Thursday, December 14, 2017

Does instability of Einstein's equations explain accelerated expansion?

The article Doing without dark energy: Mathematicians propose alternative explanation for cosmic acceleration (thanks for link to Steven Crowley) makes a very interesting claim. The instability of Einstein's equations requires accelerated expansion usually assumed to be due to a small value of cosmological constant. I understood that the instability of Einstein' cosmological solutions around cosmological solutions is however not proven.

What is remarkable that the exact analog of this instability occurs in TGD.

  1. I believed for a long time that Kähler action alone determines the dynamics. The special feature of Kähler action was its huge vacuum degeneracy, which I interpreted in terms of 4-D spin glass nature of theory and did not regard it as a problem. This instability however destroyed all hopes about path integral approach to the quantum TGD and led to the notion of "world of classical worlds". It became soon clear that it really works and leads to a beautiful physical interpretation. Mistakes sometimes force to see a really big problem and even solve it!

    In particular, for the canonically imbedded empty Minkowski space, which should give rise to an analog of massless field theory, the field equations give 0=0! The propagator defined by the kinetic term vanishes identically. The situation if of course mathematically very singular and the interpretation is as instability since the infinite-D matrix defined by the second order functional derivatives has not only some vanishing eigenvalues but vanishes identically. One expects a hierarchy of singularities with increasing number of non-vanishing eigenvalues.

  2. Few years ago my views changed as I started to think about twistorialization of TGD at the level of space-time dynamics. The basic idea is simple: in TGD framework particles are massless in 8-D sense but can be massive in 4-D sense. 8-D twistorialization could solve the basic problem of ordinary twistorialization due to massive particles.

    Twistor lift of space-time surfaces is needed. This requires the introduction of 6-D twistor space of space-time surface as a dynamical entity: a sphere bundle of space-time surface receiving twistor structure by induction from the product of twistor spaces for M4 and CP2.

    What puts bells ringing is that M4 and CP2 are the unique 4-D manifolds with twistor space possessing Kähler structure. This makes possible the generalization of Kähler action to its 6-D variant in the 12-D twistor space of M4×CP2. The existence of twistor lift of TGD would lead to standard model symmetries and fix TGD completely!

    The allowed solutions of field equations/preferred externals should be twistor spaces of spacetime surfaces. The natural guess is that they are also extremals of 6-D Kähler action, which is a generalization of Maxwell action. Dimensional reduction for 6-D Kähler action to sum of Kähler action and volume term serving as analog of cosmological term is proposed to determine the 6-D preferred extremals, which should correspond to 6-D twistor spaces of 4-D space-time surfaces (sphere bundles with space-time surface as base space). It however seems that cosmological term at GRT limit of TGD corresponds to the sum of Kähler action and volume term rather than only volume term: here I must be however cautious.

    Twistor space property for 6-surface should determine the dynamics completely. This generalizes Penrose's approach reducing Maxwell's equations to holomorphy. A generalization of the approach of Penrose from gauge fields to induced gauge fields would be in question.

Preferred extremals for Kähler action plus volume term come in two classes.
  1. Minimal surface solutions for which field equations reduce to holomorphy conditions. One has minimal surfaces and the equations for Kähler action and volume term are separately satisfied and reduce to holomorphy conditions. These solutions are analogs of light-like geodesic lines: massless particles but in 8-D sense allowing massive particles in 4-D sense so that the basic problem of ordinary twistor approach is solved.

  2. Second type of solution corresponds to an analog for the motion of massless particle in Abelian gauge field, which is however internally determined and vanishes in equiibrium situations: that is for external particles entering causal diamond. Physically these solutions describe interaction regions and minimal surfaces to external particles with interactions coupled off.

The addition of volume term solves the instability/degeneracy problem and the analog of volume term is indeed cosmological constant term in GRT! The spin glass degeneracy could quite well remain as approximate property since the cosmological constant in recent cosmology is extremely small and just takes care that the degeneracy disappears. At the limit of infinitely long p-adic length scale cosmological constant vanishes and one has vacuum degeneracy. The reason is that cosmological constant depends on p-adic length scale going like 1/p-adic length scale squared propto 1/p. This predicts that cosmological constant evolves and approaches its maximal and very large value in the early Universe. Its value is not "un-natural" anymore. One should however be critical and check for whether two strong assumptions are made. Everything is guesswork after all.
  1. The preferred extremals in the interaction regions correspond at the level of M8 (recall M8-H duality) to space-time surfaces, which are not associative/quantum critical (having quaternionic (associative) tangent or normal space) so that they cannot be mapped to surfaces in M4 ×CP2 (requires quaternionicity of tangent space). It is however enough to do this only for external particles which are associative surfaces and correspond to quantum criticality. Kähler action +volume term take care of the time evolution inside CDs once 3-surfaces at boundaries of CD are known.

  2. For minimal surfaces defining external particles dynamics is determined by holomorphy and holomorphy is the key feature of twistorialization. Could it be that twistor bundle property for the 6-D sphere bundle is true only for external particles? This would correspond to associativity of external particles at the level of M8. Could it be that twistor space property (characterizing also for standard twistors free gauge fields) fails in interaction regions - CDs - and is true only for external particles? Just asking;-).

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Tuesday, December 12, 2017

DMT: connector to God or bio-chemical waste?

In FB I got a link to a very interesting article about DMT. DMT is psychedelic or hallucinogen - depending on one's attitudes. DMT is used for spiritual and healing purposes in many cultures. The effect is short-lasting: from 5 to 15 minutes. DMT induces mystical experiences, euphoria, dynamical geometric hallucinations of geometric forms, experiences about meeting of higher intelligences, extraterrestrials, elves, and even God.

First some facts about DMT.

  1. DMT is found in both plants and animals and is the only naturally occurring psychedelic. Its occurrence in the pineal gland of rodents and therefore also of mammals has been reported.

  2. Chemically DMT is a structural analog of serotonin and melatonin and involves aromatic 6-cycle and 5-cycle with common edge appearing in amino-acid tryptophan. Also DNA nucleotides A and G have this double cycle structure but have however more than one nitrogen atom.

  3. The biosynthesis of DMT from amino-acid L-tryptophan (occurring endogenously in plants but not in animals) has been detected in rabbit's lungs. Whether DMT is produced by brain is still an unsettled question. It has been even argued that DMT is mere waste.

    In TGD framework aromatic cycles serve as indication that molecule contains paired valence electrons with the value of heff/h=n higher than its standard value: this explains the delocalization of electrons to longer than atomic length scale. n would serve as a kind of intelligence quotient: the larger the value of n is, the larger the maximal value of entanglement negentropy of the system is (understanding of this statement requires going outside the framework of the mathematical framework of standard physics: I call this framework adelic physics).

