Saturday, November 28, 2015

Could leptoquarks be squarks in TGD sense?

The basic problem of TGD inspired SUSY has been the lack of experimental information allowing to guess what might be the p-adic length scale associated with sparticles. The massivation as such is not a problem in TGD: the same mass formula would be obeyed by particles and sparticles and SUSY breaking would mean only different p-adic mass scales for stable particle states. One can even consider the possibility that particles and sparticles have identical masses but sparticles have non-standard value of heff behaving therefore like dark matter.

The solution of the problem could emerge from experiments in totally unexpected manner. Indications for the existence of leptoquarks have been accumulating gradually from LHC. Leptoquarks should have same quantum numbers as pairs of quark and right-handed neutrino and would thus correspond to squarks in N=2 SUSY of TGD.

Both Jester and Lubos have written about leptoquarks. Jester lists 3 B-meson potential anomalies, which leptoquarks could resolve :

  • A few sigma deviation in differential distribution of B → K*μ+- decays.

  • 2.6 sigma violation of lepton flavor universality in B → Dμ+μ- vs. K→ D e+e- decays.

  • 3.5 sigma violation of lepton flavor universality, but this time in B → Dτν vs. B → Dμν decays.
There is also a 3 sigma discrepancy of the experimentally measured muon magnetic moment, one of the victories of QED. One explanation has been in terms of SUSY, and I have also considered explanation in terms of N=2 SUSY strongly suggested by TGD. It has been is claimed that leptoquark with quantum numbers of D νR, where D denotes D type quark - actually s quark, which in TGD framework corresponds to genus g=1 for the corresponding partonic 2-surface - could explain all these anomalies.

TGD allows to consider two explanations for the observed breaking of leptonic universality in induced by quark self energy diagrams involving emission of virtual W- boson decaying normally to lepton pair.

The breaking of lepton universality for charged lepton pair production would be following. Penguin diagram involving self energy loop for b quark is involved. b quark transforms to t quark by emitting virtual W decaying to charged lepton and antineutrino. Antineutrino decays to leptoquark and s quark (say) and leptoquark fuses with top quark to charged antilepton. Charged lepton pairs is obtained and the presence of CKM matrix elements implies breaking of universality. Breaking of universality becomes possible also in the production of lepton-neutrino pairs. This option is discussed in an article and also in blog posting .

TGD allows also an alternative mechanism based on the (almost-)predicted existence of higher gauge boson generations, whose charged matrices are orthogonal to those of ordinary gauge bosons with charge matrix which in the 3-D state space associated with three families is unit matrix for the ordinary gauge bosons. For higher generations the charge matrices must break universality by orthogonality condition. Hence emission of virtual gauge boson of higher generation would explain the breaking of universality. For more details see the article and blog posting .

But what about TGD based SUSY, which should have N=2 and should be generated by adding right-handed neutrino or antineutrino to particle state assignable to a pair of wormhole contacts and basically to single wormhole throat as fermion line? Is there any hope that the p-adic mass scale corresponds to either k=89 (Mersenne) or more plausibly k=79 (Gaussian Mersenne)?

An interesting possibility is that light leptoquarks (using CP2 mass scale as unit) actually consist of quark and right-handed neutrino apart from possible mixing with left-handed antineutrino, whose addition to the one-particle state generates broken N=2 supersymmetry in TGD. The model for the breaking of universality is consistent with this interpretation since leptoquark is assumed to be scalar (squark!) and to consist of right-handed neutrino and quark. This would resolve the long-standing issue about the p-adic mass scale of sparticles in TGD. SUSY would be there - not N=1 SUSY of standard unifiers but N=2 SUSY of TGD reducing to CP2 geometry. I have made also other proposals - in particular the idea that sparticles could have same p-adic mass scales as particles but appear only as dark in TGD sense- that is having non-standard value of Planck constant.

It must be made clear that TGD SUSY differs radically from standard N=1 SUSY. For instance, lepton and baryon numbers are separately conserved and both fermion number 2 and 0 sparticles (in particular lepton number two particles) are predicted. The recipe for building sparticles by adding right-handed neutrinos distinguishes TGD SUSY in a unique manner from the other variants of SUSY and the direct observation of the leptoquarks is THE signature kills entire classes of competing theories leaving - as it seems - only TGD in the battlefield!

With a lot of good luck both mechanisms are involved and leptoquarks are squarks in TGD sense. If also M89 and M79 hadron make themselves visible at LCH (there are several pieces of evidence for this), a breakthrough of TGD would be unavoidable. Or is it too optimistic to hope that the power of truth could overcome academic stupidity, which is after all the strongest force of Nature?

For background see the article Leptoquarks as first piece of evidence for TGD based view about SUSY? and chapters SUSY in TGD Universe and New Particle Physics Predicted by TGD: Part I of "p-Adic Physics".

For a summary of earlier postings see Links to the latest progress in TGD.

Thursday, November 26, 2015

Why the non-trivial zeros of Riemann zeta should reside at critical line?

Riemann Hypothess (RH) states that the non-trivial (critical) zeros of zeta lie at critical line s=1/2. It would be interesting to know how many physical justifications for why this should be the case has been proposed during years. Probably this number is finite, but very large it certainly is. In Zero Energy Ontology (ZEO) forming one of the cornerstones of the ontology of quantum TGD, the following justification emerges naturally. I represented it in the answer to previous posting, but there was stupid error in the answer so that I represent the corrected argument here.

  1. The "World of Classical Worlds" (WCW) consisting of space-time surfaces having ends at the boundaries of causal diamond (CD), the intersection of future and past directed light-cones times CP2 (recall that CDs form a fractal hierarchy). WCW thus decomposes to sub-WCWs and conscious experience for the self associated with CD is only about space-time surfaces in the interior of CD: this is a trong restriction to epistemology, would philosopher say.

    Also the light-like orbits of the partonic 2-surfaces define boundary like entities but as surfaces at which the signature of the induced metric changes from Euclidian to Minkowskian. By holography either kinds of 3-surfaces can be taken as basic objects, and if one accepts strong form of holography, partonic 2-surfaces defined by their intersections plus string world sheets become the basic entities.

  2. One must construct tangent space basis for WCW if one wants to define WCW Kähler metric and gamma matrices. Tangent space consists of allowed deformations of 3-surfaces at the ends of space-time surface at boundaries of CD, and also at light-like parton orbits extended by field equations to deformations of the entire space-time surface. By strong form of holography only very few deformations are allowed since they must respect the vanishing of the elements of a sub-algebra of the classical symplectic charges isomorphic with the entire algebra. One has almost 2-dimensionality: most deformations lead outside WCW and have zero norm in WCW metric.

