About the Nature of Contemporary Mathematics

I found from Not Even Wrong a link to a very nice popular article The Nature of Contemporary Core Mathematics by topologist and topological quantum field theorist Frank Quinn. To my own surprise I had several times the impression of understanding (perhaps the aging brain of scientists learns to generate this experience when required;-)). Core mathematics differs from pure and applied mathematics in Quinn's classification in that it can but need not yet have direct applications.

I have been following the work of John Baez and others based on category theoretical inspirations and I admit my frustration because I am unable to follow the technicalities and fail to see the connection to quantum physics. Quinn represents interesting comments about this work which I could use as an excuse for giving up totally my attempts to understand what they are doing;-).

First of all Quinn notices the potential fatal consequences coming from the lack of a direct connection with physics. It is easy to agree: the lack of a concrete connection makes it possible for a brilliant mathematician to generate endlessly formal structures as generalizations of existing ones and to generate theorems as analogs of existing ones. This is not wrong as such but the lack of the evolutionary pressures leads to an inflation of these mathematical life forms and eventually the mass extinction is unavoidable since the academic metabolic resources are finite. I also think that something genuinely new and irreducible is required. Deformations of existing structures - what most of recent day theoretical physics is - are not enough.

The second point of Quinn is more technical. He claims that the decomposition structure of categories (composition of arrows) cannot hold true in the physically interesting 4-D case even in topological QFTs. What decomposition means here is the assumption that S-matrices - the important arrows now- are parametrized by the value of a continuous time parameter telling the duration of time evolution between initial and final states. This implies that one can decompose S-matrix to a product in many manners (arrow as product of arrays). One can do the same also for path integral (but only formally). Quinn interprets this as locality. One can indeed imagine of decomposing the S-matrix to a product of infinite number of S-matrices associated with infinitesimal values of time parameterm and to obtain representations as an exponent of interaction Hamiltonian. The relationship between what happens by two points separated by a wall can be reconstructed from what happens at the wall. This is how Quinn states it.

For a short time I was enthusiastic about cobordism category and S-matrices as as representation of this category and talked about TGD as almost topological QFT but soon realized that this does not lead to anywhere. My own objection against the decomposition is based on the same observation as Quinn's but formulated differently. The decomposition means that the counterpart of unitary time evolution in the sense of exponentiation of interaction Hamiltonian) is assumed. This is impossible in TGD framework as became clear during the first months of TGD when I learned that Hamiltonian formalism makes no sense in TGD because of the extreme non-linearity of any general coordinate invariant variational principle. Within about 7 years this led to the vision about physics as infinite-dimensional geometry of world of classical worlds (or configuration space as I used to say then) and the last five years I have been talking about zero energy ontology formulated in terms of causal diamonds (CDs) defined as intersections of future and past directed lightcones.

1. The temporal distance between the tips of CD is quantized in powers of two (p-adic length scale hypothesis) and also the relative position of tips forms a discrete lattice like set in 3-D hyperboloid of future light-cone. Unions of CDs are allowed and they can also intersect and there are CDs within CDs so that one can speak about fractal hierarchy. Most of this is very relevant for the notions like radiative correction, coupling constant evolution, virtual particle, finite measurement resolution, second law, and even quantum cosmology (when one considers very large CDs). I feel that these fundamental quantum physical notions must be feeded explicitly to the mathematics at the fundamental level. I would be astonished if an approach starting from existing mathematical notions such as categories having motivations coming from the internal structure of mathematics of a particular era- in particular the idea to of transferring the results from one branch of mathematics to another one by using functors- could miraculously reproduce these notions.

2. One can assign M-matrix ("complex" square root of density matrix decomposing to a product of positive square root of diagonal density matrix and unitary S-matrix) to any CD as a representation of zero energy state. The collection of M-matrices orthonormal as zero energy states defines unitary U-matrix. There is a fractal hierarchy of M-matrices (again a physical input) but the product property fails. One cannot arrange CDs to a sequences of CDs so that product decomposition fails and one cannot speak of cobordism category.

3. Product property implying a representation of S-matrix as an exponential of interaction Hamiltonians is also inconsistent with number theoretical universality stating that M-matrices make sense in all number fields. In p-adic context the continuous unitary time evolution in non-sensical as follows from the fact that p-adic exponent function does not have the physical properties of real exponent function. To define the counterparts of the exponent of Hamiltonian one must introduce the counterparts of phases exp(iEt) as roots of unity appearing in algebraic extension of p-adic numbers. Discretization and number theoretical quantization are unvoidable. One has chronons and the classical Hamiltonian flow picture fails.

Quinn says many other things but just these points stimulated sufficient interest in me to write these comments. I recommend the article warmly for physicists willing to understand how mathematicians see the science.

Considerable progress in generalized Feynman diagrammatics

The following is expanded and somewhat edited response in Kea's blog. For reasons that should become obvious the response deserves to be published also here although I have done this implicitly via links to pdf files in earlier postings. My sincere hope is that at least single really intelligent reader might realize what is is involved;-). This might be enough.

I have been working with twistor program inspired ideas in TGD framework for a couple of years. The basic conceptual elements are following.

1. The notion of generalized Feyman diagram defined by replacing lines of ordinary Feynman diagram with light-like 3-surfaces (elementary particle sized wormhole contacts with throats carrying quantum numbers) and vertices identified as their 2-D ends - I call them partonic 2-surfaces. Speaking somewhat loosely, generalized Feynman diagrams plus background space-time sheets define the "world of classical worlds" (WCW).

2. Zero energy ontology (ZEO) and causal diamonds (intersections of future and past directed lightcones). The crucial observation is that in ZEO it is possible to identify off mass shell particles as pairs of on mass shell particles at throats of wormhole contact since both positive and negative signs of energy are possible. The propagator defined by modified Dirac action does not diverge (except for incoming lines) although the fermions at throats are on mass shell. In other words, the generalized eigenvalue of the modified Dirac operator containing a term linear in momentum is non-vanishing and propagator reduces to G=i/λγ , where γ is modified gamma matrix in the direction of stringy coordinate. This means opening of the black box of off mass shell particle-something which for some reason has not occurred to anyone fighting with the divergences of QFTs.

3. Representation of 8-D gamma matrices in terms of octonionic units and 2-D sigma matrices. Modified gamma matrices at space-time surfaces are quaternionic/associative and allow a genuine matrix representation. As a matter fact, TGD and WCW can be formulated as study of associative local sub-algebras of the local Clifford algebra of 8-D imbedding space parameterized by quaternionic space-time surfaces. Central conjecture is that quaternionic 4-surfaces correspond to preferred extremals of Kähler action identified as critical ones (second variation of Kähler action vanishes for infinite number of deformations defining super-conformal algebra) and allow a slicing to string worldsheets parametrized by points of partonic 2-surfaces.

4. Number theoretic universality requiring the existence of Feynman amplitudes in all number fields when one allows suitable algebraic extensions: roots of unity are certainly required in order to realize plane waves. Also imbedding space, partonic 2-surfaces and WCW must exist in all number fields and their extensions. These constraints are enormously powerful and the attempts to realize this vision have dominated quantum TGD for last 20 years.

5. As far as twistors are considered, the first key element is the reduction of the octonionic twistor structure to quaternionic one at space-time surfaces and giving effectively 4-D spinor and twistor structure for quaternionic surfaces.

Quite recently quite a dramatic progress took place in this approach. It was just the simple observation -I should have made if for already half year ago!- that on mass shell property puts enormously strong kinematic restrictions on the loop integrations. With mild restrictions on the number of parallel fermion lines appearing in vertices (there can be several since fermionic oscillator operator algebra defining SUSY algebra generates the parton states)- all loops are manifestly finite and if particles has always mass -say small p-adic thermal mass also in case of massless particles and due to IR cutoff due to the presence largest CD- the number of diagrams is finite. Unitarity reduces to Cutkosky rules automatically satisfied as in the case of ordinary Feynman diagrams.

This is about momentum space aspects of Feynman diagrams but not yet about the functional (not path-) integral over small deformations of the partonic 2-surfaces. It took some time to see that also the functional integrals over WCW can be carried out at general level both in real and p-adic context.

