The vanishing of super-conformal charges as a gauge conditions selecting preferred extremals of Kähler action

Classical TGD involves several key questions waiting for clearcut answers.

1. The notion of preferred extremal emerges naturally in positive energy ontology, where Kähler metric assigns a unique (apart from gauge symmetries) preferred extremal to given 3-surface at M⁴ time= constant section of imbedding space H=M⁴× CP₂. This would quantize the initial values of the time derivatives of imbedding coordinates and this could correspond to the Bohr orbitology in quantum mechanics.
   
   
2. In zero energy ontology (ZEO) initial conditions are replaced by boundary conditions. One fixes only the 3-surfaces at the opposite boundaries of CD and in an ideal situation there would exist a unique space-time surface connecting them. One must however notice that the existence of light-like wormhole throat orbits at which the signature of the induced metric changes (det(g₄)=0) its signature might change the situation. Does the attribute "preferred" become obsolete and does one
   lose the beautiful Bohr orbitology which looks intuitively compelling and would realize quantum classical correspondence?
   
   
3. Intuitively it has become clear that the generalization of super-conformal symmetries by replacing 2-D manifold with metrically 2-D but topologically 3-D light-like boundary of causal diamond makes sense. Generalized super-conformal symmetries should apply also to the wormhole throat orbits which are also metrically 2-D and for which conformal symmetries respect detg(g₄)=0 condition. Quantum classical correspondence demands that the generalized super-confornal invariance has classical counterpart. How could this classical counterpart be realized?
   
   
4. Holography is one key aspect of TGD and mean that 3-surfaces dictate everything. In positive energy ontology the content w of this statement would be rather obvious and reduce to Bohr orbitology but in ZEO situation is different. On the other hand, TGD strongly suggests strong form of holography based stating that partonic 2-surfaces (the ends of wormhole throat orbits at boundaries of CD) and tangent space data at them code for quantum physics of TGD. General coordinate invariance would be realied in strong sense: one could formulate the theory either in terms of space-like 3-surfaces at the ends of CD or in terms of light-like wormhole throat orbits. This would realize Bohr orbitology also in ZEO by reducing the boundary conditions to those at partonic 2-surfaces. How to realize this explicitly at the level of field equations? This has been the challenge.
   
   

Answering questions is extremely useful activity. During last years Hamed has posed continually questions related to the basic TGD. At this time Hamed asked about the derivation of field equations of TGD. In "simple" field theories involving some polynomial non-linearities the deduction of field equations is of course totally trivial process but in the extremely non-linear geometric framework of TGD situation is quite different.

While answering the questions I made what I immediately dare to call a breakthrough discovery in the mathematical understanding of TGD. To put it concisely: one can assume that the variations at the light-like boundaries of CD vanish for all conformal variations which are not isometries. For isometries the contributions from the ends of CD cancel each other so that the corresponding variations need not vanish separately at boundaries of CD! This is extremely simple and profound fact. This would be nothing but the realisation of the analogs of conformal symmetries classically and give precise content for the notion of preferred external, Bohr orbitology, and strong form of holography. And the condition makes sense only in ZEO!

I attach below the answers to the questions of Hamed almost as such apart from slight editing and little additions, re-organization, and correction of typos.

The physical interpretation of the canonical momentum current

Hamed asked about the physical meaning of Tⁿ_k== ∂ L/∂(∂_n h^k) - normal components of canonical momentum labelled by the label k of imbedding space coordinates - it is good to start from the physical meaning of a more general vector field

T^α_k == ∂ L/∂(∂_α h^k)

with both imbedding space indices k and space-time indices α - canonical momentum currents. L refers to Kähler action.

1. One can start from the analogy with Newton's equations derived from action
   principle (Lagrangian). Now the analogs are the partial derivatives ∂ L/∂(dx^k/dt). For a particle in potential one obtains just the momentum. Therefore the term canonical momentum current/density: one has kind of momentum current for each imbedding space coordinate.
   
   
2. By contracting with generators of imbedding space isometries (Poincare and color) one indeed obtains conserved currents associated with isometries by Noether's theorem:
   

   j^{A α}= T^α_kj^Ak .
   

   By field equations the divergences of these currents vanish and one obtains conserved charged- classical four-momentum and color charges:
   

   D_α T^{A α}=0 .
   
   

3. The normal component of conserved current must vanish at space-like boundaries if one has such
   

   T^An=0
   

   if one has boundaries with Minkowskian signature of induced metric. Now one has wormhole throat orbits which are not genuine boundaries albeit analogous to them and one must be very careful. The quantity Tⁿ_k determines the values of normal components of currents and must vanish at possible space-like boundaries.
   

Note that in TGD field equations reduce to the conservation of isometry currents as in hydrodynamics where basic equations are just conservation laws.

The basic steps in the derivation of field equations

First a general recipe for deriving field equations from Kähler action - or any action as a matter of fact.

1. At the first step one writes an expression of the variation of the Kähler action as sum of variations with respect to the induced metric g and induced Kähler form J. The partial derivatives in question are energy momentum tensor and contravariant Kähler form.
   
   
2. After this the variations of g and J are expressed in terms of variations of imbedding space coordinates, which are the primary dynamical variables.
   
   
3. The integral defining the variation can be decomposed to a total divergence plus a term vanishing for extremals for all variations: this gives the field equations. Total divergence term gives a boundary term and it vanishes by boundary conditions if the boundaries in question have time-like direction.
   

   If the boundary is space-like, the situation is more delicate in TGD framework: this will be considered in the sequel. In TGD situation is also delicate also because the light-like 3-surfaces which are common boundaries of regions with Minkowskian or Euclidian signature of the induced metric are not ordinary topological boundaries. Therefore a careful treatment of both cases is required in order to not to miss important physics.
   
   

Expressing this summary more explicitly, the variation of the Kahler action with respect to the gradients of the imbedding space coordinates reduces to an integral of

T^α_k ∂_αδ h^k + (∂ L/∂ h^k) δ h^k .

The latter term comes only from the dependence of the imbedding space metric and Kähler form on imbedding space coordinates. One can use a simple trick. Assume that they do not depend at all on imbedding space coordinates, derive field equations, and replaced partial derivatives by covariant derivatives at the end. Covariant derivative means covariance with respect to both space-time and imbedding space vector indices for the tensorial quantities involved. The trick works because imbedding space metric and Kähler form are covariantly constant quantities.

The integral of T^α_k ∂_αδ h^k decomposes to two parts.

1. The first term, whose vanishing gives rise to field equations, is integral of
   

   D_α T^α_k δ h^k .
   
   

2. The second term is integral of
   

   ∂_α (T^α_k δ h^k) .
   

   
   This term reduces as a total divergence to a 3-D surface integral over the boundary of the region of fixed signature of the induced metric consisting of the ends of CD and wormhole throat orbits (boundary of region with fixed signature of induced metric). This term vanishes if the normal components Tⁿ_k of canonical momentum currents vanishes at the boundary like region.
   

In the sequel the boundary terms are discussed explicitly and it will be found that their treatment indeed involves highly non-trivial physics.

Boundary conditions at boundaries of CD

In positive energy ontology one would formulate boundary conditions as initial conditions by fixing both the 3-surface and associated canonical momentum densities at either end of CD (positions and momenta of particles in mechanics). This would bring asymmetry between boundaries of CD.

In TGD framework one must carefully consider the boundary conditions at the boundaries of CDs. What is clear that the time-like boundary contributions from the boundaries of CD to the variation must vanish.

1. This is true if the variations are assumed to vanish at the ends of CD. This might be however too strong a condition.
   
   
2. One cannot demand vanishing of T^t_k (t refers to time coordinate as normal coordinate) since this would give only vacuum extremals. One could however require quantum classical correspondence for any Cartan sub-algebra of isometries, whose elements define maximal set of isometry generators. The eigenvalues of quantal variants of isometry charge assignable to second quantized induced spinors at the ends of space-time surface are equal to the classical charges. Is this actually formulation of Equivalence Principle, is not quite clear to me.
   

While writing this a completely new idea popped to my mind. What if one poses the vanishing of the boundary terms at boundaries of CDs as additional boundary conditions for all variations except isometries? Or perhaps for all conformal variations (conformal in TGD sense)? This would not imply vanishing of isometry charges since the variations coming from the opposite ends of CD cancel each other! It soon became clear that this would allow to meet all the challenges listed in the beginning!

1. These conditions would realize Bohr orbitology also to ZEO approach and define what "preferred extremal" means.
   
   
2. The conditions would be very much like super-Virasoro conditions stating that super conformal generators with non-vanishing conformal weight annihilate states or create zero norm states but no conditions are posed on generators with vanishing conformal weight (now isometries). One could indeed assume only deformations, which are local isometries assignable to the generalised conformal algebra of the δ
   M⁴_+/-× CP₂. For arbitrary variations one would not require the vanishing. This could be the long sought for precise formulation of super-conformal invariance at the level of classical field equations!
   

   It is enough co consider the weaker conditions that the conformal charges defined as integrals of corresponding Noether currents vanish. These conditions would be direct equivalents of quantal conditions.
   
   

3. The natural interpretation would be as a fixing of conformal gauge. This fixing would be motivated by the fact that WCW Kähler metric must possess isometries associated with the conformal algebra and can depend only on the tangent data at partonic 2-surfaces as became clear already for more than two decades ago. An alternative, non-practical option would be to allow all 3-surfaces at the ends of CD: this would lead to the problem of eliminating the analog of the volume of gauge
   group from the functional integral.
   