  3. One can express the deformations of the space-like 3-surface at the ends of space-time using a suitable function basis. For CP2 degrees of freedom color partial waves with well defined color quantum numbers are natural. For light-cone boundary S2× R+, where R+ corresponds to the light-like radial coordinate, spherical harmonics with well defined spin are natural choice for S2 and for R+ analogs of plane waves are natural. By scaling invariance in the light-like radial direction they look like plane waves ψs(r)= rs= exp(us), u=log(r/r0), s= x+iy. Clearly, u is the natural coordinate since it replaces R+ with R natural for ordinary plane waves.

  4. One can understand why Re[s]=1/2 is the only possible option by using a simple argument. One has super-symplectic symmetry and conformal invariance extended from 2-D Riemann surface to metrically 2-dimensional light-cone boundary. The natural scaling invariant integration measure defining inner product for plane waves in R+ is
    du= dr/r =dlog(r/r0) with u varying from -∞ to +∞ so that R+ is effectively replaced with R. The inner product must be same as for the ordinary plane waves and indeed is for ψs(r) with s=1/2+iy since the inner product reads as

    ⟨ s1,s2⟩ == ∫0 (ψ*s1) ψs2dr= ∫0 exp(i(y1-y2)r-x1-x2 dr .

    For x1+x2=1 one obtains standard delta function normalization for ordinary plane waves:

    ⟨s1,s2⟩ = ∫-∞+∞exp[i(y1-y2)u] du∝ δ (y1-y2) .

    If one requires that this holds true for all pairs (s1,s2), one obtains xi=1/2 for all si. Preferred extremal condition gives extremely powerful additional constraints and leads to a quantisation of s=-x-iy: the first guess is that non-trivial zeros of zeta are obtained: s=1/2+iy. This identification would be natural by generalised conformal invariance. Thus RH is physically extremely well motivated but this of course does not prove it.

  5. The presence of the real part Re[s]=1/2 in eigenvalues of scaling operator apparently breaks hermiticity of the scaling operator. There is however a compensating breaking of hermiticity coming from the fact that real axis is replaced with half-line and origin is pathological. What happens that real part 1/2 effectively replaces half-line with real axis and obtains standard plane wave basis. The integration measure becomes scaling invariant - something very essential for the representations of super-symplectic algebra. For Re[s]=1/2 the hermicity conditions for the scaling generator rd/dr in R+ for s=1/2+iy reduce to those for the translation generator d/du in R but with Re[s] dropped away.

This relates also to the number theoretical universality and mathematical existence of WCW in an interesting manner.
  1. If one assumes that p-adic primes p correspond to zeros s=1/2+y of zeta in 1-1 manner in the sense that piy(p) is root of unity existing in all number fields (algebraic extension of p-adics) one obtains that the plane wave exists for p at points r= pn. p-Adically wave function is discretized to a delta function distribution concentrated at (r/r0)= pn- a logarithmic lattice. This can be seen as space-time correlate for p-adicity for light-like momenta to be distinguished from that for massive states where length scales come as powers of p1/2. Something very similar is obtained from the Fourier transform of the distribution of zeros at critical line (Dyson's argument), which led to a the TGD inspired vision about number theoretical universality .

  2. My article Strategy for Proving Riemann Hypothesis (for a slightly improved version see this written for 12 years ago relies on coherent states instead of eigenstates of Hamiltonian. The above approach in turn absorbs the problematic 1/2 to the integration measure at light cone boundary and conformal invariance is also now central.

  3. Quite generally, I believe that conformal invariance in the extended form applying at metrically 2-D light-cone boundary (and at light-like orbits of partonic 2-surfaces) could be central for understanding why physics requires RH and maybe even for proving RH assuming it is provable at all in existing standard axiomatic system. For instance, the number of generating elements of the extended supersymplectic algebra is infinite (rather than finite as for ordinary conformal algebras) and generators are labelled by conformal weights defined by zeros of zeta (perhaps also the trivial conformal weights). s=1/2+iy guarantees that the real parts of conformal weights for all states are integers. By conformal confinement the sum of ys vanishes for physical states. If some weight is not at critical line the situation changes. One obtains as net conformal weights all multiples of x shifted by all half odd integer values. And of course, the realisation as plane waves at boundary of light-cone fails and the resulting loss of unitary makes things too pathological and the mathematical existence of WCW is threatened.

  4. The existence of non-trivial zeros outside the critical line could thus spole the representations of super-symplectic algebra and destroy WCW geometry. RH would be crucial for the mathematical existence of the physical world! And physical worlds exist only as mathematical objects in TGD based ontology: there are no physical realities behind the mathematical objects (WCW spinor fields) representing the quantum states. TGD inspired theory of consciousness tells that quantum jumps between the zero energy states give rise to conscious experience, and this is in principle all that is needed to understand what we experience.
See the chapter Number Theoretical Vision or the article Why the non-trivial zeros of Riemann zeta should reside at critical line?.

For a summary of earlier postings see Links to the latest progress in TGD.

Wednesday, November 18, 2015

Does Riemann Zeta Code for Generic Coupling Constant Evolution?

Understanding of coupling constant evolution and predicting it is one of the greatest challenges of TGD. During years I have made several attempts to understand coupling evolution.

  1. The first idea dates back to the discovery of WCW Kähler geometry defined by Kähler function defined by Kähler action (this happened around 1990) (see this). The only free parameter of the theory is Kähler coupling strength αK analogous to temperature parameter αK postulated to be is analogous to critical temperature. Whether only single value or entire spectrum of of values αK is possible, remained an open question.

    About decade ago I realized that Kähler action is complex receiving a real contribution from space-time regions of Euclidian signature of metric and imaginary contribution from the Minkoswkian regions. Euclidian region would give Kähler function and Minkowskian regions analog of QFT action of path integral approach defining also Morse function. Zero energy ontology (ZEO) (see this) led to the interpretation of quantum TGD as complex square root of thermodynamics so that the vacuum functional as exponent of Kähler action could be identified as a complex square root of the ordinary partition function. Kähler function would correspond to the real contribution Kähler action from Euclidian space-time regions. This led to ask whether also Kähler coupling strength might be complex: in analogy with the complexification of gauge coupling strength in theories allowing magnetic monopoles. Complex αK could allow to explain CP breaking. I proposed that instanton term also reducing to Chern-Simons term could be behind CP breaking

  2. p-Adic mass calculations for 2 decades ago (see this) inspired the idea that length scale evolution is discretized so that the real version of p-adic coupling constant would have discrete set of values labelled by p-adic primes. The simple working hypothesis was that Kähler coupling strength is renormalization group (RG) invariant and only the weak and color coupling strengths depend on the p-adic length scale. The alternative ad hoc hypothesis considered was that gravitational constant is RG invariant. I made several number theoretically motivated ad hoc guesses about coupling constant evolution, in particular a guess for the formula for gravitational coupling in terms of Kähler coupling strength, action for CP2 type vacuum extremal, p-adic length scale as dimensional quantity (see this). Needless to say these attempts were premature and a hoc.

