Does the quantal gravitational force vanish below critical radius in average sense?

Nottale's gravitational constant hbar_gr= GM_Dm/v₀ contains dark mass M_D as a parameter. At the surface of Earth M_D much smaller than M_D and for the planets  one has M_D=M_Sun. It turns out that in the  average sense  M_D must grow to M.   This is  required by  the condition that  Bohr radii correspond to the classical radii in the average sense. The actual dependence of M_D on r  is expected to  be a staircase like function.

At the quantum level, this   effectively eliminates  the average  gravitational force in the scales below the critical radius r_cr above  which M_D=M is true.   Indeed, due to the average M_D∝ r dependence,  gravitational potential would be constant on the average. 

 Could one regard this   effective elimination of  the gravitational force as a kind of    Quantum Equivalence Principle or   as an analog of asymptotic freedom?

See the article Two alternative generalizations of Nottale's hypothesis or the chapter About the Nottale's formula for h_gr and the relation between Planck length and CP₂ length.

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

Articles and other material related to TGD.

The idea of Connes about inherent time evolution of certain algebraic structures from TGD point of view

Alan Connes has proposed that certain mathematical structures known as hyperfinite factors contain in their structure inherent time evolution.This time evolution is determined only modulo unitary automorphism analogous to a time evolution determined by Hamiltonian so that this time evolution seems to be too general for the purposes of a physicist.

Zero energy ontology of TGD combined with adelic physics leads to a vision that the sequences of state function reductions implies a mathematical evolution in the sense that the extensions of rationals characterizing the space-time region increases gradually. This induces the increase of algebraic complexity implying time evolution as the analog of biological evolution.

The dimension of extension corresponds to an effective Planck constant assumed to label dark matter as phases of ordinary matter. Therefore quantum coherence lengths increase in this evolution.

This generalization of the idea of Connes is discussed in the framework provided by the recent view about TGD. In particular, the inclusion hierarchies of hyper-finite factors, the extension hierarchies of rationals, and fractal inclusion hierarchies of subalgebras of supersymplectic algebra isomorphic with the entire algebra are proposed to be more or less one and the same thing in TGD framework.

See the article The idea of Connes about inherent time evolution of certain algebraic structures from TGD point of view.

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

Articles and other material related to TGD.

Pomeron and Odderon as direct support for the notion of color magnetic body

The following comments were inspired by a popular article"> telling about the empirical support for a particle christened Odderon. As the name tells, Odderon is not well-understood in QCD framework.

Odderon is a cousin of Pomeron which emerged already about half century ago in the so called Regge theory to explain the logarithmically rising (rather than decreasing) cross sections in proton-proton and proton-antiproton collisions. Pomeron is part of low energy phenomenology and perturbative QCD cannot say much about it. Since the charge parity is C=1 for Pomeron C=-1 for Odderon, these states are analogous to pion with spin 0 and ρ meson with spin 1.

Pomeron and Odderon have not been in the interests of the frontier of theoretical physics: they represent for an M-theorist a totally uninteresting and primitive low energy phenomenology - as all that we used to call physics before the first superstring revolution -, and does not therefore deserve the attention of an ambitious superstring theorist more interested in the marvels of brane words, landscape, swampland, and multiverse.

I have written about Pomeron for years ago. The following is something different since the view about low energy strong interactions according to TGD (see this) has developed considerably (see for instance this and this)

One can go first to Wikipedia to learn about Pomeron.

1. Pomeron exchange in the t-channel was postulated to explain the slowly (logarithmically) rising scattering cross sections in proton-proton and proton-antiproton collisions. For quarks and gluons the scattering cross sections fall down rather rapidly with energy (by dimensional argument like inverse 1/s of cm energy squared) so that something else would be in question.
2. The cross sections did not depend on the charges of the colliding baryons. The usual shower of Cerenkov radiation was missing from Pomeron exchange events. The absence of pions usually present was interpreted as absence of color charge and therefore. This suggests that quarks and gluons do not participate the Pomeron events. There is often also a large rapidity gap in which no outgoing particles are observed.
3. In the Regge theory which later was concretized in terms of the hadronic string model. Pomeron would correspond to a Regge trajectory for which the Reggeon would have quantum numbers of vacuum except for mass and angular momentum. Regge trajectory would satisfy the formula M²= M₀² =α(s) J, M mass, J angular momentum. Odderon would be Pomeron like state with an odd charge parity C=-1 instead of C=1.
4. In the QCD picture Pomeron and Odderon are assumed to be associated with the gluonic exchanges. Pomeron would be a many-gluon state.