    In this picture the interpretation as a waste does not look sensible and the proposal that DMT is produced by brain or some other parts of body looks more reasonable. Biology does not usually manufacture anything without purpose. Especially so, if the manufacturing process requires metabolic energy. The biosynthesis of DMT from tryptophan does not occur spontaneously and requires N-methyltransferase enzyme as a catalyst. Also the highly non-trivial positive effects of DMT on consciousness suggests that it cannot be waste.

To understand what the purpose of DMT could be, one must have some idea about sensory perception in TGD Universe (I have already earlier written about DMT and psychedelics, see this).
  1. TGD view about sensory perception relies on the idea that sensory qualia are at the level of sensory organs: this view makes sense if one accepts macroscopic quantum coherence (see this). TGD based view about time (zero energy ontology (ZEO)) allow to circumvent basic objections such as phantom leg: pain in phantom leg would be sensory memory of pain and in geometric past when the leg still existed. These sensory memories can be produced by stimulating parietal lobes in any subject person. One also avoids the challenge of explaining why structures consisting of essentially identical neutrons can produce so different sensory qualia.

  2. This model however requires virtual visual feedback from brain realized as dark photons, which leak to ordinary photons identifiable as biophotons with energied in visible and UV range. The presence of virtual visual input could explain why the retina has inverted structure not expected in engineerish thinking.

    Sensory percept would be an artwork created by the perceiver. This conforms with the fact that when congenitally blind people receive their vision, they report only seeing of diffuse light. The percept would be a standardized sensory mental images emerging as an outcome of iteration in which dark photons signals travel forth and back and give rise to a pattern recognition by transforming sensory input to standardized input nearest to it.

  3. Dark photon signals would travel along magnetic flux tubes between brain to sensory organs and even between brain and magnetic body (MB) in much longer scales. Flux tubes would gives rise to a connection network analogous to a telephone network. This network would have permanent part and dynamical part consisting of switches allowing to connect two flux tubes to single flux tube by a short bridge. Information molecules such as neurotransmitters, hormones, and messengers could act as switches/bridges: as the information molecule attaches to a receptor, the bridge is formed and signals can propagate.

    Also nerve pulses could induce flux tube bridges between neurons of the neuronal pathway by using neurotransmitters and learning as amplification of synaptic connections would be essentially the gradual stabilization of these flux tube bridges. Nerve pulse patterns need not serve as communications inside brain but could only make possible communications in much shorter time scales using dark photons. For 1 meter long axons about million forth and back signals are possible during millisecond.

    Nerve pulses would however frequency modulate Josephson radiation from the generalized Josephson junctions defined by membrane proteins serving as ion channels. This modulation would code nerve pulse patterns to signals to MB mediated by EEG: EEG could also have fractally scaled variants corresponding to various layers of MB. This would explain the function of EEG.

  4. Virtual sensory input need not always end up down to the sensory organs: there would be some kind of blocking stopping the virtual sensory input to higher level so that one would have only almost sensory percept: an imagined sensory experience. The virtual sensory input associated with imagination could proceed along different route than that associated with the buildup of percept. Also imagined motor actions would be halted motor actions. During REM sleep the blocking would not be present and the virtual sensory input would enter to sensory organs, in particular retina.

  5. Pineal gland represents a kind of photoreceptor, "third eye", which still serves as eye in some animals. Could the dark photons involved with imagination be received in pineal gland. Could they continue to travel to sensory organs during dreams and hallucinations? Pineal gland would be an organ of imagination besides serving as seat of soul! What is nice from the point of view of biological economy is that pineal gland would not be useless evolutionary remnant but would have found a new function.

Accepting this schematic view one can ask about the possible function of DMT.
  1. DMT molecules could make possible REM dreams by providing the bridges making possible the propagation of dark photons to the retina. Pineal gland would be the natural relay station. Same mechanism could work for other sensory modalities if dark photons mediate the virtual sensory input transformed to ordinary percept at sensory organs. Also hallucinations would rely on this mechanism.

  2. MB has very large layers, there is even evidence that galactic magnetic field is in contact with personal MB (personal MB could have flux tubes inside flux tubes of galactic magnetic field). Since magnetic field in Maxwellian world extends to infinity and since in TGD systems have field identity (field body/MB), one can even image that there are connections to distant civilizations with very weak magnetic field strengths at corresponding flux tubes carrying dark matter.

    These connections could make possible a genuine sharing of sensory experiences and the encounters with ETs and alike could be genuine remote meetings! We might have these encounters during sleep quite routinely but would not remember anything since the sensory information would stop at the third eye! Only during dreams situation might change but also now sensory input would be virtual and represent imaginations.

Remark: I have told many times that I am working intensely and close my eyes lightly, I see a dim flow consisting of points and resembling an incompressible hydrodynamic flow. There are vortices and the flow goes back and forth. The flow lines are mathematically equivalent with field lines of a magnetic field in Maxwell's theory and in TGD with flux tubes of MB in 1-1 correspondence with the points of the flow. Could this be seeing MB with the "third eye"?

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Sunday, December 10, 2017

LIGO: no gravitational radiation from cosmic strings

LIGO has reported that there is no evidence for so called cosmic strings, which are a basic prediction of GUTs. It is becoming painfully clear that GUTs have led the entire theoretical physics to a wrong track. Regrettably, we have spent for more than four decades at this wrong track now. Also superstring models and M-theory assume GUT as their limit at long length scales so that this finding should finally wake up even the most sleepy colleagues.

As Peter W*it tells in N*t Even Wr*ng (for some reason Lubos wants to write "o":s as "*":s in this context), cosmic strings has been one of so called qualitative predictions of many variants of superstring theory. This is true but since Lubos is one of the few remaining superstring fans, Woit's blog post made him very irritated.

What about TGD? Do I have reasons to get irrirated? Cosmic strings appear also in TGD but are very different objects than those of GUTs. They differ also from those of superstrings theories, where they can appear at the GUT limit or as very long fundamental strings.

Cosmic strings in GUTs and superstring theories

What mainstream cosmic strings are?

  1. In GUTs cosmic strings are 1-D defects associated with singular gauge field configurations. There is a phase, which grows by a multiple of 2π as one goes around the defect line. One has essentially vortex line locally. At the singularity the modulus of field variable associated with the phase must vanish.

    Here comes in the fundamental difference between gauge fields in GUTs and in TGD where they are induced and QFT limit of TGD does not allow either GUT cosmic strings, GUT monopoles, nor instantons implying strong CP breaking plaguing QCD.

  2. In superstring theories one also has these defects almost unavoidably if one believes that some kind of GUT defines the long length scale limit of superstring theories. Superstring theories also suggests that fundamental strings somehow give rise to very long fundamental cosmic strings: I cannot say anything about the details of the proposed mechanism.

The dynamics of string like objects is almost universal.

  1. The first parameter is string tension μ predicted by GUTs. There are strong bounds on μ in terms of 1/G. The upper bound μG ≈10-7 emerges from the fact that cosmic strings have not been found yet. The string tension of TGD cosmic strings satisfies this condition.