  3. The vision about hierarchy of Planck constants heff=n× h and the connection heff= hgr= GMm/v0, where v0<c=1 has dimensions of velocity (see this>) forced to consider very seriously the hypothesis that Kähler coupling strength has a spectrum of values in one-one correspondence with p-adic length scales. A separate coupling constant evolution associated with heff induced by αK∝ 1/hbareff ∝ 1/n looks natural and was motivated by the idea that Nature is theoretician friendly: when the situation becomes non-perturbative, Mother Nature comes in rescue and an heff increasing phase transition makes the situation perturbative again.

    Quite recently the number theoretic interpretation of coupling constant evolution (see this> or this in terms of a hierarchy of algebraic extensions of rational numbers inducing those of p-adic number fields encouraged to think that 1/αK has spectrum labelled by primes and values of heff. Two coupling constant evolutions suggest themselves: they could be assigned to length scales and angles which are in p-adic sectors necessarily discretized and describable using only algebraic extensions involve roots of unity replacing angles with discrete phases.

  4. Few years ago the relationship of TGD and GRT was finally understood (see this>) . GRT space-time is obtained as an approximation as the sheets of the many-sheeted space-time of TGD are replaced with single region of space-time. The gravitational and gauge potential of sheets add together so that linear superposition corresponds to set theoretic union geometrically. This forced to consider the possibility that gauge coupling evolution takes place only at the level of the QFT approximation and αK has only single value. This is nice but if true, one does not have much to say about the evolution of gauge coupling strengths.

  5. The analogy of Riemann zeta function with the partition function of complex square root of thermodynamics suggests that the zeros of zeta have interpretation as inverses of complex temperatures s=1/β. Also 1/αK is analogous to temperature. This led to a radical idea to be discussed in detail in the sequel.

    Could the spectrum of 1/αK reduce to that for the zeros of Riemann zeta or - more plausibly - to the spectrum of poles of fermionic zeta ζF(ks)= ζ(ks)/ζ(2ks) giving for k=1/2 poles as zeros of zeta and as point s=2? ζF is motivated by the fact that fermions are the only fundamental particles in TGD and by the fact that poles of the partition function are naturally associated with quantum criticality whereas the vanishing of ζ and varying sign allow no natural physical interpretation.

    The poles of ζF(s/2) define the spectrum of 1/αK and correspond to zeros of ζ(s) and to the pole of ζ(s/2) at s=2. The trivial poles for s=2n, n=1,2,.. correspond naturally to the values of 1/αK for different values of heff=n× h with n even integer. Complex poles would correspond to ordinary QFT coupling constant evolution. The zeros of zeta in increasing order would correspond to p-adic primes in increasing order and UV limit to smallest value of poles at critical line. One can distinguish the pole s=2 as extreme UV limit at which QFT approximation fails totally. CP2 length scale indeed corresponds to GUT scale.

  6. One can test this hypothesis. 1/αK corresponds to the electroweak U(1) coupling strength so that the identification 1/αK= 1/αU(1) makes sense. One also knows a lot about the evolutions of 1/αU(1) and of electromagnetic coupling strength 1/αem= 1/[cos2WU(1). What does this predict?

    It turns out that at p-adic length scale k=131 (p≈ 2k by p-adic length scale hypothesis, which now can be understood number theoretically (see this ) fine structure constant is predicted with .7 per cent accuracy if Weinberg angle is assumed to have its value at atomic scale! It is difficult to believe that this could be a mere accident because also the prediction evolution of αU(1) is correct qualitatively. Note however that for k=127 labelling electron one can reproduce fine structure constant with Weinberg angle deviating about 10 per cent from the measured value of Weinberg angle. Both models will be considered.

  7. What about the evolution of weak, color and gravitational coupling strengths? Quantum criticality suggests that the evolution of these couplings strengths is universal and independent of the details of the dynamics. Since one must be able to compare various evolutions and combine them together, the only possibility seems to be that the spectra of gauge coupling strengths are given by the poles of ζF(w) but with argument w=w(s) obtained by a global conformal transformation of upper half plane - that is Möbius transformation (see this) with real coefficients (element of GL(2,R)) so that one as ζF((as+b)/(cs+d)). Rather general arguments force it to be and element of GL(2,Q), GL(2,Z) or maybe even SL(2,Z) (ad-bc=1) satisfying additional constraints. Since TGD predicts several scaled variants of weak and color interactions, these copies could be perhaps parameterized by some elements of SL(2,Z) and by a scaling factor K.

    Could one understand the general qualitative features of color and weak coupling contant evolutions from the properties of corresponding Möbius transformation? At the critical line there can be no poles or zeros but could asymptotic freedom be assigned with a pole of cs+d and color confinement with the zero of as+b at real axes? Pole makes sense only if Kähler action for the preferred extremal vanishes. Vanishing can occur and does so for massless extremals characterizing conformally invariant phase. For zero of as+b vacuum function would be equal to one unless Kähler action is allowed to be infinite: does this make sense?. One can however hope that the values of parameters allow to distinguish between weak and color interactions. It is certainly possible to get an idea about the values of the parameters of the transformation and one ends up with a general model predicting the entire electroweak coupling constant evolution successfully.

To sum up, the big idea is the identification of the spectra of coupling constant strengths as poles of ζF((as+b/)(cs+d)) identified as a complex square root of partition function with motivation coming from ZEO, quantum criticality, and super-conformal symmetry; the discretization of the RG flow made possible by the p-adic length scale hypothesis p≈ kk, k prime; and the assignment of complex zeros of ζ with p-adic primes in increasing order. These assumptions reduce the coupling constant evolution to four real rational or integer valued parameters (a,b,c,d). One can say that one of the greatest challenges of TGD has been overcome.

For details see the article Does Riemann Zeta Code for Generic Coupling Constant Evolution?.

For a summary of earlier postings see Links to the latest progress in TGD.

Wednesday, November 04, 2015

About Fermi-Dirac and Bose-Einstein statistics, negentropic entanglement, Hawking radiation, and firewall paradox in TGD framework

In quantum field theories (QFTs) defined in 4-D Minkowski space spin statistics theorem forces spin statistics connection: fermions/bosons with half-odd integer/integer spin correspond to totally antisymmetric/symmetric states. TGD is not a QFT and one is forced to challenge the basic assumptions of 4-D Minkowskian QFT.

  1. In TGD framework the fundamental reason for the fermionic statistics are anticommutation relations for the gamma matrices of the "World of Classical Worlds" (WCW). This naturally gives rise to geometrization of the anticommutation relations of induced spinor fields at space-time surfaces. The only fundamental fields are second quantized space-time spinors, which implies that the statistics of bosonic states is induced from the fermionic one since they can be regarded as many-fermion states. At WCW level spinor fields are formally classical.