1. The p-adic generalization of Fourier analysis allows to algebraize integration- the horrible looking technical challenge of p-adic physics- for symmetric spaces for functions allowing the analog of discrete Fourier decomposion. Symmetric space property is indeed essential also for the existence of Kähler geometry for infinite-D spaces as was learned already from the case of loop spaces. Plane waves and exponential functions expressible as roots of unity and powers of p multiplied by the direct analogs of corresponding exponent functions are the basic building bricks and key functions in harmonic analysis in symmetric spaces. The physically unavoidable finite measurement resolution corresponds to algebraically unavoidable finite algebraic dimension of algebraic extension of p-adics (at least some roots of unity are needed). The cutoff in roots of unity is very reminiscent to that occurring for the representations of quantum groups and is certainly very closely related to these as also to the inclusions of hyper-finite factors of type II₁ defining the finite measurement resolution.

2. WCW geometrization reduces to that for a single line of the generalized Feynman diagram defining the basic building brick for WCW. Kähler function decomposes to a sum of "kinetic" terms associated with its ends and interaction term associated with the line itself. p-Adicization boils down to the condition that Kähler function, matrix elements of Kähler form, WCW Hamiltonians and their super counterparts, are rational functions of complex WCW coordinates just as they are for those symmetric spaces that I know of. This allows straightforward continuation to p-adic context. Incredibly simple!
3. As far as diagrams are considered, everything is manifestly finite as the general arguments (non-locality of Kähler function as functional of 3-surface) developed two decades ago indeed allow to expect. General conditions on the holomorphy properties of the generalized eigenvalues λ of the modified Dirac operator can be deduced from the conditions that propagator decomposes to a sum of products of harmonics associated with the ends of the line and that similar decomposition takes place for exponent of Kähler action identified as Dirac determinant. This guarantees that the convolutions of propagators and vertices give rise to products of harmonic functions which can be Glebsch-Gordanized to harmonics and only the singlet contributes to the WCW integral in given vertex. The still unproven central conjecture is that Dirac determinant equals the exponent of Kähler function.

Ironically, twistors which stimulated all these development do not seem to be absolutely necessary in this approach although they are of course possible. Situation changes if one does not assumes small p-adically thermal mass due to the presence of massless particles and one must sum infinite number of diagrams. Here a potential problem is whether the infinite sum respects the algebraic extension in question.

For a more detailed representation of generalized Feynman diagrammatics see the last section of the pdf article Weak form of electric-magnetic duality, electroweak massivation, and color confinement. For Feynman diagrams and WCW integration see the article How to define generalized Feynman diagrams? summarizing the basic formulas. See also the chapter Does the Modified Dirac Equation Define the Fundamental Action Principle?.

Strong CP breaking observed in BBbar system?

Both Lubos Motl, Tommaso Dorigo, and Jester comment the strong breaking of CP symmetry in B-Bbar system claimed by D0 collaboration. The claimed symmetry breaking is about 50 times larger than the breaking predicted by the standard model, and manifests itself as an asymmetry in the production of μ⁺μ⁺ and μ^-μ^- pairs in the decays producing B⁰Bbar⁰ pairs. The asymmetry is due to the oscillations between almost mass degenerate states B⁰ and Bbar⁰. It is the mass difference which is much larger than predicted one.

In TGD framework one can imagine a very general CP breaking mechanism due to the presence of imaginary exponent of the instanton density associated with Kähler action. A second very geometric mechanism is suggested by zero energy ontology. The basic notion is causal diamond (CD) defined as the intersection of future and past directed lightcones of Minkowski space (times CP₂ to be precise). The moduli space for CDs within given CD defining a preferred rest system consists of translations of the lower tip of sub-CD, which are continuous plus discrete moduli space for the relative position of the upper tip of the sub-CD relative to lower tip. This dicretization has turned out to be necessary for the p-adicization program and it could resolve also some cosmological mysteries as I have explained in earlier postings.

One could argue that the asymmetry between CDs could induce CP breaking. One could also argue that the overall cm degrees of freedom are associated with entire CD rather than lower tip so that no CP breaking should results. I am not sure. It might be that the rest system of larger CD is the natural one and indeed induces a spontaneous CP breaking within it.

Loops involving a decay to W bosons by top quark exchange are responsible for the CP breaking in standard model and the obvious guess is that there are new heavy fermions which contribute to the loops inducing 50 times larger CP breaking as expected. In TGD framework it is easy to imagine this kind of new fermions. One possibility is p-adically scaled up variant of top: I told about this in earlier posting. The new M₈₉ hadronic physics would provide new fermions which could also contribute to the CP breaking. In principle everything is calculable since only weak interactions are involved unless the M₈₉ hadrons couple to M₆₁ weak bosons rather than the ordinary M₈₉ ones. In this case they would have virtually no weak interactions. This possibility cannot be excluded.

How to perform WCW integrations in generalized Feynman diagrams?

The formidable looking challenge of quantum TGD is to calculate the M-matrix elements defined by the generalized Feynman diagrams. Zero energy ontology (ZEO) has provided profound understanding about how generalized Feynman diagrams differ from the ordinary ones. The most dramatic prediction is that loop momenta correspond to on mass shall momenta for the two throats of the wormhole contact defining virtual particles: the energies of the energies of on mass shell throats can have both signs in ZEO. This predicts finiteness of Feynman diagrams in the fermionic sector. Even more: the number of Feynman diagrams for a given process is finite if also massless particles receive a small mass by p-adic thermodynamics. The mass would be due to IR cutoff provided by the largest CD (causal diamond) involved.

The basic challenges are following.

1. One should perform the functional integral over world of classical worlds (WCW) for fixed values of on mass shell momenta appearing in internal lines. After this one must perform integral or summation over loop momenta.

2. One must achieve this also in the p-adic context. p-Adic Fourier analysis relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly that the loop momenta are discretized and ZEO predicts this kind of discretization naturally.

The realization that p-adic integrals could be defined if the manifold is symmetric space as the world of classical world (WCW) is proposed to be raises the hope that the WCW integration for Feynman amplitudes could be carried at the general level using Fourier analysis for symmetric spaces. Even more, the possibility to define p-adic intergrals for symmetric spaces suggests that the theory could allow elegant p-adicization. This indeed seems to be the case. It seems that the dream of transforming TGD to a practical calculational machinery does not look non-realistic at all.

I do not bother to type more but give a link to a short article summarizing the basic formulas. For more background see also the article Weak form of electric-magnetic duality, electroweak massivation, and color confinement and the chapter Does the Modified Dirac Equation Define the Fundamental Action Principle?.

Weak form of electric-magnetic duality, particle concept, and Feynman diagrammatics

The notion of electric magnetic duality emerged already two decades ago in attempts to formulate the Kähler geometric of world of classical worlds. Quite recently a considerable step of progress took place in the understanding of this notion. Every new idea must be of course taken with a grain of salt but the good sign is that this concept leads to an identification of the physical particles as string like objects defined by magnetic charged wormhole throats connected by magnetic flux tubes. The second end of the string contains particle having electroweak isospin neutralizing that of elementary fermion and the size scale of the string is electro-weak scale would be in question. Hence the screening of electro-weak force takes place via weak confinement. This picture generalizes to magnetic color confinement.

Zero energy ontology in turn inspires the idea that virtual particles correspond to pairs of on mass shell states assignable to the opposite throats of wormhole contacts: in TGD framework the propagators do not diverge although particles are on mass shell in standard sense. This assumption leads to powerful constraints on the generalized Feynman diagrams giving excellent hopes about the finiteness of loops. Finiteness has been obvious on basis of general arguments but has been very difficult to demonstrate convincingly in the fermionic sector of the theory. In fact, there are good arguments supporting that only a finite number of diagrams contributes to a given reaction: something inspired by the vision about algebraic physics (infinite sums lead out of the algebraic extension used). The reason is that the on mass shell conditions on states at wormhole throats reduce the phase space dramatically, and already in the case of four-vertex loops leave only a discrete set of points under consideration. This implies also finiteness. This wisdom can be combined with the new stringy view about particles to build a very concrete stringy view about generalized Feynman diagrams.

The coutcome of the opening of the black box of virtual particle -an idea forced by the twistorial approach and made possible by zero energy ontology- is something which I dare to regard as a fulfillment of 32 year old dream.