In the many-sheeted space-time of TGD, hadrons are many-sheeted objects.

1. There is a hadronic space-time sheet and quark and gluon space-time sheets are glued to this. There is a magnetic body (MB) of hadron having a layered structure. In particular, there are em/color/weak MBs consisting of flux tubes and "tentacles", which are U-shaped flux tubes.

   Low energy hadron physics would be described in terms of reconnections of these tentacles. This is a rather new element in the picture. In a reasonable approximation, flux tubes are strings and the reconnection of closed strings appears as a basic reaction vertex for closed strings. This gives a connection with the hadronic string model. TGD indeed emerged as a generalization of the hadronic string model 43 years ago (and also as a solution of the energy problem of GRT).

2. Most of the energy of hadron is assumed to be carried by color MB: quarks and gluons carry only a small part of energy. In QCD space-time dynamics is not present and the analog of hadron as space-time surfaces would be a gluon condensate of some kind.
3. Low energy hadron reactions would consist of reconnections of the U-shaped flux tubes of the colliding color MBs. Besides this there are also the collisions of quarks and gluons having approximate description in terms of QCD. The already mentioned connection with hadronic string model suggests a connection with Regge and string model descriptions of Pomeron/Odderon.
4. Hadrons have U-shaped flux tubes acting like tentacles and reconnect to form a bridge of two flux tubes between colliding hadrons. This topological interaction mechanism would be universal and occur in all scales. In biology the ability of reacting biomolecules to magically find each other in the dense molecular soup would rely on this mechanism. It would be also a mechanism of high Tc - and biological superconductivity.

Could this explain the basic properties of the Pomeron?

1. Charge independence and absence of pion emission assignable to quark-gluon reactions can be understood. Gluons and quarks of colliding hadrons would not meet each other at all. The two colliding hadrons would just touch each other with their "tentacles" which would transfer some momentum between them in elastic collisions. This would explain the rapidity gap.
2. What about the slow dependence on collision energy? Why the cross section describing the probability of the formation of reconnection would not depend on collision energy?
   1. One could visualize the cross section in cm frame geometrically as the area of a 2-D surface cylinder parallel to the line connecting the colliding particles. The area of this cylinder would tell the probability for the formations of reconnection. If I try to touch some object in darkness, its area tells how probable the success is.
   2. In elastic scattering the t-channel momentum exchange would be orthogonal to this cylinder and have vanishing energy component. It would not change in Lorentz boosts increasing the cm collision energy. If the contribution to the cross section depends only on t, it would be independent of collision energy.

The TGD view about this finding is described in the article Some unexpected findings in hadron and nuclear physics from TGD point of view and in a chapter with the same title.

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

Articles and other material related to TGD.

MeshCODE theory from TGD point of view

Benjamin Goult has made an interesting proposal in an article The Mechanical Basis of Memory the MeshCODE Theory published in Frontiers of Molecular Neuroscience (see this).

The proposal is that the cell - or at least synaptic contacts - realize mechanical computation in terms of adhesive structures consisting of hundreds of proteins known as talins, which act as force sensors. Talins are connected to integrins in the extracellular matrix, to each other, and to the actins in the cell interior. This proposal has far reaching consequences for understanding formation of memomies as behaviors at the synaptic level.

This proposal does not conform with the TGD vision but inspires a series of questions leading to a rather detailed general vision for how magnetic body (MB) receives sensory input from biological body (BB) coded into dark 3N-photons a representing genes with N codons and as a response activates corresponding genes, RNA or proteins as a reaction. Sensory input and the response to it would be coded by the same dark genes.

See the article MeshCODE theory from TGD point of view or the chapter An Overall View about Models of Genetic Code and Bio-harmony.

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

Articles and other material related to TGD. 


