What next in TGD?

Last night I was thinking about possible future project in TGD. The construction of scattering amplitudes has been the dream impossible that has driven me for decades. Maybe the understanding of fermionic M⁸-H duality provides the needed additional conceptual tools.

1. M⁸ picture looks simple. Space-time surfaces in M⁸ can be constructed from real polynomials with real (rational) coefficients, actually knowledge of their roots is enough. Discrete data - roots of the polynomial!- determines space-time surface as associative or co-associative region! Besides this one must pose additional condition selecting 2-D string world sheets and 3-D light-like surfaces as orbits of partonic 2-surfaces. These would define strong form of holography (SH) allowing to map space-time surfaces in M⁸ to M⁴×CP₂.
2. Could SH generalize to the level of scattering amplitudes expressible in terms of n-point functions of CFT?! Could the n points correspond to the roots of the polynomial defining space-time region!

   Algebraic continuation to quaternion valued scattering amplitudes analogous to that giving space-time sheets from the data coded SH should be the key idea. Their moduli squared are real - this led to the emergence of Minkowski metric for complexified octonions/quaternions) would give the real scattering rates: this is enough! This would mean a number theoretic generalization of quantum theory.

3. One can start from complex numbers and string world sheets/partonic 2-surfaces. Conformal field theories (CFTs) in 2-D play fundamental role in the construction of scattering string theories and in modelling 2-D statistical systems. In TGD 2-D surfaces (2-D at least metrically) code for information about space-time surface by strong holography (SH) .

   Are CFTs at partonic 2-surfaces and string world sheets the basic building bricks? Could 2-D conformal invariance dictate the data needed to construct the scattering amplitudes for given space-time region defined by causal diamond (CD) taking the role of sphere S² in CFTs. Could the generalization for metrically 2-D light-like 3-surfaces be needed at the level of "world of classical worlds" (WCW) when states are superpositions of space-time surfaces, preferred extremals?

The challenge is to develop a concrete number theoretic hierarchy for scattering amplitudes: R→C→Q→O - actually their complexifications.

1. In the case of fermions one can start from 1-D data at light-like boundaries LB of string world sheets at light-like orbits of partonic 2-surfaces. Fermionic propagators assignable to LB would be coded by 2-D Minkowskian QFT in manner analogous to that in twistor Grassmann approach. n-point vertices would be expressible in terms of Euclidian n-point functions for partonic 2-surfaces: the latter element would be new as compared to QFTs since point-like vertex is replaced with partonic 2-surface.
2. The fusion (product?) of these Minkowskian and Euclidian CFT entities corresponding to different realization of complex numbers as sub-field of quaternions would give rise to 4-D quaternionic valued scattering amplitudes for given space-time sheet. Most importantly: there moduli squared are real! A generalization of quantum theory (CFT) from complex numbers to quaternions (quaternionic "CFT").
3. What about several space-time sheets? Could one allow fusion of different quaternionic scattering amplitudes corresponding to different quaternionic sub-spaces of complexified octonions to get octonion-valued non-associative scattering amplitudes. Again scattering rates would be real. A further generalization of quantum theory?

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

M8-H duality for fermions

M⁸-H duality in bosonic sector is rather well understood but the situation is different in the fermionic sector. The basic guideline is that also fermionic dynamics should be algebraic and number theoretical.

1. Spinors should be octonionic. I have already earlier considered their possible physical interpretation.
2. Dirac equation as linear partial differential equation should be replaced with a linear algebraic equation for octonionic spinors which are complexified octonions. The momentum space variant of the ordinary Dirac equation is an algebrac equation and the proposal is obvious: PΨ=0, where P is the octonionic continuation of the polynomial defining the space-time surface and multiplication is in octonionic sense. The masslessness condition restricts the solutions to light-like 3-surfaces m_klP^kP^l=0 in Minkowskian sector analogous to mass shells in momentum space - just as in the case of ordinary massless Dirac equation. P(o) rather than octonionic coordinate o would define momentum. These mass shells should be mapped to light-like partonic orbits in H.
3. This picture leads to the earlier phenomenological picture about induced spinors in H. Twistor Grassmann approach suggests the localization of the induced spinor fields at light-like partonic orbits in H. If the induced spinor field allows a continuation from 3-D partonic orbits to the interior of X⁴, it would serve as a counterpart of virtual particle in accordance with quantum field theoretical picture.

   Addition: A really pleasant surprise that came this morning-9.7.2020 - sounds melodramatic but I do not want to forget it - it could have come more than decade ago but did not. The octonionic inner product for complexified octonionic 8-momenta with conjugation with respect to commuting imaginary unit i gives 8-D Minkowski norm squared. Same about quaternonic norm for complexified quaternionic momenta. Minkowski space with signature of (1,-,-1,-1) for metric follows from number theory alone! This conforms with the very idea of M⁸-H duality that geometry and number theory are dual in physics. Already this single finding makes M⁸-duality a "must".