For a more detailed representation of weak electric-magnetic duality see the last section of the pdf article Weak form of electric-magnetic duality, electroweak massivation, and color confinement. For Feynman diagrams and WCW integration see the article How to define generalized Feynman diagrams? summarizing the basic formulas. See also the chapter Does the Modified Dirac Equation Define the Fundamental Action Principle?.

Does top quark has scaled up variant?

Tommaso Dorigo writes in Quantum Diaries Survivor about The 450 GeV Quark That Wouldn't Go Away. What has been observed in CDF is indication for what looks like a scaled up copy of top quark with mass of 450 GeV. It is fun to test various new physics prediction of TGD. As I have told again and again, p-adic length scale hypothesis allows scaled up variants of quarks with masses coming as half octaves. The mass obtained by multiplying top quark mass 170 GeV with a factor 2^3/2 is 480 GeV and and 6 per cent higher than the rough experimental estimate.

Solution to dark energy problem?

Paul Frampton tells in the blog of Lubos about his proposal explaining dark energy in terms of an argument relying on the observation that the amount of matter in the observed Universe is not far from the mass of a black hole of same radius. Frampton's article Possible solution of dark matter, solution of dark energy and Gell-Mann as great theoretician can be found from archive.

It is assumed that in a reasonable approximation we live inside a blackhole. Hawking temperature (quantal notion) is deduced from the mass of the Universe. After this Unruh formula expressing the temperature of the radiation observed from a system in an accelarating motion is used. Also this formula is quantal. Usually the temperature is deduced from acceleration but now acceleration is deduced from temperature using existing formula so that one goes outside the original context. The assignment of this acceleration with the growth of the radius of the blackhole is second step out-of-context. The third step out-of-context is the identification of the acceleration-essentially given by Hubble constant- as the acceleration of the cosmic expansion. The outcome happens to be consistent with observations.

One can forget the steps leading to the conclusion and notice that the acceleration for purely dimensional reasons is apart from a numerical constant equal to Hubble constant unless one is willing to bring in some genuinely new physics. That the acceleration is proportional to Hubble constant is what should be the starting point since it suggests that the solution of the negative energy puzzle might be "kinematical" in some sense. Despite all of these out-of-contexts I see the emergence of this kind of papers as a positive sign. Theoretical physics is gradually beginning to recover from the social pressures of super string ideology and problem centered approach is beginning to become in fashion again.

This numerical co-incidence could reflect something deeper. What might be essential is that space-time is replaced with a finite region of it: now it is the interior of a black hole in order to get the 3-D surface and the familiar formulas to get numbers which we so much appreciate. Blackhole as such need not be essential. Holography is something respectable but fuzzy enough to justify the adhoc identification of Unruh acceleration reproducing the Hawking temperature as the acceleration for the expansion of the Universe.

In TGD framework space-time surface is replaced with many-sheeted space-time so that one obtains effective boundaries: effective they correspond to pairs of wormhole throats and inside wormhole throats the induced metric is Euclidian. Also holography is key element of TGD. "Partonic" 2-surfaces plus their 4-D tangent space distributions at partonic 2-surfaces code for the information about the physical states in zero energy ontology. The motivation for the "partonic" is that also elementary particles correspond to this kind of 2-surfaces -very tiny in this case.

In TGD inspired quantum cosmology the continuous cosmic expansion is replaced with a sequence of short periods of accelerating expansion followed by longer periods during which a given space-time sheet does not expand. There is a fractal hierarchy of cosmologies within cosmologies. By criticality the period of the accelerated expansion obeys a universal dynamics. The mere condition that 3-space is flat (criticality tolerates no dimensional parameters) and imbeddable to M⁴×CP₂ fixes the Robertson-Walker metric apart from a parameter telling the duration of the expansion period. The duration is necessarily finite for both critical and over-critical cosmology. Accelerated expansion is due to a negative "pressure" and implied by the sub-manifold constraint so that there is no need for mysterious particles with negative kinetic energy nor for cosmological term. This gives a meaning for the "kinematic". Sub-manifold constraint solves the same basic problems of standard cosmology as inflation in terms of flatness of 3-space but avoids the inflation of inflations plaguing the inflationary scenario. It also explains all standard model quantum numbers and leads to a highly predictive scenario for new physics effects. This adds a further meaning to the "kinematic".

While writing this I realized that for more than two decades I have tried to tell about this beautiful solution to the colleagues but in vain! Tells something about the deph of the intellectual abyss in theoretical physics. People waste their time to long discussions about ad hoc dimensional analysis tricks by old names interpreting old formulas outside their original context instead of seeing the trouble of learning something genuinely new. It is so safe and so much easier than trying to understand long arguments leading to completely new formulas!

New anomaly in CDF

Jester told about Another Anomaly from CDF. For 18 months ago I spent a quite hectic period with the first CDF anomaly, which turned out to have TGD inspired interpretation in terms of a production of meson like states from from color octet excitations of tau leptons (see for instance this blog posting). Color excitations of leptons and of quarks represent a basic prediction of quantum TGD and already earlier evidence for colored excitations of electron (already at seventies!) and muon had emerged. Since the facts did not fit the standard model and its standard extensions, they were forgotten again, as so many times before. To paraphrase Wheeler: Phenomenon exists only if it is understood phenomenon!

The period ended up with a beautiful model for the anomaly. Also an amusing episode telling much about the intellectual and ethical standards of the decision makes of Helsinki University took place. I lost the possibility to use university computer for my web page (this had been the only positive gesture towards my work) and they even refused to guide visitors to the new URL!

The data relating to the new anomaly is from the same experiment as those for 18 months ago. The cross section for the production of charged particles is three orders of magnitude higher than the QCD prediction at transversal momenta about 100 GeV. In A note on the CDF high-pt charged particle excess it shown that the results cannot be understood in QCD framework. It is also found that the cross section for producing single charge particle is essentially the same than for producing a jet so that the jet should consist of essentially single charged particle. Possible explanations for the findings are discussed and the high value of production cross section is found to be very difficult to understand.

TGD model is based on the production of tau-pions in the strong non-orthogonal magnetic and electric fields of colliding quarks. The subsequent decays of neutral tau-pion coherent state would produce charged tau-pions. The final outcome is mostly muons. This mechanism is not something coming out from standard Feynman diagrammatics but has a justification in terms of anomaly argument: the production amplitude -essentially Fourier component of the instanton density E.B for the electromagnetic field of colliding quarks- is fixed completely from anomaly considerations. I do not have time to work with this but my bet is that the explanation is same as for the former CDF anomaly.

The presence of non-orthogonal electroweak fields implies in TGD framework necessarily parity breaking and an interesting question is whether the vacuum in question could correspond to an almost vacuum extremal of Kähler action. These extremals led to a breakthrough in understanding TGD inspired quantum biology as I told in the earlier posting.

What makes me happy that facts do not seem to care about the desires of power holders. Truth is eventually the winner.

For details about the physics of colored leptons and for the explanation for the first CDF anomaly see the chapter Recent Status of Leptohadron Hypothesis of the book "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".

Strange: quasars do not show time dilation in their dynamics

Lubos Motl told about Discovery that quasars don't show time dilation mystifies astronomers by Hawkins. I also received a link from Kram about this: thank you. The finding is rather strange.

Consider first what one expects. Lorentz invariance implies red shift for frequencies and in time domain this means the stretching of time intervals so that the evolution of distant objects should look the slower the longer their distance from the observer is. In the case of supernovae this seems to be the case. What was studied now were quasars at distances of 6 and 10 billion years. The time span of the study was 28 years. Their light was red shifted by different amounts as one might expect but their evolution went on exactly the same rhythm! This looks really strange.

One must notice that the frequency assigned to electromagnetic signature is not ordinary light frequency. For instance, is it analogous to a frequency assignable to massive particle or massless particle? Consider ordinary Doppler effect as an analog. If the redsift is effectively that of a massive particle then the redshift is given by f→ (1-v²)^1/2f =(1+z)f and for small relative velocities the redshift is about z=Δf/f =v² smaller than for massless case f→ ((1-v)/(1+v))^1/2× f=zf giving z=Δ f/f =v in the same approximation. In the recent case however redshifts are large. From z+1= Hr, with redshift z=7 associated with r=.75 billion years one deduces z=56 for 6 billion ly and z=93.3 for 10 billion ly. Therefore the redshifts for massive and massless case are related by a factor of 2 as one easily finds.