  2. Second parameter characterizes the dynamics of string networks and is reconnection probability p for strings. It would be p≈ 10-1 for strings with topological origin (GUT strings) and p≈ 10-3 for possibly existing long superstrings. Using these parameters one can build dynamical models and perform numerical simulations. In LIGO article several models are discussed together with their predictions.

Reconnections lead to a generation of oscillating string loops and these would generate gravitational radiation at harmonics of the frequency, which is essential the inverse of the length of the string. In particular, the kinks and cusps (string moves with light-velocity locally) propagating along these strings would generate gravitational radiation.
  1. One expects that kinks and cusps correspond to delta function singularities in energy momentum tensor serving as sources of gravitational radiation. In cusps the determinant of 2-D induced metric vanishes and the energy momentum tensor proportional to 2-D contravariant metric diverges like 1/det(g). This seems to produce a singularity.

  2. Energy momentum tensor serving as the source of gravitational radiation seems to be however only discontinuous at kinks. Naively one might think that the ordinary divergence of energy momentum tensor having delta function singularity tells how much energy momentum goes out from string as gravitational radiation. My guess is that one must add to the action an additional term corresponding to the discontinuity and depending on Christoffel symbols at the discontinuity to describe curvature singularity. This term would serve as a source of gravitational radiation.

    This term is essentially the second fundamental form for the imbedding of the singularithy as a 3-surfaces and its trace would define the interaction term just as the naive picture would lead to expect. The interpretation of this term is essentially as the analog of acceleration and accelerating particle indeed creates radiation, in particular gravitational radiation. As a matter fact, this kind of term must be also added in 2-D case to the curvature scalar to get correctly Gauss-Bonnet law for polygons having corners.

There are two kinds of space-time surfaces in TGD Universe

To discuss the question whether cosmic strings radiate in TGD one must say something general about the dynamics of space-time surfaces in TGD.

There are two kinds of space-time surfaces in TGD Universe. These two kinds fo space-time surfaces appear at the boths sides of M8-H duality: here one has H=M4× CP2. In the following I stay at the H-side of the duality.

There is a rather precise analogy with the vision about what happens in particle reactions. External particles decouple from interactions and interactions take place in interaction regions, where interactions are in some sense coupled on. This is realized for the preferred extremals of the action determining space-time surfaces in rather precise sense. The twistor lift of TGD predicts that the action is sum of Kähler action and volume term analogous to cosmological term.

  1. The preferred exremals can be minimal surfaces in which case field equations are satisfied separately for Kähler action and volume term: the two interactions effectively decouple. The dynamics reduces to holomorphy conditions and coupling constants disappear completely from it. This corresponds to the universal dynamics of quantum criticality.

    The minimal 4-surfaces are direct 4-D analogs of geodesic lines, free particles. Also cosmic strings are surfaces or this kind and presumably also the magneti flux tubes. In Zero Energy Ontology (ZEO) these surfaces represent external particles entering or leaving causal diamond (CD). Free particles do not emit any kind of radiation and this would be indeed realized now.

  2. Inside CDs Kähler action and volume term do not decouple and there is genuine interaction between them. One does not have minimal surfaces anymore and coupling constants appear in the dynamics. In this region the emission of radiation and also of gravitational radiation is possible.

Cosmic strings in TGD sense

Also TGD predicts what I call cosmic strings.

  1. Ideal cosmic strings a la TGD string like objects, space-time surfaces. They are not singular densities of matter in 4-D space-time which would be small deformation of Minkowski metric. Rather, they are 4-D surfaces havng 2-D string world sheets as M4 projection. String world sheet and string like object are minimal surfaces and should emit no radiation.

    Remark: Since M4 projection is not 4-D GRT limit does not make sense for cosmic strings and the GRT based calculation for gravitational radiation does not apply in TGD framework.

  2. Cosmic strings dominate the dynamics in very early universe. In reasonable approximation one could speak about gas of cosmic strings in M4- or strictly speaking in M4× CP2. The transition to radiation dominated era is the TGD counterpart for inflationary period: the space-time in GRT sense emerges as space-time sheets having 4-D M4 projection. Stringlike objects topologically condense at 4-D space-time sheets. Also their M4 projection becomes 4-D and begins to thicken during cosmic evolution so that magnetic field strength starts to weaken.

    Cosmic strings can carry Kähler magnetic monopole flux explaining the mysterious long ranged magnetic fields in cosmological scales. Reconnection and formation of closed loops is possible. Many-sheetedness is an important aspect: there are flux tubes within flux tubes.

    Cosmic strings/magnetic flux tubes play a key role in the formation of galaxies and larger (and even smaller) structures. Galaxies are along cosmic strings like pearls along necklace: the simplest model assumes that pearls are knots along cosmic strings (note the amusing analogy with DNA having coding regions as nucleosomes along it). Flux tubes and their reconnections play also key role in TGD inspired quantum biology.

Does TGD survive the findings of LIGO?

The question of the title reduces to the question whether the cosmic strings in TGD sense emit gravitational radiation.

  1. If cosmic strings are idealizable as minimal surfaces and therefore as stationary states outside CDs they do not produce any kind of radiation. Radiation and gravitational radiation can emerge only in space-time regions, where there is a coupling between Kähler action and volume term. In particular, the purely internal dynamics of ideal cosmic strings cannot produce gravitational radiation.

  2. One can of course argue that topologically condensed thickened cosmic strings actually interact and ought to be described as something inside CD. In any case, there is a coupling between Kähler degrees of freedom and geometry of string and this means that GRT based model cannot apply. This is of course clear already from the fact that string like objects in TGD sense are hardly describable as a singular mass distribution in slightly curved piece of M4.

    One can of course ask whether GRT based calculation for the emission of gravitational radiation makes sense for thickened cosmic strings having 4-D M4 projection. This requires going to the GRT-QFT limit involving the approximation of the many-sheeted space-time with GRT space-time: this means replacing sheets with single sheet and identifying deviation of the metric from M4 metric and gauge potentials with sums of the corresponding induced quantities.

    There would be however no emission in the approximation with genuinely 2-D objects and the calculation must involve also other than purely geometric degrees of freedom. There is also the question about whether kinks and cusps are possible for preferred extremals satisfying extremely tight symmetry conditions realizing strong form of holography. If not, they are not expected at QFT limit either.

See the article Three findings by LIGO or the chapter Quantum Astrophysics of "Physics in Many-Sheeted Space-time".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Tuesday, December 05, 2017

Model for RNA life

Ulla gave a link to a very interesting paper about the possible mechanism giving life-like properties to RNA system during the conjectured RNA era. The title of the article is "The life story of hydrogen peroxide II: a periodic pH and thermochemical drive for the RNA world. "Life-like" would mean "breathing" realized as these oscillations and would require a metabolic energy source.

I try to interpret the proposal on basis of my own model bringing in the control of chemistry by magnetic body (MB). The idea is that MB adapts to the chemical dynamics and gets a control over it by driving forces realized in terms of dark cyclotron radiation form MB resonating with the chemical oscillations. "Breathing" would basically correspond to the periodic formation of flux tube network with high connectivity giving rise to crystal-like or gel-like state and subsequent decay to plasma-like state with low connectivity and would require metabolic energy feed.