   
4. The conditions would also define precisely the notion of holography and its reduction to strong form of holography in which partonic 2-surfaces and their tangent space data code for the dynamics.
   

Needless to say, the modification of this approach could make sense also at partonic orbits.

Isometry charges are complex

One must be careful also at the light-like 3-surfaces (orbits of wormhole throats) at which the induced metric changes its signature.

1. Should one assume that det(g₄)^1/2 is imaginary in Minkowskian and real in Euclidian region? For Kähler action this is sensible and Euclidian region would give a real negative contribution giving rise to exponent of Kähler function of WCW ("world of classical worlds") making the functional integral convergent. Minkowskian regions would give imaginary contribution to the exponent causing interference effects absolutely essential in quantum field theory. This contribution would correspond to Morse function for WCW.
   

   The implication would be that the classical four-momenta in Euclidian/Minkowskian regions are imaginary/real. What could the interpretation be? Should one accept as a fact that four-momenta are complex.
   
   

2. Twistor approach to TGD is now in quite good shape. M⁴× CP₂ is the unique choice is one requires that the Cartesian factors allow twistor space with Kähler structure and classical TGD allows twistor formulation.
   

   In the recent formulation the fundamental fermions are assumed to propagate with light-like momenta along wormhole throats. At gauge theory limit particles must have massless or massive four-momenta. One can however also consider the possibility of complex massless momenta and in the standard twistor approach on mass shell massless particles appearing in graphs indeed have complex momenta. These complex momenta should by quantum classical correspondence correspond directly to classical complex momenta.
   
   

3. A funny question popping in mind is whether the massivation of particles could be such that the momenta remain massless in complex sense! The complex variant of light-likeness condition would be
   

   p²_Re= p²_Im , p_Re• p_Im=0 .
   

   Could one interpret p²_Im as the mass squared of the particle? Or could p²_Im code for the decay width of an unstable particle?
   
   

Boundary conditions at the wormhole throat orbits and connection with quantum criticality and hierarchy of Planck constants defining dark matter hierarchy

The contributions from the orbits of wormhole throats are singular since the contravariant form of the induced metric develops components which are infinite (det(g₄)=0). The contributions are real at Euclidian side of throat orbit and imaginary at the Minkowskian side so that they must be treated as independently.

1. One can consider the possibility that under rather general conditions the normal components Tⁿ_kdet(g₄) ^1/2 approach to zero at partonic orbits since det(g₄) is vanishing. Note however the appearance of contravariant appearing twice as index raising operator in Kähler action. If so, the vanishing of Tⁿ_kdet(g₄) ^1/2 need not fix completely the "boundary" conditions. In fact, I assign to the wormhole throat orbits conformal gauge symmetries so that just this is expected on physical grounds.
   
   
2. Generalized conformal invariance would suggest that the variations defined as integrals of Tⁿ_kdet(g₄) ^1/2δ h^k vanish in a non-trivial manner for the conformal algebra associated with the light-like wormhole throats with deformations respecting det(g₄)=0 condition. Also the variations defined by infinitesimal isometries (zero conformal weight sector) should vanish since otherwise one would lose the conservation laws for isometry charges. The conditions for isometries might reduce to Tⁿ_kdet(g₄) ^1/2→ 0 at partonic orbits. Also now the interpretaton would be in terms of fixing of conformal gauge.
   
   
3. Even Tⁿ_kdet(g₄) ^1/2=0 condition need not fix the partonic orbit completely. The Gribov ambiguity meaning that gauge conditions do not fix uniquely the gauge potential could have counterpart in TGD framework. It could be that there are several conformally non-equivalent space-time surfaces connecting 3-surfaces at the opposite ends of CD.
   

   If so, the boundary values at wormhole throats orbits could matter to some degree: very natural in boundary value problem thinking but new in initial value thinking. This would conform with the non-determinism of Kähler action implying criticality and the possibility that the 3-surfaces at the ends of CD are connected by several space-time surfaces which are physically non-equivalent.
   

   The hierarchy of Planck constants assigned to dark matter, quantum criticality and even criticality indeed relies on the assumption that h_eff=n× h corresponds to n-fold coverings having n space-time sheets which coincide at the ends of CD and that conformal symmetries act on the sheets as gauge symmetries. One would have as Gribov copies n conformal equivalence classes of wormhole throat orbits and corresponding space-time surfaces. Depending on whether one fixes the conformal gauge one has n equivalence classes of space-time surfaces or just one representative from each conformal equivalent class.
   
   

4. There is also the question about the correspondence with the weak form of electric magnetic duality. This duality plus the condition that j^αA_α=0 in the interior of space-time surface imply the reduction of Kähler action to Chern-Simons terms. This would suggest that the boundary variation of the Kähler action reduces to that for Chern-Simons action which is indeed well-defined for light-like 3-surfaces.
   

   If so, the gauge fixing would reduce to variational equations for Chern-Simons action! A weaker condition is that classical conformal charges vanish. This would give a nice connection to the vision about TGD as almost topological QFT. In TGD framework these conditions do not imply the vanishing of
   Kähler form at boundaries. The conditions are satisfied if the CP₂ projection of the partonic orbit is 2-D: the reason is that Chern-Simons term vanishes identically in this case.
   
   

5. A further intuitively natural hypothesis is that there is a breaking of conformal symmetry: only the generators of conformal sub-algebra with conformal weight multiple of n act as gauge symmetries. This would give infinite hierarchies of breakings of conformal symmetry interpreted in terms of criticality: in the hierarchy the integers n_i would satisfy n_i divides n_i+1.
   

   Similar degeneracy would be associated with the space-like ends at CD boundaries and I have considered the possibility that the integer n appearing in h_eff has decomposition n=n₁n₂ corresponding to the degeneracies associated with the two kinds of boundaries. Alternatively, one could have just n=n₁=n₂ from the condition that the two conformal symmetries are 3-dimensional manifestations of single 4-D analog of conformal symmetry.
   
   

As should have become clear, the derivation of field equations in TGD framework is not just an application of a formal recipe as in field theories and a lot of non-trivial physics is involved!

See the chapter The recent vision about preferred extremals and solutions of the modified Dirac equation or the article The vanishing of super-conformal charges as a gauge conditions selecting preferred extremals of Kähler action.

About sterile neutrinos, SUSY partners, antimatter, and dark matter

The links in Thinking Allowed Original inspired the following considerations related to sterile neutrinos, SUSY, antimatter, and dark matter.

Sterile neutrino as dark matter particle?

Sterile neutrino is one of the many candidates explaining dark matter. Sterility means that would have no electroweak or color interactions. Lightest SUSY particle is another candidate and there are many others. There is also entire zoo of WIMPS which are weakly interacting and massive.

There are some experiments proposing that the decays of sterile neutrino explain the un-identified line at about 3.5-3.6 keV in the X-ray spectrum of galaxy clusters. The mechanism of decay producing photons remains to me unclear: personally I find this kind of decay infeasible because of the defining properties of sterile neutrino. There is however rather strong evidence that sterile neutrinos do not exist. The number of neutrinos deduced from cosmic microwave background according to standard cosmology is in good approximation equal to 3, not 4.

The experimental finding (if true) could be explained in many manners. My personal proposal for anomalous X rays is based on a new kind of nuclear physics at energy range of keV (MeV is the energy range of ordinary nuclear physics and 1000 times higher). The energy scale would be that for exotic states "almost-predicted" by TGD: they would look electromagnetically/chemically just like ordinary isotopes of nuclei but would have slightly different masses. The X rays radiation from Sun could excite these states and imply annually varying anomalies in nuclear decay rates since the distance to Sun is varying. This has been observed.

Suppose that sterile neutrino exists and is dark? How this would affect cosmology. Usually all particles - including the dark ones - are assumed to couple to gravitons with strength proportional to their mass. This would exclude sterile neutrinos.

Dark matter in TGD Universe

In TGD Universe dark matter corresponds to phases of ordinary matter with non-standard value of Planck constant h_eff=n× h.

1. The most natural assumption is that only particles with same value of Planck constant h_eff=n× h appear in the same vertex. Since graviton and other elementary particles have similar anatomy in TGD Universe, this would naturally apply also to gravitons and would distinguish between TGD dark matter and the usual dark stuff.
   

   Gravitational constant is proportional to the CP₂ length scale R squared: this gives G= k R²/X, where X has dimensions of Planck constant. Should one take X=h, the minimal value of h_eff or should one take X=h_eff (k is a numerical constant). In the latter case the gravitational constant would be weaker than for ordinary matter. Another, more plausible option is that one uses X=g_K² where g_K² is the square of Kähler coupling having dimensions of h.
   
   

2. What about classical gauge fields and gravitational fields? Here the direct touching of space-time sheets would induce interaction and the given test particle would experience the forces assignable to the space-time sheets that it touches and one would experience the effective linear superposition of fields in good approximation. This leads to a view about how GRT space-time emerges from TGD: one can think that GRT space-time is obtained by slashing the space-time time sheets to single slightly curved region of M⁴ space-time: various effective fields are sums of those associated with the sheets.
   

   Could phases with different value of h_eff have classical interactions mediated by touching. To formulate this concretely, a concrete view about what large h_eff = n×h means at the level of space-time geometry and topology and the most general assumption is that classical fields mediate the interaction.
   

