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.

Pollack's findings about fourth phase of water

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

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

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

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

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

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

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

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

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

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

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

Morphogenesis, morphostasis, and learning in TGD framework

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

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

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

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

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

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