Gravitational Mother Gaia and life

In an earlier posting I have told about considerable progress in understanding TGD inspired quantum biology. The basic result is that the gravitatational Planck constant h_gr inspired by Nottale's observations and h_eff inspired by the effects of ELF radiation on vertebrate brain can be one and same thing at least in elementary particle scales where h_gr is defined for a pair formed by elementary particle (say) and Earth, or Sun or some massive body. It is of course possible that heavier objects than elementary particle can appear as second member in the pair. The objects are connected by gravitational flux tubes mediating gravitational interaction.

The big surprise was that h_gr is indeed of same order of magnitude as needed for the energies of EEG photons to be in visible-UV range so that their decay products can be interpreted as biophotons. Dark cyclotron photons with universal energy spectrum in this range would control bio-chemical reactions by resonance mechanism in living matter.

This picture generalizes to other interaction and the notion of h_em= Z₁Z₂e²/v₀. Now the surprising numerical accident is that for ATP synthase which is motor with rotating shaft rotating with velocity v₀ and generating three ATPs from ADP during single turn h_em seems is same order of magnitude as h_gr(particle,Earth) for elementary particles.

These findings lead to fascinating speculations about the role of quantum gravitation in living systems.

Negentropic entanglement (NE) is one of the key notions of TGD inspired quantum biology. For instance, it would seem that NE would look more natural metabolic resource than energy. Nutrients should carry it. NE is however not single particle property but between nutrient and some other system in the recent case. What can one say about this system? Can it be part of nutrient? Could it correspond to oxygen molecules? Or could it be gravittional Mother Gaia identified in some sensible manner?

If one believes on the presence of gravimagnetic flux tubes and their role as generator of macroscopic quantum coherence in biology then one is forced to consider seriously also NE between its ends. If this is the case then the view of religions about life might be nearer to truth than that of hard-born materialists.

To make this more concrete, let us first look what the transfer of NE could mean.

1. Suppose that nutrient N has NE with unknown system A which a priori could be part of nutrient. Assume that the transfer of NE of nutrient with A is formed by reconnection of U-shaped flux tubes associated with N (or glucose G produced from it) and A so that two parallel flux tubes connecting N and A are formed.
   
   
2. The basic operation allowing transformation of N-A NE to P-A NE is following. The two flux tube portions of U-shaped flux associated with the receiver R are reconnected with the two parallel flux tubes connecting N and A so that two flux tubes connecting R to A are formed. NMP strongly suggests that the entanglement remains negentropic in the process.
   
   
3. NE is first transferred to P using this process so that P and A are now NE-connected. After this P attaches to ADP to yield ATP and ATP attaches to B and the transfer process leads to NE between B and A.
   

   For ATP synthase the h_em consisting two elementary charges is of the same order as h_gr. This is probably not an accident. Could this mean that this kind of flux tube can reconnect with gravitational flux tube? Could this make possible a reconnection transforming N-Earth NE to P-Earth NE? This looks plausible.
   
   

Consider now the identification of A.

1. If one assumes that the negentropic entanglement corresponds to gravitational flux tubes for N-Earth system then A should be gravitational Mother Gaia, whatever its precise definition might be. N (and glucose) molecules would be alive in the sense that they have
   NE with Mother Gaia.
   
   
2. Could oxygen have some deeper role? For instance, could O₂ molecules serve as analogs of cell membrane receptors for Mother Gaia meaning that gravitational flux tubes go through O₂ molecules? This does not look plausible since metabolism is possible also as fermentation involving no oxygen.
   
   
3. In this picture the role of breathing and fermentation would be to make possible the transfer of NE from nutrients to the living system.
   
   

This picture allows to imagine about what might happen in biological death. Biological death takes first place only at the highest level of self hierarchy assignable to the our biological body. Cells continue for some time their life even after the last breath. The notion of h_gr together with Equivalence Principle suggests that the living biological body has negentropic flux tube connections to both electromagnetic magnetic body (personal magnetic body) and to gravitational Mother Gaia (MG) (especially during sleep) representing collective consciousness in the scale of Earth. Also connections to higher levels are possible. Also personal magnetic body and MG have connections. At the moment of biological death the negentropic flux tube pairs connecting the personal magnetic body to biological body are split and only those with MG remain or are generated in this process. This would happen later at lower levels of biological self hierarchy such as organ and organelles and eventually for cells and biopolymers. The magnetic bodies of the resulting decay products have negentropic entanglement with MG and and can be used as nutrients to transfer this entanglement to bio-molecules.

The quantum model for metabolism allows to understand life as a process in which negentropic entanglement of gravitational Mother Gaia with nutrients is transformed to that of molecules of biological body with personal magnetic body and further processed and enriched. At the moment of biological death this information returns to the personal magnetic body which now connects only gravitational Mother Gaia or higher levels in the hierarchy. By NMP information is not lost but increases steadily giving rise to "Akashic records". This view conforms with the core ideas of spiritual and religious teachings.

For the details the reader can consult the article Implications of strong gravimagnetism for TGD inspired quantum biology.

String world sheets, partonic 2-surfaces and vanishing of induced (classical) weak fields

Well-definedness of the em charge is the fundamental on spinor modes. Physical intuition suggests that also classical Z⁰ field should vanish - at least in scales longer than weak scale. Above the condition guaranteeing vanishing of em charge has been discussed at very general level. It has however turned out that one can understand situation by simply posing the simplest condition that one can imagine: the vanishing of classical W and possibly also Z⁰ fields inducing mixing of different charge states.

1. Induced W fields mean that the modes of Kähler-Dirac equation do not in general have well-defined em charge. The problem disappears if the induced W gauge fields vanish. This does not yet guarantee that couplings to classical gauge fields are physical in long scales. Also classical Z⁰ field should vanish so that the couplings would be purely vectorial. Vectoriality might be true in long enough scales only. If W and Z⁰ fields vanish in all scales then electroweak forces are due to the exchanges of corresponding gauge bosons described as string like objects in TGD and represent non-trivial space-time geometry and topology at microscopic scale.
   
   
2. The conditions solve also another long-standing interpretational problem. Color rotations induce rotations in electroweak-holonomy group so that the vanishing of all induced weak fields also guarantees that color rotations do not spoil the property of spinor modes to be eigenstates of em charge.
   

One can study the conditions quite concretely by using the formulas for the components of spinor curvature .

1. The representation of the covariantly constant curvature tensor is given by
   
   

   
   R₀₁= e⁰ ∧ e¹-e²∧ e³ , R₂₃= e⁰∧ e¹- e²∧ e³ ,
   

   R₀₂=e⁰∧ e²-e³ ∧ e¹ , R₃₁ = -e⁰∧
   e²+e³∧ e¹ ,
   

   R₀₃ = 4e⁰∧ e³+2e¹∧ e²
   , R_{12 = 2e⁰∧ e³+4e¹∧ e² .}
   

   R₀₁=R₂₃ and R₀₃= R₃₁ combine to form purely left handed classical W boson fields and Z⁰ field corresponds to Z⁰=2R₀₃.
   

   Kähler form is given by
   

   J= 2(e⁰∧e³+e¹∧ e²) .
   
   

2. The vanishing of classical weak fields is guaranteed by the conditions
   

   e⁰∧ e¹-e²∧e³ =0 ,
   

   e⁰∧ e²-e³ ∧e¹ ,
   

   4e⁰∧ e³+2e¹∧e² .
   
   

3. There are many manners to satisfy these conditions. For instance, the condition e¹= a× e⁰ and e²=-a×e³ with arbitrary a which can depend on position guarantees the vanishing of classical W fields. The CP₂ projection of the tangent space of the region carrying the spinor mode must be 2-D.
   

   Also classical Z⁰ vanishes if a²= 2 holds true. This guarantees that the couplings of induced gauge potential are purely vectorial. One can consider other alternaties. For instance, one could require that only classical Z⁰ field or induced Kähler form is non-vanishing and deduce similar condition.
   
   

4. The vanishing of the weak part of induced gauge field implies that the CP₂ projection of the region carrying spinor mode is 2-D. Therefore the condition that the modes of induced spinor field are restricted to 2-surfaces carrying no weak fields sheets guarantees well-definedness of em charge and vanishing of classical weak couplings. This condition does not imply string world sheets in the general case since the CP₂ projection of the space-time sheet can be 2-D.
   