   The physical picture is following. Large h_eff gives rise to long range quantal correlations and fluctuations naturally assignable to quantum - and perhaps even ordinary criticality. Criticality means non-determinism and this means that the two 3-surfaces at the light-like boundaries of causal diamonds are connected by large number of space-time surfaces with n-sheets co-inciding at ends. Each sheet can be deformed by conformal gauge symmetries and n is the number of conformal equivalence classes for these connecting surfaces.
   

   Technically speaking, space-time can be regarded as a singular n-fold covering space. I see no obvious rule preventing the multi-sheeted covering from touching ordinary space-time sheets or the other ones with different values of n. Whether all sheets can touch the test particle simultaneously or not is not quite clear. If not, then the interaction could be weaker.

The conclusion might be following.

1. Interactions between ordinary and dark phases of matter with different Planck constants would be due to the transitions transforming particles with different Planck constant to each other. The rate for these transitions could be rather low but TGD inspired model for biomatter as ordinary matter controlled by dark matter requires these.
   
   
2. Phases with different values of h_eff can interact also via exchange of gravitons but the interaction strength is expected to be proportional to the transition amplitude between different values of h_eff. Classical gravitational forces act between dark and ordinary matter and the simplest guess is that the interaction strengths are same as for the exchange of gravitons suffering h_eff changing phase transition.
   
   
3. In this framework - just one possible scenario - one would have large number of weakly interacting cosmologies and CMB would only tell about one particular cosmology. Multiverse would be realized but the laws of physics would be same for various sub-verses apart from the different value of Planck constant. Living matter would be basic example about the interaction of sub-verses.
   

The counterpart of sterile neutrino in TGD as generator of N=2 SUSY?

TGD cannot remain outsider as far as the fate of sterile neutrino is considered. The right- handed neutrino ν_R predicted by TGD is indeed "sterile" in that it does not couple to electro-weak gauge potentials. ν_R can however mix with left-handed neutrino since induced gamma matrices contain both M⁴ and CP₂ parts and the latter mix different M⁴ chiralities. Neutrinos are massive so that mixing seems to occur. The chirality mixing caused by the induced gamma matrices is purely TGD based mechanism of massivation and reflects directly the fact that space-times are assumed to be 4-surfaces.

The least broken part of supersymmetry in TGD relies on right-handed neutrino.

1. One takes ordinary particle and adds right-handed neutrino or antineutrino or both to get superpartners.
   
   
2. Is SUSY broken or exact? If SUSY is not broken, the resulting state must be dark (large h_eff) just because it is not observed! Could SUSY partners be dark matter that is sparticles with h_eff>h? SUSY breaking would mean only different h_eff, not mass!
   
   
3. Or do spartners have h_eff=h so that SUSY must be broken and spartners have large masses. For this option I encounter a problem similar to that in SUSYs What is the p-adic mass scale for the superpartners, which would obey same mass formula but with different and higher p-adic mass scale (smaller prime p). It should be probably heavier than LHC scale. Note however that TGD SUSY is different from standard one practically excluded at LHC energies.
   
   
4. These two options are extremes: also their hybrid is possible. p-Adic mass scale and h_eff could be different for particles and their spartners.
   

Could antimatter be dark matter in TGD sense?

The experimental absence of dark matter is one of the poorly understood aspects of cosmology.

1. One natural looking explanation in TGD framework is that antimatter is at different space-time sheets at different regions of M⁴ so that the approximate GRT space-time obtained by squishing the sheets to single one contains only matter or antimatter. The central regions of large voids with size of 10⁸ lys are possible candidates in this respect. This kind of regions would have been created as an outcome of annihilation of particles and antiparticles during early cosmology. A slight difference in their densities induced by CP breaking could lead to the separation of matter and antimatter in recent day Universe.
   
   
2. Could antimatter be dark matter with different Planck constants and remain very weakly interacting. Dark and visible matter would see each other only via emission of various gauge bosons and gravitons suffering h_eff changing phase transition during propagation. As proposed, this could apply also to gravitons.
   
   
3. Also a hybrid of these views can be considered. The transformation rates of particles and antiparticles to their dark variants were different in the early universe so that the densities were slightly different before the annihilation began and left only ordinary matter and dark antimatter. The h_eff changing phase transition should be CP breaking for this option.
   

   This would allow to localize CP breaking to a mixing like phenomenon. Interestingly, also the CKM mixing of quarks and leptons breaks CP: in TGD framework it corresponds to topological mixing of the topological of partonic 2-surfaces.
   
   

What is worrying me that I have ended up dangerously near to multiverse: both sparticles and antimatter would belong to different but weakly interacting sectors of the multiverse. What makes me happy is that the interactions inside these sectors would be the same ones except that the value of h_eff would be different. Cosmologists are not of course happy if they learn that the standard cosmology is only about one sector of multiverse!

Cosmic redshift as a purely kinematic effect

In cosmic redshift the frequency of the photon or graviton decreases and wave length increases with distance from the source. E= h×f implies that also the energy decreases. This is what Hubble's law says.

The redshift looks somewhat problematic prediction since it seems to be in conflict with the conservation of energy and momentum unless there exists a mechanism which explains how massless particle loses its four momentum gradually. In general relativity one might accept this since the very notions of energy and momentum become ill-defined. In TGD the situation is different. Four-momentum is conserved and one must understand how cosmic redshift manages to be consistent with this.

One must be very careful here since the values of wavelength and frequency, and four-momentum depend on the state of motion for the measuring system relative to the emitting system.

1. Consider first empty Minkowski space. If the measuring system is in motion with respect to source with constant velocity, one obtains a redshift or blueshift depending on the velocity and direction of the motion. The Lorentz boost inducing the shift relates different orientations of time axis for the source and receiver. The 3-D tangent space of time= constant section of receiver is obtained by Lorentz boost from that for source and the velocity associated with this boost determines the redshift.
   
   
2. Consider now what happens if time=constant slice is replaced with the cosmic time=constant slice of future directed light-cone. This surface is hyperboloid and mathematically equivalent with cosmic time=constant section of empty Robertson-Walker cosmology predicting cosmic redshift. The cosmic redshift can be understood using very simple argument. The redshift is determined by the relative orientations of the 3-D tangent spaces of hyperboloid at the positions of the source and receiver at the hyperboloid. The Lorentz boost relating the orientations of 3-D tangent spaces depends on the mutual distance and gives the cosmic redshift in empty Robertson-Walker cosmology defined by future light-cone. Cosmic redshift is mostly purely kinematical effect present already in empty space.
   
   
3. Consider next 4-D space-time surface so that also the small effects of matter are included. The time coordinate of the space-time surface could be anything but in zero energy ontology, where space-time surfaces are inside causal diamonds (intersections of future and past directed lightcones) the light-cone proper time associated with either light-like boundary of CD is the natural time coordinate defining cosmic time. Now one considers the M⁴ projections of the 3-D tangent space of the 3-D time= constant section of the space-time surface and the Lorentz boost relating the 3-D projections for source and receiver determines the redshift. The non-flatness of space-time surface gives some small corrections to the formula obtained for the case of future light-cone.
   
   
4. What about the energy of photon or graviton? Does it decrease with the distance from the sender as E=h× f requires? And is this consistent with the conservation of energy and momentum? In General Relativity one would of course have a serious problem and GRT indeed forces to give up conservation laws of four-momentum and angular momentum in long scales since these notions are not even well-defined. This was the basic motivation for TGD.
   

   In TGD there is no need to give up the conservation laws since the reduction of four-momentum predicted by redshift formula is a purely kinematic effect since the tangent spaces of sender and receiver corresponds to different states of motion.
   

The motivation for writing this comment came from proposals that cosmic redshift could be understood in terms of Planck constant, which would decrease with time in such a manner that that E=h×f would remain constant and energy would therefore be conserved despite the fact that frequency decreases (see this). At first the idea looks attractive in TGD framework, where energy is conserved. The purely kinematical explanation is however exponentially more feasible.

I have however proposed the possibility that at least part of gravitons are dark as one implication of h_gr = GMm/v₀ hypothesis. The gravitons with given frequency would have much larger energies than expected and this might dramatically affect the detection of gravitational radiation since the dark gravitons could be sees as bunches of ordinary gravitons carrying much larger energy than ordinary gravitons and could be discarded as noise. If most of gravitons are dark, the experiments trying to detect gravitons might give null results.

Further progress in the understanding of dark matter and energy in TGD framework

At Thinking Allowed Original (thanks for Ulla!) there was an extremely interesting link to a popular article about a possible explanation of dark matter in terms of vacuum polarization associated with gravitation. The model can make sense only if the sign of the gravitational energy of antimatter is opposite to that of matter and whether this is the case is not known. Since the inertial energies of matter and antimatter are positive, one might expect that this is the case also for gravitational energies by Equivalence Principle but one might also consider alternative and also I have done this in TGD framework.

The popular article lists four observations related to dark matter that neither cold dark matter (CMD) model nor modified gravitation model (MOND) can explain, and the claim is that the vacuum energy model is able to cope with them.

Consider first the TGD based model.

1. The model assumes that galaxies are like pearls along strings defined by cosmic strings expended to flux tubes during cosmic expansion survives also these tests. This is true also in longer scales due to the fractality if TGD inspired cosmology: for instance, galaxy clusters would be organized in a similar manner.
   