   See the article Fermionic variant of M⁸-H duality or the chapter Does M⁸ duality reduce classical TGD to octonionic algebraic geometry?: Part III.

   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.

John Baez about Noether's theorem in algebraic approach

John Baez gives very nice summary (see this of the triple of states, observables, and generators of symmetries from purely algebraic point of view. Jordan Banach algebra with commutative product A*B= (AB+BA)/2 would play the role of observables. The operators correspond to symmetry generators commuting with observables and the unitary evolutions generated by them in this algebra are trivial. One could say that this defines analogy of Noether's theorem usually deduced for the symmetries of action principle.

To me the weakness of the algebraic approach is that it says very little about the dynamics- it woul be just unitary evolution generation by some generator of symmetry. Second problem is mentioned at the end of the posting is how classical relates to quantal. And there is nothing about quantum measurement problem so that basically an attempt to reproduce wave mechanics using operators is in question.

My own view - zero energy ontology (ZEO) - goes much beyond quantum mechanics of simple systems.

1. The basic problem of quantum measurement theory is the starting point. The notion of quantum state is modified. In wave mechanics and quantum field theories it is based on initial value problem in configuration space (space of positions for particle). Initial state is wave function - a superposition of possible initial values in configuration space. Time evolution is formulated in terms of unitary evolution defined by exponential of Hamiltonian and reduces to Schroedinger equation.

   What happens in quantum measurements is not consistent with this time evolution. This is the problem.

   1. In TGD one replaces initial value problem with a boundary value problem with boundary corresponding to values at times t1 and t2 (this is a simplification).
   2. One defines states as superpositions of deterministic classical time evolutions - preferred extremals - analogous to Bohr orbits having the property that boundary value problem is equivalent to initial value problem. Once on knows configuration at t1, one knows it at t2.
   3. Quantum states are superpositions of these preferred extremals from t1 to t2 and quantum jump replaces this kind of superposition with a new one. I call this approach zero energy ontology (ZEO).
   4. The basic problem of quantum measurement theory disappears since there are two causalities: that of quantum jump and classical causality, and there is no need to break the deterministic time evolution analogous to that given by Schroedinger equation in quantum jump. There are two times: experienced time as sequence of quantum jumps and geometric time. One ends up with a theory of consciousness without moment of consciousness identifiable as state function reduction. Also a ZEO theory of self-organization emerges. This is of course only the basic idea. For instance, one must understand how correlation between experienced time and geometric time emerges.
   5. One the many implications of ZEO is new view about quantum tunnelling: it must have classical time evolution as quantum correlate. This leads to a new view about tunnelling in nuclear reactions relying essentially on the change of the arrow of time in ordinary state function reduction. Just today I received link telling about strange phenomenon occurring in what is believe to be ordinary electron tunnelling. The electron getting through the barrier radiates energy which increases with the height of the barrier. I discusse the ZEO based explanation in a related posting New support for TGD view about quantum tunnelling .

   How to realize this picture and how unique is it? Here one must leave the realm of wave mechanics.

   1. Loosely speaking, in TGD framework point-like particle is replaced with 3-D surface in M⁴× CP₂ and its orbit as preferred extremal of action principle, whatever it might be, defines space-time region. A generalization of string model is in question. Also a generalization of general relativity solving its problem due to the loss of Poincare symmetries is in question.
   2. This leads to a generalization of Einstein's geometrization program: replace configuration space with the "world of classical worlds" (WCW) and give it Kaehler geometry to realize geometrization of quantum theory. Points of WCW are 3-surfaces or equivalently 4-surfaces: this reduces holography and reduces it to general coordinate invariance.

      WCW spinor fields would represent physical states as "wave functions". Configuration space gamma matrices would be superpositions of fermionic oscillator operators so tha also fermions are geometrized. The mere existence of WCW Kaehler geometry requires maximal isometries and this fixes TGD highly uniquely. Freed realize the uniqueness for loop spaces.