   

How string world sheets could emerge?

1. Additional consistency condition to neutrality of string world sheets is that Kähler-Dirac gamma matrices have no components orthogonal to the 2-surface in question. Hence various fermionic would flow along string world sheet.
   
   
2. If the Kähler-Dirac gamma matrices at string world sheet are expressible in terms of two non-vanishing gamma matrices parallel to string world sheet and sheet and thus define an integrable distribution of tangent vectors, this is achieved. What is important that modified gamma matrices can indeed span lower than 4-D space and often do so (massless extremals and vacuum extremals representative examples). Induced gamma matrices defined always 4-D space so that the restriction of the modes to string world sheets is not possible.
   
   
3. String models suggest that string world sheets are minimal surfaces of space-time surface or of imbedding space but it might not be necessary to pose this condition separately.
   
   

In the proposed scenario string world sheets emerge rather than being postulated from beginning.

1. The vanishing conditions for induced weak fields allow also 4-D spinor modes if they are true for entire spatime surface. This is true if the space-time surface has 2-D projection. One can expect that the space-time surface has foliation by string world sheets and the general solution of K-D equation is continuous superposition of the 2-D modes in this case and discrete one in the generic case.
   
   
2. If the CP₂ projection of space-time surface is homologically non-trivial geodesic sphere S², the field equations reduce to those in M⁴× S² since the second fundamental form for S² is vanishing. It is possible to have geodesic sphere for which induced gauge field has only em component?
   
   
3. If the CP₂ projection is complex manifold as it is for string like objects, the vanishing of weak fields might be also achieved.
   
   
4. Does the phase of cosmic strings assumed to dominate primordial cosmology correspond to this phase with no classical weak fields? During radiation dominated phase 4-D string like objects would transform to string world sheets.Kind of dimensional transmutation would occur.
   
   

Right-handed neutrino has exceptional role in K-D action.

1. Electroweak gauge potentials do not couple to ν_R at all. Therefore em neutrality condition is un-necessary if the induced gamma matrices do not mix right handed neutrino with left-handed one. This is guaranteed if M⁴ and CP₂ parts of Kähler-Dirac operator annihilate separately right-handed neutrino spinor mode. Also ν_R modes can be interpreted as continuous superpositions of 2-D modes and this allows to define overlap integrals for them and induced spinor fields needed to define WCW gamma matrices and super-generators.
   
   
2. For covariantly constant right-handed neutrino mode defining a generator of super-symmetries is certainly a solution of K-D. Whether more general solutions of K-D exist remains to be checked out.
   
   

See the chapter The recent vision about preferred extremals and solutions of the modified Dirac equation of "TGD: "Physics as infinite-dimensional geometry" or the article.

Further progress concerning the relationship between TGD and GRT and Kähler-Dirac action

The earlier attempts to understand the relationship between TGD and GRT have been in terms of solutions of Einstein's equations imbeddable to M⁴× CP₂ instead of introducing GRT space-time as a fictive notion naturally emerging from TGD as a simplified concept replacing many-sheeted space-time. This resolves also the worries related to Equivalence Principle. TGD can be seen as a "microscopic" theory behind TGD and the understanding of the microscopic elements becomes the main focus of theoretical and hopefully also experimental work some day.

The understanding of Kähler Dirac action has been second long term project. How can one guarantee that em charge is well-defined for the spinor modes when classical W fields are present? How to avoid large parity breaking effects due to classical Z⁰ fields? How to avoid the problems due to the fact that color rotations induced vielbein rotation of weak fields? The common answer to these questions is restriction of the modes of induced spinor field to 2-D string world sheets (and possibly also partonic 2-surfaces) such that the induced weak fields vanish. This makes string picture a part of TGD.

For details see the chapter TGD and GRT of "Physics in Many-Sheeted Space-time" or the article Further progress concerning the relationship between TGD and GRT and Kähler-Dirac action.

Implications of strong gravimagnetism for TGD inspired quantum biology

Physicists M. Tajmar and C. J. Matos and their collaborators working in ESA (European Satellite Agency) have made an amazing claim of having detected strong gravimagnetism with gravimagnetic field having a magnitude which is about 20 orders of magnitude higher than predicted by General Relativity.

Tajmar et al have proposed the gravimagnetic effect as an explanation of an anomaly related to the superconductors. The measured value of the mass of the Cooper pair is slightly larger than the sum of masses whereas theory predicts that it should be smaller. The explanation would be that actual Thomson field is larger than it should be because of gravimagnetic contribution to quantization rule used to deduce the value of Thomson field. The required value of gravimagnetic Thomson field is however 28 orders of magnitude larger than General Relativity suggests.

TGD inspired proposal is based on the notion of gravitational Planck constant assignable to the flux tubes connecting to massive objects. It turns out that the TGD estimate for the Thomson field has correct order of magnitude. The identification h_eff=h_gr at particle physics
and atomic length scales emerges naturally.

A vision about the fundamental role of quantum gravitation in living matter emerges. The earlier hypothesis that dark EEG photons decay to biophotons with energies in visible and ultraviolet range receives strong quantitative support. Also a mechanism for how magnetic bodies couple bio-chemistry emerges. The vision conforms with Penrose's intuitions about the role of quantum gravity in biology.

For the details the reader can consult the article Implications of strong gravimagnetism for TGD inspired quantum biology.

BICEP results are challenged

I have commented in several postings (this , this , this , and this ) the BICEP claim of having detected primordial B-modes in the polarization of cosmic microwave background (CMB). The claim was that effect was produced by the interaction of microwave photons from the effects caused by primordial gravitons on the space-time geometry caused by the presence of the gravitons. The effect was unexpectedly large and challenges quantum field theoretic description used in inflation paradigm: note that inflation paradigm postulates the existence of Higgs like particle called inflaton.

Now Jester tells that there are rumours that BICEP2 group might have underestimated the effect of galactic foreground. There is also a little article in Science Now.

BICEP signal is taken only at single frequency: 150 GHz. Planck has published a polarization at 353 GHz demonstrating that there may be a significant foreground emission from the galactic dust in the parts of sky studied by BICEP. The Planck collaboration has masked the results in BICEP patch: this does not certainly help BICEP team in their work. It is a pity that competition between research groups leads to this kind of secrecy.

Whether or not the BICEP finding is correct does not affect much neither inflationary models or TGD model. In inflationary approach there are so many variants to consider that one can always find candidate models. The reduction of B-mode contribution would be actually well-come since it would allow to get rid of the internal consistency problem. In TGD framework there is also rapid accelerating expansion analogous to that of inflationary expansion but the no inflatons are needed. Quantum criticality implies vanishing 3-curvature and this fixes the cosmology apart from the duration of the critical phase. The model is not quantum field theoretic anymore: gas of cosmic strings inside Minkowski space light-cone prevails before the inflationary period which is critical period for the phase transition to a radiation dominated cosmology. The problem is that one (more precisely, I) cannot really calculate precise prediction for the size of the effect.

The B-mode contribution should be disentangled from two foreground contributions from synchrotron radiation and galactic dust. The problems with BICEP are possibly related to the latter one. I cannot of course say anything interesting about the experimental side of the problem.

One can however ask TGD might predict new kind of synchrotron contribution. In TGD Universe magnetic flux tubes in various scales are basic objects and essential also in the model for temperature fluctuations and polarization of CMB resulting from slightly different temperatures for the two polarization of CMB. The magnetic flux tubes carry monopole fluxes making their existence possible without currents generating then. Their magnetic energy can be identified as dark energy. They carry also dark variants of ordinary particles identified as phases with Planck constant coming as integer multiple of the ordinary one. Could the charged particles - in particular electrons - rotating at cyclotron orbits at these flux tubes produce cyclotron radiation at CMB frequencies and thus giving rise to its apparent polarization?

Concerning cyclotron radiation one can consider relativistic/non-relativistic and classical/quantal situations.