Consider now the situation in TGD framework.

1. Causal diamond defined as the intersection of future and past directed light-cones is the fundamental geometric object in zero energy ontology. In cosmological scales a possible interpretation of CD is as sub-cosmology. In particular, our comology would correspond to this kind of CD having sub-CDs having .... CDs possess moduli space. CD has M⁴ position identified as say that of the lower tip. One can perform Lorentz boosts for CD leaving the lower tip invariant. The proper time distance between tips of CD is Lorentz invariant and defines an internal time standard of CD. For instance, for electron, d, and u quarks this time is .1 seconds, 1/1.28 milliseconds, and 6.5 milliseconds defining fundamental biorhytms.

2. p-Adic length scale hypothesis follows if the light-cone propert time distance between the tips of the CD is quantized in powers of two. This means that future light-cone is replaced with a union of light-cone proper time constant hyperboloids with size scales coming as powers of two. Cosmic time identified as the distance between the tips would be quantized and cosmic time would increase in jumps. As a matter fact, the relative coordinate between the tips should be quantized quite generally so that the light-cone proper time constant hyperbloids would be replaced with discrete lattice like structures. This would predict quantization of cosmic redshifts and explain the claimed strange phenomena like God's fingers containing galaxies along the line of sight with a quantized redshift.

3. Could the quantization of cosmic time relate to the strange observation? What does the dynamics of objects with a frozen value of cosmic time look like when viewed from Earth? What is clear that the distant object does not recede away during the studied evolution period. The overall redshift for the studied events during its evolution is same. No dilation of the time interval between periodic events would takes place. But isn't this the case in good approximation also in the measurements? And obviously this argument does not say anything about the time dilations associated with the samples at different distances.

   This means that the time-like direction defined by the vector connecting tips of CD in M⁴ is same as the direction of the time-like vector pointing from the tip of the very big CD defining what we call our Big Bang cosmology a to the M⁴ point at which the CD containing astrophysical object is located. This position characterizes all points of given CD so that the time dilation is constant the for internal dynamics of systems inside the CD.

4. Why the Lorentz boosts of quasar CDs in the two samples should be identical? Could the explanation relate to the fact that quasars are extremely distant objects meaning that the corresponding CDs are very large? Could the quasars in the two samples belong to the same CD?! If so then the internal dynamics would obey same rhytm but there would be a purely cosmological redshift! This effect would be basic prediction of zero energy ontology in cosmological scales and would become visible in very long length scales.

For background see TGD and Cosmology.

Quantum model for qualia, sensory receptor, and hearing

I am continung the updating the books about TGD inspired theory of consciousness. I just finished the chapter about quantum model of hearing- certainly the ugliest duckling in the flock represented by the books about TGD and TGD inspired theory of consciousness.

The key idea was inspired by a model of photoreceptors. The question was whether nearly vacuum extremals of Kähler action for which parity breaking is large due to the presence of classical Z⁰ field might explain chiral selection in living matter and provide model for a sensory receptor and even cell membrane space-time sheet in general as a critical system. The completely unexpected discovery was that the peak frequencies of photoreceptors coincide with Josephson frequencies of the 4 biologically most important ions in the effective membrane potential containing also Z⁰ contribution provided the value of Weinberg angle is sin²(θ_W)=.0295. After this observation the ideas started to flow rapidly and it took two weeks to build a reasonably stable general picture.

1. Josephson photons have a dual interpretation as large hbar EEG photons and as biophotons: these two phenomena are reflections of one and same thing. This is a victory for the hierachy of Planck constants.
2. DNA as topological quantum computer model led to the identification of the fundamental sensory qualia as quantum numbers assignable to quark pair (or pair of them depending on option) in turn associated with flux tube connecting DNA nucleotide and lipid.
3. Cell membrane (at least axon) makes cell (at least neuron) a kind of homunculus with each lipid/nucleotide representing a pixel colored by different fundamental qualia.
4. Qualia obey quantum synesthesia in the sense that the composites of spin, electroweak, and color numbers are analogous the synesthetic associations of basic qualia: this has nothing to do with ordinary synesthesia. This could make associative neurons in associative areas quantum synesthetes binding various sensory inputs to colors of single pixel of axonal membrane. Cell and genome would be also sensory holograms.
5. The model for the magnetic body and its function becomes much more detailed and the vision about spectroscopy of consciousness- one of the ultra-romantic ideas which I have felt shame for- is realized since Josephson frequencies code for qualia.

I attach below the abstract of Quantum Model of Hearing. The material about the model for qualia can be also found from General Theory of Qualia.

The quantum model of hearing has evolved through several twists and turns. The emergence of zero energy ontology, the explanation of dark matter in terms of a hierachy of Planck constants requiring a generalization of the notion of imbedding space, the view about life as something in the intersection of real and p-adic worlds, and the notion of number theoretic entanglement negentropy led to the breakthrough in TGD inspired quantum biology and also to the recent view of qualia and sensory representations including hearing allowing a precise quantitative model at the level of cell membrane. This also modified dramatically the speculative ideas about the role of neutrinos in hearing.

Also in the recent view long range weak play a key role. They are made possible by the exotic ground state represented as almost vacuum extremal of Kähler action for which classical em and Z⁰ fields are proportional to each other wheras for standard ground state classical Z⁰ fields are very weak. Neutrinos are present but it seems that they do not define cognitive representations in the time scales characterizing neural activity. Electrons and quarks for which the time scales of causal diamonds correspond to fundamental biorhythms, take this role.

The ensuing general model of how cell membrane acts as a sensory receptor has unexpected implications for the entire TGD inspired view about biology.

1. The most important implication concerning the model of sensory receptors relates to the vacuum degeneracy of Kähler action. It has been clear from the beginning that the nearly vacuum extremals of Kähler action could play key role key role in living systems. The reason is their criticality making them ideal systems for sensory perception. These extremals carry classical em and Z⁰ fields related to each other by a constant factor and this could explain the large parity breaking effects characterizing living matter. The assumption that cell membranes are nearly vacuum extremals and that nuclei can feed their Z⁰ charges to this kind of space-time sheets in living matter leads to a modification of the model for cell membrane as Josephson junction. Also a model of photoreceptors explaining the frequencies of peak sensitivity as ionic Josephson frequencies and allowing the identification of biophotons as Josephson radiation emerges and will be discussed in the sequel. The value of Weinberg angle in this phase is fixed to sin²(θ_W)=.0295, whereas in standard phase the value is given by sin²(θ_W)=.23.

2. DNA as topological quantum computer model plus certain simplifying assumption leads to the conclusion that the spectrum of net quantum numbers of quark antiquark pair define the primary qualia assignable to a nucleotide-lipid pair connected by a magnetic flux tube. The most general prediction is that the net quantum numbers of two quark pairs characterize the qualia. In the latter case the qualia would be assigned to a pair of receptor cells.

3. Composite qualia result when one allows the nucleotide-lipid pairs of the membrane to be characterized by a distribution of quark-antiquark pairs. Cell membrane -or at least the axonal parts of neurons- would define a sensory representation in which is a pair of this kind defines a pixel characterized by primary qualia. Cells would be sensory homunculi and DNA defines a sensory hologram of body of or of part of it. Among other things this would give a precise content to the notion of grandma cell.

4. Josephson frequencies of biologically important ions are in one-one correspondence with the qualia and Josephson radiation could re-generate the qualia or map them to different qualia in a one-one and synesthetic manner in the neurons of the sensory pathway. For large values of Planck constant Josephson frequencies are in EEG range so that a direct connection with EEG emerges and Josephson radiation indeed corresponds to both biophotons and EEG. This would realize the notion of sensory pathway which originally seemed to me a highly non-realistic notion and led to the vision that sensory qualia can be realized only at the level of sensory organs in TGD framework.

5. At the level of brain motor action and sensory perception look like reversals of each other. In zero energy ontology motor action can be indeed seen as a time reversed sensory perception so that the model of sensory representations implies also a model for motor action. Magnetic body serves as a sensory canvas where cyclotron transitions induced by Josephson frequencies induce conscious sensory map entangling the points of the magnetic body with brain and body.

The model for hearing follows as a special case from the general model for sensory receptor and representations.