  1. The periodic drive is central in TGD based model and gives rise to "breathing". Metabolic energy feed must be involved. In the model for life-like properties of plastic ball system it would be dark nucleosynthesis. In another experimental system acoustic wave feeds energy to the magnetic body (MB). The peroxide (H-O-O-H) bond between oxygens would be the source of the metabolic energy. Peroxide - usually regarded as a mere nuisance (highly Reactive Oxygen Species causing biological damage) - would serve as the "food" of the system. This is the new and radical idea. According to the article the primary energy source would be solar or geothermal. In TGD one can consider dark nucleosynthesis preceding ordinary nucleosynthesis as the source (it might have even given rise to Fe in the core of Earth!).

  2. Figure 1 in the article illustrates that peroxide H2O2 would produce in presence of S2O3-2 or S2O3-1 thermal and pH oscillations: "breathing". Peroxide is also told to produce oxidized sulfur species and oxidixe RNA nucleotides: this could also liberate metabolic energy stored in RNA. The outcome would be the replication of RNA. Oxidation of thiosulfate ion by H2O2 mentioned in the abstract would naively mean that S2O3-n, n=-1 or -2, gives 1 or 2 electrons to H2O2. Table 1 listing various reactions involved in oxidation is however rather complex. It begin to accept that I will never really understand what chemists mean with oxidation! In any case, also the oxidation reaction for S2O3-1 can happen in several steps.

Consider next the situation from quantum TGD point of view.
  1. Periodic oxidation would correspond to breathing generating repeatedly connected magnetic body with quantum coherence and larger heff - following the model for breathing plastic ball system as a periodic formation of crystal-like and plasma-like states.

  2. Cyclotron radiation from cyclotron condensates of some important ions would serve as clocks - breathing in several time scales. What are these ions? In plastic ball system protons and Argon ions. 300 Hz is the frequency for B=Bend=.2 Gauss and also the rate of ATP:s produced by ATPase: of course, it was not present at that time. Thiosulfate cyclotron frequency would be 5.4 Hz in Bend for charge of -2 units.

    The chemical oscillation periods emerging in the model of authors are measured in fraction of hour whereas the cyclotron periods for ions are fractions of second for ions for B=Bend. Therefore the strength of the magnetic field is much lower than that of Earth. Intergalactic magnetic fields are of order nanoTesla and this would bring scale factor of about 104 to cyclotron periods and they would be of same order of magnitude as the time scales coming from chemical kinetics. For proton the cyclotron period would be 33 seconds. For S2O3-2 cyclotron time scale would be scaled up by the atomic weight 112 giving roughly 40 minutes. This suggests that RNA era occurred in intergalactic space if it occurred at all. If it continues in recent biology, the dark matter must reside at the flux tubes of intergalactic magnetic field. This does not make sense in Maxwell's theory but makes sense in the many-sheeted space-time of TGD Universe.

  3. pH oscillation means that at least dark protons would be involved. pH could be quite generally a direct measure for the density of dark protons. The density of dark protons oscillating periodically meaning formation of cyclotron condensate and its decay could correspond to oscillating pH.

See the articles Life-like properties observed in a very simple system and About a model for the control of biological body by magnetic body.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Questions inspired by quantum associations

Associations have (or seem to have) different meaning depending on whether one is talking about cognition or mathematics. In mathematics the associations correspond to different bracketings of mathematical expressions involving symbols denoting mathematical objects and operations between them. The meaning of the expression - in the case that it has meaning - depends on the bracketing of the expression. For instance, one has a(b+c)≠ (ab)+c , that is ab+ac≠ ab+c). Note that one can change the order of bracket and operation but not that of bracket and object.

For ordinary product and sum of real numbers one has associativity: a(bc)=(ab)c and a+(b+c) = (a+b)+c. Most algebraic operations such as group product are associative. Associativity of product holds true for reals, complex numbers, and quaternions but not for octonions and this would be fundamental in both classical and quantum TGD.

The building of different associations means different groupings of n objects. This can be done recursively. Divide first the objects to two groups, divide these tow groups to to two groups each, and continue until you jave division of 3 objects to two groups - that is abc divided into (ab)c or a(bc). Numbers 3 and 2 are clearly the magic numbers.

This inspires several speculative questions related to the twistorial construction of scattering amplitudes as associative singlets, the general structure of quantum entanglement, quantum measurement cascade as formation of association, the associative structure of many-sheeted space-time as a kind of linguistic structure, spin glass as a strongly associative system, and even the tendency of social structures to form associations leading from a fully democratic paradise to cliques of cliques of ... .

  1. In standard twistor approach 3-gluon amplitude is the fundamental building brick of twistor amplitudes constructed from on-shell-amplitudes with complex momenta recursively. Also in TGD proposal this holds true. This would naturally follow from the fact that associations can be reduced recursively to those of 3 objects. 2- and 3-vertex would correspond to a fundamental associations. The association defined 2-particle pairing (both associated particles having either positive or negative helicities for twistor amplitudes) and 3-vertex would have universal structure although the states would be in general decompose to associations.

  2. Consider first the space-time picture about scattering (see this). CD defines interaction region for scattering amplitudes. External particles entering or leaving CD correspond to associative space-time surfaces in the sense that the tangent space or normal space for these space-time surfaces is associative. This gives rise to M8-H correspondence.

    These surfaces correspond to zero loci for the imaginary parts (in quaternionic sense) for octonionic polynomial with coefficients, which are real in octonionic sense. The product of ∏iPi) of polynomials with same octonion structure satisfying IM(Pi)=0 has also vanishing imaginary part and space-time surface corresponds to a disjoint union of surfaces associated with factors so that these states can be said to be non-interacting.

    Neither the choice of quaternion structure nor the choice of the direction of time axis assignable to the octonionic real unit need be same for external particles: if it is the particles correspond to same external particle. This requires that one treats the space of external particles (4-surfaces) as a Cartesian product of of single particle 4-surfaces as in ordinary scattering theory.

    Space-time surfaces inside CD are non-associative in the sense that the neither normal nor tangent space is associative: M8-M4× CP2 correspondence fails and space-time surfaces inside CD must be constructed by applying boundary conditions defining preferred extremals. Now the real part of RE(∏iPi) in quaternionic sense vanishes: there is genuine interaction even when the incoming particles correspond to the same octonion structure since one does not have union of surfaces with vanishing RE(Pi). This follows from s rather trivial observation holding true already for complex numbers: imaginary part of zw vanishes if it vanishes for z and w but this does not hold true for the real part. If octonionic structures are different, the interaction is present irrespective of whether one assumes RE(∏iPi)=0 or IM(∏iPi)=0. RE(∏iPi)=0 is favoured since for IM(∏iPi)=0 one would obtain solutions for which IM(Pi)=0 would vanish for the i:th particle: the scattering dynamics would select i:th particle as non-interacting one.