   
2. The dark magnetic energy of the string like object (flux tube) is identifiable as dark energy and the pearls would correspond to dark matter shells with a universal mass density of .8 kg/m² estimated from Pioneer and Flyby anomalies assuming to be caused by spherical dark matter shells assignable to the orbits of planets. This value follows from the condition that the anomalous acceleration is identical with Hubble acceleration. Even Moon could be accompanied by this kind of shell: if so, the analog of Pioneer anomaly is predicted.
   
   
3. The dark matter shell around galactic core could have decayed to smaller shells by h_eff reducing phase transition. This phase transition would have created smaller surfaces with smaller values of h_eff=h_gr. One can consider also the possibility that it contains all the galactic matter as dark matter. There would be nothing inside the surface of the gigantic wormhole throat: this would conform with holography oriented thinking.
   

I checked the four observations listed in the popular article some of which CMD (cold dark matter) scenario and MOND fail to to explain. TGD explains all of them.

1. It has been found that the effective surface mass density σ = ρ₀R₀/3 (volume density times volume of ball equals to effective surface density times surface area of the ball for constant volume density) of galactic core region containing possible halo is universal and its value is .9 kg/m² (see the article). Pioneer and Flyby anomalies fix the surface density to .8 kg/m². The difference is about 10 per cent! One must of course be cautious here: even the correct order of magnitude would be fine since Hubble acceleration parameter might be different for the cluster than for the solar system now.
   

   Note that in the article the effective surface density is defined in the article as σ= ρ₀r₀, where r₀ is the radius of the region and ρ₀ is the density at its center. The correct definition for a constant 3-D density inside ball is σ= ρ₀r₀/3 and I use this so that the value given in the article is scaled down by factor 1/3.
   
   

2. The dark matter has been found to be inside core region within few hundred parsecs. This is just what TGD predicts since the velocity spectrum of distant stars is due to the gravitational field created by dark energy identifiable as magnetic energy of cosmic string like object - the thread containing galaxies as pearls.
   
   
3. It has been observed that there is no dark matter halo in the galactic disk. Also this is an obvious prediction of TGD model.
   
   
4. The separation of matter - now plasma clouds between galaxies - and dark matter in the collisions of galaxy clusters (observed for instance for bullet cluster consisting of two colliding clusters) is also explained qualitatively by TGD. The explanation is qualitatively similar to that in the CMD model of the phenomenon. Stars of galaxies are not affected except from gravitational slow-down much but the plasma phase interacts electromagnetically and is slowed down much more in the collision. The dominating dark matter component making itself visible by gravitational lensing separates from the plasma phase and this is indeed observed: the explanation in TGD framework would be that it is macroscopically quantum coherent (h_eff=h_gr) and does not dissipate so that the thermodynamical description does not apply.
   

   In the case of galaxy clusters also the dark energy of cosmic strings is involved besides the galactic matter and this complicates the situation but the basic point is that dark matter component does not slow down as plasma phase does.
   

   CMD model has the problem that the velocity of dark matter bullet (smaller cluster of bullet cluster) is higher than predicted by CMD scenario. Attractive fifth force acting between dark matter particles becoming effective at short distances has been proposed as an explanation: intuitively this adds to the potential energy negative component so that kinetic energy is increased. I have proposed that gravitational constant might vary and be roughly twice the standard value: I do not believe this explanation now.
   

   The most feasible explanation is that the anomaly relates to the presence of thickened cosmic strings carrying dark energy as magnetic energy and dark matter shells instead of 3-D cold dark matter halos. This additional component would contribute to gravitational potential experienced by the smaller cluster and explain the higher velocity.
   

If I want to believe in something I have two options to choose. TGD indeed allows to understand dark matter and much more or Universe is playing cruel game with me by arranging all these numerical co-incidences.

For details see the chapter TGD and Astrophysics or the article Pioneer and Flyby anomalies for almost ten years later.

Solar spots, life time expectancy, and well-being of magnetic body

Lubos tells about rather interesting claim of Norwegian researchers that sunspots during pregnancy shorten baby's life by 5 years. In my case this is not a good news: around my year of birth 1950 there was a sunspot maximum! Well, this looks non-feasible even to me in my most open-minded mind frame;-). But let us pretend for a moment that we believe the claim. How would you explain this in your pet theory of everything?

The authors of the paper suggest UV radiation, which indeed damages DNA, is responsible for the effect. Note that Earth's atmosphere, in particular ozone layer, filters out most of UV radiation above 10 eV. In TGD Universe one must however worry also about the well-being of magnetic body besides that of the biological body so that life becomes really difficult with the hedonistic attitude of modern man. My nightmare is that the people in future - thanks to TGD - must also worry how good-looking their magnetic bodies are!

Could the primary damage occur for the magnetic body receiving an increased radiation dose during magnetic storms induced by the the solar wind shock waves accompanying the sunspot activity. The solar wind shock wave would be a slap against magnetic face.

The incoming radiation would be physical violence but at the level of magnetic bodies with onion like structure having size scales even larger than Earth size scale (Schumann resonance). This violence would deform the shape of the magnetic body, in particular change the thickness of the flux tubes and in this manner affect magnetic field strengths and cyclotron frequencies crucial for the resonant communications with the biological body. The communications between biological and magnetic body could suffer and sensory input to and motor actions of the magnetic body would be disturbed. This could even lead to a loss of consciousness as is indeed reported to happen sometimes during auroras known to involve magnetic reconnections induced by solar wind at the dark side of the Earth. A possible experimental signature would be the direct effects of magnetic storms on EEG and also direct negative effects such on general well-being.

I have a personal experience about very unpleasant effects possibly caused by magnetic storm during a travel in Sweden. Suddenly I got a horrible migraine like headache. We were guessing for possible reasons and someone noticed that magnetic storms were occurring just at that time. Somehow me and my magnetic body regarded this explanation more feasible than the other ones.

So the question is whether one could one feel the magnetic storms directly - for instance as pains projected to some biological body part? If the layers of the magnetic body carry maps of the biological body parts as I have proposed, this might be the case. The effect would be the analog of projected pain. This projection would occur very generally. For instance, the very unpleasant feeling near a precipice could be due to the actual motion of magnetic body mimicking the falling down from the precipice. Also various out-of-body experiences such as levitation could take place at the level of magnetic body in the virtual magnetic world representing also the environment.

Note that from this it is not a long way to the speculation that the positions of planets dictating the periodically occurring mutual interactions of their magnetic bodies could affect the life cycle so that your birth day would matter and the basic idea behind horoscope might make sense although horoscopes as such would not!

Was ribosome the first self-replicator?

In the group Thinking Allowed Original there as a link to a popular article describing a highly interesting work by M. Root-Bernstein and R. Root-Bernstein (daughter and father). The title of the popular article "Forget the selfish gene: Evolution of life is driven by the selfish ribosome, research suggests". As a matter of fact, the article itself is not selling anything of type "selfish X", a dogma which to my opinion is more or less dead: synergy and quantum coherence are much more promising notions relevant to biomatter. "Selfish X" is a paradigm, which suits much better to the description of cancer. The title of the article "The ribosome as a missing link in the evolution of life" would have been much more appropriate also for the popular article.

First a summary of motivations by authors. The basic problem relates to the emergence of life and there are many theories. The models can be divided to "genetics first" and "metabolism first" type models.

1. RNA world is basic example of "genetics first" models. The problem of the "genetics first models" is that it is difficult to understand how prebiotic life could have coped before the complex molecular machinery of metabolism. The second problem of RNA world is that polynucleotides and proteins almost certainly co-evolved. So called compositional replication models start from this assumption but have difficulties in explain replication schemes. Both approaches fail to explain how complex cells emerged from molecular evolution. It is however known that lipid layers of cell membrane are emergent structures not coded by genes (soap films).
   
   
2. Second class of models try to proceed from complexity to simplicity by assuming the first replicator (pro-cell typically) but are not able to answer the question "What before this?". The natural assumption is that simple bio-molecules gradually evolved to polymers and polymer aggregates and eventually cell membrane emerged.
   
   

According to authors, the challenge is to bridge the gap between self-replicating polymers and fully functional cell by identifying intermediate structures able to replicate, restore and replicate information, capture metabolic components and energy, and transform all these into biochemical networks.

Trying to catch the idea

The basic idea of the authors is simple and brilliant. Ribosome is the transcription machinery transforming DNA to proteins. Also the first replicator must have contained the transcription machinery. Perhaps the first replicator was minimal and contained just this machinery! Perhaps ribosome or its predecessor ("pre-ribosome") indeed was the first self-replicator. One would have beautiful self-reference: ribosome would be the recipe for making a copy about the recipe! Brings in mind Gödel-Escher-Bach!

This assumption is highly non-trivial. In the following I try to sketch for myself what this could mean. In the following I drop "pre"or notational convenience with understanding that ribosome, RNA, amino-acid etc. means "pre-ribosome", "pre-RNA", "pre-amino-acid", "pre-tRNA" etc.. In TGD framework pre-ribosome could be of non-biochemical nature and realized at the level of dark matter.

1. It seems natural to assume that the basic raw material consisted of RNA and amino-acid molecules in the environment. Ribosome could use them to build copies of itself. The question how these were generated will not be considered now.
   
   
2. Ribosome consists of rRNA and proteins and uses tRNA to associated to mRNA sequence amino-acid sequence. If ribosome was the first replicator realizing genetic code as mRNA-amino-acid correspondence it had to use its own rRNA as a template for the translation to a corresponding protein.
   