1. Concerning hearing, the basic questions relate to the precise identification of the hearing quale, to the representation of pitch of the sound at the magnetic body, and to the representation of various geometric data about sound. The electromagnetic charge of the quark pair (or equivalently electroweak isospin) looks like an excellent candidate in this respect so that charge increment would define one fundamental hearing quale.

   This quale need not correspond to pitch. The vision about hearing as a frequency quale suggests that cyclotron transition frequency corresponds to the pitch. Sound frequency would be coded to an increment of cyclotron frequency and pitch would be a quale assignable to magnetic body rather than biological body. Hearing would in a well-defined sense represent a higher level sense not understandable without the notion of magnetic body. The strength of the magnetic field would code for cyclotron frequency and therefore for the pitch. One of the mysteries related to hearing is the ability to hear frequencies much higher than the maximum rate of nerve pulses which is below kHz. The coding by Josephson frequencies and representation of them as quale of the magnetic body resolves this mystery.

2. At quantative level the first challenge is to understand the typical hearing ranges (humans, mice, bats, sea mammals) and here the time scales of CDs associated with quarks and leptons give intriguing hints. Also their cyclotron frequencies are involved and large values of Planck constant are unavoidably involved. Josephson frequencies are given by the effective membrane potential (Z⁰ potential must be included) divided by Planck constant and it is possible to represent arbitrarily low frequencies in terms of membrane potential by allowing Planck constant to have high enough values.

3. The extreme rapidity of signalling from hair cells to brain is one of the mysteries of hearing and here Josephson radiation (biophotons) provides a direct neuronal window with practically instantaneous communication. Microtubles could be associated with the flux tubes along which Josephson radiation propagates and also microtubular conformational waves could be involved.

4. Hearing represent in many respects an exceptional quale: consider only music experience, language, internal speech, the understanding and production of speech, and right brain sings- left brain talks metaphor. This conforms with the assumption that magnetic body is involved in essential manner with hearing. Zero energy ontology leads to a vision explaining basic aspects of music experience and the notion of memetic code plus possible realization of genetic code as temporal patterns could provide first principle understanding of language.

What quark masses have to do with biology?

The latest estimates for the of u and d quarks have emerged. The masses are 2 +/- .12 MeV for u quark and 4.79+/-.16 MeV for quark.

In TGD inspired neuroscience and biology elementary particle mass scales play a fundamental role since the time scale of causal diamond associated with the elementary particle (CD is defined as intersection of future and past directed light-cones, for details see previous postings) coming as an octave of the fundamental CP₂ is an additional characteristic of elementary particle in zero energy ontology. The amazing prediction is that these secondary p-adic time scales are macroscopic. An equally amazing observation is that these time scales are highly interesting biologically.

For electron which corresponds to k=127 by p-adic length scale hypothesis the time scale is .1 seconds defining the fundamental 10 Hz biorhythm. For d quark with mass 5 MeV the time scale corresponds to k=120 and the time scale is 1/1.128 ms and corresponds to 1280 Hz (kHz cortical synchrony and duration of action potential). The mass of u quark is 2 MeV and 4 times the mass of electron so that the mass of p-adic time scale 6.25 ms corresponds to k=123 and is 16 times shorter and corresponds to 160 Hz frequency. Also this frequency should be interesting biologically.

Clicking 160 Hz in Google brought the following Journal of Neuroscience article Inactivation of Calcium-Binding Protein Genes Induces 160 Hz Oscillations in the Cerebellar Cortex of Alert Mice. Could it be that this oscillation is analog of 40 Hz oscillation in cortex?

Does harmonic complexity reduce to 3-adicity?

I have been updating the chapter Self and Binding of TGD inspired theory of consciousness. The goal is to base the theory from the beginning on ideas like zero energy ontology, hierarchy of Planck constants aand its connection with dark matter, p-adic physics as physics of cognition and intentionality -and in in particular, life as something residing in the interection real and p-adic worlds. The notion of number theoretic entropy makes it possible to assign to rational or even algebraic entanglement probabilities a positive negentropy and this has meant a breakthrough in the understanding of TGD inspired theory of consciousness and life. These updatings are extremely fruitful -not only because they force to throw away the ancient and obsolete stuff- but because the interaction of new ideas with old ones produces something completely unexpected new ideas.

The understanding of music experience is especially fascinating challenge for a consciousness theorists. In TGD framework quite nice vision about the basic aspects of music experience emerges. Octave phenomenon can be reduced to p-adic length scale hypothesis implied if the causal diamonds defined as intersections of future and past directed lightcones and playing key role in quantum TGD have discrete size spectrum coming as octaves of CP₂ length. Also the preferred role of certain rational frequencies can be understood in the p-adic context from the fact that sine waves in p-adic context can be defined only by introducing an algebraic extension of p-adic numbers allowing the needed roots of unity. Plane waves are defined p-adically only in discrete subset of points and for harmonics of the fundamental frequency. This implies automatically the preferred role of a limited set of rational valued multiples of the fundamental.

The following little excerpt from the updated chapter provides a inspired vision about one particular aspect of music experience, namely the harmony and allows to interpret Pythagorean vision about music scale in terms of 3-adicity, to deduce a measure for a harmonic measure of the chord, and to replace the Pythagorean tuning of 12-tone system based on perfect fifths with a unique tuning based on 3-adicity.

An interesting question relates to the conditions guaranteing that a chord is experienced as harmonious in the Pythagorean sense. Pythagorean tuning is based on the notion of perfect fifths identified as a scaling by 3/2 producing the sequence C,G,D,A,E,.. In this tuning major-C scale corresponds to ratios C= 1/1, D=9/8, E=81/64, F=4/3, G= 3/2, A=27/16, B= 243/128, C=2/1. Eb and F# correspond to ratios 2⁵/3³ and 3⁶/2⁹. All notes are expressible as powers of two and three. Since the multiplication of any note by a power of two does not affect the harmony it should be to drop the powers of two from the integers characterizing the notes in the ratio of three notes. For instance, C-E-G reduces 3:3⁴:1, C-Eb-G to 3⁴:1:3³, and tritonus C-Eb-F# to 3⁹:1:3³.

The problem of Pythagorean tuning is that one cannot represent 2 as an exact integer power of 3/2 and the scalings give infinite number of tones. If the construction starts from Gb then F# and Gb correspond to frequencies, which are not quite identical in Pythagorean tuning. One could make compromize by introducing the geometric mean of F# and Gb but this would bring in 3^1/2 and would force to leave the world of pure rationals. For string instruments and electronic instruments the Pythagorean tuning is practical but for instruments like piano the transposition of the scale is impossible.

One should be able to characterize a given chord harmonically by a function F(a,b,c), which is symmetric under the permutations of the reduced pitches a, b and c obtained by dropping powers of two and is invariant under over all scaling of the reduce frequencies. The elementary symmetric functions F(a,b,c)=[a²(b+c)+b²(a+c)+c²(a+b)]/abc and G(a,b,c)=[a³+b³+c³]/abc are the simplest functions of this kind. Either of these functions or their product or ratio could be considered as a measure for the harmonic complexity. The value of the denominator abc equals to 3ⁿ, n=3,7,12 in the cases considered. The numerator has in all cases 3-adic norm equal to one for both F and G. This suggests that the 3-based logarithm of the 3-adic norm 1/|abc|₃=|F|₃=|G|₃ having the values 3,7, and 12 for C-major, C-minor, and tritonus could serve as the measure for the complexity. It is indeed smallest for major and largest for tritonus. 3-adic norm for the product 1/a₁a₂...a_n of n tones of the chord defines a measure of complexity in more general case. A good guess is that the 3-adic norms of the elementary symmetric functions give rise to the same measure.

For the chords C-E-G, F-A-C, and G-H-D appearing as basic chords in C- major scale the values of the harmonic measure are 3, 2, and 8. This means that the basic chords are not harmonically equivalent in Pythagorean system whereas in equally tempered system they would be. One might think that this explains why the tonic is remembered. The anomalously low value for F-A-C relates to the fact that it is only tone for which the power of 3 is negative. Situation changes of F is identified as a minimal power of 3 giving F equivalent with Pythagorean F within the resolution of ear to pitch which is about |Δ f/f|= 4.3 per cent . F=3⁵/2⁸ gives |Δ f/f|= 4.8 per cent. This F would give for F-A-C the harmonic measure 8 which equals to that for G. This looks more reasonable than the purely Pythagorean value. This definition would also allow to find a unique choice of powers of three for 12-chord system. For instance, F# is favored over Gb since it corresponds to a positive power of 3.

