BICEP2 might have detected gravitational waves

BICEP2 team has announced a detection of gravitational waves via the effects of gravitational waves on the spectrum on polarization of cosmic microwave background (CMB). What happens that gravitational waves (or possibly some other mechanism) transforms so called E modes which correspond the curl free part of polarization field expressible as gradient to B modes responsible for the divergenceless part of polarization field expressible as curl of vector field.

Interaction of photons with gravitons would induce this polarization changing transformation: this is discussed in earlier post by Lubos. The signal is unexpectedly strong constraints on possible models, in particular to the inflationary models which are currently in fashion. There is excellent popular summary of the physics behing scalar, vector, and tensor perturbations of CMB here. The map produced by BICEP describes the vorticity of the polarization field at the sky and one can clearly see it.

There has been a lot of pre-hype about the finding as proof for inflation, which it is not. Even Scientific American falls in the sin of inflationary hyping which is a pity. Inflationary theory is only the dominating theory which might be able to explain the finding.

In the following the findings are discussed in the framework of TGD based cosmology in which the flatness of 3-space is interpreted in terms of quantum criticality rather than inflation. The key role is played by gradually thickening cosmic strings carrying magnetic monopole flux, dark energy as magnetic energy and dark matter as large h_eff phases at cosmic strings. Very thin cosmic strings dominate the cosmology before the emergence of space-time as we know it and quantum criticality is associated with the phase transition between these two phases. Later cosmic strings serve as seeds of various cosmological structures by decaying partially to ordinary matter somewhat like inflaton fields in inflationary cosmology. Cosmic strings also explain the presence of magnetic fields in cosmos difficult to understand in standard approch. The crucial point is that - in contrast to ordinary magnetic fields - monopole fluxes do not require for their creation any currents coherent in long scales.

Liam McAllister's summary about the findings of BICEP2 team

Liam McAllister from Cornell University has written an excellent posting about the discovery and its implications in Lubos's blog. McAllister discusses the finding from several points of view. Can one trust that the finding is real? How should one interpret the result? What are its implications? A brief summary is in order before going to details.

1. Consideration is restricted to inflationary scenarios but it is made clear that they are not the only option. It is emphasized that a huge amount of inflationary parameter space is excluded by the unexpectedly high strength of the effect. Also the general problems of inflationary models are made explicit - a great favor for those who are not inflationary enthusiasts and might have something else in mind.
   
   
2. Also other than gravitonic mechanisms transforming E modes to B modes can be imagined. For instance, the signal might not be primordial but caused by polarized foreground sources: BICEP claims that these contributions have been eliminated.
   
   
3. The most important conclusion is of course that a direct detection of gravitational waves - maybe even quantal ones - has been achieved. Earlier gravitational radiation has been detected only a slowing down of rotation rate of pulsars (Hulse-Taylor binary pulsar).
   
   

Comparison of inflationary models and TGD

Further conclusions depend on the cosmological model adopted and McAllister considers the situation in the framework of inflationary models and lists the basic aspects of inflationary model.

1. The Universe on large scales should be approximately homogenous, isotropic and flat.
   
   
2. The primordial scalar density perturbations should be correlated on super-horizon scales and be approximately Gaussian, adiabatic, and approximately scale-invariant.
   

In TGD framework inflationary cosmology is replaced with a cosmology fixed almost uniquely by the criticality of the mass density when combined with imbeddability to N⁴× CP₂ as Lorentz invariant 4- surface. The only free parameter is the finite durationkenotau of the critical period. This kind of critical - it seems even quantum critical - periods are predicted to appear in various scales so that Russian doll cosmology is strongly suggested as in case of inflationary models. Scalar fields (inflaton fields) are replaced with cosmic strings, which evolve by thickening their M⁴ projections from string world sheets to 4-D ones. Magnetic energy replaces dark energy and has interpretation as counterpart for the energy of inflation field. Dark matter at magnetic flux tubes corresponds to large hbar phases (see this , this , and this ).

1. In TGD framework the long range correlations would be due to quantum criticality rather than extremely rapid expansion during inflationary period. The Universe in large scales should be also now homogenous, isotropic, and flat.
   
   
2. The primordial density perturbations reflect the presence of cosmic strings (see this) before the phase transition period. These cosmic strings have 2-D M⁴ projection, which is minimal surface, so that these object behave for all practical purposes like strings, and CP₂ projection is e 2-D holomorphic surface in CP₂. During primordial period cosmic strings dominate and the mass density behaves like 1/a², where a is proper time coordinate of the light-cone. The mass per comoving volume goes to zero at the moment of big bang so that initial singularity is smoothed out and big bang transforms to "a silent whisper amplified to big bang". For radiation dominated cosmology mass density would behave as 1/a⁴ giving rise to infinite energy per comoving volume at the moment of Big Bang.
   
   
3. Cosmic strings gradually thicken their M⁴ projections and the huge primordial magnetic fields carrying quantized monopole flux weaken. These fields differ crucially from the ordinary magnetic fields in that no current is needed to create them - this is due the fact that CP₂ Kähler form defines a self-dual magnetic monopole (instanton). Amazingly, even the magnetic fields penetrating to super-conductors could be this kind and perhaps even those associated with ferromagnets.
   

   This can explain why primordial and recent Universe is full of magnetic fields in length scales, where they should not exist since the currents creating them cannot exist in long scales. The thickening of the remnants of cosmic strings would give rise to birth of galaxies organised like pearls in necklace along big cosmic strings: galaxies are indeed known to be organized into long string like structures and density perturbations would correspond to these strings.
   

   No vacuum expectations of Higgs like scalar fields are needed. Even in elementary particle physics Higgs expectation is replaced with string tension assignable to string like structures accompanying elementary particles.
   

   Cosmic strings would carry dark energy as magnetic energy and dark matter as phases with large values of Planck constant coming as integer multiple of ordinary Planck constant. Ordinary matter would be formed when cosmic strings and dark matter "burn" to ordinary matter: this would be the TGD counterpart for the decay of inflaton field to ordinary matter.
   
   

4. Cosmic strings would define the density perturbations having correlations on super-horizon scales. In the first approximation they are certainly Gaussian. Whether they are adiabatic (no exchange of heat with environment) is an interesting question: if they correspond to large values of Planck constant, this is certainly what one expects. The perturbations would be approximately scale invariant: p-adic length scale hypothesis would formulate this quantitatively by replacing continuum of scales with a hierarchy of discrete p-adic length scales coming as powers of square root of 2 (half octaves).
   
   
5. One can of course ask about spectrum of Planck constant coming as integer multiples of ordinary Planck constant: could it realize the presence of large number of length scales characterizing criticality? Could the spectrum of length scales implied by spectrum of Planck constants be the TGD counterpart for the inflationary expansion? Does the average value of Compton length or flux tube length proportional to h_eff=nh increase with exponential rate during quantum criticality as larger and larger Planck constants emerge?
   

It seems that at this qualitative level TGD survives basic tests at qualitative level but without assuming inflation fields and exponentially fast expansion since quantum criticality predicting flat 3-space (dimensional parameters such as curvature of 3-space vanish). Cosmic strings would represent the long range fluctuations. A further bonus is that cosmic strings explain dark energy and dark matter, and also the presence of long range magnetic fields in cosmos.

Fluctuations of gravitational field

McAllister gives a nice overall summary about the physics involved if given by inflationary models.

1. It is not yet fully clear whether the fluctuations of gravitational field are quantum mechanical or classical. In TGD framework quantum classical correspondence suggests that quantal and classical identifications might be equivalent.
   
   
2. Just as the quantum fluctuations of inflaton field would give rise to the density fluctuations visible as temperature anisotropies and large scale structures, the quantum fluctuations of gravitational field would give rise to the observed B modes in inflationary scenario. The correlation functions of gravitons in the background metric would tell everything. The problem is that we do not yet have quantum theory of gravitation allowing to really calculate everything except in QFT approximation.
   
   
3. In TGD framework the fluctuations should physically correspond to cosmic strings and the question is whether gravitons can be identified as massless modes for the cosmic strings so that string like objects would give all. In fact, elementary particles are in TGD framework identified as string like objects! Ironically, TGD as generalization of string model realizes stringy dream in all scales and even for ordinary elementary particles!
   

Since gravitons couple to energy the formula for the energy density at which inflationary period begins should determine the spectrum of gravitational waves. Inflationary models predict this energy scale as the fourth root of the energy density in the beginning of inflation: the formula is given by in the article of McAllister. This formula contains single dimensionless parameter called r, and BICEP measurements give a rather large value r=.2 for it.

The natural expectation is that any theory explaining the findings in terms of gravitons produces similar prediction but with the energy density of scalar field replaced with something else. In TGD the energy density assignable to cosmic strings so that the square root of the energy density of cosmic string multiplied by some numerical factor should be the relevant parameter now.