    Strong form of holography (SH) forced by strong form of General Coordinate Invariance (SGCI) implies that induced spinor fields are localized at string world sheets. 2-dimensionality of the basic objects (string world sheets and partonic 2-surfaces inside space-time surfaces) makes possible braid statistics, which is more complex than the ordinary one. The phase corresponding to 2π rotation is not +/-1 but a root of unitary and the phase can be even replaced with non-commuting analog of phase factor.

    What about the ordinary statistics of QFTs expected to hold true at the level of imbedding space H =M4× CP2? Can one deduce it from the q-variants of anticommutation relations for fermionic oscillator operators - perhaps by a suitable transformation of oscillator operators? Is the Fermi/Bose statistics at imbedding space level an exact notion or does it emerge only at the QFT limit when many-sheeted space-time sheets are lumped together and approximated as a slightly curved region of empty Minkowski space?

  2. Zero energy ontology (ZEO) means that physical systems are replaced by pairs of positive and negative energy states defined at the opposite boundaries of causal diamond (CD). CDs form a fractal hierarchy. Does this mean that the usual statistics must be restricted to coherence regions defined by CDs rather than assume it in entire H? This assumption looks reasonable since it would allow to milden the rather paradoxical looking implications of statistics and quantum identify for particles.

Interesting questions relate to the notion of negentropic entanglement (NE).

  1. Two states are negentropically entangled if their density matrix is proportional to a projection operator and thus proportional to unit matrix. This require also algebraic entanglement coefficients. For bipartite entanglement this is guaranteed if the entanglement coefficients form a matrix proportional a unitary matrix. The so called quantum monogamy theorem (see ) has a highly non-trivial implication for NE. In its mildest form it states that if two entangled systems are in a 2-particle state which is pure, the entire system must be de-entangled from the rest of the Universe. As a special case this applies to NE. A stronger form of monogamy states that two maximally entangled qubits cannot have entanglement with a third system. It is essential that one has qubits. For 3-valued color one can have maximal entanglement for 3-particle states (baryons). For instance, the negentropic entanglement associated with N identical fermions is maximal for subsystems in the sense that density matrix is proportional to a projection operator.

    Quantum monogamy could be highly relevant for the understanding of living matter. Biology is full of binary structures (DNA double strand, lipid bi-layer of cell membrane, epithelial cell layers, left and right parts of various brain nuclei and hemispheres, right and left body parts, married couples,... ). Could given binary structure correspond at some level to a negentropically entangled pure state and could the system at this level be conscious? Could the loss of consciousness accompany the formation of a system consisting of a larger number of negentropically entangled systems so that 2-particle system ceases to be pure state and is replaced by a larger pure state. Could something like this take place during sleep?

  2. NE seems to relate also to the statistics. Totally antisymmetric many-particle states with permutations of states in tensor product regarded as different states can be regarded as negentropically entangled for any subsystem since the density matrix is projection operator. Here one could of course argue that the configuration space must be divided by the permutation group of n objects so that permutations do not represent different states. It is difficult to decide which interpretation is correct so that let us considere the first interpretation.

    The traced out states for subsystems of many-fermion state are not pure. Could fermionic statistics emerge at imbedding space-level from the braid statistics for fundamental fermions and Negentropy Maximization Principle (NMP) favoring the generation of NE? Could CD be identified as a region inside which the statistics has emerged? Are also more general forms of NE possible and assignable to more general representations of permutation group? Could ordinary fermions and bosons be also in states for which entanglement is not negentropic and does not have special symmetry properties? Quantum monogamy plus purity of the state of conscious system demands decomposition into de-entangled sub-systems - could one identify them as CDs? Does this demand that the entanglement due to statistics is present only inside CDs/selves?

  3. At space-time level space-time sheets (or space-like 3-surfaces or partonic 2-surfaces and string world sheets by SH) serve as natural candidates for conscious entities at space-time level. At imbedding space level elementary particles associated with various space-time sheets inside given CD would contain elementary particles having NE forced by statistics. But doesn't this imply that space-time sheets cannot define separate conscious entities?

    The notion of finite resolution for quantum measurement, cognition, and consciousness suggests a manner to circumvent this conclusion. One has entanglement hierarchies assignable to the length scale hierarchies defined by p-adic length scales, hierarchy of Planck constants and hierarchy of CDs. Entanglement is defined in given resolution and the key prediction is that two systems unentangled in given resolution can be entangled in an improved resolution. The space-time correlate for this kind of situation are space-time sheets, which are disjoint in given resolution but contain topologically condensed smaller space-time sheets connected by thin flux tubes serving as correlates for entanglement.

    The paradoxical looking prediction is that at a given level of hierarchy characterized by size scale for CD or space-time surface two systems can be un-entangled although their subsystems are entangled. This is impossible in standard quantum theory. If the sharing of mental images by NE between subselves of separate selves makes sense, contents of consciousness are not completely private as often assumed in theories about consciousness. For instance, stereo vision could rely on fusion and sharing of visual mental images assignable to left and right brain hemispheres and generalizes to the notion of stereo consciousness making to consider the possibility of shared collective consciousness. An interpretation suggesting itself is that selves correspond to space-time sheets and collective levels of consciousness to CDs.

    Encouragingly, dark elementary particles would provide a basic example about sharing of mental images. Dark variants of elementary particles could be negentropically entangled by statistics condition in macroscopic scales and form part of a kind of stereo consciousness, kind of pool of fundamental mental images shared by conscious entities. This could explain why for instance the secondary p-adic time scale for electron equal to T= .1 seconds corresponds to a fundamental biorhythm.

  4. Quantum monogamy relates also to the firewall problem of blackhole physics.

  5. There are two entanglements involved. There is entanglement between Alice entering the blackhole and Bob remaining outside it. There is also the entanglement between blackhole and Hawking radiation implied if Hawking radiation is only apparently thermal radiation and blackhole plus radiation defines a pure quantum state. If so, Hawking evaporation does not lead to a loss of information. In this picture blackhole and Hawking radiation are assumed to form a single pure system.

    Since Alice enters blackhole (or its boundary), one can identify Alice as part of the modified blackhole being entangled with the original blackhole and forming a pure state. Thus Alice would form an entangled pure quantum state with both Bob and Hawking blackhole. This in conflict with quantum monogamy. The assumption that Alice and blackhole are un-entangled does not look reasonable. But why Alice, Bob and blackhole could not form pure entangled 3-particle state or belong to a larger entangled state?