1. In Wikipedia there is article about classical model for cyclotron radiation. One expects that the qualitative aspects remain the same in quantal treatment. For planar motion around magnetic field the radiation has dipole pattern around the axis of motion in non-relativistic situation. In relativistic situation it is strongly peaked around the direction of motion at frequency of order γ³/ρ where ρ is the radius of the orbit which gradually decreases. Most of the radiation is in the plane orthogonal to the orbit and the polarization in the plane of the orbit is parallel to the plane and orthogonal to the line of sight.
   
   
2. Quantum model might be relevant if the charged particles are in large h_eff phase at magnetic flux tubes and emit dark photons with scaled up energies. Dark photons would later transform to bunches of ordinary photons and if their energies are in the region corresponding to CMB they might produces additional contribution.
   

   In quantum case the charged particles behaves like a 2-D harmonic oscillator in degrees of freedom orthogonal to the magnetic field and energy is quantized as multiples of the cyclotron energy E= n× h_effω, ω = ZeB/m. Note the upwards scaling of energy by h_eff. The frequencies of the emitted radiation come a multiples of the cyclotron frequency and can be rather high. The Bohr radii of the orbits are quantized and the spiral orbit with decreasing radius is replaced with a sequence of circular orbits with instantaneous jumps to orbit with smaller radius. One expects that the general polarization characteristics are same as in the classical case and that classical description is a good approximation also now.
   

Could this kind of radiation give an apparent contribution to CMB? The following very naive scaling estimate is an attempt to answer the question.

1. The local direction of the vector field defined by the local polarization of CMB photons should be equal to the local direction of magnetic flux tubes in question so that the polarization map would give a map of flux tubes carrying dark matter. This would be of course extremely nice.
   
   
2. The condition that the radiation is in CMB range implies that the frequency is of order 100 GHz. Electron or electron Cooper is the best candidate for the dark charged particle in question. The cyclotron frequency of electron is $f= 6×10⁵ Hz in the magnetic field of .2 Gauss (familiar to me from TGD inspired quantum biology!). From this one deduces that a magnetic fields in question should be in Tesla range if they are to affect the CMB background.
   
   
3. If one requires quantization of the flux then minimal flux quantum for ordinary value of Planck constant would have a minimal thickness of order R=10 nm. By naive scaling the flux quantum is proportional to h_eff so that by a naive scaling the minimal radius of flux tube would scale like h_eff^1/2 and be thus larger than 10 nm lower bound.
   

   Macroscopic situation would correspond to very large thickness scaling as n^1/2, where integer n characterizes the quantized flux. Macroscopic effective thickness is of course required by data. Very large values of h_eff or n would be required to give realistic values for the flux tube radius. In the fractal Universe of TGD a fractal hierarchy of flux tubes within flux tubes picture is expected and one could have bunches of flux tubes with thickness h_eff^1/2× R.
   
   

I leave it for the reader to guess whether this contribution could mimic the CMB polarization detected by BICEP;-).

For details of TGD model see the chapter TGD and Cosmology or the article BICEP2 might have detected gravitational waves.

Pollack's findings and quantum model of cell membrane using square root of thermodynamics

Zero energy ontology (ZEO) is one of the basic differences between TGD and standard quantum theory based on positive energy ontology. One can say that TGD is as quantum theory square root of thermodynamics. Density matrix is replaced with its hermitian square root multiplied by unitary S-matrix same for all states. The general formalism is very beautiful but application has been lacking.I have now first real life application of TGD as square root of thermodynamics.

The existing model of cell membrane is thermodynamical: Coulomb energy differences and chemical potentials over the cell membrane play a key role in the description of osmosis, which is essential element but regarded as the "dirty" part of biophysics. I remember when I was something 20 +something and read in library about osmosis and felt disgust. Osmosis is however a real phenomenon: only its description is ugly, not the phenomenon.

Osmosis means the presence of pumps and channels - various transmembrane proteins. Pollack's findings about fourth gel-like phase of water and many other discoveries challenge this model, and it is not consistent with macroscopic quantum coherence. For instance, the description of metabolism requires that the chemical potential - a purely thermodynamical notion - is considerably larger than Coulomb energy for proton and dominates in metabolic energy of about .5 eV to be compared with Coulomb energy which is smaller by a factor .1-.2. This makes the skeptic inside me very alert.

Could it be that chemical potential could correspond to genuine energy: say cyclotron energy difference as suggested by TGD inspired quantum biology?

Even more, could one see osmosis as a gate to a new physics - maybe that involving magnetic body, dark matter and hierarchy of Planck constants, ZEO, etc... In TGD framework the thermodynamical description of cell membrane should be replaced with a quantal description using square root of thermodynamics. It would go roughly like follows.

• Transmembrane proteins become generalized Josephson junctions. What is new is that chemical potential, which dominates over the Coulomb energy for proton in the model for production of ATP from ADP, is replaced with the difference of cyclotron energies over the Josephson junction. Therefore the purely thermodynamical notions of proton gradient and protonmotive force become more concrete.
  
  
• Thermodynamical distibutions are replaced with their complex square roots - essentially Schroedinger amplitudes but proportional to the square root of Boltzmann weight so that ensemble property becomes single particle property and temperature has quantum mechanical meaning at single particle level as in p-adic thermodynamics too (about which one must also take square root to be be consistent).
  

For details see the TGD inspired model for Pollack's findings about water which helped to end up with this model.

The model can be applied to improve the earlier model of EEG: the energy of dark Josephson photon identifiable as EEG photon (say) is replaced with generalized Josephson energy including the difference of cyclotron energies for flux tube portions outside and inside the cell membrane and arriving from DNA (this was assumed already in the model of model DNA as topological quantum computer). Also the model of nerve pulse will become more detailed: the phase transitions changing the Planck constant at either or both sides of membrane introduce change of ion distributions as happens in nerve pulse. The new physics model for life is becoming more and more detailed and quantitative.

I have now a CMAP representation of TGD at my homepage. It gives kind of cognitive maps about basic ideas, notions, and arguments appearing in TGD. My hope is that they might help to get an idea about what TGD really is.

Possible implications of Pollack's findings for pre-biotic life in TGD Universe

I discussed in previous posting the fourth phase of water whose existence is convincingly demonstrated by Gerald Pollack and known with many other names: one of them is Brown's gas known for a long time - standard scientists have refused to admit its existence. In TGD framework the fourth phase of water has nice interpretation in terms of magnetic body and dark proton strings at its flux tubes giving rise to a realization of genetic code. If the fourth phase of water defines pre-biotic life form then the phase transition generating fourth phase of water and its reversal are expected to be fundamental elements of the ordinary metabolism, which would have developed from the pre-biotic metabolism. The following argument demonstrates that the findings of Pollack interpreted in this manner allow to understand what happens in photosynthesis and metabolism at deeper level and also shed light to the newest dramatic discovery related to metabolic pathways.

1. Cell interiors, in particular the interior of the inner mitochondrial membrane are negatively charged as the regions formed in Pollack's experiments. Furthermore, the citric acid cycle, which forms the basic element of both photosynthesis and cellular respiration, involves electron transport chain in which electron loses gradually its energy via production of NADP and proton at given step. Protons are pumped to the other side of the membrane and generates proton gradient serving as metabolic energy storage just like battery. The interpretation for the electron transport chain in terms of Pollack's experiment would be in terms of generation of dark protons at the other side of the membrane.
   
   
2. When ATP is generated from ADP three protons per ATP flow back along the channel formed by the ATP synthase molecule (perhaps Josephson junction) and rotate the shaft of a "motor" acting as a catalyst generating three ATP molecules per turn by phosphorylating ADP. The TGD based interpretation is that dark protons are transformed back to ordinary ones and possible negentropic entanglement is lost.
   
   
3. ATP is generated also in glycolysis, which is ten-step process occurring in cytosol so that membrane like structure need not be involved. Glycolysis involves also generation of two NADH molecules and protons. An open question (to me) is whether the protons are transferred through an endoplasmic reticulum or from a region of ordered water (fourth phase of water) to its exterior so that it would contribute to potential gradient and could go to magnetic flux tubes as dark proton. This would be natural since glycolysis is realized for nearly all organisms and electron transport chain is preceded by glycolysis and uses as input the output of glycolysis (two pyruvate molecules).
   