Inflation should begin at GUT mass scale

The first implication of the findings is that if inflation explains the findings, it should have begun in GUT scale 10¹⁶ GeV, which is very high. The findings cut off a gigantic portion of the parameter space of inflationary models and leaves only inflation potentials that are approximately translationally invariant.

In TGD framework one expects that the energy scale corresponds to that in which quantum critical period begins after string dominated primordial period. This scale should be given by CP₂ mass scale apart from some numerical factor. CP₂ mass corresponds to m(CP₂)=hbar/R(CP₂), where R(CP₂) is CP₂ radius. p-Adic mass calculations predict the value of electron mass and assign to electron the largest Mersenne prime M₁₂₇ having the property that the p-adic length scales kenosqrtpR(CP₂) is not completely super-astronomical. This fixes R(CP₂) and m(CP₂). The outcome is m(CP₂)∼ 4× 10¹⁵ GeV.

A numerical constant can be present in the estimate for the energy scale at which quantum critical period begins. In particular, the factor 1/α_K^1/4 should be present since Kähler action is proportional to 1/α_K, which by simple argument is in excellent approximation equal to the inverse of the fine structure constant equal to 137. This would rise the estimate for the energy scale to about 10¹⁶ GeV if the same formula for it is used also in TGD (which might of course be wrong!). With a considerable dose of optimism one could say that TGD allows to understand why the measured value of r is what it is.

Difficulties of the inflationary approach

What is nice that McAllister discusses also so the difficulties of inflationary approach.

1. So called Lyth bound gives lower bound for the distance that inflaton's vacuum expectation must move in field space in order to generate detectably large primordial waves: that is the duration of the inflationary expansion. The lower bound is given by Planck mass M_P: Δ Φ >M_P.
   
   
2. There is however a problem. This distance should be not larger than the cutoff scale Λ of the quantum field theory. But if standard wisdom is taken granted, Λ should be smaller than Planck mass M_P giving Δ Φ<M_P!
   
   
3. One can certainly invent all kinds of tricky mechanisms to circumvent the problem: the proposal considered by McAllister is that the couplings of Φ are suppressed to heavy degrees of freedom so that the UV theory respects the approximate shift symmetry Φ→ Φ+Δ Φ. This is true for massless scalar field but this field does not develop vacuum expectation value. McAllister mentions that for V=m²Φ²/2 the approximate shift symmetry is true. Maybe it is for small enough values of m: exact symmetry would require m=0 .
   
   
4. The physical interpretation of masslessness implied by strict shift invariance would be in terms of conformal invariance. In TGD framework quantum criticality implies conformal invariance also in 2-D sense and quantum criticality corresponds to the absence of dimensional parameters from Higgs potential making Higgs mechanism impossible.
   

To my humble opinion, this difficulty means a strong blow against the idea about Higgs mechanism as source of vacuum energy density in cosmology. As already mentioned, the decay of the dark energy identifiable as magnetic energy and large h_eff dark matter associated with the evolving primordial cosmic strings would produce ordinary matter in TGD Universe.

Also the ordinary Higgs mechanism is plagued by the loss of naturalness and predictivity by the fact that the Higgs particle has too low mass and SUSY has not been found in low enough mass scales to stabilize Higgs mass. In TGD framework the string tension of string like objects assignable to elementary particles would give the dominating contribution to gauge boson masses and p-adic thermodynamics in its original form the dominating contribution to fermion masses (see this and this). The couplings of fermions to Higgs are gradient couplings and the coupling is same for all fermions in accordance with naturality and universality.

The overall conclusion is that TGD survives the new findings at qualitative and even partially quantitative level.

For details see the chapter TGD and Cosmology of "Physics in Many-sheeted Space-time" , or the article BICEP2 might have detected gravitational waves.

Pollack's findings about fourth phase of water

I have already earlier proposed a model of Brown's gas with inspiration coming from Moray B. King's lectures about splitting of water. I found that the model can be replaced by a simpler one proposed as a model for water memory as I tried to understand the experimental findings described by Gerald Pollack about fourth gel like phase of water in his Youtube lecture (see this).

I list first some basic experimental findings discovered in the laboratory led by Pollack.

1. If one as gel water boundary a layer of thickness of ordermicrons is formed. All impurities in this layer are taken outside the layer. The layer consists of layers of molecular thickness and in these layers the stochiometry is H_1.5O. The layer is negatively charged. The outside region carries compensating positive charge. This kind of blobs are formed in living matter. Also in the splitting of water producing Brown's gas negatively charged regions are reported to emerge.
   
   
2. The process requires energy and irradiation by visible light or thermal radiation generates the layer. Even the radiation on skin can induce the phase transition. For instance, the blood flow in narrow surface veins requires metabolic energy and irradiation forces the blood to flow.
   
   
3. The layer can serve as a battery: Pollack talks about a form of free energy deriving basically from solar radiation. The particles in the layer are taken to the outside region, and this makes possible disinfection and separation of salt from sea water. One can even understand how clouds are formed and mysteries related to the surface tension of water as being due the presence of the layer formed by
   H_1.5O.
   
   
4. In the splitting of water producing Brown's gas having a natural identification as Pollack's fourth phase of water the needed energy can come from several alternative sources: cavitation, electric field, etc...
   
   

While listening the lecture of Pollack I realized that the original model for dark water is enough to explain the properties of the exotic water according to experiments done in the laboratory of Pollack. There is no need to assume sequences of half-dark water molecules.

1. The dark proton sequences with dark proton having size of order atomic nucleus would reside at the flux tubes of dark magnetic field which is dipole like field in the first approximation and defines the magnetic body of the negatively charged water blob. This explains the charge separation if the flux tubes have length considerably longer than the size scale of the blob which is given by size of small cell. In the model inspired (see this) by Moray B. King's lectures (see this and this) charge separation is poorly understood.
   
   
2. An interesting question is whether the magnetic body is created by the electronic currents or whether it consists of flux tubes carrying monopole flux: in the latter case no currents would be needed. This is obviously purely TGD based possibility and due to the topology of CP₂.
   
   
3. This means that in the model inspired by the lectures of Moray B. King discussed above, one just replaces the sequences of partially dark water molecules with sequences of dark protons at the magnetic body of the H_1.5O blob. The model for the proto-variants of photosynthesis and metabolism remain as such. Also now genetic code would be realized.
   

   These primitive forms of photosynthesis and metabolism form could be key parts of their higher level chemical variants. Photosynthesis by irradiation would induce a phase transition generating dark magnetic flux tubes (or transforming ordinary flux tubes to dark ones) and the dark proton sequences at them. Metabolism would mean burning of the resulting blobs of dark water to ordinary water leading to the loss of charge separation. This process would be analogous to the catabolism of organic polymers liberating energy. Also organic polymers in living matter carry their metabolic energy as dark proton sequences: the layer could also prevent their hydration. That these molecules are typically negatively charged would conform with the idea that dark protons at magnetic flux tubes carry the metabolic energy.
   

   The liberation of energy would involve increase of the p-adic prime characterizing the flux tubes and reduction of Planck constant so that the thickness of the flux tubes remains the same but the intensity of the magnetic field is reduced. The cyclotron energy of dark protons is liberated in coherent fashion and in good approximation the frequencies of the radiation corresponds to multiplies of cyclotron
   frequency: this prediction is consistent with that in the original model for the findings of Blackman and others.
   

   The phase transition generating dark magnetic flux tubes containing dark proton sequences would be the fundamental step transforming inanimate matter to living matter and the fundamental purpose of metabolism would be to make this possible.
   

This picture raises a question relating to the possible problems with physiological temperature.

1. The Josephson radiation generated by cell membrane has photon energies coming as multiples of ZeV, where V is membrane potential about .06 V and Z=2 is the charge of electron Cooper pair. This gives E=.12 eV.
   
   
2. There is a danger that thermal radiation masks Josephson radiation. The energy for photons at the maximum of the energy density of blackbody radiation as function of frequency is given as the maximum of function x³/(e^x-1), x= E/T, given by e^-x+x/3-1=0. The maximum is given approximately by x=3 and thus E_max≈ 3 T (in units c=1, k_B=1). At physiological temperature T= 310 K (37 C) this gives .1 eV, which is slightly below Josephson energy: living matter seems to have minimized the value of Josephson energy - presumably to minimize metabolic costs. Note however that for the thermal energy density as function of wavelength the maximum is at E≈ 5T corresponding to 1.55 eV, which is larger than Josephson energy. The situation is clearly critical.
   
   
3. One can ask whether also a local reduction of temperature around cell membrane in the fourth phase of water is needed.
   
   
   1. "Electric expansion" of water giving rise to charge separation and presumably creating fourth phase of water is reported to occur (see this and this).
      
      
   2. Could the electric expansion/phase transition to dark phase be adiabatic involving therefore no heat transfer between the expanding water and environment? If so, it would transform some thermal energy of expanding water to work and reduce its temperature. The formula for the adiabatic expansion of ideal gas with f degrees of freedom for particle (f=3 if there are no other than translational degrees of freedom) is (T/T₀) = (V/V₀)^-γ, γ= (f+2)/f. This gives some idea about how large reduction of temperature might be involved. If p-adic scaling for water volume by a power of two takes place, the reduction of temperature can be quite large and it does not look realistic.
      