Zero energy states as scattering amplitudes and subjective time evolution as sequence of SSFRs

Zero energy states code for the ordinary time evolution in the QFT sense described by the S-matrix. Construction of zero energy is reasonably well understood (see this, this, and this ).

This is not yet the whole story. One should also understand the subjective time evolution defined by a sequence of "small" state function reductions (SSFRs) as analogs of "weak" measurements followed now and then by BSFRs. How does the subjective time evolution fit with the QFT picture in which single particle zero energy states are planewaves associated with a fixed CD?

1. The size of CD increases at least in statistical sense during the sequence of SSFRs. This increase cannot correspond to M⁴ time translation in the sense of QFTs. Single unitary step followed by SSFR can be identified asa scaling of CD leaving the passive boundary of the CD invariant. One can assume a formation of an intermediate state which is quantum superposition over different size scales of CD: SSFR means localization selecting single size for CD. The subjective time evolution would correspond to a sequence of scalings of CD.
2. The view about subjective time evolution conforms with the picture of string models in which the Lorentz invariant scaling generator L₀ takes the role of Hamiltonian identifiable in terms of mass squared operator allowing to overcome the problems with Poincare invariance. This view about subjective time evolution also conforms with super-symplectic and Kac-Moody symmetries of TGD.

   One could perhaps say that the Minkowski time T as distance between the tips of CDs corresponds to exponentiated scaling: T= exp(L₀t). If t has constant ticks, the ticks of T increase exponentially.

The precise dynamics of the unitary time evolutions preceding SSFRs has remained open.

1. The intuitive picture that the scalings of CDs gradually reveal the entire 4-surface determined by polynomial P in M⁸: the roots of P as "very special moments in the life of self" would correspond to the values of time coordinate for which SSFRs occur as one new root emerges. These moments as roots of the polynomialdefining the space-time surface would correspond to scalings of the size of both half-cones for which the space-time surfaces are mirror images. Only the upper half-cone would be dynamical in the sense that mental images as sub-CDs appear at "geometric now" and drift to the geometric future.
2. The scaling for the size of CD does not affect the momenta associated with fermions at the points of cognitive representation in X⁴⊂ M⁸ so that the scaling is not a genuine scaling of M⁴ coordinates which does not commute with momenta. Also the fact that L₀ for super symplectic representations corresponds to mass squared operator means that it commutes with Poincare algebra so that M⁴ scaling cannot be in question.
3. The Hamiltonian defining the time evolution preceding SSFR could correspond to an exponentiation of the sum of the generators L₀ for super-symplectic and super-Kac Moody representations and the parameter t in exponential corresponds to the scaling of CD assignable to the replaced of root r_n with root r_n+1 as value of M⁴ linear time (or energy in M⁸). L₀ has a natural representation at light cone boundaries of CD as scalings of light-like radial coordinate.
4. Does the unitary evolution create a superposition over all over all scalings of CD and does SSFR measure the scale parameter and select just a single CD?

   Ordoes the time evolution correspond to scaling? Is it perhaps determined by the increase of CD from the size determinedby the root r_n as "geometric now" to the root r_n+1 so that one would have a complete analogy with Hamiltonian evolution? The scaling would be the ratio r_n+1/r_n which is an algebraic number.

   Hamiltonian time evolution is certainly the simplest option and predicts a fixed arrow of time during SSFR sequence. L₀ identifiable essentially as a mass squared operator acts like conjugate for the logarithm of the logarithm of light-cone proper time for a given half-cone.

   One can assume that L₀ as the sum of generators associated with upper and lower half-cones if the fixed state at the lower half-cone is eigenstate of L₀ not affect in time evolution by SSFRs.

How does this picture relate to p-adic thermodynamics in which thermodynamics is determined by partition function which would in real sector be regarded as a vacuum expectation value of an exponential exp(iL₀t) of a Hamiltonian for imaginary time t=iβ β=1/T defined by temperature? Here L₀ is proportional to mass squared operator.