   If nothing has changed after the emergence of the recent replication mechanisms, the testable prediction is that ribosome amino-acids are images of rRNA sequences under genetic code. One of course expects that the stricture of ribosome has not conserved in precise sense so that this prediction could be too strong.
   
   

3. tRNA is a molecule of form RNA-X-amino-acid and rRNA should have contained the genetic information allowing to transcribe and translate the RNA and amino-acid polymers appearing in tRNA.
   
   

According to the article these predictions are indeed tested in the work considered for Escheria Coli bacterium and it is found that the findings are consistent with the hypothesis.

On basis of these observations one can try to imagine how the ribosome or its predecessor "pre-ribosome" might have replicated.

1. Both the basic units of RNA sequences and corresponding amino-acid polymers of rRNA had to replicate. The most economic assumption is that this occurred simultaneously.
   
   
2. One can imagine that rRNA "gene" and the protein coded by it arranged themselves so that they were parallel. The amino-acid coded by rRNA codon acted as a catalyzer for the attachment of a conjugate of rRNA codon to the growing rRNA sequence just as in DNA replication promoter catalyzes the replication. rRNA codon in turm acted as a catalyzer for the addition of new amino-acid to the growing protein. tRNA molecules of form RNA-X-amino-acid from the environment provided the needed RNA codon and amino-acid.
   

   Remark: I have already earlier considered an RNA world scenario in which amino-acids of tRNA catalyzed the replication of RNA sequences. When DNA emerged, the roles would have changed and amino-acid sequence was formed instead of the replication of RNA.
   

   This replication differs from ordinary transcription. In transcription incoming mRNA sequences produce amino-acid sequences as tRNAs attach to the mRNA codons of mRNA attached to the ribosome. tRNA looses its amino-acid but keeps RNA. Now tRNA loses both amino-acid and RNA codon and only the unit X in tRNA? RNA-X-amino-acid remains.
   

   At some step of evolution the replication of rRNA would have ceased to occur and tRNA would have kept its RNA in the double translation process. Is this possibly biologically?
   
   

3. Concerning tRNA there are many possibilities. One can imagine that ribosome and Xs could have served as co-replicators. The reaction X→ RNA-X-amino-acid and its inverse could have occurred spontaneously. The resulting complex would have attached to the end of RNA-amino-acid sequence associated with some portion of mRNA just as it does in ordinary translation . In the replication or ribosome RNA-X-amino-acid would have attached to ribosome and X:s would have been produced in the replication of X forming a part of ribosome. In the environment the attachment of RNA and corresponding amino-acid to X would have taken place.
   

A possible objection is based on ontogenesis-recapitulates-phylogeny vision (ORP). The replicating pre-ribosomes should be still there but they are not. There should be some very simple mechanism preventing the replication but still one can ask whether the ribosomal replication could not occur in special circumstances.

How the pre-ribosome as first replicator relates to TGD approach?

TGD framework predicts that replication as a splitting of 3-surfaces to two copies is a fundamental mechanism of quantum TGD analogous to the 1→ 2 decay of elementary particle and the replication of DNA, cells, etc... should reduce to a hierarchy of replications starting from long length scales and proceeding as replications at shorter length scales with master slave relationship between the subsequent levels of the scale hierarchy.

This identification of replication as a mere splitting of 3-surfaces saying nothing about what happens for the quantum states associated with them is too general to allow to talk about unique primary replicator. If one however restricts the consideration to systems consisting of RNA and amino-acid sequences the idea about ribosome as primary replicator becomes highly non-trivial.

In TGD framework it is possible that pre-biopolymers were not bio-polymers but their dark counterparts formed from dark protons sequences at magnetic flux tubes with states of dark proton in 1-1 corresponds with DNA ,RNA, amino-acids and tRNA. If so pre-ribosome was realized at the level of dark matter as dark ribosome - a complex formed by dark analogs of bio-polymers.

If so, then pre-ribosome consisting of dark matter at flux quanta could be the primary replicator and the formation of its bio-molecular counterpart would be induced from that of dark pre-ribosome like the dynamics of slave in master slave hierarchy.

This raises questions. How does this replication proceed? Does ribosome still replicate as all other biological structures do and induce replication of low ever level structures in the dark matter hierarchy? Does the ordinary biomatter induced at the lowest level of hierarchy would only make visible this replication?

In the following I briefly summarize the basic TGD based notions involved in attempt to answer these questions.

4-D self-organization and magnetic body

One class of questions concerns the roles of self-organization and genetices. Even the definition of the notion of self-organization is poorly defined. In TGD zero energy ontology (ZEO) forms the basic framework of both quantum TGD proper and its applications to consciousness and biology. In zero energy ontology (ZEO) self-organization is replaced with self-organization by quantum jump sequence leading to the emergence of not only 3-D spatial patters but also of 4-D behavioral patterns: one can say that living system is 4-dimensional and also its geometric past changes in quantum jumps (Libet's findings).

1. Various motor actions of magnetic body appear as basic processes of the quantum self-organization. This includes braiding and knotting, h_eff changing phase transitions changing the lengths fo flux tubes, reconnections allowing to build connections between different system consisting of flux tube pairs, and also replication. Also signalling by dark photons is an essential part of the picture and the general hypothesis is that dark photons have same universal energy spectrum as bio-photons and thus in the energy range of molecular transition energies.
   
   
2. Replication in TGD framework occurs at the fundamental level as a replications of 3-surface and is completely analogous to 1→ 2 decay for point elementary particle. This replication could take place for the magnetic flux quanta representing various biopolymers and higher level structures and induced the replication at the level of visible matter. As noticed, this replication is not enough in biology and must be accompanied by the replication of the quantum states associated with 3-surfaces.
   
   
3. One key question is how the bio-molecular processes arranged into a functional network. Here the hypothesis that magnetic flux tubes form a 3-D grid analogous to coordinate grid with points of grid at intersections of 3 flux tubes and flux tubes as coordinate lines is very attractive. This Indra's web would be behind the gel like structure of cellular water and make it single coherent unit. Behavioral modes would be time evolutions of this grid: motor actions of the magnetic body - or hierarchy of them.
   
   

Does dark matter induced the dynamics of visible biomatter?

The idea that dark matter induces the dynamics of biomatter is extremely attractive since the enormous complexity of biochemistry would be only adaptation to the dynamics of the much simple almost topological dynamics of the master represented as flux tubes carrying dark matter.

1. In TGD framework there are good reasons to believe that water contained the prebiotic life forms as dark analogs of various biomolecules consisting of dark proton sequences at magnetic flux tubes with the states of dark proton in 1-1 correspondence with various bio-polymers (DNA,RNA, amino-acids, tRNA). These string like objects would be dark nuclei but with a large value of Planck h_eff=n× h constant and with same size scale as biopolymers. The proposal is that they are present also in living matter and that is interaction between various levels based on dark photons which give bio-photons as decay products.
   
   
2. All the basic processes such as transcription, translation, and replication would be realized already at this level. The analogs of these processes assigning to dark analogs of biopolymers the biopolymers themselves would have evolved later. (ORP) suggests that ordinary biopolymers are accompanied by parallel flux tubes carrying dark protons sequences representing them. Ordinary manner would condense around dark matter.
   

   The strongest assumption is that dark processes induce their bio-chemical counterparts as biomolecules attach to the magnetic flux tubes for which they form images at the level of visible matter. This might explain why strong dehydration leads to denaturation of biomolecules and why denatured biomolecules are not biologically active. Dark DNA would represent the "soul" of DNA not present in denatured DNA! Same of course would apply to other biopolymers: the loss of dark matter would induce the in vivo → in vitro transformation.
   

   I have proposed the identification of dark counterparts of RNAs and amino-acids as complex braided and knotted structures with braiding carrying information making possible topological quantum computation like processes and topological realization of memory. DNA would provide a symbolic representation coding also the braiding characteristics of the dark amino-acid sequence. Dark amino-acid sequence would represent the braiding physically ad dark DNA as a sequence of symbols.
   

   Cyclotron frequencies are crucial for communication and the strength of magnetic field on flux tubes emanating transversally from dark amino-acid sequence would be determined by the state of dark proton. The correspondence between dark RNA and amino-acid would be determined by the condition that cyclotron frequencies are identical for the corresponding dark proton states (DNA and mRNA, RNA and amino-acid) so that resonant interaction is possible.
   
   

3. This picture conforms with the chemical properties of DNA, RNA and proteins.
   
   
   1. RNA does not appear as double strands and in unfolded form is much less stable than DNA. This conforms with the fact that DNA serves as an information storage providing symbolic representation of RNA and amino-acids including their folding or at least braiding. RNA in turn would provide the concrete representation for braiding and folding.
      
      
   2. DNA double strand is stable against hydrolysis but only inside cell - this could be due to the fact that the phase of water is ordered and ice-like so that it cannot induce hydrolysis by providing water molecules - perhaps the fourth phase of water discovered by Pollack and leading to the formation of dark proton sequences in TGD framework is in question.
      
      
   3. The braiding structure of DNA is repetitive and carries no information. This conforms with the idea that DNA and its dark variant provide a purely symbolic representations in terms of genetic code for the corresponding amino-acid - and RNA polymers including also their braiding.
      
4. One can invent objections against the hypothesis that the dynamics of biopolymers is induced from that for their dark variants.
   
   
   1. RNA is not stable against hydrolysis but it can gain stability by folding. Thus the shape of RNA molecule would not be determined by its dark variant in conflict with induction hypothesis. One can however consider the much weaker possibility that dark sector determines only topological dynamics. Only the braiding of the fold RNA molecules would determined by the braiding of dark variant.
      