   
4. Biopolymers - including DNA and ATP - are typically negatively charged. They could thus be surrounded by fourth phase of water and neutralizing protons would reside at the magnetic bodies. This kind of picture would conform with the idea that the fourth phase (as also magnetic body) is fractal like. In phosphorylation the metabolic energy stored to a potential difference is transferred to shorter length scales (from cell membrane scale to molecular scale).
   
   

One of the basic questions of biology is whether metabolism preceded basic biopolymers or vice versa. RNA world scenario assumes that RNA and perhaps also genetic code was first.

1. The above view suggests that both approaches are correct to some degree in TGD Universe. Both metabolism and genetic code realized in terms of dark proton sequences would have emerged simultaneously and bio-chemistry self-organized around them. Dark proton sequences defining analogs of amino-acid sequences could have defined analogs of protein catalysts and played a key role in the evolution of the metabolic pathways from the primitive pathways involving only the phase transition between ordinary water and fourth phase of water.
   
   
2. There is very interesting article telling that complex metabolic pathways are generated spontaneously in laboratory environments mimicking hot thermal vents. Glycolysis and pentose phosphate pathway were detected. The proposal is that these pathways are catalyzed by metals rather than protein catalysts.
   
   
3. In standard biology these findings would mean that these metabolic pathways emerged before basic biopolymers and that genetic code is not needed to code for the metabolic pathways during this period. In TGD framework dark genetic code would be there, and could code for the dark pathways. Dark proton strings in one-one correspondence with the amino-acid sequences could be responsible for catalysts appearing in the pathways. Only later these catalysts would have transformed to their chemical counterparts and might be accompanied by their dark templates. One cannot even exclude the possiblity that the chemical realization of the DNA-aminoacid correspondence involves its dark analog in an essential manner.
   

For details see the chapter Meditation, Mind-Body Medicine and Placebo: TGD point of view of "TGD based view about living matter and remote mental interactions" or the article Pollack's findings about fourth phase of water: TGD view.

What is EEG made of?

The usual classification of EEG frequencies by EEG bands is more or less a convention and the definitions of various bands vary in frustratingly wide ranges. In a more ambitious approach bands should be replaced with some substructures identified on basis of their physical origin and function. In the proposed framework this is possible. This identification of substructures of course applies only to that part of EEG from which evoked potentials, noise, and possible other contributions are subtracted.

In the article What is EEG made of? a TGD inspired model for EEG as a communication and control tool of magnetic body is discussed.

1. Sensory data are communicated from cell membrane to magnetic body as Josephson radiation and induced transitions at harmonics of cyclotron frequencies determined by the mass number A and charge Z of ion in question (also electron and proton are included) plus the local strength of the magnetic field B_end having nominal value B_end=.2 Gauss in the simplest situation.
   

   Communications take place at resonance so that one has f_J= ZeV/h_eff=f_c= ZeB_end/2πAm_p, h_eff=2^k× A× h, where A is the atomic weight of the ion for the fundamental frequencies a more general resonance condition for harmonics reads as mf_J=nf_c. This condition is a new ingredient to the earlier model and is extremely restrictive - especially so if one assumes only bosonic ions forming Bose-Einstein condensates. Also electron and proton are needed to represent frequencies which are of order kHz or higher: this is true for hearing for which frequency range to be represented varies up 20 kHz.
   
   

2. Information is coded in frequency modulations of Josephson frequency induced by neural activity and feedback from the magnetic body coming via DNA at harmonics of cyclotron frequencies. Frequencymodulations have emotional content in music, which suggests that the "sensory experiences" of magnetic body defined by the Josephson radiation have emotional content dictated by the frequency modulation.
   

   Also the variations of resting potential induces frequency modulations and the quantum model for hearing suggests that the variations of the voltage could define analog of music scale consisting of discrete spectrum of resting potentials corresponding to cyclotron frequencies of ions belonging to the octave 10-20 Hz and having frequencies f_c∼ 10 Hz in alpha band as basic frequency.
   
   

3. Basic facts about EEG at various stages of sleep and the fact that octaves of 10 Hz frequency appear as resonance frequencies together with music metaphor suggests that EEG can be regarded as superposition of frequencies spectra very much analogous to frequency spectra associated with music scale. In particular, octaves of h_eff=2^km and B_end suggested also by p-adic length scale hypothesis appear. In the simplest situation the EEGs associated with various ions would be time scaled versions of each other making possible "stories" as representations of same events in various time scales: this is believed to be a basic ingredient of intelligence.
   
   
4. The model leads to a detailed identification of sub-bands of EEG in terms of cyclotron frequencies assignable to bosonic ions. One can understand the basic features of various EEG bands, why conscious experiences possible occurring during sleep are not remembered and the four stages of sleep, why beta amplitudes are low and tend to be chaotic, the origin of resonance frequencies of EEG. Also a model for how Schumann resonances could affect consciousness emerges.
   

   Music metaphor allows to develop in more detail the earlier proposal that nerve pulse patterns defined a languages with "phonemes" having duration of .1 seconds and obeying genetic code with 6 bits. Also the right brain signs metaphor can be given a detailed quantitative content in terms of the analog of music scale associated with the resting potential.
   
   

To sum up, the model gives very strong quantitative support for the notion of magnetic body and makes several testable predictions.

For background and details see the chapter Quantum model for EEG or the article What is EEG made of?.

Still about TGD and inflation

Quantum criticality is the TGD counterpart of the inflation and the flatness of 3-space follows from the condition that no local dimensional quantities are present in 3-geometry. Also the imbeddability fo M⁴ is an important piece of story and restricts the set the parameters of imbeddable cosmologies dramatically.

One can try to understand the situation microscopically in terms of the cosmic strings which gradually develop higher than 2-D M⁴ projection during cosmic evolution and become magnetic flux tubes carrying magnetic monopole fluxes explaining the presence of magnetic fields in cosmology.

At microscopic level magnetic flux tubes are the key structural elements. The phase transitions increasing Planck constant for the matter associated with flux tubes and thus also the lengths of magnetic flux tubes should be important as also the phase transitions increasing p-adic prime and reducing Planck constant originally emerged in the modelling of TGD inspired quantum biology are highly suggestive. First transitions would mean adiabatic expansion with no heat generation and latter transitions would liberate magnetic field energy since flux conservation forces field strength to be reduced and leads to liberation of magnetic energy producing ordinary matter and dark matter. Dark energy in turn is identifiable as magnetic energy.

The key question concerns the mechanism causing the isotropy and homogeny of the cosmology. There are two possible identifications.

1. According to two decades old TGD proposal primordial cosmology before the emergence of space-time sheets could be regarded as string gas in M⁴₊× CP₂ at Hagedorn temperature determined by CP₂ radius: T_H∼ hbar/R(CP₂). This phase could be present also after the transition to radiation dominated cosmology and consist of strings, whose thickness is gradually increasing and which contain carry dark energy and dark matter. The horizon radius is infinite for this cosmology thus providing at least partial explanation for the homogeny and isotropy and visible matter would represent deviations from it.
   
   
2. The accelerating expansion period towards the end of the critical period could smooth out inhomogenities and thus provide an additional mechanism leading to homogenous and isotropic Big Bang. This for given space-time sheet representing R-W cosmology: in many-sheeted cosmology one can imagine distribution of parameters for the cosmology. The rapid expansion period could however also develop large fluctuations! Indeed, the time a_F<a₁ (density would be infinite for a₁) for its end - and therefore local mass density - must have a distribution after the rapid expansion ends. This expansion would generate separate smoothed out radiation dominated space-time sheets with slightly different mass densities and cosmic temperatures. A splitting to smooth radiation dominated sub-cosmologies would take place.
   
   

Therefore TGD scenario could be very different from inflationary scenario. The problem is to decide which option is the most feasible one.

The formulas used to make back of the envelope (see this) calculations in inflation theory discussed in a guest posting in Lubos's blog given some idea about TGD counterpart for the generation of gravitons. Inflationary period is replaced with essentially unique critical cosmology containing only its duration as a free parameter. The fluctuations in the duration of this parameter explain scalar temperature fluctuations assoiated with CMB.

How the local polarization of CMB is generated?

