind we know that although theorists are true believers, they of also realize when it is not worth of continuing. Of course. Therefore "Postponed breakthrough of TGD" would have been the proper title of this section and probably already that of the earlier section. And now I also realize that I have been implicitly insulting my brilliant colleagues by suggesting that they might have spent ten years after first super-string revolution without realizing that super string model does not work! My sincere apologies. Take this as low quality science fiction, nothing more.
Matti Pitkanen

Tuesday, January 10, 2006

Are spontaneous decay and completion of dark N-hydrogen atoms behind DNA replication and lock and key mechanism?

The replication of DNA has remained for me a deep mystery and I dare to doubt that the reductionistic belief that this miraculous process is well-understood involves self deceptive elements. Of course the problem is much more general: DNA replication is only a single very representative example of the miracles of un-reasonable selectivity of the bio-catalysis. I take this fact as a justification for some free imagination inspired by the notion of dark N-atom discussed in the previous posting "What inherently dark atoms could be?".

1. Dark fermionic molecules can replicate via decay and spontaneous completion

Dark fermionic λk-molecule is ideally suited for replication. First of all, N=λk means that the analog of closed electronic shell is in question so that this (maximum) value of N is especially stable. The analogy with full Fermi electronic sphere and magic nuclei makes also sense.

Suppose that N=λk-molecule decays into N1-molecule and N2-molecule with N2k-N1. If λ is even it is possible to have N1= N2k/2 and the situation is especially symmetric. If fermionic N<λkk-sheeted) dark molecules are present, one can imagine that these molecules tend to be completed to full λk-molecules spontaneously. Thus spontaneous decay and completion would favor the spontaneous replication and dark molecules could be ideal replicators. Needless to say, the idea that the mechanisms of spontaneous decay and completion of dark N-particles somehow lurk behind DNA replication and various high precision bio-catalytic processes is extremely attractive and would trivialize the deepest mystery of biology.

2. Reduction of lock and key mechanism to spontaneous completion

DNA replication and molecular recognition by the lock and key mechanism are the two mysterious processes of molecular biology. As a matter fact, DNA replication reduces to spontaneous opening of DNA double strand and to the lock and key mechanism so that it is enough to understand the opening of double strand in terms of spontaneous decay and lock and key mechanism in terms of spontaneous completion of N-particle ("particle" refers to atom or molecule in the sequel).

Consider bio-molecules which fit like a lock and key. Suppose that they are accompanied by dark N-particles, such that one has N1+N2k so that in the formation of bound state dark molecules combine to form λk-molecule analogous to a full fermionic shell or full Fermi sea. This is expected to enhance the stability of this particular molecular complex and prefer it amongst generic combinations.

For instance, this mechanism would make it possible for a nucleotide and its conjugate, DNA and mRNA molecule, and tRNA molecule and corresponding aminoacid to recognize each other. Spontaneous completion would allow to realize also the associations characterizing the genetic code as a map from RNAs to subset of RNAs and associations of this subset of RNAs with amino-acids (assuming that genetic code has evolved from RNA → RNA code as discussed here ).

As such this mechanism allows a rather limited number of different lock and key combinations unless λk is very large. There is however a simple generalization allowing to increase the representative power so that lock and key mechanism becomes analogous to a password used in computers. The molecule playing the role of lock resp. molecule would be characterized by a set of n letters represented by N-particles with N in {N1,1,....N1,n} resp. {N2,1k-N1,1,..., N2,n= λk-N1,n}.. The molecules with conjugate names would fit optimally together. N-molecules would be like letters of a text characterizing the name of the molecule.

The mechanism generalizes also to the case of n >2 reacting molecules. The molecular complex would be defined by a partition of n copies of integer λk to a sum of m integers Nk,i: ∑i Nk,ik.