    In TGD framework the firewall problem seems to be mostly due to the use of poorly defined terms. The first poorly defined notion is blackhole as a singularity of GRT. In TGD framework the analog for the interiors of the blackhole are space-time regions with Euclidian signature of induced metric and accompany all physical systems. Second poorly defined notion is that of information. In TGD framework one can define a measure for conscious information using p-adic mathematics and it is non-vanishing for NE. This information characterizes always two-particle system - either as a pure system or part of a larger system. Thermodynamical negentropy characterizes single particle in ensemble so that the two notions are not equivalent albeit closely related. Further, in the case of blackhole one cannot speak of information going down to blackhole with Alice since information is associated with a pair formed by Alice and some other system outside blackhole like objects or perhaps at its surface. Finally, the notion is hierarchy of Planck constants allows NE in even astrophysical scales. Therefore entangling Bob, Alice, and TGD counterpart of blackhole is not a problem. Hence the firewall paradox seems to dissolve.

  6. The hierarchy of Planck constants heff=n×h connects also with dark quantum gravity via the identification heff= hgr, where hgr= GMm/v0, v0/c≤ 1, is gravitational Planck Planck constant. v0/c< 1 is velocity parameter characterizing system formed by the central mass M and small mass m, say elementary particle.

    This allows to generalize the notion of Hawking radiation (see this, this, and this ), and one can speak about dark variant of Hawking radiation and assign it with any material object rather than only blackhole. The generalized Hawking temperature is proportional to the mass m of the particle at the gravitational flux tubes of the central object and to the ratio RS/R of the Schwartschild radius RS and radius R for the central object. Amazingly, the Hawking temperature for solar Hawking radiation in the case of proton corresponds to physiological temperature. This finding conforms with the vision that bio-photons result from dark photons with heff= hgr. Dark Hawking radiation could be very relevant for living matter in TGD Universe!

    Even more (see this
    and this) , one ends up via SH to suggest that the Hawking temperature equals to the Hagedorn temperature assignable to flux tubes regarded as string like objects! This assumption fixes the value of string tension and is highly relevant for living matter in TGD Universe since it guarantees that subsystems can become time-reversed with high probability in state function reduction. The frequent occurrence of time reversed mental images makes possible long term memory and planned action and one ends up with thermodynamics of consciousness. This is actually not new: living systems are able to defy second law and the notion of syntropy was introduced long time ago by Fantappie.

  7. Does one get rid of firewall paradox in TGD Universe? It is difficult answer the question since it is not at all clear that there exists any paradox anymore. For instance, the assumption that blackhole represents pure state looks in TGD framework rather ad hoc and the NE between blackhole and other systems outside it looks rather natural if one accepts the hierarchy of Planck constants.

    It would however seems to me that the TGD analog of dark Hawking radiation along flux tubes is quite essential for communications and even more, for what it is to be Alice and Bob and even for their existence! The flux tube connections of living systems to central star and planets could be an essential part of what it is to be alive as I have already earlier suggested with the inspiration coming from heff= hgr. In this framework biology and astrophysics would meet in highly non-trivial manner.

See the article About statistics, negentropic entanglement, Hawking radiation, and firewall paradox in TGD framework.

For a summary of earlier postings see Links to the latest progress in TGD.

Thursday, October 22, 2015

Could one apply the thermodynamical approach of England in TGD framework?

It turns out possible to gain amazing additional insights about TGD inspired view of life and consciousness by generalizing England's approach discussed in previous posting. Several puzzling co-incidences find an explanation in the thermodynamical framework and the vision about solar system as a living quantum coherent entity gains additional support.

  1. The situation considered in England's approach is a system - say biomolecule - in heat bath so that energy is not conserved due the transfer of energy between reactants and heat bath.

  2. The basic equation is equilibrium condition for the reaction i→ f and its time reversal f*→ i*. The initial and final state can be almost anything allowing thermodynamical treatment: states of biomolecule or even gene and its mutation. The ratio of the rates for the reaction and its time reversal is given by the ratio of the Boltzmann weights in thermal equilibrium:

    R(i→ f)/R(f*→ i*)= R , R= e-(Ei-Ef)/T .

    Ei and Ef denote the energies of initial and final state. This formula is claimed to hold true even in non-equilibrium thermodynamics. It is important that the ratio of the rates does not depend at all on various coupling constant parameters. The equilibrium condition must be modified if initial and final states are fermions but it is assumed that states can be described as bosons. Note that in heat bath even fermion number need not be conserved.

  3. If the energy eigenstates are degenerate, the ratio R of Boltzman factors must be modified to include the ratio of state degeneracies

    R→ (D(Ei)/D(Ef) × e-(Ei-Ef)/T .

    This generalization is essential in the sequel.

    One can imagine two possible reasons for the presence of exponentially large factors compensating Boltzmann weights D(Ei). The first reason is that for heff=n× h the presence of n-fold degeneracy due to the n-fold covering of space-time surface reducing to 1-fold covering at its ends at the ends of CD is essential. Second possible reason is that the basic object are magnetic flux tubes modellable as strings with exponentially increasing density of states. These mechanisms could quite well be one and same.

Consider now the basic idea inspired by this formula in TGD framework.
  1. Since magnetic flux tubes are key entities in TGD inspired quantum biology, stringy dynamics suggests itself strongly. The situation thus differs dramatically from the standard biochemical situation because of the presence of dark matter at magnetic flux tubes to which one can assign fermion carrying strings connecting partonic 2-surfaces defining correlates for particles in very general sense.

  2. The key aspect of stringy dynamics is Hagedorn temperature. Slightly below Hagedorn temperature the density of states factor, which increases exponentially, compensates for the Boltzmann factor. Hagedorn temperature is given by

    THag = (61/2/2π) × (1/α')1/2 ,

    where α' is string tension. In superstring models the value of string tension is huge but in TGD framework the situation is different. As a matter fact, the temperature can be rather small and even in the range of physiological temperatures.

  3. What makes THag so special is that in the equilibrium condition reaction and its reversal can have nearly the same rates. This could have profound consequences for life and even more - make it possible.

    In ZEO based quantum measurement theory and theory of consciousness time reversal indeed plays key role: self dies in state function reduction to the opposite boundary of CD and experiences re-incarnation as a time-reversed self. This process is essential element of memory, intentional action, and also remote metabolism, which all rely on negative energy signals travelling to geometric past assignable to time reversed sub-selves (mental images). The above formula suggests that intelligent life emerges near THag, where the time reversed selves are generated with high rate so that system remembers and pre-cognizes geometric future as it sleeps so that memory planned action are possible.

  4. String tension cannot be determined by Planck length as in string models if it is to be important in biology. This is indeed the case in TGD based quantum gravity. The gravitational interaction between partonic 2-surfaces is mediated by fermionic strings connecting them. If string tension were determined by Planck length, only gravitational bound states of size of order Planck length would be possible. The solution of the problem is that the string tension for gravitational flux tubes behaves like 1/heff2.