      
   3. The electric expansion of water need not however involve the increase of Planck constant for water volume. Only the Planck constant for flux tubes must increase and would allow the formation of dark proton sequences and the generation of cyclotron Bose-Einstein condensates or their dark analog in which fermions (electrons in particular) effectively behave as bosons (the anti-symmetrization of wave function would occur in dark degrees of freedom corresponding to multi-sheeted covering formed in the process).
      

For details see the chapter Meditation, Mind-Body Medicine and Placebo: TGD point of view of "TGD based view about consciousness, living matter, and remote mental interactions".

Morphogenesis, morphostasis, and learning in TGD framework

According to Michael Levin, the basic challenge of morphogenetics and morphostasis is to understand how the shape of the organism is generated and how it is preserved. The standard local approach based on belief on genetic determinism does not allow answer these questions satisfactorily.

The first approach relies on self-organization paradigm in which the local dynamics of cells leads to large scale structures as self-organization patterns. In TGD framework 3-D self-organization is replaced with 4-D self-organizaton (the failure of strict determinism of classical dynamics is essential motivating zero energy ontology (ZEO)). One can speak about 4-D healing: the space-time surfaces serving as classical correlated is as a whole replaced with the original one during healing process: after the healing process the organism was never sick in geometrical sense!

Second approach could be seen as computational. The basic idea is that the process is guided by a template of the target state and morphogenesis and healing are computational processes. What Levin calls morphogenetic fields would define this template. It is known that organisms possess kind of coordinate grids providing positional information allowing cells to "decide" about the profile of genetic expression. In TGD framework magnetic body forming coordinate grid formed from flux tubes is a natural candidate for this structure. They would also realize topological quantum computation (TQC) with basic computational operations realized at the nodes of flux tubes to which it is natural to associate some biological sub-structures.

The assumption about final goal defining a template can be argued to be too strong: much weaker principle defining a local direction of dynamics and leading automatically to the final state as something analogous to free energy minimum in thermodynamics might be enough. Unfortunately, second law is the only principle that standard physics can offer. Negentropy Maximization Principle (NMP) provides the desired principle in TGD framework. Also the approach of WCW spinor field to the maximum of vacuum functional (or equivalently that of Kähler function) gives a goal for the dynamics after the perturbation of the organism causing "trauma". If Kähler function is classical space-time correlate for entanglement negentropy, these two views are equivalent.

TGD thus suggests an approach, which could be seen as a hybrid of approaches based on self-organizaton and computationalism. The magnetic body becomes the key notion and codes also for learned behaviors as TQC programs coded by the braiding of flux tubes. The replication of the magnetic body means also the replication of the programs behind behavioral patterns (often somewhat misleadingly regarded as synonymous with long term memories). This hypothesis survives the killer tests provided by the strange findings about planaria cut into two and developing new head or tail: the findings suggest that behavioral programs are preserved although planaria develops a new brain (see this).

For details see the chapter Quantum Mind, Magnetic Body, and Biological Body or the article "Morphogenesis, morphostasis, and learning in TGD framework".

Experimental evidence for sterile neutrino?

Many physicists are somewhat disappointed to the results from LHC: the expected discovery of Higgs has been seen as the main achievement of LHC hitherto. Much more was expected. To my opinion there is no reason for disappointment. The exclusion of the standard SUSY at expected energy scale is very far reaching negative result. Also the fact that Higgs mass is too small to be stable without fine tuning is of great theoretical importance. The negative results concerning heavy dark matter candidates are precious guidelines for theoreticians. The non-QCD like behavior in heavy ion collisions and proton-ion collisions is bypassed my mentioning something about AdS/CFT correspondence and non-perturbative QCD effects. I tend to see these effects as direct evidence for M₈₉ hadron physics (see this).

In any case, something interesting has emerged quite recently. Resonaances tells that the recent analysis of X-ray spectrum of galactic clusters claims the presence of monochromatic 3.5 keV photon line. The proposed interpretation is as a decay product of sterile 7 keV neutrino transforming first to a left-handed neutrino and then decaying to photon and neutrino via a loop involving W boson and electron. This is of course only one of the many interpretations. Even the existence of line is highly questionable.

One of the poorly understood aspects of TGD is right-handed neutrino, which is obviously the TGD counterpart of the inert neutrino.

1. The old idea is that covariantly constant right handed neutrino could generate N=2 super-symmetry in TGD Universe. In fact, all modes of induced spinor field would generate super-conformal symmetries but electroweak interactions would break these symmetries for the modes carrying non-vanishing electroweak quantum numbers: they vanish for ν_R. This picture is now well-established at the level of WCW geometry (see this): super-conformal generators are labelled angular momentum and color representations plus two conformal weights: the conformal weight assignable to the light-like radial coordinate of light-cone boundary and the conformal weight assignable to string coordinate. It seems that these conformal weights are independent. The third integer labelling the states would label genuinely Yangian generators: it would tell the poly-locality of the generator with locus defined by partonic 2-surface: generators acting on single partonic 2-surface, 2 partonic 2-surfaces, ...
   
   
2. It would seem that even the SUSY generated by ν_R must be badly broken unless one is able to invent dramatically different interpretation of SUSY. The scale of SUSY breaking and thus the value of the mass of right-handed neutrino remains open also in TGD. In lack of better one could of course argue that the mass scale must be CP₂ mass scale because right-handed neutrino mixes considerably with the left-handed neutrino (and thus becomes massive) only in this scale. But why this argument does not apply also to left handed neutrino which must also mix with the right-handed one!
   
   
3. One can of course criticize the proposed notion of SUSY: wonder whether fermion + extremely weakly interacting ν_R at same wormhole throat (or interior of 3-surface) can behave as single coherent entity as far spin is considered (see this)?
   
   
4. The condition that the modes of induced spinor field have a well-defined electromagnetic charge eigenvalue (see this) requires that they are localized at 2-D string world sheets or partonic 2-surfaces: without this condition classical W boson fields would mix the em charged and neutral modes with each other. Right-handed neutrino is an exception since it has no electroweak couplings. Unless right-handed neutrino is covariantly constant, the modified gamma matrices can however mix the right-handed neutrino with the left handed one and this can induce transformation to charged mode. This does not happen if each modified gamma matrix can be written as a linear combination of either M⁴ or CP₂ gamma matrices and modified Dirac equation is satisfied separately by M⁴ and CP₂ parts of the modified Dirac equation.
   
   
5. Is the localization of the modes other than covariantly constant neutrino to string world sheets a consequence of dynamics or should one assume this as a separate condition? If one wants similar localization in space-time regions of Euclidian signature - for which CP₂ type vacuum extremal is a good representative - one must assume it as a separate condition. In number theoretic formulation string world sheets/partonic 2-surfaces would be commutative/co-commutative sub-manifolds of space-time surfaces which in turn would be associative or co-associative sub-manifolds of imbedding space possessing (hyper-)octonionic tangent space structure. For this option also
   right-handed neutrino would be localized to string world sheets. Right-handed neutrino would be covariantly constant only in 2-D sense.
   

   One can consider the possibility that ν_R is de-localized to the entire 4-D space-time sheet. This would certainly modify the interpretation of SUSY since the number of degrees of freedom would be reduced for ν_R.
   
   

6. Non-covariantly constant right-handed neutrinos could mix with left-handed neutrinos but not with charged leptons if the localization to string world sheets is assumed for modes carrying non-vanishing electroweak quantum numbers. This would make possible the decay of right-handed to neutrino plus photon, and one cannot exclude the possibility that ν_R has mass 7 keV.
   

   Could this imply that particles and their spartners differ by this mass only? Could it be possible that practically unbroken SUSY could be there and we would not have observed it? Could one imagine that sfermions have annihilated leaving only states consisting of fundamental fermions? But shouldn't the total rate for the annihilation of photons to hadrons be two times the observed one? This option does not sound plausible.
   

   What if one assumes that given sparticle is charactrized by the same p-adic prime as corresponding particle but is dark in the sense that it corresponds to non-standard value of Planck constant. In this case sfermions would not appear in the same vertex with fermions and one could escape the most obvious contradictions with experimental facts. This leads to the notion of shadron: shadrons would be (see this) obtained by replacing quarks with dark squarks with nearly identical masses. I have asked whether so called X and Y bosons having no natural place in standard model of hadron could be this kind of creatures.
   
   

The interpretation of 3.5 keV photons as decay products of right-handed neutrinos is of course totally ad hoc. Another TGD inspired interpretation would be as photons resulting from the decays of excited nuclei to their ground state.