This mechanism would provide a universal explanation for the miraculous selectivity of catalysts and this selectivity would have practically nothing to do with ordinary chemistry but would correspond to a new level of physics at which symbolic processes and representations based on dark N-particles emerge.

3. Connection with the number theoretic model of genetic code?

The emergence of partitions of integers in the labelling of molecules by N-particles suggests a connection with the number theoretical model of genetic code , where DNA triplets are characterized by integers n in {0,...,63} and aminoacids by integers 0,1 and 18 primes p< 64. For instance, one can imagine that the integer n means that DNA triplet is labelled by n-particle. λ=63 would be the obvious candidate for λ and conjugate DNA triplet would naturally have nc=63-n.

The model relies on number-theoretic thermodynamics for the partitions of n to a sum of integers and genetic code is fixed by the minimization of number theoretic variant of Shannon entropy which can be also negative and has thus interpretation as information. Perhaps these partitions could correspond to states resulting in some kind of decays of n-fermion to nk-fermions with ∑k=1r nk=n. The nk-fermions should not however correspond to separate particles but something different. A possible interpretation is that partitions correspond to states in which n1 particle is topologically condensed at n2> n1 particle topologically nr> nr-1-particle. This would also automatically define a preferred ordering of the integers ni in the partition.

An entire ensemble of labels defined by the partitions would be present and depending on the situation codon could be labelled not only by n-particle by any partition n=∑i=1r ni corresponding to the state resulting in the decay of n-particle to r N-particles.

4. Reduction of DNA replication to a spontaneous decay of λk-particle

DNA replication could be induced by a spontaneous decay of λk-particle inducing the instability of the double strand leading to a spontaneous completion of the component strands.

Strand and conjugate strand would be characterized by N1-particle and N2k-N1-particle, which combine to form λk-particle as the double strand is formed. The opening of the double strand is induced by the decay of λk-particle to N1- and N2-particles accompanying strand and its conjugate. After this both strands would complete themselves to double strands by the completion to λk-particle.

It would be basically the stability of λk-particle which would make DNA double strand stable. Usually the formation of hydrogen bonds between strands and more generally, between the atoms of stable bio-molecule, is believed to explain the stability. Since the notion of hydrogen bond is somewhat phenomenological, one cannot exclude the possibility that these two mechanisms might be closely related to each other. I have already earlier considered the possibility that hydrogen bond might involve dark protons : this hypothesis was inspired by the finding that there seems to exist two kinds of hydrogen bonds (New Scientist 154 (2087):40–43, 21 June 1997).

The reader has probably already noticed that the participating N-molecules in the model of lock and key mechanism are like sexual partners, and since already molecules are conscious entities, one might perhaps see the formation of entangled bound states with positive number theoretic entanglement entropy accompanied by molecular experience of one-ness as molecular sex. Even more, the replication of DNA brings in also divorce and process of finding of new companions!

5. What the N-particles labelling bio-molecules could be?

What the dark N-particles defining the letters for the names of various bio-molecules could be? The obvious requirement is that the names of molecules cannot weigh too much. In the optimal situation there are just two options.

Dark N-hydrogen atoms are the lightest candidates for the names of bio-molecules. This mechanism would also conform with the belief that hydrogen bonds guarantee the stability of bio-molecules. At least, dark N-hydrogen atoms should be localizable in the vicinity of hydrogen bonds.

This idea is not a mere speculation. The first experimental support for the notion of dark matter came from the experimental finding that water looks in atto-second time scale from the point of view of neutron diffraction and electron scattering chemically like H1.5O: as if one fourth of hydrogen atoms would be dark (references can be found here). Attosecond time scale would presumably correspond to the first level of dark matter hierarchy and also higher level dark hydrogen could be present.