    In TGD framework string tension can be identified as an effective parameter in the expression of Kähler action as stringy action for preferred extremal strongly suggested by strong form of holography (SH) allowing the description of the situation in terms of fermionic strings and partonic 2-surfaces or in terms of interiors of space-time surfaces and Kähler action. 1/heff2 dependence can be derived from strong form of holography assuming electric-magnetic duality for Kähler form, and using the fact that the monopoles associated with the ends have same magnetic and electric charges.

  5. The discussion of the analog of Hawking radiation in TGD framework led to an amazing prediction: the TGD counterpart of Hawking
    temperature turns out to be in the case of proton very near to the physiological temperature if the big mass is solar mass (see this). This suggests that the entire solar system should be regarded as quantum coherent living system. This is also suggested by the general vision about EEG. Could Hawking temperature be near to the Hagedorn temperature but below it?

One can make this vision more detailed.
  1. In ZEO the notion of heat bath requires that one considers reactants as subsystems. The basic mathematical entity is the density matrix obtained by tracing over entanglement with environment. The assumption that dark matter is in thermal equilibrium with ordinary matter can be made but is not absolutely crucial. The reactions transforming visible photons to dark photons should take care of the equilibrium. One could even assume that the description applies even in case of the negentropic entanglement since thermodynamical entropy is different from entanglement entropy negative for negentropic entanglement.

  2. In TGD inspired quantum biology one identifies the gravitational Planck constant introduced by Nottale with heff=n× h. The idea is simple: as the strength of gravitational interaction becomes so strong that perturbation series fails to converge, a phase transition increasing the Planck constant takes place. hgr=GMm/v0= heff=n× h implies that v0/c<1 becomes the parameter defining the perturbative expansion. hgr is assigned with the flux tubes mediating gravitational interaction and one can say that gravitons propagate along them.

    Note that this assumption makes sense for any interaction - say in the case of Coulomb interaction in heavy atoms: this assumption is indeed made in the model of leptohadrons (see this) predicting particles colored excitations of leptons lighter the weak bosons: this leads to a contradiction with the decay widths of weak bosons unless the colored leptons are dark. They would be generated in the heavy ion collisions when the situation is critical for overcoming the Coulomb wall.

    The cyclotron energy spectrum of dark particles at magnetic flux tubes is proportional to hgr/m does not depend on particle mass being thus universal. In living matter cyclotron energies are assumed to be in the energy range of bio-photons and thus includes visible and UV energies and this gives a constraint on hgr if one makes reasonable assumption about strengths of the magnetic fields at the flux tubes (see this). Bio-photons are assumed to be produced in the transformation of dark photons to ordinary photons. Also (gravitational) Compton length is independent on particle mass being equal to Lgr=GM/v0: this is crucial for macrosopic quantum coherence at gravitational flux tubes.

  3. The basic idea is that Hawking radiation in TGD sense is associated with all magnetic flux tubes mediating gravitational
    interaction between large mass M, say Sun, and small mass m of say elementary particle. How large m can be, must be left open.
    This leads to a generalization of Hawking temperature (see this) assumed to make sense for all astrophysical objects at the flux tubes connecting them to external masses:

    TGR=hbar (GM/RS2 2π) = hbar/(8 π GM).

    For Sun with Schwartschild radius rS=2GM=3 km one has TGR= 3.2× 10-11 eV.

    Planck constant is replaced with hgr=GMm/v0= heff=n× h in the defining formula for Hawking temperature. Since Hawking temperature is proportional to the surface gravity of blackhole, one must replace surface gravity with that at the surface of the astrophysical object with mass M so that radius RS=2GM of the blackhole is replaced with the actual radius R of the astrophysical object in question. This gives

    THaw= (m/8 π v0) ×(RS/R)2 .

    The amazing outcome is that for proton the estimate for the resulting temperature for M the solar mass, is 300 K (27 C), somewhat below the room temperature crucial for life!

    Could Hagedorn temperature correspond to the highest temperature in which life is possible - something like 313 K (40 C)? Could it be that the critical range of temperatures for life is defined by the interval [THaw,THag]? This would require that THaw is somewhat smaller THag. Note that Hawking temperature contains the velocity parameter v0 as a control parameter so that Hawking temperature could be controllable. Of course, also THaw=THag can be considered. In this case the temperature of environment would be different from that of dark matter at flux tubes.

  4. The condition THaw≤ THag allows to pose an upper bound on the value of the effective string tension

    (α')-1/2≥ (m/4×61/2v0) × (RS/R) .

For details see the article Jeremy England's vision about life and evolution: comparison with TGD approach.

For a summary of earlier postings see Links to the latest progress in TGD.

Wednesday, October 21, 2015

Jeremy England's vision about life

We had an intensive discussion with my son-in-law Mikko about the work of Jeremy England. The article of the link is probably the most aggressive hyping I have ever seen but this should not lead to think that a mere hype is in question. There is also another, not so heavily hyped popular article. The material at england lab homepage gives a good view about the work of England for those who cannot tolerate hyping.

England's work is indeed very interesting also from TGD point of view although it is based on standard physics.

Basic ideas of England's theory

I try first to summarize England's vision.

  1. Non-equilibrium thermodynamics (NET) is the starting point. NET has been for decades the theoretical framework underlying the attempts to understand living matter using the principles of self-organization theory. Living matter is never an isolated system: dissipation would take it to a totally dead state in this case - nothing would move. Water in the pond when there is no wind, is a good example.

    Self-organization requires an external energy feed - gravitational potential energy liberated in water flow in river or electric power feed to the hot plate below a teapot. This energy feed drives the system to a non-stationary state far from a thermal equilibrium state. Dissipation polishes out all details and leads to an asymptotic spatio-temporal self-organization patterns. The flow in a river and convection in the heated teapot. With high enough energy feed chaos emerges: water fall or boiling of tea pot.

  2. The basic hypothesis of England is that evolution means increase in the ability to dissipate. This looks intuitively rather obvious. The evolving system tends to get to a resonance with the energy feed by oscillating with the same frequency so that energy feed becomes maximal and therefore also dissipation. The basic rule is simple: choose the easy option, ride on the wave rather than fighting against it! For instance, the emergence of photosynthesis means that the systems we call plants become very effective in absorbing the energy of sunlight. In this framework essentially all systems are alive to some degree.

    Dissipation means generation of entropy. Evolution of life and conscious intelligence would mean maximal effectivenes in the art of producing disorder. Now I am perhaps exaggerating. One should speak about "system's maximal ability to transfer entropy out of it": life is not possible without paper baskets. One could argue that the development of civilization durig last decades demonstrates convincingly that evolution indeed generates systems generating disorder with a maximal rate.