1. Nuclear string model (see this) predicts that nuclei are string like objects formed from nucleons connected by color magnetic flux tubes having quark and antiquark at their ends. These flux tubes are long and define the "magnetic body" of nucleus. Quark and antiquark have opposite em charges for ordinary nuclei. When they have different charges one obtains exotic state: this predicts entire spectrum of exotic nuclei for which statistic is different from what proton and neutron numbers deduced from em charge and atomic weight would suggest. Exotic nuclei and large values of Planck constant could make also possible cold fusion
   (see this).
   
   
2. What the mass difference between these states is, is not of course obvious. There is however an experimental finding (see Analysis of Gamma Radiation from a Radon Source: Indications of a Solar Influence) that nuclear decay rates oscillate with a period of year and the rates correlate with the distance from Sun. A possible explanation is that the gamma rays from Sun in few keV range excite the exotic nuclear states with different decay rate so that the average decay rate oscillates. Note that nuclear excitation energies in keV range would also make possible interaction of nuclei with atoms and molecules (see this).
   
   
3. This allows to consider the possibility that the decays of exotic nuclei in galactic clusters generates 3.5 keV photons. The obvious question is why the spectrum would be concentrated at 3.5 keV in this case (second question is whether the energy is really concentrated at 3.5 keV: a lot of theory is involved with the analysis of the experiments). Do the energies of excited states depend on the color bond only so that they would be essentially same for all nuclei? Or does single excitation dominate in the spectrum? Or is this due to the fact that the thermal radiation leaking from the core of stars excites predominantly single state? Could E=3.5 keV correspond to the maximum intensity for thermal radiation in stellar core? If so, the temperature of the exciting radiation would be about T≈ E/3≈ 1.2× 10⁷ K. This in the temperature around which formation of Helium by nuclear fusion has begun: the temperature at solar core is around 1.57× 10⁷ K.
   
   

For background see the chapter SUSY in TGD Universe of "p-Adic Length Scale Hypothesis".

Class field theory and TGD: does TGD reduce to number theory?

The intriguing general result of class field theory) -something extremely abstract for physicist's brain - is that the the maximal Abelian extension for rationals is homomorphic with the multiplicative group of ideles. This correspondence plays a key role in Langlands correspondence (see this,this, this, and this).

Does this mean that it is not absolutely necessary to introduce p-adic numbers? This is actually not so. The Galois group of the maximal abelian extension is rather complex objects (absolute Galois group, AGG, defines as the Galois group of algebraic numbers is even more complex!). The ring Z of adeles defining the group of ideles as its invertible elements homeomorphic to the Galois group of maximal Abelian extension is profinite group. This means that it is totally disconnected space as also p-adic integers and numbers are. What is intriguing that p-dic integers are however a continuous structure in the sense that differential calculus is possible. A concrete example is provided by 2-adic units consisting of bit sequences which can have literally infinite non-vanishing bits. This space is formally discrete but one can construct differential calculus since the situation is not democratic. The higher the pinary digit in the expansion is, the less significant it is, and p-adic norm approaching to zero expresses the reduction of the insignificance.

1. Could TGD based physics reduce to a representation theory for the Galois groups of quaternions and octonions?

Number theoretical vision about TGD raises questions about whether adeles and ideles could be helpful in the formulation of TGD. I have already earlier considered the idea that quantum TGD could reduce to a representation theory of appropriate Galois groups. I proceed to make questions.

1. Could real physics and various p-adic physics on one hand, and number theoretic physics based on maximal Abelian extension of rational octonions and quaternions on one hand, define equivalent formulations of physics?
   
   
2. Besides various p-adic physics all classical number fields (reals, complex numbers, quaternions, and octonions) are central in the number theoretical vision about TGD. The technical problem is that p-adic quaternions and octonions exist only as a ring unless one poses some additional conditions. Is it possible to pose such conditions so that one could define what might be called quaternionic and octonionic adeles and ideles?
   

   It will be found that this is the case: p-adic quaternions/octonions would be products of rational quaternions/octonions with a p-adic unit. This definition applies also to algebraic extensions of rationals and makes it possible to define the notion of derivative for corresponding adeles. Furthermore, the rational quaternions define non-commutative automorphisms of quaternions and rational octonions at least formally define a non-associative analog of group of octonionic automorphisms (see this).
   
   

3. I have already earlier considered the idea about Galois group as the ultimate symmetry group of physics. The representations of Galois group of maximal Abelian extension (or even that for algebraic numbers) would define the quantum states. The representation space could be group algebra of the Galois group and in Abelian case equivalently the group algebra of ideles or adeles. One would have wave functions in the space of ideles.
   

   The Galois group of maximal Abelian extension would be the Cartan subgroup of the absolute Galois group of algebraic numbers associated with given extension of rationals and it would be natural to classify the quantum states by the corresponding quantum numbers (number theoretic observables).
   

   If octonionic and quaternionic (associative) adeles make sense, the associativity condition would reduce the analogs of wave functions to those at 4-dimensional associative sub-manifolds of octonionic adeles identifable as space-time surfaces so that also space-time physics in various number fields would result as representations of Galois group in the maximal Abelian Galois group of rational octonions/quaternions. TGD would reduce to classical number theory!
   
   

4. Absolute Galois group is the Galois group of the maximal algebraic extension and as such a poorly defined concept. One can however consider the hierarchy of all finite-dimensional algebraic extensions (including non-Abelian ones) and maximal Abelian extensions associated with these and obtain in this manner a hierarchy of physics defined as representations of these Galois groups homomorphic with the corresponding idele groups.
   
   
5. In this approach the symmetries of the theory would have automatically adelic representations and one might hope about connection with Langlands program.
   

2. Adelic variant of space-time dynamics and spinorial dynamics?

As an innocent novice I can continue to pose stupid questions. Now about adelic variant of the space-time dynamics based on the generalization of Kähler action discussed already earlier but without mentioning adeles (see this).

1. Could one think that adeles or ideles could extend reals in the formulation of the theory: note that reals are included as Cartesian factor to adeles. Could one speak about adelic or even idelic space-time surfaces endowed with adelic or idelic coordinates? Could one formulate variational principle in terms of adeles so that exponent of action would be product of actions exponents associated with various factors with Neper number replaced by p for Z_p. The minimal interpretation would be that in adelic picture one collects under the same umbrella real physics and various p-adic physics.
   
   
2. Number theoretic vision suggests that 4:th/8:th Cartesian powers of adeles have interpretation as adelic variants of quaternions/ octonions. If so, one can ask whether adelic quaternions and octonions could have some number theretical meaning. Note that adelic quaternions and octonions are not number fields without additional assumptions since the moduli squared for a p-adic analog of quaternion and octonion can vanish so that the inverse fails to exist.
   

   If one can pose a condition guaranteing the existence of inverse, one could define the multiplicative group of ideles for quaternions. For octonions one would obtain non-associative analog of the multiplicative group. If this kind of structures exist then four-dimensional associative/co-associative sub-manifolds in the space of non-associative ideles define associative/co-associative ideles and one would end up with ideles formed by associative and
   co-associative space-time surfaces.
   
   

3. What about equations for space-time surfaces. Do field equations reduce to separate field equations for each factor? Can one pose as an additional condition the constraint that p-adic surfaces provide in some sense cognitive representations of real space-time surfaces: this idea is formulated more precisely in terms of p-adic manifold concept (see this). Or is this correspondence an outcome of evolution?
   

   Physical intuition would suggest that in most p-adic factors space-time surface corresponds to a point, or at least to a vacuum extremal. One can consider also the possibility that same algebraic equation describes the surface in various factors of the adele. Could this hold true in the intersection of real and p-adic worlds for which rationals appear in the polynomials defining the preferred extremals.
   
   

4. To define field equations one must have the notion of derivative. Derivative is an operation involving division and can be tricky since adeles are not number field. If one can guarantee that the p-adic variants of octonions and quaternions are number fields, there are good hopes about well-defined derivative. Derivative as limiting value df/dx= lim ( f(x+dx)-f(x))/dx for a function decomposing to Cartesian product of real function f(x) and p-adic valued functions f_p(x_p) would require that f_p(x) is non-constant only for a finite number of primes: this is in accordance with the physical picture that only finite number of p-adic primes are active and define "cognitive representations" of real space-time surface. The second condition is that dx is proportional to product dx × ∏ dx_p of differentials dx and dx_p, which are rational numbers. dx goes to xero as a real number but not p-adically for any of the primes involved. dx_p in turn goes to zero p-adically only for Q_p.
   
   
5. The idea about rationals as points commont to all number fields is central in number theoretical vision. This vision is realized for adeles in the minimal sense that the action of rationals is well-defined in all Cartesian factors of the adeles. Number theoretical vision allows also to talk about common rational points of real and various p-adic space-time surfaces in preferred coordinate choices made possible by symmetries of the imbedding space, and one ends up to the vision about life as something residing in the intersection of real and p-adic number fields. It is not clear whether and how adeles could allow to formulate this idea.
   