1. In p-adic thermodynamics temperature T is dimensionless parameter and β=1/T is integer valued. The partition function as exponential exp(-H/T) is replaced with p^{β L₀)}, β=n, which has the desired behavior if L₀ has integer spectrum. The exponential form e^L₀/T_R), β_R= nlog(p) equivalent in the real sector does not make sense p-adically since the p-adic exponential function has p-adic norm 1 if it exists p-adically.
2. The time evolution operator exp(-iL₀t) for SSFRs (t would be the scaling parameter) makes sense for the extensions of p-adic numbers if the phase factors for eigenstates are roots of unity belonging to the extension. t= 2π k/n since L₀ has integer spectrum. SSFRs would define a clock. The scalingexp(t)= exp(2π k/n) is however not consistent with the scaling by r_n-1/r_n.

   Both the temperature and scaling parameter for time evolution by SSFRs would be quantized by number theoretical universality. p-Adic thermodynamics could have its origins in the subjective time evolution by SSFRs.

3. In the standard thermodynamics it is possible to unify temperature and time by introducing a complex time variable \tau = t+iβ, where β=1/T is inverse temperature. For the space-time surface in complexified M⁸, M⁴ time is complex and the real projection defines the 4-surface mapped to H. Could thermodynamics correspond to the imaginary part of the time coordinate?

   Could one unify thermodynamics and quantum theory as I have indeed proposed: this proposal states that quantum TGD can be seen as a "complex square root" of thermodynamics. The exponentials U=exp(\tau L₀/2) would define this complex square root and thermo-dynamical partition function would be given by UU^†= exp(-β L₀).

See the article Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂?.

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

Articles and other material related to TGD.

Still some questions about M8-H duality

There are still on questions about M⁸-H duality to be answered.

1. The map p^k→ m^k= ℏ_effp^k/p² defining M⁸-H duality is consistent with Uncertainty Principle but this is not quite enough. Momenta in M⁸ should correspond to plane waves in H.

   Should one demand that the momentum eigenstate as a point of cognitive representation associated with X⁴⊂ M⁸ carrying quark number should correspond to a plane wave with momentum at the level of H=M⁴× CP₂? This does not make sense since X⁴⊂ CD contains a large number of momentaassignable to fundamental fermions and one does not know which of them to select.

2. One can however weaken the condition by assigning to CD a 4-momentum, call it P. Could one identify P as
   1. the total momentum assignable to either half-cone of CD
   2. or the sum of the total momenta assignable to the half-cones?

The first option does not seem to be realistic. The problem with the latter option is that the sum of total momenta is assumed to vanish in ZEO. One would have automatically zero momentum planewave. What goes wrong?

1. Momentum conservation for a single CD is an ad hoc assumption in conflict with Uncertainty Principle, and does not follow from Poincare invariance. However, the sum of momenta vanishes for non-vanishing planewave when defined in the entire M⁴ as in QFT, not for planewaves inside finite CDs. Number theoretic discretization allows vanishing in finite volumes but this involves finite measurement resolution.
2. Zero energy states represent scattering amplitudes and at the limit of infinite size for the large CD zero energy state is proportional to momentum conserving delta function just as S-matrix elements are in QFT. If the planewave is restricted within a large CD defining the measurement volume of observer, four-momentum is conserved in resolution defined by the large CD in accordance with Uncertainty Principle.
3. Note that the momenta of fundamental fermions inside half-cones of CD in H should be determined at the level of H by the state of a super-symplectic representation as a sum of the momenta of fundamental fermions assignable to discrete images of momenta in X⁴⊂ H.

M⁸-H-duality as a generalized Fourier transform

This picture provides an interpretation for M⁸-H duality as a generalization of Fourier transform.

1. The map would be essentially Fourier transform mapping momenta of zero energy as points of X⁴⊂ CD⊂ M⁸ to plane waves in H with position interpreted as position of CD in H. CD and the superposition of space-time surfaces inside it would generalize the ordinary Fourier transform . A wave function localized to a point would be replaced with a superposition of space-time surfaces inside the CDhaving interpretation as a perceptive field of a conscious entity.
2. M⁸-H duality would realize momentum-position duality of wave mechanics. In QFT this duality is lost since space-time coordinates become parameters and quantum fields replace position and momentum as fundamental observables. Momentum-position duality would have much deeper content than believed since its realization in TGD would bring number theory to physics.

How to describe interactions of CDs?

Any quantum coherent system corresponds to a CD. How can one describe the interactions of CDs? The overlap of CDs is a natural candidate for the interaction region.