One can imagine also a second option. The model for homeopathy leads to a rather concrete integrated view about how magnetic body controls biological body and receives sensory input from it. The model relies on the idea that dark water molecule clusters and perhaps also dark exotically ionized super-nuclei formed as linear closed strings of dark protons perform this mimicry. Dark proton super-nuclei are ideal for mimicking the cyclotron frequencies of ordinary atoms condensed to dark magnetic flux quanta. Of course, also partially ionized hydrogen N-ions could perform the cyclotron mimicry of molecules with the same accuracy.

One can consider the possibility N-molecules/atoms correspond to exotic atoms formed by electrons bound to exotically ionized dark super-nuclei: the sizes of these nuclei are however above atomic size scale so that the dark electrons would move in a harmonic oscillator potential rather than Coulombic potential and form states analogous to atomic nuclei. The prediction would be the existence of magic electron numbers. Amazingly, there is experimental evidence for the existence of this kind of many-electron states. Even more, these states are able to mimic the chemistry of ordinary atoms.

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

Matti Pitkanen

What inherently dark atoms could be?

The basic implication of the dark matter hierarchy is that there is no need to assume that temperatures at various space-time sheets are widely different since the scaling of hbar can scale up the energies above the thermal threshold. This poses very strong constraints on TGD based view about quantum biology and increases its predictive power dramatically.

The original model for inherently dark atom relies on the scaling of hbar by λk at the kth level of the dark matter hierarchy. Here λ is integer and λ ≈ 211 defines a preferred value of λ. Also the harmonics and integer valued sub-harmonics of λ might be possible. In the case of hydrogen atom the model predicts that the energies of hydrogen atom proportional to 1/hbar2 are scaled down by 1/λ2k so that dark atoms would not be thermally stable at room temperature. In practice this would exclude dark atoms and molecules as biologically interesting inherently dark systems.

The topological condensation of ordinary atoms and molecules at λk-sheeted (now in the sense of "Riemann surfaces" over M4) dark magnetic flux quanta is however possible and means scaling up of the cyclotron energy by λk making possible cyclotron Bose-Einstein condensates at high temperatures identifiable as dark quantum plasmas. The same scaling occurs to the energy of dark plasma oscillations so that their energies can be above thermal threshold. Dark plasmoids and plasma oscillations are indeed fundamental in the TGD based model of quantum control in living matter.

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

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

1. Inherently dark atoms as radial anyons?

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

  1. Dark atoms having ordinary size and ordinary energy spectrum could be possible if the principal quantum number n is fractionized to n→n/λk. The fractionization could make sense if the atomic space-time sheet is λk-folded and atoms become radial anyons. The corresponding Bohr orbits would close in the radial direction only after λk turns. The formation of dark atoms could be interpreted as a transition to chaos by period λk-folding in radial and angular degrees of freedom. This option would differ from the original model in that radial scaling in M4 by a factor λ2k is replaced by a radial λk-folding so that the M4 projection of dark atom has the same size as in the case of ordinary atom.

  2. Since dark atom would define a λk-fold covering of M4, one expects a degeneracy of states corresponding to the phase factors exp(ikn2π/λk), k=0,...,λk-1, where n labels the sheets of the λk-fold covering of M4. The nuclei and electrons of N≤ λk dark atom could form many-particle states separately and fermionic statistics becomes effectively para-statistics for the resulting N-atoms. Note that the N electrons and nuclei would be in identical states in ordinary sense of the word since Bohr orbits must be identical: kind of fermionic Bose-Einstein condensates become thus possible.

  3. The quantum transitions of N-atoms for N=λk would give rise to dark counterparts of the photons emitted in the ordinary atomic transitions. For N ≤ λk the energies of dark photons would be N times higher than the energies liberated in the ordinary transitions. The claims of Randell Mills about the scaling up of the binding energy of the hydrogen ground state by a square k2 of an integer in plasma state might be understood as being due to the formation of dark N=k2-atoms emitting dark photons with k2-fold energies de-cohering to ordinary photons. Also nore general states are however predicted now. A fraction of plasma phase in Mills experiments would be in dark plasma state. The chemistry of bio-molecules identified as N-molecules would definitely differ from the ordinary chemistry.