There is a nice discussion about the mechanism leading to the generation of CMB polarization (see this). The polarization is generated after the decoupling of CMB photons from thermal equilibrium and is due to the scattering of photons on free electrons during decoupling. This scattering is known as Thomson scattering. The page in question contains schematic illustrations for how the polarization is generated. The scattering from electrons polarizes the photons in direction orthogonal to the scattering plane. In thermal equilibrium the net polarization of scattered radiation vanishes. If however the scattered photons from two perpendicular directions have different intensities a net polarization develops.

Polarized photons could be produced only during a short period during recombination scattering from free electrons was still possible and photons could diffuse between regions with different temperature. Polarized photons were generated when electrons from hot and cold regions where scattering on same electrons. CMB polarization indeed varies over sky but not in long length scales since photons could not diffuse for long lengths.

So called quadrupole anisotropy of CMB temperature contains information about the polarization. There are three contributions: scalar, vector, and tensor.

1. Scalar contributions is due to density fluctuations reflecting themselves as temperature fluctuations and does not distinguish between polarizations: this is what has been studied mostly hitherto. A natural TGD mechanism for their generation would be different time for the end of the critical period leading to splitting of critical cosmology to radiation dominated cosmologies with slightly different temperatures.
   
   
2. There is also so called vorticity distribution due to the flow which has vorticity and would due to defects/string like objects present also in TGD. The simplified situation corresponds to are region in which one has two flows in opposite direction locally. Depending on whether the scattering photons are upstream or down stream they are blue-shifted or red-shifter so that the temperatures are slightly different in up-stream and down.The flows in opposite direction give rise to a situation in which photons with different temperatures scatter and produce polarization. The effects of vorticity are expected to disappear during the fast expansion period. Probably because the gradients of velocity giving rise to vorticity are smoothed out.
   
   
3. The third contribution is tensor contribution and due to gravitons generating stretching and squeezing of space in two orthogonal directions defining polarization tensor. Stretching increases wavelengths and decreases temperature. Squeezing does the opposite. Therefore temperature differences distinguishing between the two directions are generated and the outcome is polarization of the CMB background much later. This corresponds to the so called E and B modes.
   
   One can decompose polarization as vector field to two parts: the first one - the E-mode - is gradient and thus irrotational and second is curl and thus rotational and with vanishing divergence (incompressible liquid flow is a good concrete example).
   

How the polarization anisotropies could be generated in TGD Universe?

One can try to understand microscopically how the polarization anisotropies are generated in TGD framework using poor man's arguments.

1. One can introduce a vision vision about fractal 3-D network of cosmic strings forming a kinds of grids with nodes in various scales. These grids would be associated with different levels of the hierarchy of space-time sheets associated with many-sheeted space-time. Coordinate grid is of course an idealization since three coordinate lines would meet in single node. A weaker form of grid would involve meeting of two coordinate lines at given node. There is data about our own galactic nucleus understood if it correspond to the node at which two magnetic flux tubes meet. Ordinary visible matter would be generated in nodes.
   

   One might say that galaxies are due to traffic accidents in which dark matter arriving along two cosmic strings collides in the crossing of the roads. Flux tubes would be attracted together by gravitational attraction so from the crossing.
   
   

2. Amusingly, the notion grid emerged also TGD inspired quantum biology as a proposal for how living system codes morphogenetic position information. Flux tubes carry dark matter and ordinary matter is associated with the nodes at which coordinate lines meet each other. This web can give rise to a generalization of topological quantum computation using 2-braids. Coordinate lines define strings which can be knotted in 3-dimensions and define braids making possible topological quantum computation using macroscopic quantum phases defined by the dark matter. The time evolutions of coordinate lines defines string world sheets and in 4-D space-time the string world sheets can be knotted and braided so that also higher level TQC becomes possible with string reconnection and going above or below the other define two bits in each node.
   
   
3. The presence of grid could also explain the honeycomb like structure of Universe with the recent typical size of honeycomb about 10⁸ ly.
   
   
4. In this framework the illustrations for how the gravitational waves induce the polarization of CMB. The radiation beams entering from opposite directions can be assigned with two magnetic flux tubes meeting at the node and in slightly different temperatures due to the interaction with gravitons much earlier. The gravitons can be regarded as larger space-time sheets at which the two flux tubes had contacts so that space associated with the flux tubes was forced to stretch or squeeze. This in turn increased of reduced photon wavelength so that photon temperature at flux tubes was different and the difference were preserved during subsequent evolution.
   
   

Back on the envelope calculations in TGD framework

One can modify the back on the envelope calculations of John Preskill (see this) in Lubos's blog to see what could happen in TGD framework. Now one however starts from the critical cosmology fixed apart from its duration and looks what it gives rather than starting from Higgs potential for inflaton field. The obvious counterpart for inflaton scalar field would be magnetic field intensity having same dimension but one should avoid too concrete correspondences.

The key question is whether the critical period generates the rapid expansion smoothing out inhomogenities or whether it generates them. The original guess that it smooths them out turns out be wrong in closer examination.

1. The basic equation in inflationary model is given by
   

   (da/dt)²= V/m_p²
   

   If V is small this has as solution a(t)= a(0)exp(Ht) if H= V^1/2/m_p is constant. De Sitter cosmology allows partial imbedding in TGD but the imbedding is naturally static and has interpretation as black-hole interior with constant mass density. One can find coordinates in which the solution looks like expanding cosmology without Big Bang but these coordinates are not natural from the view of imbedding space.
   
   

2. In TGD the expression for da/dt for critical cosmology is
   

   da/dt= [a₀²-a²]^1/2/[a₀²-R²-a²]^1/2 .
   

   a₀ is roughly the duration of cosmology and R is CP₂ radius of order 10^3.5 Planck lengths. The almost uniqueness follows from the condition that the imbedding is such that the induced metric at the 3-surfaces defined by intersections with hyperboloids of M⁴₊ is flat rather than hyperbolic. This cosmology differs from de-Sitter cosmology.
   
   

3. For a→ 0 one has
   

   da/dt ≈ a₀²/[a₀²-R²]≈ 1 .
   

   so that one has da/dt ≈ 1 and a≈ t for small values of a in accordance with the replacement of Big Bang with a "silent whisper amplified to a Big Bang" (density of matter goes as 1/a²) Hubble constant goes like H∝ 1/a so that Hubble radius divergence. This does not guarantee that horizon radius becomes infinite. Rather, the horizon is finite and given in good accuracy by the duration a₁=[a₀² R²]^1/2 of the period. One can however explain the isotropy and homogenity of the string gas in light-cone M⁴₊ carrying flux tubes carrying dark matter and energy in terms of the infinite horizon of M⁴.
   

   There is no exponential time evolution at this period since one has a≈ t in good approximation for a/a₀<<1. The TGD counterpart of V would behave like 1/a², which conforms with the idea that V corresponds to energy density.
   
   

4. As the limit a→ a₁=[ta₀²-R²]^1/2 is approached, the expansion rate approaches infinite and for a>a₁ at the latest one expects radiation dominated cosmology: otherwise a region of Euclidian signature of the induced metric results. The expectation is that a transition to radiation dominated cosmology takes place before a=a₁ at which also energy density would diverge. The question is whether this period means smoothing out of inhomogenities or generation of them or both.
   

Consider now what could happen near the end of the Minkowskian period of critical cosmology.

1. Although it is not clear whether rapidly accelerating expansion is needed to to smooth out homogenities, one can just find what conditions this would give on the parameters. For a_i= kR at which phase transition began the condition that a was increased at least by factor e⁵⁰∼ 5× 10²¹ (50 e-folds) this would give a₁≈ a₀>e⁵⁰kR. For k∼ 1 this gives something like 10^-18 seconds, which happens to correspond atomic length scale. Below it will be found that this period more naturally corresponds to the period during which large fluctuations in density distribution and metric are generated.
   
   
2. The earlier estimate for the emergence of radiation dominated cosmology assumed that the transition to radiation dominated cosmology takes place at CP₂ temperature defining Hagedorn temperature at which temperature of the string gas cannot be raised anymore since all the energy goes to the generation of string excitations rather than to kinetic energy, gives a_F∼ 10^-10 seconds, which is by factor 10⁸ larger. If this were true, the fast expansion period a_F would increase the scale factor to about 68 e-folds equivalent to 98 2-folds. p-Adic prime p≈ 2¹⁹⁶ would correspond to p-adic length scale about L(196) ∼ .1 meters. The crucial assumption would be that the the time a_F at which the expansion ends is same everywhere. There is no reason to assume this and this would mean that the period in question generates inhomogenities and isotropies of mass distribution and temperature distribution.
   