   How to realize the crucial preferred extremal property making initial value problem equivalent with boundary value problem?
   1. Here the maximal isometry group of WCW enter the game. The symmetry algebra is replaced with an analog of infinite-D symplectic algebra acting as isometries of WCW induced from symplectic transformations at delta M⁴₊xCP₂ labelled by integer valued conformal weights assignable to the radial light-like coordinate of light-cone bounary δM⁴₊ defining second boundary of causal diamond cd identified as the intersection of future and past directed light-cones.
   2. The crucial point is that this algebra - call it A - has fractal hierarchy of sub-algebras A_n with conformal weights coming as multiples of n=1,2,... which very probably corresponds to a hierarchy of hyper-finite factors of type II₁ forming inclusion hierarchies labelled by sequences ...n₁ divides n₂ divides....
   3. Infinite-D sub-algebra A_n appears would have vanishing classical Noether charges in the class of preferred extremals associated with A_n. Also [A_n,A] would have the same property.This is like posing the condition that analogous sub-algebra of say Kac-Moody algebra annilates physical states. The space-time surfaces in question would be minimal surfaces satisfying the additional condition that they extremize also what I call Kaehler action, and being analogous to Maxwell action.

   See the article Some comments related to Zero Energy Ontology (ZEO).

   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.

New support for TGD view about quantum tunnelling

There is a popular article in Phys.org describing a highly interesting finding made by condensed matter physicist Doug Natelson and his colleagues at Rice and the University of Colorado Boulder. Light emission associated with the tunnelling of electrons through a nano-scaled potential barrier between Gold electrodes has been observed. The intensity of emission is larger by factor 10,000 than predicted and this suggests new physics.

By definition tunnelling means that electrons get through the potential barrier without getting energy - classical picture would require this. Now it however seems that electron receives energy and the higher the barrier the larger energy is needed. Should one challenge the notion of tunnelling? Could it have a classical counterpart?

In TGD framework all quantum phenomena should have classical counterparts, also tunnelling. Therefore the tunnelling electron would actually get energy to get over the potential barrier classically.

1. In zero energy ontology (ZEO) solving the basic problem of quantum measurement theory quantum states are superpositions of deterministic classical time evolutions, preferred extremals. Classical physics is exact part of quantum theory. The key prediction is that in ordinary, "big", state function reductions (BSFRs) the arrow of time is changed. In small SFRs (SSFRs) - analogs of weak measurements - this does not happen. ZEO leads to a theory of self-organization in which energy feed to self-organizing system corresponds to dissipation for time reversed state associated with dissipating system.
2. Tunnelling could mean in TGD framework that electrons make a BSFR reversing the arrow of time. In time reversed state they dissipate in reverse time direction: in standard time direction of observer they receive energy in standard time direction allowing them to get over the potential barrier. In the second BSFR establishing the original arrow of time they would liberate the energy and the higher the barrier, the larger the liberated energy and the brighter the light emission. The tunnelling in this sense would be already self-organization phenomenon involving BSFR. This dynamical tunnelling does not exclude the analog of wave-mechanical tunnelling as a non-dynamical process. The dynamical tunnelling could actually lead to asymptotic states in which particle is at both sides of the forbidden region or even in forbidden region but with extraction of classical energy from environment so high that this is not forbidden anymore.

For ZEO see the article Some comments related to Zero Energy Ontology (ZEO). For TGD view about tunnelling in nuclear reactions see Solar Metallicity Problem from TGD Perspective

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

New ideas about the transition to ferromagnetic phase

I received a link to a highly interesting article about ferromagnetism. According to the article, Yi Li, a physicist working at John Hopkins University and his two graduate students, Eric Bobrow and Keaton Stubis, seem to have made a considerable progress in understanding how the system of electron spins in lattice ends up to a ferromagnetic sate. This ferromagnetism is known as itinerant ferromagnetism and involves vacancies, sites without electron, which can be moved freely without affecting the energy of the state.

1. The ideas related to the work of Li et al

The problem considered by Li et al how the ferromagnetic state could emerge from an arbitrary state with some numbers of spin up and spin down states at lattice sites connected by edges.

1. Permutation of electrons with same spin leave the ferromagnetic state invariant and does not cost energy while permutations in arbitrary configuration can do so.
2. Li et al considered a simple 4× 4 lattice with single vacancy and noticed a connection with so called 15-puzzle involving 15 tiles and single vacancy with neighboring tiles of vacancy able to move to its position. The observation is following. If one has spin lattice containing single vacancy, one can number the sites by a number running from 1 to N (now 15) in arbitrary manner. If so called connectedness condition holds true one can realize any permutation of these numbers. This means that 15-puzzle has always a solution. In particular, one can arrange the situation that the numbers form an ordered sequence from 1 to N so that numbers n and n+1 are nearest neighbors.

   The result found by Li et al first for 2-D 4× 4 lattice with single vacancy generalizes to lattices, which are non-separable in the sense the removal of a lattice site does not separate any pair of spins - they are still connected by an edge-loop.

3. The curve solving the 15-puzzle goes through all points of the 4× 4 lattice and is generally known as Hamiltonian curve. It becomes Hamiltonian cycle if the numbers 1 and N are nearest neighbors.
4. The basic problem of this approach is that the theorem is true only for single vacancy and does not allow generalization to a larger number of vacancies. It is however known that ferromagnetism is possible up to fraction 1/3 for vacancies. The challenge is to generalize the result of Li et al.