   
6. For adelic variants of imbedding space spinors Cartesian product of real and p-adc variants of imbedding spaces is mapped to their tensor product. This gives justification for the physical vision that various p-adic physics appear as tensor factors. Does this mean that the generalized induced spinors are infinite tensor products of real and various p-adic spinors and Clifford algebra generated by induced gamma matrices is obtained by tensor product construction? Does the generalization of massless Dirac equation reduce to a sum of d'Alembertians for the factors? Does each of them annihilate the appropriate spinor? If only finite number of Cartesian factors corresponds to a space-time surface which is not vacuum extremal vanishing induced Kähler form, Kähler Dirac equation is non-trivial only in finite number of adelic factors.
   

3. Objections

The basic idea is that apporopriately defined invertible quaternionic/octonionic adeles can be regarded as elements of Galois group assignable to quaternions/octonions. The best manner to proceed is to invent objections against this idea.

1. The first objection is that p-adic quaternions and octonions do not make sense since p-adic variants of quaternions and octonions do not exist in general. The reason is that the p-adic norm squared ∑ x_i² for p-adic variant of quaternion, octonion, or even complex number can vanish so that its inverse does not exist.
   
   
2. Second objection is that automorphisms of the ring of quaternions (octonions) in the maximal Abelian extension are products of transformations of the subgroup of SO(3) (G₂) represented by matrices with elements in the extension and in the Galois group of the extension itself. Ideles separate out as 1-dimensional Cartesian factor from this group so that one does not obtain 4-field (8-fold) Cartesian power of this Galois group.
   

If the p-adic variants of quaternions/octonions are be rational quaternions/octonions multiplied by p-adic number, these objections can be circumvented.

1. This condition indeed allows to construct the inverse of p-adic quaternion/octonion as a product of inverses for rational quaternion/octonion and p-adic number! The reason is that the solutions to ∑ x_i²=0 involve always p-adic numbers with an infinite number of pinary digits - at least one and the identification excludes this possibility.
   
   
2. This restriction would give a rather precise content for the idea of rational physics since all p-adic space-time surfaces would have a rational backbone in well-defined sense.
   
   
3. One can interpret also the quaternionicity/octonionicity in terms of Galois group. The 7-dimensional non-associative counterparts for octonionic automorphisms act as transformations x→ gxg^-1. Therefore octonions represent this group like structure and the p-adic octonions would have interpretation as combination of octonionic automorphisms with those of rationals.
   

   Adelic variants of of octonions would represent a generalization of these transformations so that they would act in all number fields. Quaternionic 4-surfaces would define associative local sub-groups of this group-like structure. Thus a generalization of symmetry concept reducing for solutions of field equations to the standard one would allow to realize the vision about the reduction of physics to number theory.
   
   

For background see the chapter About Absolute Galois group of "TGD as Generalized Number Theory".

Why TGD?

Hamed kindly reminded me about article "Why TGD?" that I wrote
recently: why not mention it in blog article.

The article is as an attempt to provide a popular summary about TGD, its motivations, and basic implications. This is of course mission impossible as such since TGD is something at the top of centuries of evolution which has led from Newton to standard model. This means that there is a background of highly refined conceptual thinking about Universe so that even the best computer graphics and animations do not help much. One can still try - at least to create some inspiring impressions. The artice approaches the challenge by answering the most frequently asked questions. Why TGD? How TGD could help to solve the problems of recent day theoretical physics? What are the basic principles of TGD? What are the basic guidelines in the construction of TGD?

These are examples of this kind of questions which I try to answer in the article using the only language that I can talk. This language is a dialect used by elementary particle physicists, quantum field theorists, and other people applying modern physics. At the level of practice involves technically heavy mathematics but since it relies on very beautiful and simple basic concepts, one can do with a minimum of formulas, and reader can always to to Wikipedia if it seems that more details are needed. I hope that reader could catch the basic idea: technical details are not important, it is principles and concepts which really matter. And I almost forgot: problems! TGD itself and almost every new idea in the development of TGD has been inspired by a problem.

Why TGD?

The first question is "Why TGD?". The attempt to answer this question requires overall view about the recent state of theoretical physics.

Obviously standard physics plagued by some problems. These problems are deeply rooted in basic philosophical - one might even say ideological - assumptions which boil down to -isms like reductionism, materialism, determinism, and locality.

Thermodynamics, special relativity, and general relativity involve also postulates, which can be questioned. In thermodynamics second law in its recent form and the assumption about fixed arrow of thermodynamical time can be questions since it is hard to understand biological evolution in this framework. Clearly, the relationship between the geometric time of physics and experienced time is poorly understood. In general relativity the beautiful symmetries of special relativity are in principle lost and by Noether's theorem this means also the
loss of classical conservation laws, even the definitions of energy and momentum are in principle lost. In quantum physics the basic problem is that the non-determinism of quantum measurement theory is in conflict with the determinism of Schrödinger equation.

Standard model is believed to summarize the recent understanding of physics. The attempts to extrapolate physics beyond standard model are based on naive length scale reductionism and have products Grand Unified Theories (GUTs), supersymmetric gauge theories (SUSYs). The attempts to include gravitation under same
theoretical umbrella with electroweak and strong interactions has led to super-string models and M-theory. These programs have not been successful, and the recent dead end culminating in the landscape problem of super string theories and M-theory could have its origins in the basic ontological assumptions about the nature of space-time and quantum.

How could TGD help?

The second question is "Could TGD provide a way out of the dead alley and how?". The claim is that is the case. The new view about space-time as 4-D surface in certain fixed 8-D space-time is the starting point motivated by the energy problem of general relativity and means in certain sense fusion of the basic ideas of special and general relativities.

This basic idea has gradually led to several other ideas. Consider only the identification of dark matter as phases
of ordinary matter characterized by non-standard value of Planck constant, extension of physics by including physics in p-adic number fields and assumed to describe correlates of cognition and intentionality, and zero energy ontology (ZEO) in which quantum states are identified as counterparts of physical events. These new elements generalize considerably the view about space-time and quantum and give good hopes about possibility to understand living systems and consciousness in the framework of physics.

Two basic visions about TGD

There are two basic visions about TGD as a mathematical theory. The first vision is a generalization of Einstein's geometrization program from space-time level to the level of "world of classical worlds" identified as space of 4-surfaces. There are good reasons to expect that the mere mathematical existence of this infinite-dimensional geometry fixes it highly uniquely and therefore also physics. This hope inspired also string model enthusiasts before the landscape problem forcing to give up hopes about predictability.

Second vision corresponds to a vision about TGD as a generalized number theory having three separate threads.

1. The inspiration for the first thread came from the need to fuse various p-adic physics and real physics to single coherent whole in terms of principle that might be called number theoretical universality.
   
   
2. Second thread was based on the observation that classical number fields (reals, complex numbers, quaternions, and octonions) have dimensions which correspond to those appearing in TGD. This led to the vision that basic laws of both classical and quantum physics could reduce to the requirements of associativity and commutativity.
   
   
3. Third thread emerged from the observation that the notion of prime (and integer, rational, and algebraic number) can be generalized so that infinite primes are possible. One ends up to a construction principle allowing to construct infinite hierarchy of infinite primes using the primes of the previous level as building bricks at new level. Rather surprisingly, this procedure is structurally identical with a repeated second quantization of supersymmetric arithmetic quantum field theory for which elementary bosons and fermions are labelled by primes. Besides free many-particle states also the analogs of bound states are obtained and this means the situation really fascinating since it raises the hope that the really hard part of quantum field theories -
   understanding of bound states - could have number theoretical solution.
   
   

It is not yet clear whether both great visions are needed or whether either of them is in principle enough. In any case their combination has provided a lot of insights about what quantum TGD could be.

Guidelines in the construction of TGD

The construction of new physical theory is slow and painful task but leads gradually to an identification of basic guiding principles helping to make quicker progress. There are many such guiding principles.

• "Physics is uniquely determined by the existence of WCW" is is a conjecture but motivates highly interesting questions. For instance: "Why M⁴× CP₂ a unique choice for the imbedding space?", "Why space-time dimension must be 4?", etc...
  
  
• Number theoretical Universality is a guiding principle in attempts to realize number theoretical vision, in particular the fusion of real physics and various p-adic physics to single structure.
  
  
• The construction of physical theories is nowadays to a high degree guesses about the symmetries of the theory and deduction of consequences. The very notion of symmetry has been generalized in this process. Super-conformal symmetries play even more powerful role in TGD than in super-string models and gigantic symmetries of WCW in fact guarantee its existence.
  
  
• Quantum classical correspondence is of special importance in TGD. The reason is that where classical theory is not anymore an approximation but in well-defined sense exact part of quantum theory.
  

There are also more technical guidelines.

• Strong form of General Coordinate invariance (GCI) is very strong assumption. Already GCI leads to the assumption that Kähler function is Kähler action for a preferred extremal defining the counterpart of Bohr orbit. Even in a form allowing the failure of strict determinism this assumption is very powerful. Strong form of general coordinate invariance requires that the light-like 3-surfaces representing partonic orbits and space-like 3-surfaces at the ends of causal diamonds are physically equivalent. This implies effective 2-dimensionality: the intersections of these two kinds of 3-surfaces and 4-D tangent space data at them should code for quantum states.
  