   Note that if the distribution of the time a_F<a₁ at which the critical period ends is responsible for the CMB fluctuations then the number of foldings characterizes the smoothness of given local radiation dominated cosmology and could be rather large.
   
   

3. The rapid accelerating expansion occurs as g_aa approaches zero. Indeed, for
   

   a→ a₁= [a₀²-R²]^1/2
   

   a very rapid expansion occurs and da/dt approaches infinite value. Near to a₁ one can write a/a₁=1-δ and solve δ approximately as function of t as
   

   δ =[3R²/4a₁²]^2/3 [t-t₁/a₁]^2/3 ,
   t₁= ∫₀^a₁ [1-a²/a₁²1/2/[1-a²/a₁²]^1/2 .
   

   Hubble constant behaves as
   
   

   H= (da/dt)/a = (R²/2a₁³)δ^-1/2 .
   

   
   
   

4. What is interesting is that applying the naive dimensional estimate for the amplitude of gravitational fluctuations to be δ h_T²∼ H²/m_P⁴. This would mean that at the limit a→ a_F< a₁ gravitational fluctuations become very strong and generate the strong graviton background. Same applies to fluctuations in mass density.
   
   

Summary

The possibility of very rapid expansion near a=a_F<a₁ leading to radiation dominated cosmology should have some deep meaning. The following tries to catch this meaning.

1. The explosive period could lead to a radiation dominated cosmologies from string dominated cosmology with Hagedorn temperature. It could involve h_eff increasing phase transitions for string gas during the initial period and liberation of magnetic energy during the end period as massless particles: this would explain why the mass density of the space-time sheet increases dramatically. The critical cosmology could correspond to a phase transition from a phase with Hagedorn temperature identified as T_H∝ hbar/R_H to radiation dominated cosmology.
   
   
2. The cooling of string gas would lead to the generation of hierarchy of Planck constants and liberation of the magnetic energy of strings as massless particles during the end of critical period topologically condensing to space-time sheets such as massless extremals. This process could correspond to the rapid increase of energy density towards the end of the critical period.
   
   
3. Isotropy and homogenity appear both at the level of imbedding space and space-time sheets. The infinite horizon of M⁴₊ would explain the isotropy and homogenity of string gas in H both before and after the emergence of space-time sheets at Hagedorn temperature around a∼ R(CP₂). In particular, the smoothness of the cosmology of dark matter and dark energy would find explanation. The rapid expansion would in turn smooth out inhomogenities of individual space-time sheets.
   
   
4. The Hubble scale 1/H approaches to zero as a=a_F<a₁ is approached. The rapid expansion destroys anisotropies and inhomogenities of radiation dominated space-time sheet corresponding to particular value of a_F. The distribution for values of a_F in turn explains CMB scalar fluctuations since the energy density in final state is highly sensitive to the precise value of a_F. This distribution would be Gaussian in the first approximation. One can say that the fluctuation spectrum for inflaton field is replaced with that for a_F.
   
   
5. Also the generation of gravitational radiation and its decoupling from matter could take place during the same end period. After this gravitational fields would be essentially classical and assignable to space-time sheets. Essentially formation of gravitationally bound states would be in question analogous to what happens photons decouple from matter much later. The reduction of the temperature of string gas below Hagedorn temperature could generate also the massless graviton phase decoupling from matter and inducing the temperature fluctuations and polarization during decoupling.
   

   Gravitons and also other particles would topological condense at "massless extremals" (MEs,topological light rays) and particles - in particular photons - would interact with gravitons by generating wormhole contacts to gravitonic MEs. The interaction between MEs assignable to gravitational radiation and photons would have caused the fluctuations of CMB temperature.
   

To sum up, if the TGD inspired picture is correct then Penrose would have been correct in the identification of string theory as fashion and inflationary cosmology as fantasy ( Lubos has reacted strongly to this). Also the fact that inflationary cosmology is at the verge of internal contradiction due the fact that the assumption of field theoretic description is in conflict with the large graviton background suggests that inflationary cosmology is not for long with us anymore.

For details see the chapter TGD and Cosmology or the article BICEP2 might have detected gravitational waves.

Do we live in hologram?

Sabine Hossenfelder wrote and excellent posting about holographic principle was motivated by a Youtube hype stating that "Many physicists now believe that reality is not in fact, 3-dimensional". This type of "many/leading physicists believe now" hook has become familiar from science lobbying. Sabine makes it clear that the holography principle is strongly theory dependent proposal.

Lubos reacted strongly to Sabine's comments and wrote a response full of negative emotions. It is a pity, since this posting was preceded by several excellent guest posts about Bicep2 discovery of evidence for gravitational radiation in microwave background: also Lubos wrote a nice post about the topic. I am just wondering why Lubos cannot get his emotional brain in control to avoid this kind of flops.

Lubos did the usual mud slinging with a lof of "silly":s and other similar attributes. Lubos even accused Sabine for being creationist. Towards the end Lubos's emotional brain took the lead totally and he closed the posting with a series of personal insults. Lubos writes otherwise excellently and could become a good science journalist if he only could get his aggressions in control and widen his rather narrow intellectual horizon limited by blind beliefs in string theory, supersymmetry in standard sense, in Boltzmann's thermodynamics as a final truth, recent mainstream interpretation of quantum mechanics, etc...

Is holography principle true?

A fictitious character Q starts a discussion with Sabine by posing the following question.

Q: Do we really live in hologram?

Sabine reacts to "really" and quite correctly states that its content is far from clear. "Reality" indeed leads to long philosophical discussions. Sadly, most colleagues see these discussions as esoterism. It is a pity since this attitude has halted the development of theoretical physics for almost a century. This kind of discussions were possible during the first year of quantum theory but should have been continued.

To specify what "we" means requires a quantum theory of consciousness and of life and I can only refer to the 9 books concerning the TGD view about "really" and "view" (see this)!

A more technical formulation avoiding "we"s and "realities" would be following.

Q: Is holography principle true?

And to avoid the misleading impression that there exists some universally accepted form of this principle as science lobbyist would want us to believe Q should ask:

Q: Could some form form of holography principle be true?

1. Sabine quite correctly states that gravitational holography principle is a specific conjecture stimulated by AdS/CFT correspondence introduced by Maldacena and being inspired by string model. It relates conformal quantum field theory ( N=4 SUSY) at the 4-D boundary of AdS₅, which is 4-D conformally compactified Minkowski space to string model in 10-D AdS₅× S⁵. These assumptions are very strong and not generally true in quantum field theories - say standard model. Lubos claims that a fundamental physical principle is in question. One must of course notice that now hologram is 4-D Minkowski space and something totally different from 2-D hologram provided by say black-hole horizon. A lot of conceptual sloppiness is involved with holography hyping.
   
   
2. Space-time according to standard cosmology is not conformally compactified M⁴ and standard model is not conformally invariant theory so that holography in the sense AdS/CFT correspondence is a rather specific conjecture! Certainly not a fundamental principle.
   

   Lubos however states without any justification that this conjecture can be applied also to AdS₄ that we habit. This statement of Lubos contains several bad inaccuracies since AdS₄ represents inflationary cosmology in the first approximation, and inflationary cosmology is only one of the many proposals, and inflationary cosmology does not apply during say radiation dominated period. In Lubos's own blog a string gas cosmology was discussed as a guest post and this cosmology is certainly not inflationary cosmology! By the way, in TGD framework string gas is replaced with cosmic strings and there are many common elements between these views about cosmology.
   
   

3. Both Sabine and Lubos talk about holography in quantum gravity sense: 2-D or 3-D holograms in 4-D space-time defined by black hole horizons. This holography is rather speculative notion and in principle something very different from AdS/CFT correspondence since in this case one would reduce 4-D physics to 3-D or even 2-D and in the case of Maldacena n-D physics would represented as part of n+1-D physics (Sⁿ excitations are trivial).
   
   

It should be also made clear that the AdS_n/CFT correspondence is application of the mathematics of string theory and not a part of string theory. In string theory S^10-n replaced with Calabi-Yau space so that the relationship is far from obvious.