      
   2. DNA double strand is stable and braided in repetitive and very simple manner. If chemistry determines the stability of the DNA double strand then DNA double strand would induce the braiding of dark DNA strand rather than vice versa. Now one can argue that if dark DNA appears as double strand this forces the repetitive braiding.
      
      

To how high level can one continue this parallelism. For instance, does it make sense to talk about dark variants of cell and cell membrane? Can one tell whether it was pro-cell or bio-molecules that emerged first? It seems that all these structures could have emerged simultaneously. What emerged was dark matter and its emergence involved the emergence of all the others. Hens and eggs emerged simultaneously.

1. Here the findings of Pollack about the generation of exclusion zones, which are negatively charged regions of water obeying exotic stoichiometry H_1.5O, are suggestive. The TGD based model assumes that a phase transition generating dark protons sequences at flux tubes of magnetic body outside the EZ takes place. The self-organization at the level of ordinary matter would generate dark matter at quantum criticality - a basic aspect of self-organization process leading to higher hierarchy levels taking the role of master. Dark matter
   would be the master or rather - there would be entire hierarchy of masters labelled by the values of h_eff. I have also considered the possibility that the generation of large h_eff phases happens at criticality quite universally so that life would be universal phenomenon rather than random thermodynamical fluctuation.
   
   
2. EZs with sizes about 200 microns (size of cell) could have been the prebiotic cells. There is also evidence that EZs consist of structures with size of order micron called coherent regions (CDs to be not confused with Causal Diamonds!). Could they have been the predecessors of the cell nuclei inside which dark DNA would be stable? The TGD model for the formation of EZs assumes that they are formed from CDs under irradiation.
   

   This picture leads also to a view about metabolism predict that UV radiation with energies about 12.6 eV must play a key role in metabolism. The proposal is that this radiation arrives as dark photons along magnetic flux tubes of the magnetic body and excites water molecules inside CDs so that they are energetically at distance of about .5 eV from the splitting of OH bond. The excitation of water molecules inside CDs by metabolic energy quantum of nominal value .5 eV transforms this phase to EZs of Pollack.
   
   

Emergence of life as emergence of dark matter?

Many basic questions of biology seem to be hen-egg questions such as "genetics or metabolism?", "cell membrane or biomolecules?", "DNA or RNA?", "RNA or amino-acids?", etc.. This suggests that there exists a deeper level and emergence at this level induced the emergence at the level of biochemistry and cell biology.

In TGD the emergence of living systems would reduce to the emergence of dark matter as large h_eff phases of ordinary matter taking place at quantum critical and perhaps even critical systems.

1. The question whether genetics or metabolism emerged first ceases to be relevant in this framework, where basic physics provides candidates for the fundamental mechanisms of metabolism (for instance liberation of zero point kinetic energy when the p-adic length scale of space-time sheet (magnetic flux tube) increases).
   

   Also genetic code would have been realized already before biochemistry if dark proton sequences provided the counterparts for the fundamental biomolecules. The dark biology as dark nuclear physics would make itself visible via biochemistry induced by it. We would see directly the dynamics of dark matter just by looking living systems!
   
   

2. If one takes this picture seriously, then also pre-RNA and various other pre-biopolymers could have been realized in terms dark proton sequences associated with dark magnetic flux tubes. The dark replication process could have been the arrangement of RNA and amino-acid flux tube portions in parallel and replication of the dark proton sequences with the help of the analog of tRNA attaching to the corresponding amino-acid. In this framework the notion of dark ribosome makes sense. It would however replicate only in cell replication.
   
   
3. In the biochemical scenarios also the emergence of DNA looks like mystery. In TGD framework dark DNA could have emerged at the same time as dark RNA and dark amino-acids as CDs and EZs emerged and make the stable presence of also ordinary DNA inside CDs and EZs. All basic biomolecules and prebiotic cell and metabolism would have accompanied the emergence of CDs and EZs under the irradiation of water feeding metabolic energy and giving rise to prebiotic photosynthesis (note that the negative net charge of DNAs could be due to the fact that part of protons is at dark flux tubes). Dark DNA could be interpreted as an information storage representing the braiding patterns of dark RNA and dark amino-acids symbolically.
   
   
4. In this framework the basic step of the replication is the generation of flux tube parallel to the flux tube from which one forms copy or map (say in DNA replication and and transcription). How this happens?
   

   A possible answer to the question relies on the earlier proposal that living system involves kind of coordinate grid formed from magnetic flux tubes serving as coordinate lines and meeting each other at the points of the grid. The replication process would involved translation of nearby flux parallel flux tube of the grid near to a given flux tube assignable to say DNA strand as a first step - maybe by h_eff reducing phase transition for flux tubes orthogonal the flux tube. After this the building bricks of the new biomolecule would be brought along either of the remaining locally orthogonal flux tubes - perhaps by h_eff reducing phase transition. The basic structure would be this Indras web containing visible matter at its nodes with dynamics consisting of magnetic motor actions.
   

This vision involves of course considerable challenges. One should model the dark ribosome counterparts of the replication process for dark DNA, transcription of dark DNA to dark mRNA, translation of dark mRNA to dark amino-acids, and also possible self-replication of dark ribosome.

For background see the chapter Quantum gravity, dark matter, and prebiotic evolution of "Genes and Memes". See also the article Was ribosome the first self-replicator?.

Could Podkletnov effect be understood using heff= heff hypothesis?

Podkletnov discovered his effect around 1982. There are funny co-incidences involved. I got my PhD. Podkletnov was kicked out from Tampere University and I was soon to find that it is impossible to find any funding for my work: situation is still the same! God can forgive but not colleagues. I have considered possible models for Pokletnov effect in TGD framework for years ago assuming that the propagation of gravitons along topological light rays attached to magnetic flux tubes mediate gravitational interaction. A lot of progress has taken since then. Therefore reconsideration is well-motivated.

The effect itself looks rather complex. The experiment involves a levitating disk above a toroidal magnet. Solenoids generating AC fields with frequency in the range 50-10⁶ Hz are used to rotate the disk. Above the disk at height of 15 mm is a sample of silicon with weight of 5.47834 g. The claim is that both the rotating disk and sample lose part of their weight: the estimate varies from .3 per cent to few per cent. The effect was resonance like above frequency 10⁵ Hz: below this the weight fluctuates. The size of the effect increases with rotation frequency.

Some background

It is best to start by introducing some background.

1. The first thing to notice is that f=6× 10⁵ Hz is cyclotron frequency of electrons in the magnetic field B_end=.2 Gauss introduced to explain the quantal effects of ELF em fields on brain which appear at multiples of cyclotron frequencies of biologically important ions. The recent model for bio-photons as decay products of dark protons predicts that their spectrum correspond to a spectrum of B_end. Could it be that the magnetic fields at the flux tubes involved has spectrum of B_end and resonant transfer of energy in the frequency range containing f=6× 10⁵ Hz takes place?
   
   
2. The hypothesis h_eff = h_gr = GM_D m/v₀, where M_D is the dark mass assignable with large system (Earth now) and v₀ is velocity parameter is relatively new piece of TGD inspired quantum biology. One obtains a rough estimate M_D/M ≈ 2. × 10^-4 for the fraction of dark matter in the case of Earth and assignable to the dark magnetic body of Earth. One implication of h_gr=h_eff hypothesis at gravitation mediating flux tubes is that cyclotron frequencies of particles do not depend on the mass of the particle and cyclotron energy spectrum of dark photons is universal and identifiable as that
   associated with bio-photons. Second implication is that each charged particle corresponds to particular value of Planck constant so that in many-sheeted space-time they populate different flux tubes: this could be very relevant for biology since cell would not be anymore a random soup of molecules. The model for the Pioneer and Flyby anomalies leads to the estimate M_D/M≈ 1.3× 10^-4 consistent with the above estimate.
   
   
3. I have considered recently a model for the fountain effect of superfluidity considering the possibility that dark phases of matter in TGD sense might be associated with all critical situations - both ordinary critical and quantum critical phase transitions - in which long range fluctuations correlations explained in terms of generation of dark matter are present.
   

   The superfluid is able to climb from vessel along its walls apparently defying gravitation. The TGD explanation is in terms of large Planck constant h_gr=h_eff hypothesis. The large value of h_gr implies macroscopic quantum gravitational coherence and that the quantum states in gravitational field for dark ⁴He atoms have macroscopic size. In particular, the flow along walls is effectively free flow.

The anomaly in the measurement of Cooper pair mass in rotating superconductors

One has discovered an anomalous outcome in the mass measurements of Cooper pairs in the case of rotating superconductors. The measured mass of Cooper pair in rotating super conductor is slightly larger than the mass of the pair which must be slightly below the sum of the masses. Tajmar et al try to explain the anomaly is in terms of a gigantic gravimagnetic London effect associated with a rotating superconductor.

1. Recall that in in the ordinary London effect a magnetic field proportional to the negative of rotation frequency is generated inside super-conductor: usually the magnetic field is expelled. London magnetic field corresponds to a magnetic dipole proportional the negative of the rotation frequency (this follows from the negative sign of the charge carriers). The natural expectation is that this gives rise to a dipole field outside the superconductor. The dipole moment would be generated by electron current at the surface of the superconductor.
   