  4. The fractionization n→n/λk of the integer n labelling vibrational modes and cyclotron states would be unavoidable. Single particle cyclotron states having E= hbar (k)ω of the earlier picture would in this framework correspond to single particle states having n=λk or to N=λk-ion states. Fermionic N=λk-states are expected to have a special role since these configurations are analogous to noble gas atoms with full shells of electrons and to magic nuclei with full cells of nucleons. Most biologically important ions are fermions and N=λk states would give rise to what might be regarded as fermionic analogs of Bose-Einstein condensates. For bosonic ions there is no restriction to the occupation numbers of λk single particle states involved.

2. Connection with quantum groups?

The phase q= exp(i2π/λk) brings unavoidably in mind the phases defining quantum groups and playing also a key role in the model of topological quantum computation tqc}. Quantum groups indeed emerge from the spinor structure in the "world of classical worlds" realized as the space of 3-surfaces in M4× CP2 and being closely related to von Neumann algebras known as hyper-finite factors of type II1 vNeumann}. Unfortunately, the integer n characterizing the phase cannot be identified as λ. This allows to ask whether quantum groups could emerge in two different manners in TGD framework.

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

3. Are both options for dark matter realized?

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

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

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

  1. Could it be that we can observe only the decay products of dark N-fold molecules to ordinary molecules? Is matter in vivo dark matter and matter in vitro ordinary matter? Could just the act of observing the matter in vivo in the sense of existing science make it ordinary dead matter?

  2. How can one distinguish between N-fold and ordinary molecules? Electromagnetic interactions, and more generally gauge forces, do not allow to distinguish classically between these molecules since there are no direct quantum interactions between them. The gravitational forces generated by N-molecules are too weak to allow to distinguish from N molecules.

  3. The decay of N-molecule via decay to N ordinary molecules in principle allows to conclude that N-molecule was present. But could this process mean just the replacement of DNA in vivo with DNA in vitro?

  4. The emission of dark N-photons decaying via decay to N photons can serve as a signature of N-molecules. If the molecules are fermions this would in principle allow to exclude the interpretation in terms of coherent emission of photons from Bose-Einstein condensate of N ordinary molecules. Bio-photons indeed represent this kind of radiation having no obvious explanation in standard physics context.

These questions perhaps make it clear that it is not at all obvious that the living matter could not consist of dark N-molecules at least partially.

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

Homeopathy in many-sheeted space-time

The claimed mechanisms of homeopathic healing and the method of manufacturing homeopathic potencies are not the only paradoxical aspects of homeopathy. Also the reported frequency imprinting and entrainment, codes based on field patterns, and associative learning of water look mysterious in the framework of standard physics.

1. Frequency imprinting and entrainment

Frequency imprinting and entrainment at preferred frequencies are believed to be fundamental for homeopathy and acupuncture. The data suggest that water builds representations for the chemicals it contains as space-time sheets containing water in liquid crystal form. These space-time sheets reproduce relevant part for the spectrum of rotational frequencies of the molecule in rigid rotor approximation. Also the mimicry of vibrational spectrum using sound waves can be considered possible. Besides LC water blobs also magnetic mirrors consisting of magnetic flux tube plus parallel MEs pop up naturally in the original model of frequency imprinting and entrainment.

The basic objection is that if the space-time sheets are in thermal equilibrium, the scenario partially fails in the case of fundamentally important rotational and conformational spectra which are in microwave region. TGD however suggests that also inherently dark atoms identifiable as anyonic counterparts of ordinary atoms are possible and have the same energy spectrum as ordinary atoms, and that the notion of atom and molecule generalizes to what might be called N-atom/molecule having energy spectrum scaled up by a factor 1\leq N\leq λk, hbar (k)=λkhbar0. In this case various vibrational and rotational frequencies would define a hierarchy of dark energies which can be above thermal threshold. In particular, rotational and conformational microwave spectra of bio-molecules have dark counterparts with energies above the thermal threshold. Otherwise only cyclotron energies and plasma oscillation energies can be above thermal threshold at sufficiently high levels of dark matter hierarchy.