2. Some reasons to get interested

In TGD framework there are good reasons of getting interested on these results.

1. The result of Li et al states that ferromagnetic phase transition might be understood in terms of shifting of lattice vacancy if the lattice with single defect allows deformaton of any configuration of spin labelled by numbers n running from 1 to N to a closed curve connecting nearest neighbors along which n increases. Could there be a connection with Hamiltonian curves making sense for lattice like structures (actually all graphs)? Could Hamiltonian curve have some deeper physical meaning or is it only an auxialiary notion useful for representing the possibility to realize all points of the lattice with vacancy by shifting it suitably?

   Hamiltonian curve connects neighboring points of a lattice and goes through all points without self-intersections. Icosahedral geometry appears in biology and one can ask whether this kind of cycles could be actually realized physically - say as flux tubes at icosahedron and tetrahedron, which play key role in TGD inspired biology. Flux tube are actually fundamental objects in TGD Universe in all scales. For instance, final states of stars could correspond to flux tube spaghettis consisting of single volume filling flux tube (see this).

2. If the Hamiltonian cycle is something physical it could correspond to flux tube. The notion of magnetic flux tube central in TGD might allow application to ferromagnetism. TGD predicts two kinds of flux tubes: Maxwellian ones and monopole flux tubes with magnetic fields requiring no currents to generate them: they are not not allowed by Maxwell's theory.

   The preservation of the Earth's magnetic field predicted to decay rather rapidly as currents generating it dissipate supports the view that it contains monopole flux part which from biological input would correspond to endogenous magnetic field B_end, which is a fraction 2/5 about the nominal value of B_E=.5 Gauss. The presence of magnetic fields in cosmological scales is also a mystery finding a solution in terms of monopole flux tubes.

3. Monopole flux tubes must be closed. Closed non-intersecting flux tubes connecting nearest neighbors in lattice would correspond to Hamiltonian cycles. In TGD inspired biology Hamiltonian cycles associated with icosahedron and tetrahedron provide a realization of the vertebrate genetic code (see this) but it is still somewhat of mystery why the points of icosahedron and tetrahedron, which are lattices (tesselations) at sphere, would be connected by a curve. Quantum classical correspondence suggests that magnetization corresponds to flux tubes connecting magnetic dipoles as formal analogs of monopole-antimonopole pairs. Could magnetic flux tubes provide a concrete realizaon for these Hamiltonan cycles?
4. Closed monopole flux tubes seem to be unrealistic for the description of ferromagnetism, which suggests the presence of N parallel flux tubes carrying magnetization M and defining a braid connecting opposite ends of ferromagnet. The monopole fluxes could arrive as single flux along parallel space-time sheet carrying field H defined by single thick flux tube. Test particle would experience B= M+H.

The following considerations are not much more than first impressions and probably require updating.

3. TGD based view

Flux tubes are the new element of condensed matter physics predicted by TGD. Could they provide insights into ferromagnetism?

3.1 Starting from text book picture about ferromagnetism

To develop TG view about ferromagnetism it is best to start from the text book picture.

1. In the standard model of ferromagnetism one assumes the presence of field B identified as sum B= M+H of magnetization and field H equal to B outside the magnet. M is due to magnetic dipoles besides magnetic field B and the interaction of spins with H is important. B is usually regarded as the fundamental field M and and H appear as auxiliary notions and their relation to B requires a model for the system: typically H, B, and B are assumed to be linearly related.
2. The field M could be naturally assigned with a flux tube connecting the spins - perhaps at nearest neighbor lattice points. What about H? In standard model H and B are parallel for the ferromagnetic configuration. If B is assigned with the flux tube connecting the magnetic moments and B is parallel to H, this would suggest a flux tube consisting of long straight portions parallel to each other.

   In the many-sheeted space-time of TGD M and B can reside at different space-time sheets, which are parallel so that they are on top of each other in M⁴×CP₂. The decomposition to sum would have representation as a set theoretic union.

   The test particle would experience the sum of the magnetic fields associated with the two sheets. Could M and H as the return flux associated with M and superpositing with the external contribution to H correspond to these two space-time sheets so that particle would experience their sum B=M+H? If so, ferromagnetism could be seen as a direct signature of many-sheeted space-time.

3.2 Could also monopole flux tubes be important?

There is still one important aspect related to the TGD view about magnetic field which might play important role. TGD predicts two kind of flux tubes. The first kind of flux tubes could be called Maxwellian and the corresponding magnetic fields require current to generate them. There are also flux tubes having closed cross section and carrying monopole fluxes. No currents are required to generate corresponding magnetic fields. Could also these flux tubes having no current as sources be present? This would mean new physics.