To sum up, music seems to provide a possible manifestations of 3-adicity, and the proposed measure of harmonic complexity might provide a manner to construct also a theory of aesthetically pleasing harmonic progressions.

Negentropic entanglement and the role of neural transmitters

Soon after starting to develop TGD inspired theory of consciousness, I somehow ended up to an email correspondence with Gene Johnson who insistently emailed me links to abstracts about neuroscience. I read the classic Bible about brain by Kandel et al [2] and tried to make sense of it in my own conceptual framework. This was of course hopeless task since I had only the notions of quantum jump and self. The feeling that something very simple -about which I do not and perhaps cannot ever have a slightest clue- must be behind this incredible complexity made the situation really frustrating. The deeper meaning of EEG, nerve pulse neurotransmitters, hormones- actually of entire brain chemistry and also biochemistry- remained a total mystery.

Development of ideas After required number of years however some concrete ideas began to emerge.

1. The notion of magnetic body with fractal onionlike structure meant a decisive step of progress. Also the hierarchy of Planck constants and dark matter as controller of visible matter in living systems emerged. The function of EEG as communication and control tool of magnetic body using biological body as a motor instrument and sensory receptor looked very natural. This led also to a proposal that there is an entire hierarchy of EEGs and their variants. After several trials a vision about nerve pulses as concomitants of quantum level communications emerged as also a vision about DNA as topological quantum computer based on the flux tubes connecting DNA nucleotides with the lipid layers of cell membrane emerged and providing a function for the intronic portions of genome as carriers of quantum computer programs [1].

2. Also a vision about the biochemical role of dark matter evolved. In particular, phase transitions reducing Planck constant for a magnetic flux tube would induce its contraction and force biomolecules near to each other. This would explain the miracles of DNA replication, translation, and transcription and quite generally the processes known as aggregation of proteins. The reconnection of magnetic flux tubes changing the topology of the biological Indra's net would be also a central mechanism.

3. The model of nerve pulse and the vision about living matter as a kind of dynamical Indra's net led to a first clear idea about the role of neural transmitters. Transmitters are classified to inhibitory or excitatory depending on whether they increase or reduce the magnitude of the membrane potential. This property is however a property of the receptor rather than that of the transmitter. The same transmitter can have both excitatory and inhibitory receptors although often either receptor type dominates. The proposal was that neural transmitters are associated with the ends of the links of the 4-dimensional web connecting neurons to each other. Neurotransmitter attaches to the plug defined by the receptor connecting the communication wire from presynaptic neuron to the flux tube leading to the passive portion of postsynpatic DNA strand acting as sensory receptor. This would make possible rapid communications to DNA. The corresponding active portion of DNA strand could then respond by generating an activity at the level of cell membrane. This conforms with the general idea that proteins represent only one particular outcome of the gene expression. This left open the question whether the excitatory-inhibitory dichotomy could have some deeper meaning.

4. Also it became clear the emotions and information are closely related and that peptides acting both as neurotransmitters and hormones are crucial for emotions [3]. I proposed that emotions are "entropic" qualia. Although I realized the importance of negentropic entanglement I did not have time or I was not able to realize how far reaching this notion actually is.

Is genome a fractal counterpart of brain?

Fractality replaces standard reductionism in TGD Universe. An old idea inspired by p-adic length scale hypothesis is that the binary structures associated with p-adic scales L(k) propto 2^k/2 and L(k+2) define a fractal hierarchy. Brain hemispheres would represent one example of this kind of pair, lipid layers of the cell mebrane second one, and DNA double strand third one. Just for fun one could assume that the structure and functions of brain hemispheres have fractal analogs at the level of DNA double strand and vice versa and look what kind of questions this inspires.

1. Could the identical structures of DNA strands correspond to the anatomical similarity of right and left brain and could the functional asymmetry of the strands correspond to the laterizalization of brain function? Could the genome act as the brain of cell? Could various brain areas have counterparts at the level of DNA? Could the hydrogen bonds between nucleotides serve as the counterpart of corpus callosum? Could the splitting of these bonds during transcription and replication correspond to what happens to a split brain patient?

2. Before continuing it must be made clear that the global identification of right-left dichotomy with holistic-reductionistic dichotomy is wrong. One can however consider its local variant with holism and reductionism assigned do the pairs of right and left brain areas. For instance, emotional right (left) brain (amygdala) would be reductionistic (holistic, negentropic) and intellectual right (left) would be holistic (reductionistic, entropic). The practical reason to the division to the entropic and negentropic pieces could relate to the metabolism. The entropic regions could provide the binding energy as a usable energy to the positive energy negentropic entanglement. Good is not possible without Evil! There are no winners without loosers! Right brain is specialized in spatial thinking and left brain to verbal thinking and arithmetics: the geometry-algebra division of mathematics! Right brain is not so good in motor actions as left brain as any right-handed person knows. Right brain is however better in tactile sensing: right handed persons tend to use left hand for touching objects to get an idea about their shape. Also this can be understood in holistic-reductionistic picture.

3. Apart from reflex actions almost all activities of the body seem to be controlled to a high degree by brain. Could also the activitites of cell be regarded as motor actions of the genome acting as the brain of cell receiving sensory imput from the cell membrane? Could one identify the analogs of sensory areas receiving information from cell membrane, processing, and sending it to the association areas? Could the analogs associative areas be identified as intronic portions of DNA performing topological quantum computations and communicating the outcome to the higher motor areas at the intronic portions of the of the complementary strand, wherefrom they would be communicated to the primary motor areas identifiable as the regions of DNA expressing themselves either chemically (RNA and proteins), as activitites generated directly at the level of cell membrane, or electromagnetically? For instance, could neurotransmitter in the receptor generate the feed of sensory input to the genome inducing the change of the membrane potential as the counterpart of motor action. Could prokaryotes without introns be analogous to brain with only primary sensory and motor areas or to mere ladder-like nervous system?

One could argue that the analogy between DNA are brain fails because second DNA strand is completely passive whereas both brain hemispheres express themselves via motor actions. This is not the case! Both DNA strand has regions expressing themselves but the transcription takes place in opposite directions. Hence DNA strands have motor and sensory areas as also brain does, and the natural guess is that primary motor areas correspond to the areas expressing themselves in terms of RNA, proteins, and possibly also as actions at the level of cell membrane. Primary sensory areas would correspond to to regions complementary to the primary motor regions.

1. What right brain sings-left brain talks metaphor could mean in this picture? Pitch-rhythm dichotomy is more technical expression for this dichotomy. Function providing local data and its Fourier transform providing global data is more abstract representation for this dichotomy and Uncertainty Principle for momentum and position relates closely to these two representations of information. This dichotomy could reflect the presence of two different natural time scales and millisecond time scale for nerve pulses and .1 second time scale for moments of sensory experience are the natural candidates.

   If so, this dichotomy could directly reflect the different time scales assignable to u and d type quarks (1 millisecond) and to electron (100 ms) and reduce to the level of elementary particle physics. This dichotomy would also have fractally scaled up variants made possible by the hierarchy of Planck constants. The analog of Fourier transform would be the negentropic unentanglement of sub-CDs (assignable to quarks) to single mental image inside electron's CD. The analog of function itself would be a collection of sub-CDs representing separate unentangled mental images assignable to individual nerge pulses in millisecond time scale. Also the topological quantum computations assigned to the intronic portions correspond to different time scales due and reflect quark-lepton dichotomy. The quarks in question could be the quarks assigned to the ends of flux tubes in the model of DNA as topological quantum computer.

2. This raises some questions. Could the gene expressions of the two strands somehow reflect this dichotomy? For instance, could the flux tube structures assignable to the aminoacid sequences correspond to the millisecond and 100 ms scales assignable to quarks and electron have the property that also the functioning of these proteins is characterized by these typical time scales? The time scales of protein folding indeed appear in two typical ranges beginning from ms [5] and 100 ms respectively [4]. There are also short proteins for which the folding takes place in microsecond time scales which might relate to the CD of proton.

What can one say about the function of neurotransmitters?

Can one say anything interesting about the the function of neurotransmitters if one combines this highly speculative picture- which can be defended only by the belief on fractality as universal principle- with the idea that bound state and negentropic entanglement make possible the fusion of mental images.