2. Scaling laws

Homeopathy seems to involve two kinds of scaling laws which seem to be closely related. What I call scaling law of homeopathy states that homeopathic frequencies appear in pairs (fh,fl) of high and low frequencies such that their ratio is given by fh/fl≈ 2× 1011. TGD approach explains this ratio predicts a generalization of the law. v=Lfl scaling law tells in TGD framework how the frequencies associated with generalized EEG code for the velocities of physiological waves and their frequencies fh= cfl/v. The general model for motor control by magnetic body predicts this scaling law.

3. Model for the homeopathy

The model of homeopathy must explain the effectiveness of homeopathic remedies manufactured by a repeated dilution and succussion. This can be understood if part of chemical involved is transformed to dark matter and is also represented by water clusters or dark super-nuclei formed from protons. This minimal representation involves thermally stable dark cyclotron frequencies. If inherently dark atoms and molecules with essentially same energy spectrum as ordinary ones are possible, also the mimicry of vibrational and rotational spectrum is possible by clusters of dark water molecules.

One must also understand why homeopathic remedies are manufactured from molecules which basically cause the symptoms to be cured. The explanation is that the presence of molecules mimicking the poisonous molecule makes it possible to sweep the poisonous molecules "under the rug" if they enter the organism. In the presence of Bose-Einstein condensates of dark photons generated by the mimicking particles, the poisonous molecules drop to dark space-time sheets where they are harmless: the mechanism is generalization of induced emission.

The model should also explain the associative learning and field codes. The presence of a hierarchy of dark matter levels leads to a model for how magnetic body performs motor control in terms of dark plasmoids and their quantal plasma oscillation patterns and receives sensory input from the biological body and experiences it as a kind of somatosensory representation along entire magnetic body. It would be the magnetic bodies at higher levels of dark matter hierarchy which learn rather than mere water. Context sensitive field codes emerge naturally as codes involved with all bio-control, in particular that of gene expression.

The charge entanglement by W MEs is the essentially new element in the model for generalized motor actions by magnetic body. Also the telepathic sharing of mental images could rely on charge entanglement. The reduction of charge entanglement can induce a quantum jump to a state in which local Bose-Einstein condensates become exotically ionized with certain probability depending on the intensity of W field. These Bose-Einstein condensates define pixels of generalized motor maps. Plasma oscillations in turn induce various physiological responses such as Ca++ and Mg++ waves and nerve pulses in turn giving rise to the generalized motor action. Field code is the correspondence between the spatio-temporal pattern of plasma oscillations and generalized motor action.

4. Some applications

The model of the magnetic body and the mechanism of motor control based on plasma oscillations of plasmoids can be tested by finding whether it allows to understand various enigmatic findings. Priore's machine which is a device demonstrated to induce a cure of cancer by somehow stimulating the immune system defines one such application. The findings of Sue Benford about intentionally produced tracks and dots in nuclear emulsions and microwave hearing and closely related taos hum define further applications. There is experimental evidence that electromagnetic stimulation can be used to transfer genetic information imprinted in field patterns between organisms belonging to different species. The idea about genes responsible for genetic self engineering and responding to field patterns representing foreign genes pops up naturally in dark matter inspired vision.

The general model for the magnetic body allows also to sharpen the model of remote mental interactions. In fact, these effects would be only a scaled-up exogenous versions of the effects appearing endogenously in cellular length scales and also in astrophysical length scales in communications between magnetic bodies and corresponding biological bodies.

For details see the revised chapter Homeopathy in Many-Sheeted Space-Time of "Genes, Memes, Qualia,...".

Matti Pitkanen