1. The first thing to notice is that the interpretation of magnetization M is as a magnetic field generated by magnetic moments. The usual interpretation is that spins are analogous to magnetic moments created by currents consisting of rotating charge. Now there is no such rotating charge. Second interpretation is as magnetic moments identifiable as infinitesimal monopole pairs.
2. Could one think that the flux tubes containing sequence magnetic moments correspond to monopole flux and that closing this loop could give rise to monopole magnetic field? Ordinary Maxwellian part could be also present and have current as source. How M and H would relate to these. Could M correspond to the monopole part and H the Maxwellian part?

   Are spins necessary for the existence of a monopole flux tube? Could quantum classical correspondence require this? Could dark charged matter assigned with the monopole flux tubes correspond to the magnetic moments of say dark valence electrons with non-standard value of h so that M would be represented by monopole flux tubes classically? If the return flux represented by H is absent, flux tube must give rise to a Hamiltonian cycle. If H is present, it would be enough to have flux tubes representing N braid strands fusing to single monopole flux carrying the return flux.

   Formation of a flux loop defining Hamiltonian cycle would be a new kind of phenomenon analogous to spontaneous magnetization requiring no external field H. Spontaneous magnetization would be however something different. A trivial braid consisting of N parallel strands representing M and parallel to it locally with return flux arriving along single large flux tube carrying H would be formed in ferromagnetic transition and also in spontaneous magnetization.

3.3 Bringing in thermodynamics

One can try to make this more concrete by bringing in thermodynamics.

1. Assume that there exists single flux tube - connecting all the lattice points (magnetic moments) or possibly N flux tubes parallel to local magnetization M and giving rise to a braid like structure representing the topology of flux lines of M connecting opposite boundaries of magnet.
2. In the general case, the points of the lattice could be connected by a flux tubes connecting points, which need not be nearest neighbors. The first guess is that the magnetic interaction energy of spins at the ends of the flux tube portion connecting them decreases with the distance between spins. There sould be also magnetic energy associated with the field H at the space-time sheet carrying the return flux. Thermodynamics would bring in entropy and free energy F=E-TS would be mimimized. Entropy maximization would favor long random flux tubes and energy minimization short flux tubes.

   One expects that flux tube has free energy F increasing with flux tube length. If one does not allow self-intersections - as suggested by repulsive Coulomb interaction and Fermi statistics - the flux tube could be either Hamiltonian cycle or consist of analogs of braid strands: in the case of ferromagnetism the strands would be parallel to each other. The interacton energy would be same for all Hamiltonian cycles if determined by nearest neighbour interactions.

3. In the general case with lattice replaced by graph one expects that a large number of Hamiltonian cycles not related by rotation to each other exists so that one would have large number of states with same minimum energy. Could this somehow correspond to spin glass state allowing large number of degenerate states? The flux tube need not be closed. In ferromagnetic configuration this would be the case.
4. How would the assignment of spin direction to the lattice points affect the situation? Could the numbers N₊ and N_- of spin up and spin down electrons determine the flux tube configuration by (Gibbs) energy minimization?

3.4 Could 2-braid describe the transition to ferromagnetism?

In the work of Li et al discussed in the article, the permutations of lattice points are induced by moving the vacancy around. This picture inspired the considerations above but is too limited. In fact the work of Li et al only directed attention to Hamiltonian cycles and braids formed by the non-closed analogs.

1. TGD picture brings in mind braid-knot connection. One can replace braid assiciated with M with a knot by connecting the magnetic moments at the opposite ends of the braid by trands of a trivial braid at parallel space-time sheet. This trivial braid would carry the return flux having interpretation in terms of field H.

   The flux tubes of trivial braid could also fuse to single thicker flux tube carrying the total return flux associated with M. This would conform with the idea that H provides a description of the system in longer length scale being analogous to a smoothed out total magnetic field acting as self-consistent background.

   This stimulates a critical question. Could one assume that only H assignable to big flux tube has constant direction and magnitude and that M is represented as flux tubes connecting dipoles can in principle correspond to any permutation of atoms. For this option the spontaneous magnetization would correspond to a superposition of different configurations with same weights and would be invariant under permutations as in the argument of Li et al involving no flux tubes. This option does not look attractive.

2. What braid picture allows to say about the transition to ferromagnetism? Could the transition be realized by deforming the flux tubes associated with M and forming a non-trivial braid be induced by permutation of the lattice points taking the non-trivial braid to trivial one? This would be like opening the braid. The lattice points in the initial and final state would correspond to the ends of a dynamical evolution. The permutation would be realized as a time-like braiding with braid strands in time direction.