1. CD represents the perceptive field of a conscious entity and CDs form a kind of conscious atlas for M⁸ and H. CDs can have CDs within CDs and CDs can also intersect. CDs can have shared sub-CDs identifiable as shared mental images.
2. The intuitive guess is that the interactions occur only when the CDs intersect. A milder assumption is that interactions are observed only when CDs intersect.
3. How to describe the interactions between overlapping CDs? The fact thequark fields are induced from second quantized spinor fields in in H resp. M⁸ solves this problem. At the level of H, the propagators between the points of space-time surfaces belonging to different CDs are well defined and the systems associated with overlapping CDs have well-defined quark interactions in the intersection region. At the level of M⁸ the momenta as discrete quark carrying points in the intersection of CDs can interact.

Zero energy states as scattering amplitudes and subjective time evolution as sequence of SSFRs

This is not yet the whole story. Zero energy states code for the ordinary time evolution in the QFT sense described by the S-matrix. What about subjective time evolution defined by a sequence of "small" state function reductions (SSFRs) as analogs of "weak" measurements followed now and then by BSFRs? How does the subjective time evolution fit with the QFT picture in which single particle zero energy states are planewaves associated with a fixed CD.

1. The size of CD increases at least in statistical sense during the sequence of SSFRs. This increase cannot correspond to M⁴ time translation in the sense of QFTs. Single unitary step followed by SSFR can be identified asa scaling of CD leaving the passive boundary of the CD invariant. One can assume a formation of an intermediate state which is quantum superposition over different size scales of CD: SSFR means localization selecting single size for CD. The subjective time evolution would correspond to a sequence of scalings.

   The crucial point is that scalings commute with Poincare symmetries. Subjective and Poincare time evolutions commute.

2. The view about subjective time evolution conforms with the picture of string models in which the Lorentz invariant scaling generator L₀ takes the role of Hamiltonian identifiable in terms of mass squared operator allowing to overcome the problems with Poincare invariance. This view about subjective time evolution also conforms with super-symplectic and Kac-Moody symmetries of TGD.

   One could perhaps say that the Minkowski time T as distance between the tips of CDs corresponds to exponentiated scaling: T= exp(L₀t). If t has constant ticks, the ticks of T increase exponentially.

See the article Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂?.

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

Articles and other material related to TGD.

Three unexpected findings in hadron and nuclear physics from TGD point of view

During the same week I learned about 3 unexpected findings related to hadron- and nuclear physics. This inspired 3 articles and a chapter to one of the books about TGD.

The asymmetry of antimatter in proton

The recent experiments of Dove et al (see this and this) confirm that the antiquark sea is asymmmetric in the sense that the ratio anti-d/anti-u is larger than unity. A model assuming that proton is part of time in a state consisting of neutron and virtual pion seems to fit at qualitative level into the picture.

The TGD based model relies on the already existing picture developed by taking seriously the so called X boson as 17.5 MeV particle and the empirical evidence for scaled down variants of pion predicted by TGD. Virtual mesons are replaced with real on mass shell mesons but with p-adically scaled down mass, and low energy strong interactions at the hadronic and nuclear level are described topologically in terms of reconnections of flux tubes.

See the article a The asymmetry of antimatter in proton from TGD point of view.

The strange decays of heavy nuclei

That final state nuclei from the fission of heavy nuclei possess a rather high spin has been known since the discovery of nuclear fission 80 years ago but has remained poorly understood. The recent surprising findings by Wilson et al (see this) was that the final state angular momenta for the final state nuclei are uncorrelated and must therefore emerge after the decays.

The TGD proposal is that the generation of angular momentum is a kind of self-organization process. Zero energy ontology (ZEO) and h_eff hierarchy indeed predicts self-organization in all scales. Self-organization involves energy feed needed to increase h_eff/h₀= n serving as a measure for algebraic complexity and as a kind of universal IQ in the number theoretical vision about cognition based on adelic physics.

The final state nuclei have angular momenta 6-7 hbar. This suggests that self-organization increases the values of h_eff to nh, n∈ {6,7}. Quantization of angular momentum with new unit of spin would force the generation of large spins. Zero energy ontology (ZEO) provides a new element to the description of self-organization and a model for quantum tunnelling phenomenon.