1. Suppose that the fusion of neuronal mental images is required to build higher level mental images that we experience. Suppose that neuronal mental images involve DNA in an essential manner. Suppose that magnetic flux tubes serve as correlates for the entanglement so that the transmission of nerve pulse from pre-synaptic neuron to post-synaptic one creates a flux tube connection between neurons possibly extending to the genome of the post-synaptic neuron. The transmitter at the end of flux tube attached to the receptor acting as a plug would build this connection to some part of DNA specialized to receive particular kind of sensory data from a particular region of cell membrane with complementary strand activating as a response a motor function inducing gene expression at cell membrane level. Gene expression as build-up of proteins would not be necessary and is also too slow for neural activities.

2. Suppose that the entanglement between neurons generated in this process is always negentropic as the interpretation as the idea about neural correlate for a conscious association suggests. One could also ask whether the neurons could entangled entropically and whether the entropic-inhibitory association could make sense. This does not lead to anything interesting and entropic entanglement between neurons should be regarded as a pathological condition. Note that neuron-neuron entanglemement would be naturally time-like and in this case only negentropic entanglement might be meaningful.

   1. To gain some perspective consider the activation of cell in general by some external perturbation from the resting state to the active state (here I have learned a lot from email correspondence with Vladimir Mateev) In the resting state the proteins inside cell are passive -or rather, forced to be passive- as one might expect on basis of the general vision about homeostasis. The unfolded proteins and unfolded portions of the folded proteins are connected by hydrogen bonds to ordered water so that the folding occurring otherwise spontaneously is prevented. One can say that the cellular winter prevails. The situation is however nearly critical and if external perturbation occurs cell liberates metabolic energy melting the ice and spring comes. Also the outer surfaces of globular proteins are hydrogen bonded and when the ordered water melts, spontaneous melting of the protein takes place leading to a partial unfolding.

      The resulting folded proteins and partially unfolded globular proteins interact by forming aggregates and this activity would naturally involve hbar reducing phase transitions and flux tube reconnections. In TGD based model the mechanism of both folding and melting would be the liberation of metabolic energy destroying the hydrogen bonds and the energy for this comes from the ATP containing positive energy negentropic bond between O=s of phosphates.

   2. Similar situation could prevail at the cell membrane. One can imagine that cell membrane is like a particle at the bottom of a small potential well. At the other side there is a deep well representing the generation of nerve pulse and at the other side a high wall corresponding to hyper-polarization requiring energy. Both polarization and hyperpolarization are prevented by the freezing of protein activities needed to induce them. The flux tubes connecting the presynaptic neuron and receptor and possibly genome are always negentropic and their formation can as such serve as the signal leading to the partial melting of the ordered water making possible to generate action leading to either depolarization or hyperpolarization. The signal could be just the additional metabolic energy making it possible for these transitions to occur.

   3. This picture does not require any communications from the receptor to the genome and in the simplest situation the resulting action could be seen as the analog of a reflex action. These communications could of course be present and the negentropic entanglement could make it easier to induce depolarization also now. Also the question whether excitatory-inhibitory dichotomy for the receptors has some deeper meaning apart from taking the neuron nearer to or farther from criticality for firing remains unanswered.

Bibliography

1. The chapter DNA as Topological Quantum Computer of "Genes and Memes".
2. E. R. Kandel, J. H. Schwartz, T. M. Jessel (1991), Principles of Neural Science. Prentice-Hall International Inc..
3. C. B. Pert (1997), Molecules of Emotion, Simon and Schuster Inc..
4. T. E. Creighton (1993), Proteins: Structures and Molecular Properties. W.H. Freeman and Company. New York.
5. Protein folding.

For background see the chapter TGD Inspired Model for Nerve Pulse.

EEG synchrony and negentropic entanglement

In the discussion related to the previous posting someone turned my attention to 40 Hz synchrony. If one accepts the vision about life as something in the intersection of real and p-adic worlds 40 Hz EEG synchrony can be interpreted as a correlate for the generation of negentropic entanglement between cortical neurons. Before proposing this interpretation let us first describe the experimental findings of a finnish neuroscientist Antti Revonsuo (see his article Binding and the Phenomenal Unity of Consciousness).

Findings

The interpretation for 40 Hz EEG frequency inspired by the binding hypothesis is as a synchronizing frequency necessary for the generation of unified percepts. This hypothesis has been studied using auto-stereograms. There was no detectable difference in the power spectrum at 36-44 Hz range in the situation when auto-stereogram was experienced as a set of random dots as compared to the situation when it was perceived as a coherent, symmetrical gestalt. The situation was same also in 8-13 Hz and 13-20 Hz beta bands.

On the other hand, when the conscious percept was transformed from a random set of points to a coherent gestalt, there was a detectable increase in 40 Hz power in the occipital and right posterior sites for EEG electrodes in a time window 300-500 ms before the unified percept was reported. There could be also some time lapse between the unified percept and the report about it but probably this cannot explain the entire lapse. No increase of power in beta bands was detected: this might be due to the fact that the widths of the measured bands are much wider than the widths ofthe narrow sub-bands reported masked by other EEG activity according to Nunez (Behavioral and Brain Sciences, 23, 2000). Note that in the model for a hierarchy of EEGs based on dark matter hierarchy beta band correspond to data communicated to the magnetic body (see this).

That the change in activity is associated with the emergence of a new percept suggests that the temporary increase of the EEG power could be assigned to the communications of the forming percept to the magnetic body.

Interpretation in terms of a generation of a negentropic entanglement

A fresh view about what really happens during 40 Hz synchrony came with the realization that negentropic entanglement is possible in the intersection of real and p-adic worlds. The generation of negentropic entanglement between two subselves means that the corresponding mental images are fused (see see this and this). The process is experienced by the fusing subselves as an expansion of consciousness whereas consciousness is lost when when bound state entanglement is generated. Also the meditative states begin with enchanged 40 Hz activity and interpretation would be same. Quite generally, the generation of negentropically entangled neuron groups could be a correlate for the emergence of a new idea or a new holistic pattern emerging from a chaos. Synchronous firing would be a natural correlate for the synergic state resulting in this manner. The paradoxical looking reduction of the oxiditative metabolism associated with 40 Hz firing could be seen as a signature of reduced dissipation when dissipating ensemble of neurons forms a single quantum coherent system.

What could then be the interpretation of the 300-500 ms time scale and synchronous firing in TGD framework?

1. If one assumes that only brain is involved, one must answer whether the new percept emerges after such a long time period. One would naively expect that negentropic entanglement immediately gives rise to the percept. Negentropic entanglement however means that a quantum superposition of several alternative percepts is involved. In the beginning the new percept is present with only small probability so that one would only know that the moment of heureka is quite near (this is indeed the experience that one has) and in the final situation it dominates but not completely since it requires conscious effort to preserve the percept.

2. Also magnetic body should be involved in TGD framework. The natural question is "Why this synchronous neuronal firing?". The natural answer would be that it allows to communicate the new percept as a consequence of a generation of negentropic entanglement to the magnetic body. The frequency scale of 40 Hz corresponds to a time scale of 25 milliseconds and corresponds to a length scale involved is about .75× 10⁷ m, a good candidate for the size of the part of the magnetic body involved. This time scale is much shorter than 300-500 seconds. If the layer of the magnetic body in question corresponds to the fundamental 100 millisecond time scale assignable to electron as is natural in case of sensory percepts, the time lapse could be essentially due to the communication. If one takes the time scale literally the value of Planck constant which is about 3 to 5 larger than its standard value would suggest itself. Of course, the development of the percept from a fuzzy inkling to the final heureka could involve several communication loops between brain and magnetic body so that the interpretation as a lapse due the slowness of communications need not be inconsistent with the first interpretation.

3. The time scale 300-500 ms could characterize the duration of negentropic entanglement but this is not necessarily the case since negentropic entanglement would be un-necessary after the percept has been represented symbolically so that one knows what is lurking behind the chaos.

The reported lower oxidative metabolism during the negentropic entanglement could be either due to the reduced dissipation due to the absence of dissipating neuronal selves or due the fact that magnetic body provides in this kind of situation the metabolic energy.