  3. The proposal is that the entire scattering amplitude defined by the zero energy state - is associative, perhaps in the projective sense meaning that the amplitudes related to different associations relate by a phase factor (recall that complexified octonions are considered), which could be even octonionic. This would be achieved by summing over all possible associations.

  4. Quantum classical correspondence (QCC) suggests that in ZEO the zero energy states - that is scattering amplitudes determined by the classically non-associative dynamics inside CD - form a representation for the non-associative product of space-time surfaces defined by the condition RE(∏iPi)=0. Could the scattering amplitude be constructed from products of octonion valued single particle amplitudes. This kind of condition would pose strong constraints on the theory. Could the scattering amplitudes associated with different associations be octonionic - may be differing by octonion-valued phase factors - and could only their sum be real in octonionic sense (recall that complexified octonions involving imaginary unit i commuting with the octonionic imaginary units are considered)?

One can look the situation also from the point of view of positive and negative energy states defining zero energy states as they pairs.
  1. The formation of association as subset is like formation of bound state of bound states of ... . Could each external line of zero energy state have the structure of association? Could also the internal entanglement associated with a given external line be characterized in terms of association.

    Could the so called monogamy theorem stating that only two-particle entanglement can be maximal correspond to the decomposing of n=3 association to one- and two-particle associations? If quantum entanglement is behind associations in cognitive sense, the cognitive meaning of association could reduce to its mathematical meaning.

    An interesting question relates to the notion of identical particle: are the many-particle states of identical particles invariant under associations or do they transform by phase factor under association. Does a generalization of braid statistics make sense?

  2. In ZEO based quantum measurement theory the cascade of quantum measurements proceeds from long to short scales and at each step decomposes a given system to two subsystems. The cascade stops when the reduction of entanglement is impossible: this is the case if the entanglement probabilities belong to an extension of extension of rationals characterizing the extension in question. This cascade is nothing but a formation of an association! Since only the state at the second boundary of CD changes, the natural interpretation is that state function reduction mean a selection of association in 3-D sense.

  3. The division of n objects to groups has also social meaning: all social groups tend to divide into cliques spoiling the dream about full democracy. Only a group with 2 members - Romeo and Julia or Adam and Eve - can be a full democracy in practice. Already in a group of 3 members 2 members tend to form a clique leaving the third member outside. Jules and Catherine, Jim and Catherine, or maybe Jules and Jim! Only a paradise allows a full democracy in which non-associativity holds true. In ZEO it would be realized only at the quantum critical external lines of scattering diagram and quantum criticality means instability. Quantum superposition of all associations could realize this democracy in 4-D sense.

A further perspective is provided by many-sheeted space-time providing classical correlate for quantum dynamics.
  1. Many-sheeted space-time means that physical states have a hierarchical structure - just like associations do. Could the formation of association (AB) correspond basically to a formation of flux tube bond between A and B to give AB and serve as space-time correlate for (negentropic) entanglement. Could ((AB)C) would correspond to (AB) and (C) "topologically condensed" to a larger surface. If so, the hierarchical structure of many-sheeted space-time would represent associations and also the basic structures of language.

  2. Spin glass is a system characterized by so called frustrations. Spin glass as a thermodynamical system has a very large number of minima of free energy and one has fractal energy landscape with valleys inside valleys. Typically there is a competition between different pairings (associations) of the basic building bricks of the system.

    Could spin glass be describable in terms of associations? The modelling of spin glass leads to the introduction of ultrametric topology characterizing the natural distance function for the free energy landscape. Interestingly, p-adic topologies are ultrametric. In TGD framework I have considered the possibility that space-time is like 4-D spin glass: this idea was originally inspired by the huge vacuum degeneracy of Kähler action. The twistor lift of TGD breaks this degeneracy but 4-D spin glass idea could still be relevant.

See the article From amplituhedron to associahedron or the chapter Does M8-H duality reduce classical TGD to octonionic algebraic geometry? of "Physics as generalized number theory".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

About a model for the control of biological body by magnetic body

The recent work in TGD in attempts to understand various surprising findings (see this and this) about very simple self-organizing systems assuming that they are actually macroscopic quantum systems at the level of magnetic body (MB) leads to a rather concrete model for how MB carrying dark matter identified as heff/h=n phases controls the part of system consisting of ordinary matter - biological body (BB) in biological context. The key element is magnetic body (MB) involving flux tube network able to make heff=n× h changing phase transition changing its connectivity (the extreme corresponds to phase transition between crystal-like and plasma-like states).

The control is assumed to involve Alfwen waves with the frequencies of cyclotron transitions for the dark matter. Alfwen waves induce resonant forced oscillations of the particles at the nodes of the network. MB adapts to the dynamics of BB by using quantum criticality: if the length L and transversal area S of flux tube are scaled up by n, the ratio L/S is unaffected and the energetics of the system (cyclotron energies and the magnetic energies of the flux tubes ) remains un-affected but frequencies scale by n. By a suitable choice of n system and L/S ratio MB can gain control over BB.

If MB controls basic biological processes at BB then cyclotron frequencies for biologically important ions determine the time scales of basic bio-processes involving various kinds of molecular motors. In communications from BB to MB the difference Δ fc of cyclotron frequencies of ions associated with cell membrane at different sides of cell membrane and would determine the time scales of these communications. For large enough values of n membrane potential would add a small contribution Δ f = ZeV/heff to Δ fc and code nerve pulse patterns and therefore sensory information to the Josephson radiation.

In the article About a model for the control of biological body by magnetic body this picture is discussed in biological context.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Saturday, December 02, 2017

Chinese satellite provides evidence for second generation Z boson predicted by TGD

I found in FB a link to a highly interesting popular article "Dark matter exists? Chinese satellite detects mysterious signals while measuring cosmic rays". There is an article in Nature with title Direct detection of a break in the teraelectronvolt cosmic-ray spectrum of electrons and positrons by DAMPE collaboration.

A Chinese satellite – Dark Matter Particle Explorer (DAMPE), also called Wukong or "Monkey King", is reported to have made a discovery. The energy spectrum of cosmic ray electrons and positrons is measured. The surprise was that there is a break at about .9 TeV and a strange spike at around 1.4 TeV. The conclusion is that the spike indicates a particle with a mass of about 1.4 TeV on the spectrum. To me a more natural conclusion would be that there is a particle with mass 2.8 TeV decaying to electron positron pair. Unfortunately, the popular article does not allow to conclude what is the precise finding.

In any case, TGD predicts scaled up variant of electroweak physics and there are several pieces of evidence for its existence coming from the violation of lepton and quark universality (see this). The mass scale for this physics would correspond to Gaussian Mersenne prime MG,79 = (1+i)79-1 and is obtained by scaling the mass scale of electroweak physics by a factor 32. This predicts the mass of Z boson of this physics to be 2.9 TeV. It would decay to electron positron pairs with members having energy 1.45 TeV in cm system. Also gluons could have scaled up variants and there is some evidence for this too from the breaking of the quark universality.