See the article The decays of heavy nuclei as support for nuclear string model .

The strange findings of Eric Reiner challenging basic quantum measurement theory

Eric Reiter (see this) has studied the behavior of gamma-rays emitted by heavy nuclei going through a beam splitter splitting the photon beam to two beams. Quantum theory predicts that only one detector fires. Therefore the pulses in the two detectors occur at different times. This has been verified for photons of visible light. The experiment studied the same situation for gamma-rays and the surprise was that one observes mostly half pulses in both detectors and in some cases also full pulses. Reiner has made analogous experiments also with alpha particles with the same conclusion. Also these findings pose a challenge for TGD.

See the article TGD based intepretations for the strange findings of Eric Reiner.

The TGD view about these 3 findings is described in the article Three unexpected findings in hadron and nuclear physics from TGD point of view or in the chapter with the same title.

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

Articles and other material related to TGD.

TGD based interpretation for the strange findings of Eric Reiter

I learned of rather interesting findings  claimed by Eric Reiter hosting  a public group " A serious challenge to quantum mechanics" (see this). There is a published article (see this) about  the behavior of gamma-rays emitted by heavy nuclei going through two detectors in tandem.

Quantum theory predicts that only one detector fires. It is however found that both detectors fire with the  same  pulse height and firings are causally related. The pulse height  depends on wavelength and distance between the source and detector and also on  the chemistry of the source, which does not conform with the assumption that nuclear physics and chemistry decouple from each other.    Reiter has made analogous experiments also with alpha particles with the same conclusion. These findings pose a challenge for TGD, and in this article a TGD based model for the findings is developed. 

See the article TGD based intepretations for the strange findings of Eric Reiter.

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

Articles and other material related to TGD. 


Support for the quantization of Planck constant from the decays of heavy nuclei

That final state nuclei from the fission of heavy nuclei possess a rather high spin has been known since the discovery of nuclear fission 80 years ago but has remained poorly understood.

The recent surprising finding published in Nature article "Angular momentum generation in nuclear fission" (see this) was that the final state angular momenta for the final state nuclei are uncorrelated and must therefore emerge after the decays. This represents a challenge for TGD inspired model of nuclei as nuclear strings, and one ends up to a rather detailed model for what happens in the fissions.

The TGD proposal is that the generation of angular momentum is a kind of self-organization process. Zero energy ontology (ZEO) and h_eff hierarchy indeed predicts self-organization in all scales. Self-organization involves energy feed needed to increase h_eff/h₀= n serving as a measure for algebraic complexity and as a kind of universal IQ in the number theoretical vision about cognition based on adelic physics.

The observation that the final state nuclei have angular momenta 6-7 hbar suggests that self-organization increase the values of h_eff to nh, n∈ {6,7}. Quantization of angular momentum with new unit of spin forces the generation of large spins. Also zero energy ontology (ZEO) is involved: ZEO provides a new element to the description of self-organization and a model for quantum tunnelling phenomenon.

See the article The decays of heavy nuclei as support for nuclear string model .

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

Articles and other material related to TGD.

TGD based explanation for the asymmetry between anti-u and anti-d sea quarks in proton

I encountered in FB a highly interesting popular article "Decades-Long Experiment Finds Strange Mix of Antimatter in The Heart of Every Proton" (see this).

The popular article tells about the article "The asymmetry of antimatter in the proton" of Dove et al published in Nature (see this). This article is behind the paywall but the same issue of Nature has an additional article "Antimatter in the proton is more down than up" (see this) explaining the finding.

What is found is an asymmetry for u and antiquarks in the sense that there are slightly more d-type antiquarks (anti-d) than u type antiquarks (anti-u) in quark sea. This asymmetry does not seem to depend on the longitudinal momentum fraction of the antiquark: the ratio of anti-down and anti-up distribution functions is smaller than one and constant.

A model assuming that proton is part of time in a state consisting of neutron and virtual pion seems to fit at qualitative level into the picture. Unfortunately, the old-fashioned strong interaction theory based on nuclei and pions does not converge by the quite too large value of proton pion coupling constant.