   Mathematically braid group corresponds to the covering group of permutation group and quantum group representations correspond to the representations of braid groups. The description of the transition could provide a new application of quantum groups.

The description as time-like braiding is not however complete since there isan additional structure involved: the flux tubes connecting the magnetic dipoles in lattice and defining a braid or even more complex configuration having flux tube connections between non-neighboring poins.

1. If there is no return flux assignable to H, M corresponds to a closed flux tube carrying monopole flux the dynamical time-like dynamcial braiding would lead to a Hamiltonian cycle in this case and the number of final state configurations would be finite, there is degeneracy. Could spin glass phase correspond to this situation?
2. In ferromagnetism final state would contain N parallel strands carrying the monopole flux assignable to M and the return flux H would arrive along parallel thick flux tube. In general configuration these strands can be braided. The transition to ferromagnetism would represent time-like braiding of an ordinary 3-D braiding of flux tube strands connecting the opposite boundaries of ferromagnetic. In the initial state braid would be non-trivial and the flux tubes of braid would not have minimal length and minimum energy. In the the final ferromagnetic state braid would be trivial with parallel flux tubes.

   Mathematically this process would correspond to what is called 2-braiding: I have proposed that 2-braidings are important in TGD inspired biology as a topological description of dynamical processes. An interesting interpretation is as a topological analog for problem solving. I have also proposed that in biosystems topological quantum computation programs are represented as this kind 2-braidings for flux tubes (see this and this.)

   Ferromagnetism would correspond to an opening of a non-trivial braid. If the return flux arrives along flux tubes this is possible smoothly only if the knot defined in this manner is trivial. To achieve opening, the 2-braiding must involve reconnections, which correspond to cutting the knot strand and reconnecting the pieces in new manner: this is how Alexander opened his knot. Fermi statistics and repulsive Coulomb interaction do not fabour this mechanism. If the return flux arrives along single flux tube, the opening could correspond to a smooth deformation without reconnections transferring the braidedness to the parallel space-time sheet, where it is "neutralized" by fusing the flux tubes to single flux tube.

See the article TGD based view about ferromagnetism or the chapter Quantum criticality and dark matter: part I.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Planning to move to Mars?: have you asked the opinion of your magnetic body?

There has been a lot of talk about the colonization of Mars. I was asked about possible problems involved. In the following I consider the question only from TGD point of view about life.

The new element of TGD based quantum biology is the notion of magnetic body carrying dark matter as phases of ordinary matter labelled by the effective value h_eff =nh₀ of Planck constant (h= 6h₀ is a good guess). MB is the boss controlling ordinary matter by using dark photons transforming to ordinary photon and vice versa. Actually one has hierarchy of values of h_eff and master slave hierarchy.

Cyclotron frequencies and generalize Josephson frequencies are in a central roles in the communications between MB and biological body relying on frequency and energy resonance if the values of h_eff are identical or only energy resonance if they are not same.

Frequencies are thus fundamental for the control level of life and the question is whether MB can adapt and change its frequency spectrum. Also Schumann frequency is known to be important for life and in Mars its scae 2 times that in Earth. These problems might make already the travel to Mars dangerous to say nothing about living there.

1. Cyclotron frequencies and Schumann frequencies

On basis of findings done already at seventies about unexpected effects of ELF em fields on vertebrate brain, EEG resonances seem correspond to cyclotron frequencies in endogeneous magnetic field of B_end=.2 Gauss which is 2/5 of the nominal value B_E=.5 Gauss of Earth's magnetic field. A possible interpretation is that B_end corresponds to field strength for the monopole flux part of B_E. It is stable against dissipation since no current is needed to create it unlike ordinary Maxwellian magnetic field. This explains why B_E has not decayed away long time ago by the decay of the current creating it.

Cyclotron frequencies are in a key role in TGD based quantum biology. The value spectrum of h_eff determining bio-photon energies is in central role: dark photon energies are given by E=h_eff×f.

The cyclotron energy spectrum in Earth would be in bio-photon range (visible and UV) and same for all charged particles - there is no dependence on mass of charged particle since one has hbar_eff= hbar_gr= GMm/v₀ at gravitational flux tubes. hbar_gr= GMm/v₀ is gravitational Planck constant fundamental introduced first by Nottale. v₀ is velocity parameter with value about v₀/c= 2^-11 in the case of Sun. It might relate to the parameters of the system but could be also almost universal parameter (it is near electron proton mass ratio).

The cyclotron energy spectrum in Earth would be in bio-photon range and same for all charged partcles - there is no dependence on mass since one has hbar_eff= hbar_gr= GMm/v₀ at what I call gravitational flux tubes. This would make possible the control of molecular transitions by transforming dark photons to visible and UV photons first. MB could control molecular transitions and act as "boss". Quite generally, the layers of MB with different values of h_eff would form a master slave hierarchy with ordinary biomatter at bottom.