    One could argue that the definition is too negative. Living matter is conscious and there is genuine conscious information present. The fact is that evolution involves a continual increase of conscious information: the exponential explosion of science is the best proof for this. England's vision says nothing about it. Something is missing.

    It is however quite possible to imagine that the principle of maximal entropy generation is true and that the increase of the ability to produce entropy is implied by some deeper principle allowing to speak about living matter as something tending to increase conscious information resources. To formulate this idea one needs a theory of consciousness, thermodynamics is not enough.

  3. England has a further idea. The evolution life is not climbing to Mount Everest but coming down from it. Life emerges spontaneously. This is definitely in conflict with the standard wisdom, in particular with the thermodynamical belief on thermal death of the Universe as all gradients disappear. Darwinian evolution would be a special case of a more general phenomenon, which could be called dissipation driven adaptation (DDA). I made a head-on-collision with this principle in totally different framework by starting from quantum criticality of TGD: if took time to fully realize that indeed: evolution could be seen as a sequence of phase transitions breaking in which certain infinite-dimensional symmetry was spontaneously broken to become just the same symmetry but in longer scale!

    Standard thermodynamics predicts the heat death of the Universe as all gradients gradually disappear. This prediction is problematic for England's argument suggesting that differentiation occurs instead of homogenization. Here the standard view about space-time might be quite too simplistic to overcome the objection. In TGD many-sheeted space-time comes in rescue.

    Here is an example about England's argumentation. It seems intuitively clear that replication increases entropy (it is not however clear whether just the splitting into pieces is even more effective manner to increase entropy!). This would suggest that DDA forces the emergence of replication. Very effective dissipators able to replicate, would increase the total effectiveness in dissipation and be the winners. The proposal to be tested is that bacterial mutations , which are best replicators are also best dissipators.

What is missing from England's theory?

What is missing from England's theory? The answer is same as the answer to the question what is missing from standard physics.

  1. What is conscious observer - self?

    Observer, which remains outsider to the physical world in the recent day physics - both classical and quantum. Hence one does not have a theory of consciousness and cannot speak about conscious information. Thermodynamics gives only the notion of entropy as a measure for the ignorance.

    Therefore there is a long list of questions that England's theory does not address. What are the physical correlates of attention, sensory perception, cognition, emotions relating closely to information, etc.? Is there some variational principle behing concious existence, and does it imply evolution? Could second law and DDA be seen as consequences of this variational principle ?

    England does not say much about quantum theory since he talks only about thermodynamics but his hypothesis is consistent with quantum theory. The restriction to thermodynamics allows only statistical description and notions like
    macroscopic quantum coherence are left outside.

  2. What is life?

    Again one has a long list of questions.

    What it is to be alive? What distinguishes between living and inanimate systems. What it is to die? How general phenomenon evolution is: does it apply to all matter? Also notions like self-preservation and death are present only implicitly in an example about a population of wine glasses whose members might gradually evolve to survive in an environment populated by opera sopranos.

    One can make also other kinds of questions. What really happens in replication? What is behind genetic code? Etc...

    England is a spiritual person and has made clear that the gulf between science and spirituality is something which bothers him . England even has the courage to use the word "God". Therefore it sounds somewhat paradoxical that England avoids using the concepts related to consciousness and life. This is however the only option if one does not want to lose academic respectability.

How England's theory relates to TGD?

It is interesting to see whether England's vision is consistent with TGD inspired theory of consciousness, which can be also seen as a generalization of quantum measurement theory achieved by bringing the observer part of the quantum physical world. In TGD framework several new principles are introduced and they relate to the new physics implied by the new view about space-time.

  1. The new physics involves a generalization of quantum theory by introducing a hierarchy of Planck constants heff =n×h with various quantal length and time scales are proportional to heff. heff hierarchy predicts a hierarchy of quantum coherent systems with increasing size scale and time span of memory and planned action. heff defining a kind of intelligence quotient labels the levels of a hierarchy of conscious entities.

    heff hierachy labels actually a fractal hierarchy of quantum criticalities: a convenient analogy is a ball at a top of ball at the top..... The quantum phase transitions inreasing heff occur spontaneously: this
    is the TGD counterpart for the spontaneous evolution in England's theory. Dark matter is what makes system alive and intelligent and thermodynamical approach can describe only what we see at the level of visible matter.

  2. Second key notion is zero energy ontology (ZEO). Physical states are replaced by events, one might say. Event
    is a pair of states: initial state and final state. In ZEO these states correspond to states with opposite total
    conserved quantum numbers: positive and negative energy states. This guarantees that ZEO based quantum theory is consistent with the fundamental conservation laws and laws of physics as we understand them although it allows non-determinism and free will. Positive and negative energy states are localized at opposite boundaries of a causal diamond (CD). Penrose diagram - diamond symbol - is a good visualization and enough for getting the idea.

    State function reduction (SFR) is what happens in quantum measurement. The first SFR leads to a state which is one in a set of states determined once measurement is characterized. One can only predict the probabilities of various outcomes. Repeated quantum measurements leave the state as such. This is Zeno effect - watched kettle does not boil.

    In ZEO something new emerges. The SFR can be performed at either boundary of CD. SFR can occur several times at the same boundary so that the state at it does not change. The state at the opposite boundary however changes - one can speak of the analog of unitary time evolution - and the second boundary also moves farther away. CD therefore increases and the temporal distance between its tips does so also.

    The interpretation is as follows. The sequence of reductions at fixed bounary corresponds to a conscious entity, self. Self experiences the sequence of state function reductions as a flow of time. Sensory experience and thoughts, emotions, etc.. induced by it come from the moving boundary of CD. The constant unchanging part of self which meditators try to experience corresponds to the static boundary - the kettle that does not boil.

    Self dies in the first reduction to the opposite boundary of CD. Self however re-incarnates. The boundaries of self change their roles and the geometric time identified as distance between the tips of CD increases now in opposite direction. Time-reversed self is generated.

  3. Negentropy Maximization Principle (NMP) stating roughly that the information content of consciousness is maximal. Weak form of NMP states that self has free will and can choose also non-maximal negentropy gain. The basic principle of ethics would be "Increase negentropy". p-Adic mathematics is needed to construct a measure for conscious information and the notion of negentropic entanglement (NE) emerges naturally as algebraic entanglement.

    The negentropy to which NMP refers is not the negative of thermodynamical entropy describing lack of information of outsider about state of system. This negentropy characterizes the conscious information assignable to
    negentropic entanglement (NE) characterized by algebraic entanglement coefficients with measure identified as a number theoretic variant of Shannon entropy. Hence NMP is consistent with the second law implied by the mere
    non-determinism of SFR.