  
• Quantum criticality states that Universe is analogous to a critical system meaning that it has maximal structural richness. One could also say that Universe is at the boundary line between chaos and order. The original motivation was that quantum criticality fixes the basic coupling constant dictating quantum dynamics essentially uniquely.
  
  
• The notion of finite measurement resolution has also become an important guide-line. Usually this notion is regarded as ugly duckling of theoretical physics which must be tolerated but the mathematics of von Neumann algebras seems to raise its status to that of beautiful swan.
  
  
• What I have used to call weak form of electric-magnetic duality is a TGD version of electric-magnetic duality discovered by Olive and Montonen. It makes it possible to realize strong form of holography implied actually by strong for of General Coordinate Invariance. Weak form of electric magnetic duality in turn encourages the conjecture that TGD reduces to almost topological QFT. This would mean enormous mathematical simplification.
  
  
• TGD leads to a realization of counterparts of Feynman diagrams at the level of space-time geometry and topology: I talk about generalized Feynman diagrams. The highly non-trivial challenge is to give them precise mathematical content. Twistor revolution has made possible a considerable progress in this respect and led to a vision about twistor Grassmannian description of stringy variants of Feynman diagrams. In TGD context string like objects are not something emerging in Planck length scale but already in scales of elementary particle physics. The irony is that although TGD is not string theory, string like objects and genuine string world sheets emerge naturally from TGD in all length scales. Even TGD view about nuclear physics predicts string like objects.

For details see the new article Why TGD?.

Orch-Or theory of Penrose and Hameroff and new experimental findings about microtubules

The latest news in quantum biology is the claim about corroboration of the the Orch OR theory of Penrose
Hameroff (see this). To my humble opinion the news suffer from rather heavy hyping. If the observation of the group lead by Anirban Bandyopadhyay about detection of quantum vibration in microtubule scale - their lengths vary up to 50 μm - can be replicated, one can speak about breakthrough in quantum consciousness. The results do not however prove Orch OR, which involves poorly defined vision about quantum gravitational description of state function reduction so that most predictions are just order of magnitude estimates relying on Uncertainty Principle.

The biological half of the theory relies on microtubules and for this side of the theory the claimed finding would of course be a victory. Indeed, there is a meeting in Amsterdam devoted to Orch OR theory of consciousness motivated by this finding (see this) Unfortunately, I could not find any article about the findings of Bandyopadhyay in web. I managed however to find two years old Youtube talk of Bandyopahdyay summarizing earlier experimental results supporting the vision about microtubules as macroscopic quantum systems (see this) to be discussed below.

The findings reported in the talk give support for the general TGD inspired view about TQC and allow rather detailed model in the case of microtubules. The idea is that flux tubes from a 2-D coordinate grid consisting of parallel flux tubes in two different directions: say helical Fibonacci flux tubes and their mirror images. Crossing points would be associated with tubulins and the conformational state of tubulin could define a bit coding whether the braid strands defining coordinate lines are braided or not (swap or not). In this manner any bit pattern at microtubule defines a particular TQC program. If also conformations are quantum superposed one as "quantum-quantum computation". The flux tubes could form lattice of type A whereas microtubules form always a lattice of type B - a heavy objection against Penrose-Hameroff model. This picture generalizes in the fractal universe of TGD. One can form layers of 2-D coordinate grids and connect them by vertical flux tubes to obtain 3-D grid defining TQC. Brain is known to have grid like architecture and neurons could by quantum computation produce bit/qubit defining swap or not/superposition of swap and not-swap for a larger scale TQC. One would have fractal of TQCs.

One also ends up with a very crazy idea which turned out to have lifetime longer than the time it took to type it.

1. If one piles up 2-D TQC:s one obtains 3-D TQC. In crossings one must have 4 bits to specify whether to swap or not since there are three planes for TQC and 4 pairs of crossing strands (12,13,23,23).
   
   
2. If one further piles 3D TQC:s in 4-D one obtains 4-D one making sense in zero energy ontology because failure of strict non-determinism is basic element of TGD. Single crossing would in 4-D would involve crossings of four lines in orthogonal dimensions. TGD predicts also space-time regions with Euclidian signature in all scales (lines of generalised Feynman diagrams). I have proposed that any system corresponds to an Euclidian space-time sheet having its size and shape and behaving like quantum system. In these regions the fourth piling might really make sense!
   
   
3. in 4-D This would make 6 crossing pairs corresponding to 6 planes in which particular TQC takes place - for which one must tell whether to swap or not (12,13,14,23,24,34). This makes 6 bits. DNA codons correspond to 6 bits! Could codons define crossing points of magnetic flux tubes arriving from 4 coordinate directions- perhaps at Euclidian space-time sheets? Could the planes correspond to 3 components of magnetic field and 3 components electric field. Magnetic flux tubes and electric flux tubes in 3 directions? In Euclidian regions magnetic and electric do not differ intrinsically.
   

Addition: The TGD inspired interpretation of the experiments of Bandyopadhyay in terms of flux tube coordinate grids making possible TQC architectures with tubulin dimers defining bits defining in turn TQC program looks rather natural. Coordinate grids can be fixed on basis of the experimental findings and there are 8 grids. The interpretation is in terms of different resolutions. The grids for A and B type lattices are related by 2π twist for the second end of the basic 13-unit for microtubule. An attractive interpretation for the resonance frequencies is in terms of phase transitions between A and B type lattices. If A type lattices can be generated only in phase transitions induced by AC stimulus at resonance frequencies, one could understand their experimental absence, which is a strong objection against Penrose-Hameroff model.

This would fit very nicely with the general vision about frequencies as passwords inducing not only directed attention but activities in target - also TQCs! The increase of Planck constant could be associated with the phase transition to A-phase making possible high T_c dark super-conductivity for which evidence is observed! One can even deduce estimates for h_eff/h=n if one requires that AC photons have energy above thermal threshold: n= f_visible/f_AC would be the estimate. For biophoton energies one would obtain something like n≈ 10⁸-10⁹, which pops up in different contexts in TGD framework.

For details see the chapter Quantum Mind, Magnetic Body, and Biological Body or the article "Orch-Or theory of Penrose and Hameroff and new experimental findings about microtubules".

Are microtubules macroscopic quantum systems?

There has been a lot of buzz about the claimed discovery of quantum vibrations in microtubules: see this. I have been working for two days trying to understand the work of Anirban Bandyopadhyay. Certainly, the experimental finding- if true - would be a breakthrough for quantum consciousness but certainly not for Orch-OR. Therefore I was surprised for the heavy hyping of Penrose-Hameroff theory. The result only tells that microtubules are macroscopic quantums systems, it says nothing about Orch-OR.

I did not find any article about experiment. I found and listened the earlier talk (2111) of Anirban Bandyopadhyay whose group might discovered the quantum vibrations. The talk was also was about experiments done with microtubules and looked very interesting. See this .

I got the impression that he is excellent sharply thinking experimentalist and had identified the signatures for what he interpreted in terms of Froehlich B-E condensation, topological qubit, superconductivity like state of electrons inside microtubules, and so on. One can interpret the findings differently and I have been working with TGD interpretation assuming that basic findings are correct.

What was frustrating was the fuzzy terminology: for instance, he talked about conduction pathways at micro tubular surface as topological qubits and did not explain when asked about this issue. Excellent experimentalist need not be a theorist: was this the reason? Or was the unclarity purposeful?

Also the interpretation of experiments seems to be internally inconsistent and I got the impression that it reflects his own theories. It might rely on the earlier proposal of Penrose and Hameroff, which I did not find as freely available article. The only article mentioning conduction pathways that I found from web did not help: I have the feeling that they have no detailed model but want to give the impression that they have.

The wrong interpretation need not mean catastrophe: as a good experimentalist he is looking for signatures of these phenomena, and if he has found them, there are all reasons to take the findings under serious discussion.

I also looked for the Penrose Hameroff theory. As a professional I known that the Penrose's contribution relating to speculations about gravitation does not tolerate daylight and the only calculations are just dimensional analysis involving Uncertainty Principle. I had thought that Hameroff's microtubule contribution is on less shaky grounds. I learned within few hours that this is not the case. For instance, the assumption that microtubules in brain are of type A, is simply wrong: all microtubules in living matter seem to be of type B, in particular in brain this is the case. See this .

Therefore the proposal of Penrose and Hameroff for microtubules as topological quantum computers relying on Fibonacci conduction paths (with periodicity 3,5,8, or 13) possible only for A-type microtubules is simply wrong. The same is true about Hameroff's and indian theorists Gupta's later proposal suggesting that MAPs act as quantum gates. As a matter of fact, the abstract of the article contained horrible terminological errors: I tried to explain this by language but why Hameroff did not check the language? See this .