Schumann resonances correspond to resonance frequencies for the radiation fields of Earth. In the approximation that the conductivity of the medium is infinite, the wavelengths depend on the radius R_E of Earth only. Lowest wavelength corresponds in good approximation to lambda= 2πR_E. Lowest Schumann frequency has nominal value 7.8 Hz. These frequencies are in EEG range.

Remark: I remember having read in some source that 10 Hz frequency corresponding to alpha band in brain is needed in space and is produced artificially. I could not find the original source.

2. Coupling between Schumann frequencies and cyclotron frequencies

1. Schumann frequencies are is in the range of EEG frequencies, which strongly suggests resonant coupling with the cyclotron transitions corresponding to frequencies near to Schumann frequencies.
2. For instance, the cyclotron frequency 7.5 Hz for K⁺ ions is near to the nominal value 7.8 Hz of the lowest Schumann frequency. K⁺ currents through K⁺ channels cell membrane are known to be important for what happens in anesthesia and when organism falls asleep and thus for consciousness.

   What happens when organism falls asleep is of course not quite clear. The membrane voltage increases and nerve pulse generation becomes improbable. Metabolism continues and this means consciousness in TG framework but not sensory and motor consciousness. Could the apparent loss of consciousness mean fusion of self with higher level self representing the collecting consciousness of magnetic Mother Gaia? Could it be that during sleep we could form a larger collective consciousness representing "human condition" (see this) .

3. Irradiaton by frequency around 7 Hz is also necessary in the experiments of HIV Nobelist Montagnier involve remote DNA replication (see this) and this) .
4. Irradiation by Schumann frequency around 60 Hz appears leads to healing of cancer cell population in lab (see this) .
5. Also higher Schumann resonances could represent resonant coupling between Mother Gaia and brains of vertebrates allowing realization of levels of collective consciousness. Coherent collective gene expression in various scales (organ, organism, group, population,...) is one of the possible testable implication.

3. Possible problems related to different values of magnetic fields in Earth and Mars

The first problem relates to the magnetic field of Mars. Martian magnetic field has been believed to be weak but the recent findings suggests that it might be present and order of magnitude as in Earth (see this) .

1. TGD based view about life requires B_end which could be monopole part of B_E. Flux tubes can carry monopole flux or not - the latter option is realized in the case of ordinary Maxwellian magnetic field. Monopole flux would be biologically important and it would be in Earth 2/5 of total flux. It could be of course different in Mars. Different value of B_end in Mars could lead to severe difficulties since cyclotron frequencies are in a key role in TGD based quantum biology.
2. Also the value spectrum of hbar_gr= GMm/v₀ determining biophoton energies is in central role: one has for energies E=h_eff×f. In Mars the mass parameter M and velocity parameter v₀ in h_gr could be different and this could have fatal consequences for bio-control by the magnetic body of earthly biosystems.
   1. In the case of Earth M seems to correspond to the mass of "inner inner core" of Earth. If M is same for Mars (planets would be like atoms having varying number of identical "shells"), then it would be enough to have same value B/v₀ to keep the spectrum same. The value of B is under control by varying the flux tube thickness and this control mechanism would be used in terrestial biology.
   2. The optimistic guess is that v₀ has universal spectrum and the value is same in Mars and Earth. A not necessarily good guess is that the velocity v₀ scales like the rotation frequency of planet. Here we would have good luck! The Martian day has essentially the same length as day in Earth. The value of v₀ would be same! In this case hbar_gr could be the same! Sounds too optimistic!
   3. One can imagine also second option. The strength of monopole flux magnetic field B_end =.2 Gauss at flux tubes is free parameter and magnetic bodies could vary its value by varying thickness of flux tubes: this would be a basic biological control mechanism for instance in water and allow water to develop antennas sensitive to the cyclotron frequencies of invader molecules and detect them: this would be water memory and basis of the immune system.

   4. Problems related to different Schumann frequencies

   Schumann frequency scale in Mars is roughly twice that in Earth since radius is about 2 times smaller: around 15.6 Hz instead of 7.8 Hz for lowest Schumann frequency. Schumann frequency is known to be important for us although this is not well-understood. This might cause severe problems.

   The scaling of Schumann frequencies by 2 might cause bad complications but we do not really understand their effect even in Earth.

   We of course do not have thorough knowledge about B in Mars. There are auroras but earlier it was believed that magnetic field in large scales is very small.The latest findings suggest in TGD framework that there is monopole flux tube part of order B_end (see this).

   One can consider a possible solution to Schumann frequency doubling problem. Scale also the cyclotron frequencies by factor 2!