    NMP demands that self during sequence of reductions at the same boundary generates maximum negentropy gain at the changing CD boundary. If self fails, it dies and re-incarnates (in a reduction to the opposite CD boundary more negentropy is generated). Selves do not want to die and usually they do not believe on re-incarnation, and therefore do their best to avoid what they see as a mere death. This is the origin of self-preservation. Self must collect negentropy somehow: gathering negentropic sub-selves (mental images) is a manner to achieve this. Plants achieve this by photosynthesis, which means generation of negentropy and storage of it to various biomolecules. Animals are not so saintly and simply eat plants and even other animals. We are negentropy thieves all.

    Re-incarnation also means increase of heff and getting to higher level in hierarchy and occurs unavoidably. As in England's theory, evolution occurs spontaneously: it is not climbing to Mount Everest but just dropping down.

  4. England says "Some things we consider inanimate actually may already be 'alive'." This conforms with TGD view. Even elementary particles could have self: it is however not clear whether their SFR sequences contain more that one reduction to a fixed boundary - necessary for having a sense about the flow of time. Elementary particles would even cognize: in adelic physics every system has both real and p-adic space-time surfaces as its correlates. It can even happen that system has only p-adic space-time correlates but not the real one: this kind of systems would be only imaginations of real system! This is one of the most fascinating implications of strong form of holography which follows from strong form of General Coordinate Invariance forced by the new view about space-time.

    Clearly the notion of evolution generalizes from biological context to entire physics in TGD. One can speak about
    p-adic evolution and evolution as increase of heff. The most abstract formulation is number theoretical:
    evolutioncorresponds to the increase of the complexity of extension of rationals to which the parameters characterizing space-time surfaces belong to.

  5. Does DDA emerge in TGD framework? NMP demands a lot of SFRs - also at the level of visible matter. The non-determimism of SFR alone means a loss of knowledge about the state of system and an increase of thermodynamical entropy so that living systems would generate entropy very effectively also in TGD Universe at the level of visible matter. If one believes that second law and NET imply DDA as England argues, then also TGD implies it at the level of visible matter. For dark matter the situation is different, since the outcome of SFR is not not random anymore. Seen from TGD perspective England's vision misses what is essential for life - the generation of phases of matter identifiable as the mysterious dark matter.

  6. England talks about God. In a theory of consciousness predicting infinite self hierarchy, it is easy to assign the attribute "divine" to the levels of consciousness above given level of hierarchy. Personally I have nothing against calling the Entire Universe "God".

    One could give NMP the role of God. For strong form of NMP SFR would be almost deterministic except for ordinary matter for which entanglement is not algebraic and is therefore entropic: the universe would the best possible one in dark sectors and the worst one in the visible matter sector - Heaven and Hell! Weak form of NMP makes possible even more effective generation of negentropy than its strong form but allows self to make also stupid things and even SFRs with a vanishing negentropy gain: the outcome is state with no entanglement (system is in very literal sense alone in this state). The world in dark matter sectors is not anymore the best possible one but can become better and does so in statistical sense.

  7. Replication is a crucial aspect of being alive. England argues that DDA allows to understand its emergence but does not tell about its mechanism. In TGD framework replication can be understood as an analog of particle decay - say photon emission by electron. This requires however a new notion: magnetic body. In Maxwell's theory one cannot assign any field identity to a physical system but TGD view about space-time forces to assign to a given system its field/magnetic body. The replication occurs primarily at the level of magnetic body carrying dark matter as large heff phases. Magnetic body replicates and ordinary visible matter self-organizates around the resulting copies of it. The dynamics of dark matter would induce also DNA replication, transcription and mRNA translation, and there are some indications that it is indeed "dark DNA" (dark proton sequences having DNA, RNA, amino-acids, and tRNA as biochemical counterparts), which determines what happens in transcription.

For details see the article Jeremy England's vision about life and evolution: comparison with TGD approach.

For a summary of earlier postings see Links to the latest progress in TGD.

Saturday, October 17, 2015

Quantum criticality and protein folding

In Thinking Allowed Original there was a link to a new observation about protein folding process. During folding some proteins hold single building blocks in shapes that were thought to be impossible to find in stable form. Stable shapes contained some parts, which were trapped like mosquitos in amber.

A concrete TGD based model relies on the general ideas of TGD inspired quantum biology.

  1. Biomolecules containing aromatic rings play a fundamental role. All DNA nucleotides contain them and there are 4 proteins, which also have them. trp and phe are of special importance and form a pair structurally analogous to a base pair in DNA strand. The rings are assumed to carry the analog of supra current and be in or at least be able to make transition to a state with large heff. The delocalization of electron pairs in aromatic ring could be a signature of heff/h>1.

  2. trp-phe pairing would be responsible for information molecule-receptor pairing. Information molecule and receptor would be at the ends of flux tubes serving as communication lines, and the attachment of info molecule to receptor would fuse the two flux tubes to longer one. After that communication would become possible as dark photon signals and dark supra currents. Formation of info molecule-receptor complex would be like clicking icon generating a connection between computers in net. Info molecules would generate the communication channels - they would not be the signals. This is the distinction from standard neuroscience.

  3. All quantum critical phenomena involve generation of large heff phases. Folding emerges or disappears at quantum criticality (QC) possible in certain temperature range of width about 40 K and depending on pH. The flux tubes associated with phe and trp containing aromatic rings carrying "supra current" would become dark (either h→ heff or heff> h increases) and thus much longer and reconnect temporarily and force phe and trp in a close contact after the reverse transition inducing shortening. This is a general mechanism making biomolecules able to find each other in what looks like molecular soup in the eyes of standard biochemist. The contacts between amino-acids phe and trp formed in this manner are structurally identical with the hydrogen bonding between members of DNA base pairs and they would fix the final folding pattern to high degree.
There was also a link to very interesting article about possible topological phenomena related to protein folding. Authors are Henrik and Jakob Bohr (akin to the Great Niels Bohr?) and Sören Brunak.

The article is very easy to read and explains the basic topological concepts like winding in a simple manner. The proposal is that the excitation of so called wringing modes of proteins are involved in the generation and disappearance of the protein folding. Excitation of wringing modes twisting the protein (think about how one wrings water from a wetted cloth) would make the protein folding state cold denatured unstable and transform in to stable folded (F) state. In the same manner their excitation would transform hot denatured (HD) stable state to folded state. Wringing modes could be excited by radiation.

In TGD framework the folding phase diagram CD-F-HD could be understood also in terms of quantum criticality (QC). Perhaps the simplest option is that the transitions CD-F and HD-F involve a generation of critical states leading to a generation of long range correlations (large heff) inducing the folding pattern. Absorption of photons to wringing modes would induce the criticality and the folding would proceed by the mechanism discussed above.

For background see the chapter More Precise TGD Based View about Quantum Biology and Prebiotic Evolution or article with the same title.

For a summary of earlier postings see Links to the latest progress in TGD.