Various forms of holography principle

There are very many forms of holography principle with varying degree of mathematical and physical feasibility.

1. t'Hooft proposed a holography principle relating gauge theory description to string model type description: for gauge theory in M⁴ the strings would live in M⁴ and intuitively correspond to planar Feynman diagrams forming net like structures.
   
   
2. In general relativity it is natural to make the conjecture that 2-D black-hole horizon is hologram. It is often assumed - an ad hoc assumption is in question - that single bit corresponds to an area of Planck length squared so that horizon area would could carry only finite number of bits. Sabine talks about this form of holography. Also Lubos speaks about this holography instead of better established AdS₅/CFT holography as he starts to put down Sabine.
   
   
3. Maldacena introduced super-string inspired holographies using 10-D target space with decomposition AdS_n× S^10-n. I guess that in M-theory speculations this decomposition would be replaced with AdS_m× S^11-n. AdS_m has m-1-D conformally compactified Minkowski space as boundary. For AdS₅/CFT hologram the boundary would be 4-dimensional and correspond to conformal compactification of M⁴ appearing also in twistorial approach and being motivated by 4-D conformal symmetry. QFT in M⁴ would have higher-D stringy/gravitational description.
   

   Maldecena holography must be distinguished from the gravitational holography in which one conjectures that 4-D gravitation allows 3-D or even 2-D QFT type description in terms of black hole horizons. These are quite different holographies but for some reason neither Sabine nor Lubos do not emphasize this distinction.
   
   

I do not know how feasible all these conjectured AdS_n/CFT correspondences really are.

1. It is argued that one can think that S^10-n excitations do not contribute to the physics in the scales much longer than S^10-n size so that higher-D space effectively reduces to AdS_n. Hence one would have hologram as n-1-dimensional representation for physics in n-dimensions rather than for 9-D physics in 10 dimensions.
   
   
2. This is not not enough: if one wants gravitational holography in the sense suggested by blackhole physics and t'Hooft's original argument one should be able to replace AdS_n× S^10-n with 4-dimensional space-time of general relativity and in quantum gravity one should speak about quantum superpositions of space-time surfaces. One would have "quantum holography". Whether holography extends in this manner is far from obvious. AdS₃ with 2-D with conformally compactified M² as boundary would be analogous with this holography.

What about experimental side? AdS₅× S⁵ holography have been applied in attempts to explain RHIC and later LHC results but with a rather modest success: even qualitative predictions are wrong as reported by Sabine in her earlier posting.

What looks strange to me that one is ready to introduce strings in 10-dimensional space to explain these findings in conflict with perturbative QCD but refuses to consider the possibility that a fractal copy of hadronic physics modellable using hadronic string like objects in 4-D space-time could explain the findings much more elegantly (see this)! But this is sociology of science which rational mind is not able to understand.

AdS/CFT holography has been applied also to nuclear physics and condensed matter without any breakthroughs. The description of atomic nuclei or condensed matter as blackholes in 10 dimensions has not led to any breakthroughs. Amusingly, in TGD framework atomic nuclei can be described as wounded string like objects in the familiar 4-D space-time but this is of course too science-fictive and speculative as compared to blackholes in 10 dimensions;-). Wikipedia article contains comments about these applications (see this).

Holography in TGD framework reduces to General Coordinate Invariance

In TGD framework holograms are effectively 2-D as they should be if quantum gravitational intuition is correct. The pair formed by AdS₅ and its boundary which is 4-D Minkowski space M⁴ is replaced with 4-D space-time surface in M⁴× CP₂ and its space-like boundaries or light-like "boundaries". The holography holds trued for single space-time surface in quantum superposition of them.

1. Holography in TGD sense follows from General Coordinate Invariance (GCI) in TGD framework in which gravity becomes sub-manifold gravity. Single big principle instead of two means quite a dramatic increase in conceptual economy and was in ancient times seen as a signal that theory has been able to catch something very profound about reality.
   
   
2. Also a stronger form of holography is possible. Suppose one requires that light-like "boundaries" identified as regions at which induced metric changes its signature from Minkowskian to Euclidian inside lines of generalized Feynman diagrams and space-like 3-surfaces at the ends of causal diamonds provide dual descriptions of quantum physics. If this is the case, one obtains strong form of GCI and consequently strong form of holography. The universe is effectively 2-dimensional: partonic 2-surfaces defined by intersections of these two kinds of 3-surfaces and tangent 4-D space - data at them would code for physics.
   

   It is amusing that strong form of holography is very nearly the same as the holography as we encounter it in everyday world and in sensory perception we see things as 2-dimensional! Note however that the representability of space-time as a 4-surface of M⁴× CP₂ is essential.
   
   

"Effectively" is an important limitation.

1. Quantum states contain information about actual 3-dimensionality. For instance, the integers characterizing the modes of induced spinor fields restricted at string world sheets code for this kind of information. These string world sheets accompanying magnetic flux tubes carrying monopole fluxes and connecting various partonic 2-surfaces are the counterparts of strings connecting points at the boundary of AdS₅× S⁵ so that these two holographies have a lot of common. In TGD one might perhaps speak about dual descriptions provided by partonic 2-surfaces and string world sheets. The situation is not however completely clear.
   
   
2. Zero energy ontology originally motivated by the failure of the strict determinism of Kähler action implies a hierarchy of causal diamonds (CDs) so that one obtains holography only in given UV and IR resolutions (considering single CD). Also Sabine emphasizes the importance of measurement resolution but formulates this in terms of finite area per bit condition. Discretization at space-time level is the number theoretic manner to express finite measurement resolution. Inclusions of hyper-finite factors of type II₁ provide the mathematical language to express the notion of finite measurement resolution and leads to the emergence of quantum groups and quantum spinors.
   
   
3. An additional complication is due to the fact that one does not have single space-time surface but quantum superposition of them. If quantum classical correspondence is taken really seriously, one is led to the conjecture that all space-time surface in allowed superpositions have the same classical n-point functions for coordinate invariant field like quantities as functions of M⁴ coordinates and that these n-point functions are identical with their quantal counterparts. This is very powerful constraint on quantum states and without further specifications could be too strong. "Modulo finite measurement resolution" is one such additional specification.
   
   
4. The hierarchy of CDs implies that we are 3- (or 4-) dimensional in the same as a 3-D lattice consisting of 2-D (3-D) objects is 3-D (4-D). Although quantum states are coded by data assignable to partonic 2-surfaces at boundaries of CDs, the understanding of what happens in quantum measurements requires both quantum states and and their space-time correlates since every measurement outcome is formulated in terms of classical space-time physics. Quantum numbers such as momenta, spin, charge, etc.. label quantum states whereas in space-time description one has frequencies, field intensities, etc... Both are needed.
   
   

For these reasons and as a habitant of TGD Universe I cannot agree when someone says that we live in (2-D or 3-D) hologram/are hologram. Nature just represents same information in many manners just as computers provide a large number of different representations of the same data. This does not diminish the mathematical power of strong form of GCI/holography.

Quantum critical cosmology of TGD predicts also very fast expansion

TGD inspired critical cosmology (see this) relies on the identification of 3-space as a= constant section, where a is Lorentz invariant cosmological time defined by the light-cone proper time a=(m⁰)²-r_M²)^1/2, and from the assumption that (quantum) criticality corresponds to a vanishing 3-curvature meaning that 3-space is Euclidian.

The condition that the induced metric of the a= constant section is Euclidian, fixes the critical cosmology apart from its duration a₀ from the existence of its vacuum extremal imbedding to M⁴× S²,
where S² homologically trivial geodesic sphere:

ds² = g_aada² -a² (dr² +r²dΩ²) ,

g_aa= (dt/da)²=1- ε² /(1-u²) , u=a/a₀ , ε=R/a₀ .

sin(Θ)= +/- u , Φ= f(r) ,

1/(1+r²) -ε²(df/dr))²=1 .

From the expression for dt/da one learns that for the small values of a it is essentially constant equal to dt/da=(1 ε²)^1/2. When a/a₀ approaches to (1-ε²)^1/2, dt/da approaches to zero so that the rate of expansion becomes infinite. Therefore critical cosmology is analogous to inflationary cosmology with exponential expansion rate. Note that the solution is defined only inside future or past light-cone of M⁴ in accordance with zero energy ontology.