   
2. The idea is to to introduce gravitational superconductivity for which all kinds of particles participate in the flow which would be analogous to super-fluidity. One can also speak about gravitational Meissner effect and massivation of graviton as analog of massivation of photons in the ordinary Meissner effect. Also the notion of London magnetic field might generalizes and gives rise to a dipole like gravimagnetic field outside the super-conductor. Now however negative charge is replaced by mass, which is positive so that the sign of the effect changes. The predicted effect is however completely negligible using the existing estimates for the mass of the graviton.
   
   
3. The crazy proposal of Tajmar et al is that a gravimagnetic field larger than that predicted by GRT by a factor of order 10²⁴ is associated with the rotating super-conductor and combines and produces the slight deviation of the measured mass of the Cooper pair from real when this since the Cooper pair couples also to gravimagnetic field besides magnetic field. The reason is that the effective magnetic field contains a small contribution of gravimagnetic field so that the measurement gives too large a result for the mass of the Cooper pair.
   

In standard model plus GRT this kind of effect is impossible. In TGD framework the hierarchy of Planck constants suggests two alternative explanations.

1. The London magnetic field (also gravimagnetic) is a purely quantal effect and proportional to the square h² of Planck constant. If h is replaced with say h_eff = h_gr≈ 10¹² h the effect is enormous as compared to that predicted by GRT! There is however an objection: one cannot perform this replacement for ordinary London field! Why?
   
   
2. Many-sheeted space-time allows to consider also alternative model in which the change of mass is due to a generation of the analog of dark London magnetic field at dark magnetic flux tubes: electron would couple to the sum of these fields since it would have topological sum contacts to both space-time sheets This magnetic field is proportional to dark matter density and ρ_D/ρ=M_D/M≈ 2× 10^-4 would give a correct order of magnitude estimate.
   
   
3. Since gravimagnetic and magnetic fields are expressible in terms of CP₂ coordinates and their gradients, one can wonder whether the two explanations are actually equivalent.
   
   

What about Podkletnov effect?

Also Pokdletknov effect is associated with a rotating superconductor and one can ask whether the above ideas apply also to it.

1. The vision that dark variants of elementary particles are associated with all critical phenomena suggest that a critical phenomenon is in question also now and part of the matter - at least part of Cooper pairs - are in dark phase at magnetic flux tubes satisfying h_eff= h_gr. Could large h_eff=h_gr be involved also with Podkletnov's effect? Could the reported loss of the weight of the (not necessarily) rotating disk and and of the sample by .3 per cent be due to the transformation of part of Cooper pairs to large h_eff=h_gr phase de-localized to the magnetic flux tubes along which gravitational force is mediated in a scale considerably larger than that of the sample and disk? Also the air above the rotating superconductor was reported to start to rise. Could this be that also air
   molecules lost some of their electrons to the dark flux tubes in this manner? Since electron mass is about 2^-11 fraction of proton mass, also protons and heavier particles should leak to the dark phase to achieve weight loss of order per cent. This effect would be present already for the non-rotating superconductor and would be much like the fountain effect in superfluidity according to TGD.
   
   
2. As the frequency of AC fields is increased, the weight of the sample fluctuates but above 10⁵ Hz it stabilizes and is resonant like. Levitation is essentially due to the gradient of the magnetic energy associated with AC fields. Could part of AC photons transform to dark photons and could the large energy of dark photons - in visible and UV range - mean much larger excluded magnetic energy in the volume of the gravi-superconducting sample and rotating superconducting disk and in this manner induce stronger levitating effect becoming stronges at cyclotron resonance energies. Resonance absorption would take place when the frequency is in the region of electron cyclotron frequencies for the flux tubes. Also coherence would be achieved thanks to the presence of Bose-Einstein condensates of electronic Cooper pairs.
   
   
3. One should explain also the increase of the reported loss of the weight with the rotation velocity of the superconducting disk. Rotation generating the mass current should generate dipolar gravimagnetic field with strength proportional to the rotation frequency (and accompanied by ordinary magnetic fields). The increasing strength of the gravimagnetic field would mean increase in the number of flux quanta or increase of the field strength at the flux tubes. At least in the first case more particles could end up to the dark phase leading to the reduction of effective weight of the sample and rotating disk. This gravimagnetic dipole field would naturally correspond to the gravimagnetic London field continued outside the superconducting rotating disk acting as a magnetic dipole.
   
   

For background see the chapter Quantum gravity, dark matter, and prebiotic evolution of "Genes and Memes" or the article Could Podkletnov effect be understood using h_eff= h_eff hypothesis?.

Quantization of conductance in neutral matter as evidence for many-sheeted space-time?

We are living really interesting times. Experimental sciences are producing with accelerating pace new discoveries challenging the existing theories and it is difficult to avoid the impression that a revolution is going on in physics and also in biology and neuroscience. It is a pity that colleagues do not seem to even realize what is going on. Ulla's Facebook page Quantum Biology, coherence and decoherence contained this morning a link to and article published in Nature.

The article tells about quantized conductance in neutral matter. In quantum Hall effect conductances is quantized in multiples of e²/h. Now the however is in multiples of 1/h. Looks strange! This is due to the fact that voltage is not present now: particles are neutral and electric field is replaced with the gradient of chemical potential and electric current with particle current. Hence elementary charge e is replaced with the unit for particle number which is just 1 rather than e. Hence the quantisation as multiples of 1/h but in complete analogy with Quantum Hall Effect (QHE).

What comes to my innocent in mind is that the effect is mathematically like QHE and that there is also fractional variant of it as in the case of QHE. In QHE magnetic field and cyclotron states at flux quanta of this field are in key role. But in the situation considered they are not
present if we live in the standard model world.

What is the situation in TGD?

1. In many-sheeted space-time all classical electroweak fields are present as long range fields at given sheet. This has been one of they key interpretational problems of TGD from the beginning. In particular, Kähler electric and magnetic fields are always associated with non-vacuum extremals although ordinary electric field can vanish. Note that classical electro-weak fields affect the dynamics indirectly by forcing fermions to the string world sheets! They are clever power holders!
   
   
2. This has inspired the hypothesis that induced spinor fields describing fundamental fermions are localized at string world sheets at which only em fields are non-vanishing. This assumption guarantees that electromagnetic charge is well-defined quantum number for the modes of spinor field and thus also conserved. Classical Z⁰ fields could be present below weak scale also at string world sheets. Weak scale is scaled up to macroscopic scale for large values of h_eff=n× h and this could explain the large parity breaking effects in living matter but also just the fact that fermionic fields are not where weak fields are, could explain the parity breaking effects in living matter.
   
   
3. At GRT-gauge theory limit the sheets of many-sheeted space-time are replaced with single one and interpreted as region of Minkowski space slightly curved and carrying gauge fields: now space-time is not regarded as a surface anymore. Only classical em field effectively present above weak scale since other electroweak gauge potentials associated with space-time sheets sum up to something which is zero on average at GRT limit.
   
   

These observations lead to ask whether the quantization of conductivity for neutral particles be a direct signature of many-sheeted space-time? Could the experiments probe physics at single sheet of many sheeted space-time? Could the needed magnetic and electric fields correspond to classical Z⁰ fields, which can be present at string world sheets below weak scale now scaled up by h_eff/h.

If this approach is on the correct track then the thermodynamical description in terms of chemical potential cannot be fundamental (the gradient of the chemical potential replaces that of electric potential in this description). Leaving the realm of standard model, one could however wonder whether the thermodynamical description using chemical potentials (chemistry is by definition effective theory!) is really fundamental in quantum regime and whether it could reduce to something more fundamental which standard model can describe only phenomenologically.

1. I have ended up with two alternative models of cell membrane in zero energy ontology as a generalisation of thermodynamics as square root of thermodynamics with probability densities interpreted as square roots of thermodynamical weights which are exponentials of thermal energies. These models can be also combined. Both are characterized by a large value
   of h_eff=h_gr, where h_gr is the gravitational Planck
   constant discussed in the series earlier postings about criticality and hierarchy of Planck constants (see this and earlier postings during November).
   
   
2. In the first model of the cell membrane Josephson energy determined by the voltage over the cell membrane is generalized by adding to it the difference of cyclotron energies at flux tubes at the two different sides of the membrane and the magnetic fields at flux tubes appear in the formula. This difference of cyclotron energies corresponds to chemical potential and affects the frequency associated with the Josephson current and corresponding energy proportional to h_eff and therefore above thermal energy.
   
   
3. For the second model classical Z⁰ fields explaining the large parity breaking effects in living matter are assumed to be present. Chemical potential corresponds to the difference of Z⁰ potential over the cell membrane. Could this phase be the phase in which "chemical" conductivity is quantized?
   
   
4. For the hybrid of the two models the theory of QHE would generalize by replacing em fields with combinations of em and Z⁰ fields. This framework could be used to model also the observed quantization of neutral conductivity as an analog of QHE.

The most obvious objection that the quantum of conductivity for neutral particles is 1/h rather than g²/h, where g is appropriate weak coupling strength does not bite. Experimentalists measure particle currents rather than Z⁰ currents (j= j_Z/g_Z) and use gradient of chemical potential instead of Z⁰ potentials μ= g_ZE_Z). j_Z= σ E_Z implies that the quantization of the conductance is in multiples of 1/h.

For details and references see the chapter Quantum Hall effect and hierarchy of Planck constants of "p-Adic length scale hypothesis and hierarchy of Planck constants" or the article Quantization of conductance in neutral matter as evidence for many-sheeted space-time?.