Cosmic ray electron and positron spectra are found to have peak at 1.4 TeV. Could they result in the decays of the second generation Z boson with mass 2.9 TeV? In TGD framework this boson would not however solve dark matter puzzle. In TGD Universe dark matter has explanation as heff/h=n phases of ordinary matter.

Could the spectral "break" at about .9 TeV (I am not quite sure what "break" really means) relate to massive photon of MG,79physics?

Article also mentions that the cosmic ray positron flux is higher than predicted above 70 GeV. That this energy corresponds to the mass of M89 pion, might not be an accident. The decay to gamma pairs dominates and gives a peak but the rate for the decay to gamma+ e+e- pair would be by factor of order &alpha ≈ 1/137 lower and would give a break rather than peak since the energy spectrum of pairs is continuous. Therefore support for both M89 and MG,79 physics emerges. Maybe the long-waited breakthrough of TGD might not be in too far future.

See the article Indications for the breaking of Universality in B meson decays or the chapter New Physics Predicted by TGD: I of "p-Adic physics".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Physics as number theory and number theory as physics

It seems that also mathematicians are discovering the number theoretic vision about physics - or rather - the physics inspired vision about number theory (see the article in Not Even Wrong). In TGD I call this M8-H duality, H=M4×CP2. Arithmetic geometer Minhyong Kim is realizing that rational points of certain exotic spaces encountered in number theory are very special: the space of paths emanating from rational points is speculated to have additional symmetries analogous to gauge symmetries.

In TGD the world of classical worlds (WCW) as as its points pairs or 3-surfaces with members at boundaries of CD and paths between membees correspond to what I call preferred extremals - space-time surfaces.

  1. At the level of M^8 - the arithmetic side - space-time surfaces are algebraic varieties of certain kind and satisfy algebraic equations plus associativity conditions coding quantum criticality.

  2. At the level of M^4xCP_2 - the physics side - the preferred extremals satisfy an infinite number of gauge conditions: gauge symmetry again!

Not only rational numbers but all extensions of rationals are physically very special, and evolution corresponds to increasing complexity of this extension. Therefore TGD vision is much more general. In any case. it is nice to see that mathematicians are moving to the same direction as TGD!

See the article Does M8-H duality reduce classical TGD to octonionic algebraic geometry?.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

The arrow of time is relative: experimental support

It is amazing how experimental findings pop up - almost one every day - to support TGD. Experimenters seem to work as if they knew about predictions of TGD and were systematically testing its predictions. Do they? Or does science make progress at the level of collective consciousness and are individual scientists like neutrons in brain? Certainly TGD is a curse word for the HEP-TH empire (high energy physics - theory). Last week I wrote about experiments giving support for TGD view about prebiotic forms of life. Now it is about arrow of time: the arrow of time is relative.

Remark: TGD is like the forbidden interval C-F# in music before times of Bach (the sound of ambulance by the way): it was regarded as something satanic by the church. You can find it oppoing up is the compositions of Bach again and again! Suddenly it became deeply spiritual!

What has been found that heat flows from from system with temperature T1 to a system with temperature T2> T1 if there is correlation between the two systems meaning that the density matrix for the two nuclear systems (samples consisting of hydrogen atoms and carbon atoms) is not mere tensor product of density matrices but contains an additional term describing correlation. It must be emphasized that this finding is not in conflict with the standard view about second law which only says that heat flows from system with higher temperature to that with lower temperature provided that there are no correlations between the systems.

The argument runs as follows. The mutual information for the uncorrelated systems vanishes, and since it can only increase this implies flow of heat in the standard direction. If the mutual information is non-vanishing in the initial situation (due to the correlation) it can also decrease and this can give a heat flow in non-standard direction. This has been observed.

Although one can model the finding using standard thermodynamics, one can ask whether something deeper might be involved. Should one be cautious and talk only about the changing direction of heat flow due to the breaking of the basic assumptions of thermodynamics, and avoid speaking about direction of thermodynamical time? Or could a genuine change of the arrow of time take place? Going even deeper, one must ask what thermodynamical time, the time of physicist (geometric time), and the arrow of time do really mean? What is the relationship between these two times? This leads to ponder questions about the basics of quantum measurement theory and here I can only consider TGD based vision (see this).

  1. The basic prediction of zero energy ontology (ZEO) is that the arrow of geometric time can have both signs whereas the arrow of subjective time (relating closely to thermodynamic time) defined by experience created by sequence of state function reductions is always the same. The arrow of geometric time is indeed relative. The flow of geometric time corresponds to the increase of distance between tips of causal diamond (CD) and the increase in particular reduction is at either tip of CD and in this manner defines arrow of time. CD grows either "upwards" or "downwards". A geometric measure for experienced time is that distance between the tips of CD which always increases.

    Time reflection symmetry (T) with respect tot he center of CD is broken in TGD: the classical time evolutions of space-time surfaces are not T mirror images of each other. This is true also for the quantal evolutions defined by zero energy states essentially as quantum superpositions of classical evolutions. States and their time reversals obey the initial conditions at opposite boundaries of CD. Arrow of time is forced by the place (either boundary of CD), where initial conditions are posed, not by the initial conditions themselves.

  2. One must however remember that ZEO describes genuine quantum systems whereas thermodynamics decribes ensemble, which is a highly idealized notion. In ZEO arrow of geometric time would change in each "big" quantum jump and would remain the same during the sequence of "small" state function reductions defining the counterpart of Zeno effect or weak measurement.

  3. Initial conditions breaking the basic assumptions of thermodynamics induce correlations and the heat flow in "wrong" direction in the model for the finding. The arrow of time is claimed to be changed in time interval of length of order 2 millisecond. Interestingly, millisecond happens to characterize the time scale of nerve pulse and ZEO predicts that in living matter the change of the arrow of time takes place routinely. In ZEO based description the growth of the temporal distance between the tips of CD would be of order 2 milliseconds.

    It would be however the opposite boundary of CD in geometric past that would receide farther away. One can argue that it is not possible measure the position of the past boundary of CD directly. But is it possible to measure the distance between the tips of CD indirectly from the behavior of the ensemble? ZEO would suggest that the time appearing in the Hamiltonian modelling the system corresponds to the distance between tips of CD and never decreases. The change of the direction of heat flow would correspond to the reduction to the original boundary of CD in the experiment and the correlation would make ZEO visible.

    If the two descriptions are equivalent, the initial correlations for the ensemble force should correspond to posing initial conditions at the non-standard boundary of CD leading to the reversal of the arrow of time. The very act of posing the correlations would correspond to a "big" state function reduction to opposite boundary of CD. In standard quantum measurement theory state preparation indeed corresponds to this state function reduction so that the two descriptions might be consistent.