Now Penrose and Hameroff propose explanation for the origin of EEG based on beat phenomenon for MHz frequencies: it seems that they are trying to mimic what I have done in TGD and get the honour for discovering quantum theory of consciousness;-).

I must say that I am confused. Certainly the discovery that microtubules are macroscopic quantum systems would be wonderful if true, and the claimed earlier findings of Indian experimentalist support the TGD based picture based on the identification of braids as magnetic flux tubes. But can I trust to experimentalist without name when I cannot trust on namy theorists?

To sum up, these are my first impressions after two day's listening and reading. I might have misinterpreted and misunderstood. I am writing a summary about TGD based interpretation of the earlier experiments of the group of Bandyopadhyay -assuming that experimental findings are correct (I do not believe that the interpretation is correct) - and give a link to the article later.

Addition: I wrote a short analysis of the talk of Bandyopadhyay.

Little but important step in the understanding the arrow of time

"Fractality from your blog" posed an interesting question about possible asymmetry between boundaries of causal diamond CD. The answer to the question led to recall once again the incomplete understanding of details about how the arrow of time emerges in zero energy ontology (ZEO).

The basic vision is following.

1. CDs form a fractal scale hierarchy. Zero energy states possess a wave function in moduli degrees of freedom characterizing sizes of CDs as well telling what Lorentz boost leaving boundary invariant are allowed for them. Boosts form by number theoretic constraints a discrete subgroup of Lorentz group defining analogs of lattices generated by boosts instead of translations.
   
   
2. The arrow of subjective time maps to that of geometric time somehow. The origin of arrow comes from the fact that state function reductions can occur to either boundary of given CD and reduction creates time-asymmetric state since second boundary of CD is in a quantum superposition of different sizes and there is a superposition of many-particle states with different particles numbers and quantum number distributions.
   
   
3. Subjective existence corresponds to a sequence of moments of consciousness: state function reductions at opposite boundaries of CDs. State function reduction reduction localizes either boundary but the second boundary is in a quantum superposition of several locations and size scales for CD. This predicts that the arrow of time is not constant. In fact, there is considerable evidence for the variation of the arrow of time in living systems and Fantappie introduced long time ago the notion of syntropy to describe his view about the situation.
   
   
4. The first very naive proposal was that state function reductions occur alternately to the two boundaries of CD. This assumption would be indeed natural if one considered single fixed CD rather than superposition CDs with different size and state function reduction localizing their either boundary: restriction to single CD was what I indeed did first.
   
   
5. This assumption leads to the question about why do we do not observe this alternation of the arrow of time all the time in our personal experience. Some people actually claim to have actually experienced a temporary change of the arrow of time: I belong to them and I can tell that the experience is frightening. But why do we experience the arrow of time as stable in the standard state of consciousness?
   

One possible way to solve the problem - perhaps the simplest one - is that state function reduction to the same boundary of CD can occur many times repeatedly. This solution is so absolutely trivial that I could perhaps use this triviality to defend myself for not realizing it immediately!

I made this totally trivial observation only after I had realized that also in this process the wave function in the moduli space of CDs change in these reductions. Zeno effect in ordinary measurement theory relies on the possibility of repeated state function reductions. In the ordinary quantum measurement theory repeated state function reductions do not affect the state in this kind of sequence but in ZEO the wave function in the moduli space labelling different CDs with the same boundary could change in each quantum jump. It would be natural that this sequence of quantum jumps give rise to the experience about flow of time? This option would allow the size scale of CD associated with human consciousness be rather short, say .1 seconds. It would allow to understand why we do not observe continual change of arrow of time.

Maybe living systems are working hardly to keep the personal arrow of time changed - living creatures try to prevent kettle from boiling by staring at it intensely. Maybe it would be extremely difficult to live against the collective arrow of time.

For details and background see the chapter About nature of time of "TGD Inspired Theory of Consciousness".

Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds"

The construction of Kähler geometry of WCW ("world of classical worlds") is fundamental to TGD program. I ended up with the idea about physics as WCW geometry around 1985 and made a breakthrough around 1990, when I realized that Kähler function for WCW could correspond to Kähler action for its preferred extremals defining the analogs of Bohr orbits so that classical theory with Bohr rules would become an exact part of quantum theory and path integral would be replaced with genuine integral over WCW. The motivating construction was that for loop spaces leading to a unique Kähler geometry. The geometry for the space of 3-D objects is even more complex than that for loops and the vision still is that the geometry of WCW is unique from the mere existence of Riemann connection.

The basic idea is that WCW is union of symmetric spaces G/H labelled by zero modes which do not contribute to the WCW metric. There have been many open questions and it seems the details of the earlier approach must be modified at the level of detailed identifications and interpretations. What is satisfying that the overall coherence of the picture has increased dramatically and connections with string model and applications of TGD as WCW geometry to particle physics are now very concrete.

1. A longstanding question has been whether one could assign Equivalence Principle (EP) with the coset representation formed by the super-Virasoro representation assigned to G and H in such a manner that the four- momenta associated with the representations and identified as inertial and gravitational four-momenta would be identical. This does not seem to be the case. The recent view will be that EP reduces to the view that the classical four- momentum associated with Kähler action is equivalent with that assignable to modified Dirac action supersymmetrically related to Kähler action: quantum classical correspondence (QCC) would be in question. Also strong form of general coordinate invariance implying strong form of holography in turn implying that the super-symplectic representations assignable to space-like and light-like 3-surfaces are equivalent could imply EP with gravitational and inertial four-momenta assigned to these two representations.
   
   
2. The detailed identification of groups G and H and corresponding algebras has been a longstanding problem. Symplectic algebra associated with δM⁴_+/-× CP₂ (δM⁴_+/- is light-cone boundary - or more precisely, with the boundary of causal diamond (CD) defined as Cartesian product of CP₂ with intersection of future and past direct light cones of M⁴ has Kac-Moody type structure with light-like radial coordinate replacing complex coordinate z. Virasoro algebra would correspond to radial diffeomorphisms.
   

   I have also introduced Kac-Moody algebra assigned to the isometries and localized with respect to internal coordinates of the light-like 3-surfaces at which the signature of the induced metric changes from Minkowskian to Euclidian and which serve as natural correlates for elementary particles (in very general sense!). This kind of localization by force could be however argued to be rather ad hoc as opposed to the inherent localization of the symplectic algebra containing the symplectic algebra of isometries as sub-algebra. It turns out that one obtains direct sum of representations of symplectic algebra and Kac-Moody algebra of isometries naturally as required by the success of p-adic mass calculations.
   
   

3. The dynamics of Kähler action is not visible in the earlier construction. The construction also expressed WCW Hamiltonians as 2-D integrals over partonic 2-surfaces. Although strong form of general coordinate invariance (GCI) implies strong form of holography meaning that partonic 2-surfaces and their 4-D tangent space data should code for quantum physics, this kind of outcome seems too strong. The progress in the understanding of the solutions of modified Dirac equation led however to the conclusion that spinor modes other than right-handed neutrino are localized at string world sheets with strings connecting different partonic 2-surfaces.
   

   This leads to a modification of earlier construction in which WCW super-Hamiltonians were essentially 2-D flux integrals. Now they are 2-D flux integrals with super-Hamiltonian replaced Noether super charged for the deformations in G and obtained by integrating over string at each point of partonic 2-surface. Each spinor mode gives rise to super current and the modes of right-handed neutrino and other fermions differ in an essential manner. Right-handed neutrino would correspond to symplectic algebra and other modes to the Kac-Moody algebra and one obtains the crucial 5 tensor factors of Super Virasoro required by p-adic mass calculations.
   

   The matrix elements of WCW metric between Killing vectors are expressible as anticommutators of super-Hamiltonians identifiable as contractions of WCW gamma matrices with these vectors and give Poisson brackets of corresponding Hamiltonians. The anti-commutation relates of induced spinor fields are dictated by this condition. Everything is 3-dimensional although one expects that symplectic transformations localized within interior of X³ act as gauge symmetries so that in this sense effective 2-dimensionality is achieved. The components of WCW metric are labelled by standard model quantum numbers so that the connection with physics is extremely intimate.
   
   

4. An open question in the earlier visions was whether finite measurement resolution is realized as discretization at the level of fundamental dynamics. This would mean that only certain string world sheets from the slicing by string world sheets and partonic 2-surfaces are possible. The requirement that anti-commutations are consistent suggests that string world sheets correspond to surfaces for which Kähler magnetic field is constant along string in well defined sense (J_μνε^μνg^1/2 remains constant along string). It however turns that by a suitable choice of coordinates of 3-surface one can guarantee that this quantity is constant so that no additional constraint results.

See the new chapter Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds of "Quantum TGD as Infinite-dimensional Spinor Geometry" or the article with the same title.

