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.

Pollack's findings about fourth phase of water

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

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

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

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

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

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

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

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

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

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

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

Morphogenesis, morphostasis, and learning in TGD framework

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

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

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

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

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

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

Experimental evidence for sterile neutrino?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

3. Objections

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

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

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

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

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

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

Why TGD?

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

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

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

Why TGD?

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

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

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

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

How could TGD help?

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

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

Two basic visions about TGD

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

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

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

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

Guidelines in the construction of TGD

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

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

There are also more technical guidelines.

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

For details see the new article Why TGD?.