Negentropy Maximization Principle updated

Conscious existence is continual recreation of the Universe. My own humble contribution to this magnificent activity is endless updating of the chapters of the books about TGD. During this particular cascade of quantum jumps I updated the chapter Negentropy Maximization Principle of "TGD Inspired Theory of Consciousness" so that zero energy ontology and causal diamonds, hierarchy of Planck constants, and the vision about life as something in the intersection of real and p-adic worlds - which is nothing but number theoretical criticality- are taken into account from the beginning. I managed to build a vision about what it means mathematically to be in this intersection and what it means for U-matrix. I also found an expression for U-matrix as a collection of M-matrices so that these two matrices are not independent of each other as I had erratically thought. Unitarity of U states the orthogonality for the zero energy states defined by M-matrices. Very beautiful.

Number theory enters into game strongly: for instance, different algebraic extensions of rationals are regarded formally as quantum states and there is unitary dispersion in this space. Also the notion about leakage between different number fields at the level of partonic 2-surfaces leads to amplitudes expressible in terms of points of partonic 2-surface belonging to the algebraic extension of rationals. Kind of number theoretic QFT emerges naturally. For the first time I encountered really naturally infinite collection of commutative diagrams, which mathematicians have used since the days of Adam and Eve. We theoretical physicists are rather slow in our reactions. I attach the abstract of the updated chapter below.

In TGD Universe the moments of consciousness are associated with quantum jumps between quantum histories. The proposal is that the dynamics of consciousness is governed by Negentropy Maximization Principle, which states the information content of conscious experience is maximal. The formulation of NMP is the basic topic of this chapter.

Negentropy Maximization Principle (NMP) codes for the dynamics of standard state function reduction and states that the state function reduction process following U-process gives rise to a maximal reduction of entanglement entropy at each step. In the generic case this implies at each step a decomposition of the system to unique unentangled subsystems and the process repeats itself for these subsystems. The process stops when the resulting subsystem cannot be decomposed to a pair of free systems since energy conservation makes the reduction of entanglement kinematically impossible in the case of bound states. The natural assumption is that self loses consciousness when it entangles via bound state entanglement.

There is an important exception to this vision based on ordinary Shannon entropy. There exists an infinite hierarchy of number theoretical entropies making sense for rational or even algebraic entanglement probabilities. In this

case the entanglement negentropy can be negative so that NMP favors the generation of negentropic entanglement, which need not be bound state entanglement in standard sense. Negentropic entanglement might serve as a correlate for emotions like love and experience of understanding. The reduction of ordinary entanglement entropy to random final state implies second law at the level of ensemble. For the generation of negentropic entanglement the outcome of the reduction is not random: the prediction is that second law is not a universal truth holding true in all scales. Since number theoretic entropies are natural in the intersection of real and p-adic worlds, this suggests that life resides in this intersection. The existence effectively bound states with no binding energy might have important implications for the understanding the stability of basic bio-polymers and the key aspects of metabolism. A natural assumption is that self experiences expansion of consciousness as it entangles in this manner. Quite generally, an infinite self hierarchy with the entire Universe at the top is predicted.

The identification of life as a number theoretically critical phenomenon is also consistent with the idea that the transformation of intention to action corresponds to a U-process inducing leakage between different sectors. This leakage makes sense in the intersection where same mathematical expression defines both real and p-adic partonic 2-surfaces which are the fundamental objects in TGD framework. What these statements really mean requires a construction of number theoretical variant of quantum theory applying in the intersection of real and p-adic worlds.

Besides number theoretic negentropies there are also other new elements as compared to the earlier formulation of NMP. Zero energy ontology modifies dramatically the formulation of NMP since U-matrix acts between zero energy states and can be regarded as a collection of M-matrices, which generalize the ordinary S-matrix and define what might be called a complex square root of density matrix so that kind of a square root of thermodynamics at single particle level justifying also p-adic mass calculations based on p-adic thermodynamics is in question. The hierarchy of Planck constants is a further new element having important implications for conciousness and biology. Hyper-finite factors of type II₁ represent an additional technical complication requiring separate treatment of NMP taking into account finite measurement resolution realized in terms of inclusions of these factors.

NMP has important implications for thermodynamics. In particular, one must give up the standard view about second law and replace it with a formulation taking into accoung the hierarchy of causal diamonds assigned with zero energy ontology and dark matter hierarchy labeled partially by the values of Planck constants, as well as the effects due to negentropic entanglement. In particular, in the case of living matter breaking of second law in standard sense is expected to take place and be crucial for the understanding of evolution. Self hierarchy having the hierarchy of causal diamonds as imbedding space correlate leads naturally to a thermodynamical description of the contents of consciousness and quantum jumps is very much analogous to quantum computation. This leads to a vision about the role of bound state entanglement and negentropic entanglement in the generation of sensory qualia. Negentropic entanglement leads to a vision about cognition. Negentropically entangled state consisting of a superposition of pairs can be interpreted as a conscious abstraction or rule: negentropically entangled Schrödinger cat knows that it is better to keep the bottle closed. A connection with fuzzy qubits and quantum groups with negentropic entanglement is highly suggestive. The implications are highly non-trivial also for quantum computation, which allows three different variants in TGD context. The negentropic variant would correspond to conscious quantum computation like process.

Magnetic flux tubes and ocean bacteria as super-organism

Again new evidence for the role of magnetic flux tubes in living matter (I am grateful for the link to Mark McWilliams)! Now as potential carriers of oxygen making the population of sea bacteria act as a super-organism. See the New Scientist article The real Avatar: ocean bacteria act as 'superorganism'.

Could high energy phosphate bond be negentropic bond with negative binding energy?

Most people assign the word "love" to the word "life" as their first association. There is a notable exception to this: scientists including biologists. Un-educated layman might however wonder whether one can understand life without identifying any physical counterpart for this notion (, which could be replaced with that of compassion, sex, or ability to act synergetically or just X if some of these notions sounds less un-scientific). Certainly the word "love" stimulates a deep feeling of disgust in a reductionistically conditioned scientist. But isn't the duty of scientist to win this kind of feelings and try to see whether this identification might be possible after all? The prize could be high: the understanding of what distinguishes between living and dead matter could change the entire culture. Who knows, maybe it could be possible to identify some poorly understood fundamental biological process allowing a quantitative model using a guess for what this physical correlate could be. The basic step of metabolism is at the core of life and indeed poorly understood, and I shall argue that the identification of the negentropic entanglement as the counterpart for the notion of love could allow to model quantititatively what happens in this process.

Before continuing general motivating comments about implications of negentropic entanglement are in order.

1. Ordinary bound states are stable because they have positive binding energy. One can visualize this kind of binding as a jail: the second particle resides near the bottom of a potential well. Organized marriage is a social analogy for this situation. Negentropic entanglement makes possible bound states for which binding energy can have and perhaps even has always a wrong sign. The state is not prevented from decaying to free particles in state function reduction by energy conservation: Negentropy Maximization Principle (NMP) takes care that they remain correlated. The social analogy would be a voluntary marriage based on love. Partners are competely free to leave but want to stay together.

   One implication could be explanation for the stability of highly charged basic molecules of life such as DNA and ATP.

2. The presence of the negentropic entanglement implies the directedness of the biological processes since the outcome of the state function reduction would be far from random since the behavior of negentropic bonds could be almost deterministic. In the case of time-like entanglement this would select only particular initial final state pairs so that determinism would emerge also in this sense and could lead to almost deterministic irreversible cellular automaton behavior characteristic for the living matter very different from the reversible determinism of classical physics and very difficult to understand in quantum context.

3. The determinism would of course be only partial and would allow volition not spoiled by randomness of quantum jump. This would provide a general explanation for the ability of the living matter to overcome the second law basically implied by quantum randomness predicted by the standard quantum theory. This would happen in time scales shorter than the time scale of the appropriate causal diamond (CD) only but one would have hierarchy of CD meaning that in arbitrary long time scales there are levels of hierarchy at which second law is broken. The hierarchy of Planck constants would be also crucial since it would allow zooming up to arbitrarily long time scale. Non-equilibrium thermodynamics and cellular automaton models could be seen as phenomenological descriptions for the actual breaking of second law in the intersection of real and p-adic worlds.

I do not bother to do the painful transformation of the the tex file to html so that the reader interested in details can just click the six page article Could high energy phosphate bond be negentropic bond with negative binding energy?.