   1. At Earth the lowest Schumann frequency 7.8 Hz corresponds to cyclotron frequency 7.5 Hz of K⁺ ion quite well and this might make possible resonant coupling between Mother Gaia and magnetic bodies of living system. If the B_end=.2 Gauss is scaled by factor 2 in Mars to about .4 Gauss, cyclotron frequency scale doubles and one would have 15 Hz cyclotron frequency for K⁺ not far from Schumann.
   2. Could human MB scale up the cyclotron frequencies by factor 2? Note that TGD based model for Cambrian explosion (see this) predicts that Schumann frequency doubled in geologically short time scale (extremely long from human perspective). The lifeforms that would have bursted from underground oceans to the surface survived this transition. One could test what happens if artificially produced counterpart of Schumann frequency is doubled in artificial conditions using Faraday cage.

   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.

Schumann resonances and consciousness

The role of Schumann resonances for consciousness is highly interesting in TGD framework, where the notion of magnetic body (MB) carrying dark matter as h_eff=n*h₀ phases is in key role. MB would control biological body by dark photons - probably at cyclotron frequencies - and receive information as dark generalized Josephson radiation from cell membrane with the modulation of membrane potential inducing frequency modulation coding for the sensory data (see this ) .

On basis of findings done already at seventies about unexpected effects of ELF em fields on vertebrate brain, EEG resonances seem correspond to cyclotron frequencies in endogeneous magnetic field of B_end=.2 Gauss which is 2/5 of the nominal value B_E=.5 Gauss of Earth's magnetic field. A possible interpretation is that B_end corresponds to field strength for the monopole flux part of B_E. It is stable against dissipation since no current is needed to create it unlike ordinary Maxwellian magnetic field. This explains why B_E has not decayed away long time ago by the decay of the current creating it.

Cyclotron frequencies are in a key role in TGD based quantum biology. The value spectrum of h_eff determining bio-photon energies is in central role: dark photon energies are given by E=h_eff*f. The cyclotron energy spectrum in Earth would be in bio-photon range (visible and UV) and same for all charged particles - no dependence on mass since one has hbar_eff= hbar_gr= GMm/v₀ at what I call gravitational flux tubes. This would make possible for MB to control molecular transitions and act as "boss". Quite generally, the layers of MB with different values of h_eff would form a master slave hierarchy with ordinary biomatter at bottom.

1. Schumann frequencies are is in the range of EEG frequencies, which strongly suggests resonant coupling with the cyclotron transitions corresponding to frequencies near to Schumann frequencies.
2. For instance, the cyclotron frequency 7.5 Hz for K⁺ ions is near to the nominal value 7.8 Hz of the lowest Schumann frequency. K⁺ currents through K⁺ channels cell membrane are known to be important for what happens in anesthesia and when organism falls asleep and thus for consciousness.

   What happens when organism falls asleep is of course not quite clear. The membrane voltage increases and nerve pulse generation becomes improbable. Metabolism continues and this means consciousness in TG framework but not sensory and motor consciousness. Could the apparent loss of consciousness mean fusion of self with higher level self representing the collecting consciousness of magnetic Mother Gaia? Could it be that during sleep we could form a larger collective consciousness representing "human condition" (see this) .

3. Irradiaton by frequency around 7 Hz is also necessary in the experiments of HIV Nobelist Montagnier involve remote DNA replication. See (see this and this) .
4. Irradiation by Schumann frequency around 60 Hz appears leads to healing of cancer cell population in lab (see this) .
5. Also higher Schumann resonances could represent resonant coupling between Mother Gaia and brains of vertebrates allowing realization of levels of collective consciousness. Coherent collective gene expression in various scales (organ, organism, group, population,...) is one of the possible testable implications.

   For a summary of earlier postings see Latest progress in TGD.

   Articles and other material related to TGD.

Has Pluto experienced a period of fast expansion?

The surprise of this morning was that Pluto seems to have experienced a rapid expansion and might have had underground oceans.

Actually not a surprise if one lives in TGD Universe. TGD predicts that all astrophysical objects, including planets, might have experienced this kind of periods. In general relativity these periods would correspond smooth cosmological expansion of this objects: the absence this smooth expansion is indeed an enigma - astrophysical objects co-move with expanion in large scale but do not expand themselves. Earth would have experienced this expansion during Cambrian explosion.

The underground oceans would make possible evolution of life without problems from cosmic rays and meteorites and radioactivity (for instance) could provide the metabolic energy.

This would solve Fermi's paradox: most planets could be carriers of intraplanetary invisible-to-outsider life waiting the next fast expansion and burst to the surface of the planet.

See http://tgdtheory.fi/public_html/articles/expearth.pdf .

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.