See the the article Re-examination of the basic notions of TGD inspired theory of consciousness.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Tuesday, November 28, 2017

From amplituhedron to associahedron

Lubos has a nice article (see this) explaining the proposal represented in the newest article by Nima Arkani-Hamed, Yuntao Bai, Song He, Gongwang Yan (see this). Amplituhedron is generalized to a purely combinatorial notion of associahedron and shown to make sense also in string theory context (particular bracketing). The hope is that the generalization of amplituhedron to associahedron allows to compute also the contributions of non-planar diagrams to the scattering amplitudes - at least in N=4 SYM. Also the proposal is made that color corresponds to something less trivial than Chan-Paton factors.

The remaining problem is that 4-D conformal invariance requires massless particles and TGD allows to overcome this problem by using a generalization of the notion of twistor: masslessness is realized in 8-D sense and particles massless in 8-D sense can be massive in 4-D sense.

In TGD non-associativity at the level of arguments of scattering amplitude corresponds to that for octonions: one can assign to space-time surfaces octonionic polynomials and induce arithmetic operations for space-time surface from those for polymials (or even rational or analytic functions). I have already earlier demonstrated that associahedron and construction of scattering amplitudes by summing over different permutations and associations of external particles (space-time surfaces). Therefore the notion of associahedron makes sense also in TGD framework and summation reduces to "integration" over the faces of associahedron. TGD thus provides a concrete interpretation for the associations and permutations at the level of space-time geometry.

In TGD framework the description of color and four-momentum is unified at the level and the notion of twistor generalizes: one has twistors in 8-D space-time instead of twistors in 4-D space-time so Chan-Paton factors are replaced with something non-trivial.

1. Associahedrons and scattering amplitudes

The following describes briefly the basic idea between associahedrons.

1.1 Permutations and associations

One starts from a non-commutative and non-associative algebra with product (in TGD framework this algebra is formed by octonionic polynomials with real coefficients defining space-time surfaces as the zero loci of their real or imaginary parts in quaternionic sense. One can indeed multiply space-time surface by multiplying corresponding polynomials! Also sum is possible. If one allows rational functions also division becomes possible.

All permutations of the product of n elements are in principle different. This is due to non-commutativity. All associations for a given ordering obtained by scattering bracket pairs in the product are also different in general. In the simplest case one has either a(bc) or (ab)c and these 2 give different outcomes. These primitive associations are building bricks of general associations: for instance, abc does not have well-defined meaning in non-associative case.

If the product contains n factors, one can proceed recursively to build all associations allowed by it. Decompose the n factors to groups of m and n-m factors. Continue by decomposing these two groups to two groups and repeat until you have have groups consisting of 1 or two elements. You get a large number of associations and you can write a computer code computing recursively the number N(n) of associations for n letters.

Two examples help to understand. For n=3 letters one obviously has N(3)= 2. For n=4 one has N(4)=5: decompose abcd to (abc)d and a(bcd) and (ab)(cd) and then the 3 letter groups to two groups: this gives 2+2+1 =5 associations and associahedron in 3-D space has therefore 5 faces.

1.2 Geometric representation of association as face of associahedron

Associations of n letters can be represented geometrically as so called Stasheff polytope (see this). The idea is that each association of n letters corresponds to a face of polytope in n-2-dimensional space with faces represented by the associations.

Associahedron is constructed by using the condition that adjacent faces (now 2-D polygons) intersecting along common face (now 1-D edges). The number of edges of the face codes for the structure particular association. Neighboring faces are obtained by doing minimal change which means replacement of some (ab)c with a(bc) appearing in the association as a building bricks or vice versa. This means that the changes are carried out at the root level.

1.3 How does this relate to particle physics?

In scattering amplitude letters correspond to external particles. Scattering amplitude must be invariant under permutations and associations of the external particles. In particular, this means that one sums over all associations by assigning an amplitude to each association. Geometrically this means that one "integrates" over the boundary of associahedron by assigning to each face an amplitude. This leads to the notion of associahedron generalizing that of amplituhedron.

Personally I find it difficult to believe that the mere combinatorial structure leading to associahedron would fix the theory completely. It is however clear that it poses very strong conditions on the structure of scattering amplitudes. Especially so if the scattering amplitudes are defined in terms of "volumes" of the polyhedrons involved so that the scattering amplitude has singularities at the faces of associahedron.

An important constraint on the scattering amplitudes is the realization of the Yangian generalization of conformal symmetries of Minkowski space. The representation of the scattering amplitudes utilizing moduli spaces (projective spaces of various dimensions) and associahedron indeed allows Yangian symmetries as diffeomorphisms of associahedron respecting the positivity constraint. The hope is that the generalization of amplituhedron to associahedron allows to generalize the construction of scattering amplitudes to include also the contribution of non-planar diagrams of at N=4 SYM in QFT framework.

2. Associations and permutations in TGD framework

Also in the number theoretical vision about quantum TGD one encounters associativity constraints leading to the notion of associahedron. This is closely related to the generalization of twistor approach to TGD forcing to introduce 8-D analogs of twistors (see this).

  1. By M8-H duality (H=M4× CP2) the scattering are assignable to complexified 4-surfaces in complexified M8. Complexified M8 is obtained by adding imaginary unit i commutating with octonionic units Ik, k=1,,..,7. Real space-time surfaces are obtained as restrictions to a Minkowskian subspace complexified M8 in which the complexified metric reduces to real valued 8-D Minkowski metric. This allows to define notions like Kähler structure in Minkowskian signature and the notion of Wick rotations ceases to be ad hoc concept. Without complexification one does not obtain algebraic geometry allowing to reduces the dynamics defined by partial differential equations for preferred extremals in H to purely algebraic conditions in M8. This means huge simplifications but the simplicity is lost at the QFT-GRT limit when many-sheeted space-time is replaced with slightly curved piece of M4.

  2. The real 4-surface is determined by a vanishing condition for the real or imaginary part of octonionic polynomial with RE(P) and and IM(P) defined by the composition of octonion to two quaternions: o= RE(o)+ I4IM(o), where I4 is octonionic unit orthogonal to a quaternionic sub-space and RE(o) and IM(o) are quaternions. The coefficients of the polynomials are assumed to be real. The products of octonionic polynomials are also octonionic polynomials (this holds for also for general power series with real coefficients (no dependence on Ik). The product is not however neither commutative nor associative without additional conditions. Permutations and their associations define different space-time surfaces. The exchange of particles changes space-time surface. Even associations do it. Both non-commutativity and non-associativity have a geometric meaning at the level of space-time geometry!

  3. For space-time surfaces representing external particles associativity is assumed to hold true: this in fact guarantees M8-H correspondence for them! For interaction regions associativity does not hold true but the field equations and preferred extremal property allow to construct the counterpart of space-time surface in H from the boundary data at the boundaries of CD fixing the ends of space-time surface.