Does number theoretical universality require the positivity of twistor Grassmann amplitudes?

Lubos wrote a commentary about a new article of Nima Arkani Hamed et al about the positivity of the amplitudes in in the amplituhedron. Nima et al argue using explicit calculations that positivity could be a quite general property: as if the amplitudes were analogous to generalized volumes of higher-dimensional polyhedra.

The Grassmannian twistor approach considers also positive Grassmannians. This is not the same thing but most be closely related to the positivity of amplitudes. I recall that the core idea is however that one considers higher-D analogs of polygons. Simple representative for positive space polygon would be a triangle bounded by positive x- and y-axis and the line y=-x. x and y coordinates are positive.

What is of course certain is that the entire scattering amplitude cannot be positive since it is complex number. Rather, it must decompose into a product of "trivial" part determined by symmetries and non-trivial part which for some reason must be positive. What does this mean? Lubos considers this question in his posting: the idea is roughly that the real amplitude in question is an exponential and this guarantees positivity. Bundle theorist might speak about global everywhere non-vanishing section of vector bundle having geometric and topological meaning in algebraic geometry. Below I try to interpret positivity in terms of number theoretic arguments.

Does number theoretical universality require positivity?

Number theoretical universality of physics is one of the key principles of TGD and states that real physics must allow algebraic continuation to p-adic physics and vice versa. I suggest that number theoretical universality requires the positivity.

1. The p-adicization of the amplitudes requires positivity. The "non-trivial" factor of the amplitude is mapped to its p-adic counterpart by a variant of canonical identification mapping p-adics to non-negative reals and vice versa and is well-defined only for non-negative real numbers. Hence positivity. This condition could also explain why positive Grassmannians are needed: the preferred coordinates must be positive in order to have well-defined p-adic counterparts and vice versa.
   

   The basic reason for positivity is that p-adic numbers are not well-ordered. When one has two p-adic numbers with the same p-adic norm, one cannot tell which of them is the larger one. This makes it impossible to tell whether a given p-adic number is positive or negative and one cannot talk about p-adic boundaries. p-Adic line segment has no ends. As a consequence, definite integral is very difficult notion p-adically although the notion of integral function can be defined. p-Adic counterparts of differential forms are also far from trivial to define.
   
   

2. What about the symmetry determined parts of amplitudes, which are typically analogs of partial waves depending on angular coordinates and are complex and cannot be positive? Also here one encounters a technical problem related to another conceptual challenge of p-adicization program: the notion of angle is not well-defined in p-adic context and one can talk only about discrete phases. More precisely, one can define exponential function exp(x) if x has p-adic norm smaller than one but it does not have the properties of the ordinary exponential function (it has p-adic norm 1 for all values of x). One can define also trigonometric functions with the help of exp(ix) for p mod 4=3 formally but the trigonometric functions are not periodic. Something is missing.
   

   In the case of ordinary trigonometry the only way out is to perform algebraic extension of p-adic numbers by adding roots of unity representing phases associated with corresponding angles: phases replace angles. For instance, U_n=exp(i2π/n) exists in an algebraic extension of p-adic numbers. Angle degrees of freedom are discretized.
   

   In the case of hyperbolic geometry, one can add roots of e to obtain p-adic counterparts of e⁽1/n) (note that e^p is ordinary p-adic number so that these extensions are finite-dimensional algebraically and e is completely unique real transcendental in that it is algebraic number p-adically!): this extension allows to get the counterparts of ordinary exponential functions in extension.
   

   One can also multiply the points of discretization by p-adic numbers of norm smaller than 1 (or some negative power of p) to get something as near as possible to continuum. Hence discretization in both hyperbolic and trigonometric degrees of freedom by algebraic extension solves the problems quite generally for amplitudes defined in highly symmetric spaces. In Grassmann twistor approach one indeed considers projective spaces.
   
   

3. Consider as an example the p-adic counterpart of Euclidian 2-space with coordinates (ρ,φ). ρ is non-negative radial coordinate and has p-adic counterpart obtained by canonical identification or its variant. The values of φ are replaced with discrete phase factors U_n characterizing the values of φ coordinate. One has a collection of n rays emanating from origin instead of entire plane. One obtains infinite number of variants of E² labelled by n characterizing the angular resolution.
   

   The p-adicization of Cartesian representation of real Euclidian 2-space defined using (x,y) coordinates would give only the first quadrant since negative x and y have no p-adic counterparts. In both cases cognitive representations lose a lot of information for purely number theoretical reasons. Cognitive analog of Uncertainty Principle is suggestive.
   
   

4. Obviously General Coordinate Invariance is broken at the level of cognition which is actually not so surprising after all since the worlds in which mathematician has chosen to used Cartesian resp. spherical coordinates must differ in some delicate manner! Of course, the resulting discretized spaces are very different.
   
   

How should one p-adicize?

The p-adicization of various spaces and amplitudes is needed. p-Adicization means that one assigns to a real (or complex) number a p-adic variant by some rule. In the case of trigonometric and hyperbolic angles one can use discretization and algebraic extension but what about other kinds of coordinates? There are two guesses.

1. Consider only rationals or their algebraic extension and maps only them to their p-adic counterparts in the needed extension of p-adic numbers. This correspondence is however extremely discontinuous since real numbers which are arbitrary distant can be arbitrary near p-adically and vice versa. What is nice that this map respects symmetries suggesting that one has symmetries below some rational cutoff defining measurement resolution. This conforms with the general philosophy about measurement resolution realized in terms of inclusions of hyper-finite factors realizing measurement resolution as analog of dynamical gauge symmetry.
   
   
2. Use canonical identification mapping p-adic numbers to p-adic numbers by canonical identification: x= ∑ x_npⁿ → ∑ x_np^-n is the first option. It indeed works only for non-negative real numbers: hence positivity! Canonical identification is continuous but does not respect differentiability nor symmetries. Direct identification via common rationals in turn does not respect continuity.
   
   

The resolution of the problems is a compromize based on the use of two cutoffs. In some length scale range above p-adic UV cutoff L_UV and scale L a direct correspondence between common rationals is assumed. Between L IR cutoff L_IR canonical identification is used. Outside the range [L_UV, L_IR] there is no correspondence and conditions like smoothness dictate the details at both sides.

p-Adic space-time surfaces as cognitive maps of real ones and real space-time surfaces as correlates for realized intentions

One wants to talk about real topological invariants also in p-adic context: p-adic space-time surface should be a kind of cognitive representation of real space-time surface.

1. Space-time surfaces are extremals of Kähler action (real/p-adic) but have a discrete set of common rational points. The notion of p-adic manifold for which p-adic regions are mapped to real chart leafs (rather than to p-adic ones!) formalizes this concept and allows to avoid the problem that p-adic balls are either disjoint or nested so that the usual construction of manifold does not make sense. The problem that there exists an endless variety of coordinate choices and each would give different notion of p-adic manifold.
   
   
2. The cure comes from space-time as a surface property, and from symmetries allowing to induce manifold structure from the level of imbedding space the level of space-time surfaces. In TGD imbedding space is M⁴ × CP₂. CP₂ allows very natural p-adicizations by using complex coordinates transforming linearly under maximal subgroup of isometries and one obtains discrete variants of coset space with points labeled by phases in the algebraic extensions of p-adic numbers. One can also have a generalization in which each discrete point corresponds to a continuum of p-adic units.
   

   In the case of M⁴ one has more options but if one requires that the coordinate which is mapped by canonical identification to its real counterpart, the natural choices is the cosmic coordinates assignable to the future or past light-cone of causal diamond. Light-cone proper time would correspond to non-negative coordinate and the remaining coordinates would be ordinary angles hyperbolic angle and mappable to phase factors and real exponential which exists if one introduces finite number of roots of e and discretizes the hyperbolic angle. Note that p-adic causal diamond (CD) is p-adically non-trivial manifold requiring two chart leafs and this might deeply relate to the fact that state function reductions occur to either boundary of CD.
   
   

3. Surface property implies that the correspondence between real and p-adic space-time surfaces is induced from that between the corresponding imbedding spaces and thus dictated to high degree by symmetries. Preferred imbedding space coordinates and their discretizations induce coordinates and discretizations at space-time surfaces so that there is a huge reduction in the number of different but cognitively non-equivalent discretizations.
   
   
4. This could make possible in practice to define the notion of p-adic space-time surface as a cognitive map of real space-time surface and real space-surface as a realization of intention represented by p-adic space-time surface. The real extremal of Kähler action is mapped to p-adic one only in a given resolution. A subset of discrete points of the space-time surface is mapped to p-adic ones and vice versa and this discrete skeleton is continued to a p-adic extremal of Kähler action. The outcome is interpreted as cognitive representation or its inverse (transformation of intention to action) and need not be unique. The mapping taking p-adic skeleton to real one is up to some cutoff pinary digit just identification along common rationals respecting symmetry and above that canonical identification up to the highest allowed pinary digit.
   

To sum up, number theoretic universality condition for scattering amplitudes could help to understand the success of twistor Grassmann approach. The existence of p-adic variants of the amplitudes in finite algebraic extensions is a powerful constraint and I have argued that they are satisfied for the polylogarithms used. Positive Grassmannians and positivity of the amplitudes might be also seen as a manner to satisfy these constraints.

For background see the chapter Some fresh ideas about twistorialization of TGD of "Towards M-matrix" or the article Positivity of N=4 scattering amplitudes from number theoretical universality?.