Magnetic hysteresis, super string sociology, catastrophe theory, Higgs mechanism, and ferromagnets in many-sheeted space-time

Ferromagnets are simple but fascinating systems and spontaneous magnetization represents a situation analogous to Higgs mechanism. In the following I will discuss the hysteresis phenomenon for ferromagnets on basis of thermodynamical description: hysteresis model applies also to phenomenon of mass hysteria in sociology. This all is standard but the understanding of ferromagnets in many-sheeted space-time involves some new elements: in particular the possibility that the magnetic fluxes of permanent magnets consist of monopole fluxes.

Standard definitions

Let us begin with basic definitions. The magnetic field H is defined in terms of magnetization M and magnetic induction B (often called just magnetic field) via he formula H= B/μ₀-M quite generally. For historical reasons different units are used for B and H but in vacuum they are essentially one and the same thing. In the case of magnets the situation changes.

Paramagnets and diamagnets are linear: M= χ_m H in good approximation. The sign of χ_m determines whether the behavior is diamagnetic (induced magnetization reduces the external field inside magnet) or whether its paramagnetic (induce magnetization increases the external field inside magnet). For the ferromagnets the behavior
is non-linear and M is non-vanishing for vanishing H.

The behavior at the boundary between magnet and external world is important for understanding magnets. If the exterior of the magnet is vacuum, one has H=μ₀M and the fields H and B are one and the same thing. Inside magnet magnetization implies that the two fields are not same. By the absence of magnetic charges the normal component of magnetic field is continuous. Therefore the normal component satisfies B_n(in)= μ₀H_in+M= B_n(out)=μ₀H_out.

Hysteresis for ferromagnets

For ferromagnets the relationship between H M is non-linear and many-valued, and one has hysteris so that the effects of increasing and decreasing the magnetic field are different in saturation. The hysteresis cycle characterizes this behavior quite nicely.

1. The plot can be understood easily when one realizes that magnetization M corresponds microscopically to the density of magnetic dipoles typically realized as electrons spins. The field H corresponds essentially to the difference between external magnetic field and that caused by magnetization. As one starts from H=0 to increase the magnitude of H, M gradually increases as for paramagnets but above some critical value M starts to increase and reaches the saturation value. The interpretation is that electron spins change they direction in phase transitions producing magnetized regions. This behavior can be understood only quantum mechanically and can be seen as an outcome of exchange interaction for spins relating to fermion statistics. Essentially collective behavior is in question: when the number of spins in direction of external field is large enough all other spins "follow the fashion".
   
   
2. One can also gradually decrease the value of H in saturation. Now M decreases smoothly as some spins here and there change their direction but no phase transition like reduction of M occurs since "follow the fashion" behavior is possible only when the number of reversed spins is high enough. Therefore one proceeds along the lower part of the hysteresis cycle: inside the cycle the behavior is reversible for small enough changes of H and irreversibily occurs only near the ends.
   
   
3. At some point one has a situation in which the added external field vanishines: H=0. There is a net magnetization and the normal component of external field is essentially this magnetization at the surface of the magnet. This field is known as remanescence. This corresponds to a magnetization without any added external field H.
   
   
4. As H is reduced further so that its sign changes, eventually "follow the fashion" behavior sets in and most spins change their direction to opposite and the direction of magnetization changes. The magnitude of the magnetic field at which this occurs is known as coercivity. Coercivity and remanescence characterize the magnetic in the first approximation.
   
   
5. The mathematical description of Higgs mechanism is very similar to the idealized description of spontaneous magnetization. In spontaneous magnetization one has however large number of magnetized regions which means that the direction of magnetization does not change instantaneously since the analog of overheating and overcooling are possible for all these regions.
   

Hysteresis (and hysteria) in sociology

The hysteresis model applies also in sociology. Superstring fashion represents an excellent example about hysteresis phenomenon in the sociology of science. There are two kinds of people involved: those who really understand (H) and those who just follow the fashion (M). Some fraction p of those who understand, believes in superstrings. The remaining fraction 1-p does not. H dould correspond mathematically to the difference (p-p₀)/p₀, where p₀ is a critical propability analogous to remanesence in ferromagnetism. As p increases a sudden phase transition occurs at critical fraction satisfying p-p₀=Δ p_cr, and everyone suddenly believes that super strings are not only a promising theory but even the only possible one. Δ p_cr is analogous to coercivity.

The return along upper part of hysteris curve means that the per cent of the believers who really understand starts to decrease as people who have not suffered the fate of becoming a string guru are learning about the deep problems of the theory and start to worry about them publicly. Eventually the number of the non-gurus who understand and do not believe becomes so high that the followers of fashion make the decision to not believe anymore on superstrings, and everyone suddenly "knows" that super strings are pseudoscience. Except certain billionaire who decides to make super string theorists millionaires;-) . This billionaire does not follow the fashion, which is nice. He does not even follow those who understand, which is not so nice. To my humble opinion, it would be more rational to build an institute supporting the study of alternatives for super string models than drowning theoreticians to money which is not even their primary interest.

Hysteresis in magnets cannot be understood microscopically without introducing quantum effects. One can of course ask, whether also hysteresis involves quantum mechanics but now in macroscopic length and time scales applying in sociology.

Ferromagnetism, catastrophe theory, and Higgs mechanism

The model for magnetism can be also understood in terms of catastrophe theory using cusp catastrophe. This applies to Higgs mechanism (not the manner in which particle massivation is described in TGD) too. Catastrophe theory brings in also the temperature as external parameter besides H. This is the simplest interesting catastrophe and involves two parameters/control variables: (temperature T and added external field H) plus one behavior variable (magnetization M). Above certain critical temperature (Curie temperature) there is no magnetization. Below Curie temperature there is a magnetization in certain range for field H. As the magnitude of H is increased, one reaches at critical magnitude of H (coercivity) a situation when the only possible manner to continue is to jump from the boundary of the cusp to the sheet below or above it. A sudden phase transition like change changing the sign of magnetization takes place.

Above we have assumed that the external contribution H to the field is in the same direction as magnetization. What happens if this is not the case? And what happens when the external field H changes the direction of magnetization: is it enough apply the basic criterion to the vector sum H= B/μ₀-M. Presumably this is the case. If it were not, it would be mentioned in Wikipedia!

Catastrophe theory provides a rough description and does not say anything about the microscopic mechanism of hysteresis. In the case of Higgs mechanism one can expect the same to be true: there should exist a microscopic thermodynamical description replacing Higgs mechanism, which is only capable of reproducing the particle masses but not predicting them and suffers from un-naturality. In TGD framework p-adic thermodynamics provides this microscopic thermodynamical description.

Since QFT is in rough sense square root of thermodynamics, one can argue that also p-adic thermodynamics must have also square root and characterizes single particle states rather than ensembles. This is the case. In zero energy one can say that quantum theory is square root of thermodynamics. U-matrix characterizes the physics. I call the rows M_i of unitary U-matrix M-matrices, which are products of mutually orthogonal hermitian square roots P_i^1/2 of density matrices P_i with a unitary S-matrix S. One has M_iM_j^†= P_iδ_ij and Tr(M_iM_j^†)=δ_ij. U defines negentropic entanglement in time direction. In p-adic thermodynamics the Hermitian matrix P_i^1/2 corresponds to a diagonal matrix defined by the square roots of eigenvalues of mass squared operator expressible as vibrational part of scaling generator L₀ of conformal algebra. The unitary matrix S is the counterpart of the ordinary S-matrix.

Permanent magnet in many-sheeted space-time

How could one understand permanent magnet in the framework of many-sheeted space-time?

1. It seems that one must consider two space-time sheets. That of magnet at which magnetization M alone defines the magnetic field B₁=μ₀M and that of external world at which external added field defines the magnetic field B₂=μ₀ H_in. Test particle has topological sum contacts on both space-time sheets and effectively experiences the sum B₁+B₂: the fields do not however sum at same space-time sheet - only their effects on spins are additive so that '+' is replaced with a set theoretic union inTGD. This applies quite generally and saves TGD from the catastrophe caused otherwise by the fact that linear superposition of fields is not possible at given space-time sheet even approximately.
   
   
2. The spins inside the space-time sheet of magnet also experience B₂ and when B₂ is above critical value (coercivity), a phase transition changing the direction of spins occurs and magnetization is generated. It seems that TGD does not add much to the model of how spontaneous magnetization takes place and what is behind the hysteresis.
   
   
3. The notion of magnetic field in TGD differs from that in Maxwell's theory. In TGD Universe it is quite possible that the flux tubes have closed cross section (sphere) instead of disk and that they carry a monopole flux. One would have magnetic flux tube without a circulating current at its boundary generating the magnetic field inside it as in the case of electromagnets, which are typically flux tubes with current carrying helical wire. Could the static magnetic field of permanent magnet consist of monopole flux tubes with a closed rather than disk-like cross section requiring no circular currents at their boundaries?
   

   If this kind of flux tubes are possible, one could understand why cosmos is populated by magnetic fields in all scales. In Maxwell's theory this is not possible since coherent currents defining flux tubes are not possible in primordial cosmology. In superconductors the flux quanta associated with this monopole like fields would become visible as they penerated the super-conductor.