    Associativity poses quantization conditions on the coefficients of the polynomial determining it. The conditions are interpreted in terms of quantum criticality. In the interaction region identified naturally as causal diamond (CD), associativity does not hold true. For instance, if external particles as space-time surfaces correspond to vanishing of RE(Pi) for polynomials representing particles labelled by i, the interaction region (CD) could correspond to the vanishing of IM(Pi) and associativity would fail. At the level of H associativity and criticality corresponds to minimal surface property so that quantum criticality corresponds to universal free particle dynamics having no dependence on coupling constants.

  4. Scattering amplitudes must be commutative and associative with respect to their arguments which are now external particles represented by polynomials Pi This requires that scattering amplitude is sum over
    amplitudes assignable to 4-surfaces obtained by allowing all permutations and all associations of a given permutation. Associations can be described combinatorially by the associahedron!

    Remark:. In quantum theory associative statistics allowing associations to be represented by phase factors can be considered (this would be associative analog of Fermi statistics). Even a generalization of braid statistics can be considered.

Yangian variants of various symmetries are central piece also in TGD although supersymmetries are realized in different manner and generalized to super-conformal symmetries: these include generalization of super-conformal symmetries by replacing 2-D surfaces with light-like 3-surfaces, supersymplectic symmetries and dynamical Kac-Moody symmetries serving as remnants of these symmetries after supersymplectic gauge conditions characterizing preferred extremals are applied, and Kac-Moody symmetries associated with the isometries of $H$ . The representation of Yangian symmetries as diffeomorphisms of the associahedron respecting positivity constraint encourages to think that associahedron is a useful auxiliary tool also in TGD. 3. Is color something more than Chan-Paton factors?

Nima et al talk also about color structure of the scattering amplitudes usually regarded as trivial. It is claimed that this is actually not the case and that there is non-trivial dynamics involved. This is indeed the case in TGD framework. Also color quantum numbers are twistorialized in terms of the twistor space of CP2, and one performs a twistorialization at the level of M8 and M4× CP2. At the level of M8 momenta and color quantum numbers correspond to associative 8-momenta. Massless particles are now massless in 8-D sense but can be massive in 4-D sense. This solves one of the basic difficulty of the ordinary twistor approach. A further bonus is that the choice of the imbedding space H becomes unique: only the twistor spaces of S4 (and generalized twistor space of M4 and CP2 have Kähler structure playing a crucial role in the twistorialization of TGD. To sum up, all roads lead to Rome. Everyone is well-come to Rome!

See the articles Does M 8 − H duality reduce classical TGD to octonionic algebraic geometry? and From amplituhedron to associahedron.

Addition: Marni Lee Sheppard wrote a thesis in which the notion of associahedron appeared. I remember discussions in some net group. Her motivations came from category theory. Marni had bad luck. Big boys rarely remember who proposed the idea first if she/he is not a name.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Friday, November 24, 2017

Misbehaving Ru atoms and valence electrons as dark electrons

The understanding of dark matter in TGD sense has been evolving rapidly recently. Dark matter at magnetic flux tubes appears to be part of ordinary chemistry and even more a part of organic chemistry. Non-equilibrium-thermodynamics has popped up also as a natural application of tensor networks formed from flux tubes carrying dark matter perform quantum phase transitions. The ideas about how to generate systems with life-like properties are getting rather precise. Dark matter and flux tubes are suddenly everywhere! Also this piece of text relates to this revolution.

In FB I received a link to a highly interesting article. The title of the article was "Breakthrough could launch organic electronics beyond cell phone screens" and is tailored to catch the attention of techno-oriented leader. My attention was however caught for different reasons. The proposed technology would rely on the observation that Ruthenium atoms do not behave as they are expected to behave.

Ru atoms appear as dimers of two Ru atoms in the system considered. Free Ru atoms with one valence electron are however needed: they would become ions by giving up their valence electrons, and these electrons would serve as current carriers making the organic material in question semi-conductor. Irradiation by UV light was found to split Ruthenium dimers to single Ru atoms. If the total energy of Ru dimer is smaller than that for two Ru atoms, thermodynamics predicts that the Ru atoms recombine to dimers after the irradiation ceases. The did not however happen!

Can one understand the mystery in TGD framework?

  1. Ruthenium atoms have one outer s-electron at 5:th shell. One would expect that Ru dimer has valence bond with shared 5s electrons. I recently learned about mysteriously disappearing valence electrons of rare Earth metals caused by heating. This gives strong support for the idea that valence electrons of free atoms can become dark in TGD sense: that is their Planck constant increases and the orbitals become large. The analogy with Rydberg atoms is obvious and it could be that Rydberg atoms in some case have dark valence electrons. Since electron's binding energy scale scales like 1/heff2, the creation of these states requires energy and therefore heating is required. Also irradiation by photons with energy equal to energy difference between ordinary and dark states should give rise to the same phenomenon. This would provide a manner to create dark electrons and a new technology.

  2. This also inspired the proposal that valence bond (thought to be understood in chemistry with inspiration coming from the reductionistic dogma) involves flux tube pair and heff/h= n which is larger than for ordinary quantum theory. This provides new very concrete support for the view that the transitions from atomic physics to chemistry and from chemistry to organic chemistry could involve new physics provided by TGD.

    The step from atomic physics to chemistry with valence bond would involve new physics: the delocalization of valence electrons to flux tubes due to the increase of heff! Valence electrons would be dark matter in TGD sense! The step from chemistry to organic chemistry would involve delocalization of proton as dark proton by similar mechanism and give rise to hydrogen bond and also many other new phenomena.

  3. The increase of heff would reduce the binding energy from the expected. This would be the case for so called ( and somewhat mysterious) high energy phosphate bond. This picture conforms with the fact that biological energy storage indeed relies on valence bonds.

    If this vision is correct, the breaking of valence bond would split the flux tube pair between two Ru atoms by reconnection to flux loops associated with Ru atom. The resulting pair of free Ru atoms would have lower energy than Ru dimer and would be favored by thermodynamics. The paradox would disappear.

A couple of critical questions are in order.
  1. Why irradiation would be needed at all? Irradiation would kick the dimer system over a potential wall separating it from a state two free Ru atoms. Also the magnetic energy of the flux tube would contribute to the energy of dimer and make it higher than that of free state.

  2. Why Ru dimers would not decay spontanously to pairs of free Ru atoms? This is the case if the energy needed to overcome the potential wall is higher than thermal energy at temperatures considered. One could also argue that electronic states with different values of heff/h=n are not in thermal equilibrium: one has far-from-equilibrium thermodynamical state. These electrons would indeed represent dark matter in TGD sense and interact rather weakly with ordinary matter so that it would take time for thermal equilibrium to establish itself.

    TGD indeed leads to the proposal that the formation of states regarded as far-from-thermal equilibrium states in standard physics approach means formation of flux tubes networks with heff/h=n larger than for the original state (see this and this). If this interpretation is correct, then one can also consider the possibility that the energy of the free state is higher than that of the dimer as assumed by the experimenters.

See the article Mysteriously disappearing valence electrons of rare Earth metals and hierarchy of Planck constants or the chapter Quantum criticality and dark matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.