After this a transition to Euclidian signature of metric happens (also a transition to radiation dominated cosmology is possible): this is something completely new as compared to the general relativistic model. The expansion begins to slow down now since dt/da approaches infinity at a/a₀=1. In TGD framework the regions with Euclidian signature of the induced metric are good candidates for blackhole like objects. This kind of space-time sheets could however accompany all physical systems in all scales as analogs for the lines of generalized Feynman diagrams. For sin(Θ)=1 at a/a₀=1 the imbedding ceases to exist. One could consider gluing together of two copies of this cosmology together with sin(Θ)= sin(π-Θ)= a/a₀ to get a closed space-time surface. The first guess is that the energy momentum tensor for the particles defined by wormhole contacts connecting the two space-time sheets satisfies Einstein's equations with cosmological constant.

Quantum criticality would be associated with the phase transitions leading to the increase of the length and thickness of magnetic flux tubes carrying Kähler magnetic monopole fluxes and explaining the presence of magnetic fields in all length scales. Kähler magnetic energy density would be reduced in this process, which is analogous to the reduction of vacuum expectation value of the inflation field transforming inflaton vacuum energy to ordinary and dark matter.

At the microscopic level one can consider two phase transitions. These phase transitions are related to the hierarchy of Planck constants and to the hierarchy of p-adic length scales corresponding to p-adic primes near powers of 2.

1. The first phase transition increases Planck constant h_eff=nh in a step-wise manner and increases the length and width of the magnetic flux tubes accordingly but conserves the total magnetic energy so that no magnetic energy is dissipated and one has adiabaticity. This sequence of phase transitions would be analogous to slow roll inflation in which the vacuum expectation of inflation field is preserved in good approximation so that vacuum energy is not liberated. The flux tubes contain dark matter.
   
   
2. Second phase transition increases the p-adic length scale by a power of 2^1/2 and increases the length and width of magnetic flux tubes so that the value of the magnetic field is reduced by flux conservation (magnetic flux tubes carry monopole fluxes made possible by CP₂ homology). This phase transition reduces zero point kinetic energy and in the case of magnetic fields magnetic energy transforming to ordinary and dark matter.
   
   
3. The latter phase transition can be accompanied by a phase transition reducing Planck constant so that the length of the flux tubes is preserved. In this transition magnetic energy is liberated and dark matter is produced and possibly transformed to ordinary matter. This kind of phase transitions could take place after the inflationary adiabatic expansion and produce ordinary matter. As a matter fact, I
   have originally proposed this kind of phase transition to be the basic phase transition involved with the metabolism in living matter (see
   this), which suggests that the creation of ordinary matter from dark magnetic energy could be seen as kind of metabolism in cosmological scales.
   

   In zero energy ontology one can ask whether one could assign to the Minkowskian and Euclidian periods a sequence of phase transitions increasing Planck constants but proceeding in opposite time directions.
   
   

4. During the inflationary period the size scale of the Universe should increase by a factor of order 10²⁶ at least. This corresponds to 2⁸⁷ - that is 87 2-foldings, which is a more natural notion than e-folding now. If the size of the sub-Universe is characterized by a p-adic length scale, this would correspond in the final state to p∼ 2¹⁷⁴ at least: this p-adic length scale is about 4× 10^-5 meters roughly and thus of order cell size. If the foldings correspond to increase of secondary p-adic length scale characterizing causal diamond, 89 foldings would correspond to Mersenne prime assignable to weak bosons.
   

5. How the transition to radiation dominated cosmology takes place is an interesting question. The decay of the magnetic energy to ordinary matter should take place during the Euclidian period initiating therefore the radiation dominated period. For the radiation dominated cosmology the scale factor behaves as t∝ a² so that dt/da approaches zero. Since this occurs also when the Euclidian period starts, the guess is that space-time sheets with radiation dominated sub-cosmologies assignable to sub-CDs (CD is shorthand for causal diamond) begin to be created.
   
   

Although this picture is only an artist's vision and although one can imagine many alternatives, I have the feeling that the picture might contain the basic seeds of truth.

For details see the chapter TGD and Cosmology or the article BICEP2 might have detected gravitational waves.

Could TGD allow inflationary cosmology?

A natural question is whether TGD could allow inflationary cosmology. In the lowest order this would require imbedding of the De Sitter space. De Sitter space allows two basic coordinate slicings.

1. The first one corresponds to a stationary metric having interpretation in terms of interior of an object with constant mass density. The line element reads
   

   ds² =Adt²-Bdr²-r²dΩ² ,
   

   A =1-(r/l)² , B= 1/A .
   

   l has natural interpretation as outer boundary of the object in question. It will be found that TGD suggests 2-fold covering of this metric.
   
   

2. Second coordinatization has interpretation as simplest possible inflationary cosmology having flat 3-space:
   

   ds²= dt₁²-e^2t₁/l dr²-r₁²dω² .
   
   

3. The two coordinatizations are related to each other by the formulas deducible from the general transformation property of metric tensor:
   

   t =t₁+ log[1+(r₁/l)²e^2t₁/l]/2 ,
   

   r =e^t₁/lr₁ .
   

In TGD framework also the imbedding of space-time as surfaces matters besides the metric which is purely internal property. The most general ansatz for the imbedding of De Sitter metric into M⁴× CP₂ is as a vacuum extremal for for Kähler action with the understanding that small deformation carries energy momentum tensor equal to Einstein tensor so that Einstein's equations would old true in statistical sense.

1. The general ansatz for the stationary form of the metric is of same general form as that for Schwartchild metric. One can restrict the consideration to a homologically trivial geodesic sphere S² of CP₂ with vanishing induced Kähler form and standard spherical metric. This means that CP₂ is effectively replaced with S². This imbedding is a special one but gives a good idea about what is involved.
   

   Denoting by (m⁰,r_M,θ,φ) the coordinates of M⁴ and by (Θ, Φ) the coordinates of S², a rather general ansatz for the imbedding is
   

   m⁰= t+ h(r) , r_M=r ,
   

   Rω × sin(Θ (r))= +/- r/l , Φ= ω t+ k(r) .
   
   

2. The functions h(r), k(r), and Θ (r) can be solved from the condition that the induced metric is the stationary metric. For Schwartschild metric h(r) and k(r) are non-vanishing so that the imbedding cannot be said to be stationary at the level of imbedding space since t=constant surfaces correspond to m⁰ h(r_M)=constant surfaces.
   

   De Sitter metric is however very special. In this case one can assume h(r)=k(r)=0 for Rω=1. The imbedding reduces simply to an essentially unique imbedding
   

   sin(Θ(r))=+/- r/l= r_M/l , Φ= t/R= m⁰/R .
   

   This imbedding is certainly very natural and would describe stationary non-expanding cosmology with constant mass density. Not that the imbedding is defined only for r_M<l. Unless one allows 3-space to have boundary, which for non-vacuum extremals does not seem plausible option, one must assume double covering
   

   sin(Θ(r))= sin(π-Θ(r))= +/- r_M/l
   

   Stationarity implies that there is no Big Bang.
   
   

3. The transition to the inflationary picture looks in TGD framework very much like a trick in which one replaces radial Minkowski coordinate with r₁ =exp(-t₁/l) r_M and in these new coordinates obtains Big Bang and exponential expansion as what looks like a coordinate effect at the level of imbedding space. Also the transition to radiation dominated cosmology for which the hyperbolic character of M⁴₊ metric ds²=da² a²(dr²/(1+r²) +r²dΩ²) is essential, is difficult to understand in this framework. The transition should correspond to a transition from a stationary cosmology at the level of imbedding space level to genuinely expanding cosmology.

The cautious conclusion is that sub-manifold cosmology neither excludes nor favors inflationary cosmology and that critical cosmology is more natural in TGD framework. In TGD Universe De Sitter metric looks like an ideal model for the interior of a stationary star characterized by its radius just like blackhole is characterized by its radius. It seems that TGD survives the new findings at qualitative and even partially quantitative level.

For details see the chapter TGD and Cosmology or the article BICEP2 might have detected gravitational waves.

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.