I looked at the situation in more detail and developed a simple TGD based model based on the already existing picture developed by taking seriously the so called X boson as 17.5 MeV particle and the empirical evidence for scaled down variants of pion predicted by TGD (see this). What TGD can give is the replacement of virtual mesons with real on mass shell mesons but with p-adically scaled down mass and a concrete topologicaldescription of strong interactions at the hadronic and nuclear level in terms of reconnections of flux tubes.

1. Basic data about quark and nucleon masses

To get a quantitative grasp about the situation, one can first see what is known about masses of u and d quarks.

1. One estimate for u and d quark masses (one must taken the proposals very cautiously) can be found here.

   The mass ranges are for u 1.7-3.3 MeV and and for d 4.1-5.8 MeV.

2. In the first approximation n-p mass difference 1.3 MeV would be just d-u mass difference varying in the range 1.2 MeV-4.1 MeV and has correct sign and correct order of magnitude. 4.1 MeV for d and 3.3 MeV for u would produce the n-p mass difference correctly.
3. Coulomb interactions give a contribution which is vanishing for p and and negative for neutron

   E_c(n) =-α× ℏ/3R_e,

   R_e is proton's electromagnetic scale.

   This contribution reduces neutron mass. If R_em is taken to be proton Compton radius this gives about E_c≈ - 3.2 MeV. This would predict mass n-p difference in the range -1.1-0.9 MeV. This favors maximal n-p mass difference 4.1 MeV and m(u)= 1.7 MeV and md =5.8 MeV: d-u mass difference would be 4.1 MeV roughly 4 times electron mass.

2. TGD based picture about hadronic an nuclear interactions

Consider first the TGD inspired topological model for hadronic an nuclear interactions.

1. The notion of magnetic body (MB) assignable to color and em and electroweak interactions is essential. Interactions are described by virtual particle exchanges in quantum field framework. In TGD they are described by reconnections of U-shaped flux tubes which are like tentacles.

   In interaction these tentacles reconnect and give rise to a pair of flux tubes connecting the particles. The flux tubes would carry monopole flux so that single flux tube cannot be split. These flux tube pairs serve also as correlates of entanglement replacing wormholes as their correlates in ER-EPR picture.

   This picture looks rather biological and was developed first as a model of bio-catalysis. The picture should apply quite generally to short range interactions at least.

2. The U-shaped flux tubes of color MB replace virtual pion and and rho meson exchanges in the old fashioned picture about strong interactions. They represent in TGD framework real particles but with p-adically scaled down mass. For instance, pions are predicted to have scaled down variants with masses different by a negative power of 2 from pion mass. Same is true for rho. Now the masses would be below MeV range, which is the energy scale of nuclear strong interactions.

   Also nuclear strong interactions would occur in this manner. The fact that flux tubes have much longer length than nuclear size would explain the mysterious finding that in nuclear decay the fragments manage to generate their angular momenta after the reaction: the flux tubes would make possible the exchange of angular momentum required by angular momentum conservation.

3. A model for the anti-quark asymmetry

Consider now a model anti-quark asymmetry for sea quarks.

1. Quarks and antiquarks would appear at these flux tubes. The natural first guess is meson like states are in question.

   The generation of u-anti-d type pion or rho would transform proton to neutron if the valence u transforms to valence d and W boson with scaled down mass.

   Note that the scaling down would make weak interaction stronger since weak boson exchange amplitude is proportional to 1/m_W²).

   This would give the analog of neuron plus charge virtual pion. Taking two sea quarks would lead to trouble with the too large Coulomb interaction energy about -10 MeV of negatively charged sea with positively charged valence part of proton if the sea is of the same size as proton.

2. Does the scaled down W decay to u-anti-d forming a scaled down meson? Or should one regard u-anti-d as a scaled down W having also the spin zero state analogous to pion since it is massive?
3. Here comes a connection with old-fashioned and long ago forgotten hadron physics. Thepartially conserved axial current hypothesis (PCAC) gives a connection between strong and weak interactions forgotten when QCD emerged as the final theory. PCAC says that the divergence of axial weak currents associated with weak bosons are proportional to pions.

   Are the two pictures more or less equivalent? Virtual pion exchange could be regarded as a weak interaction! Also conserved vector current hypothesis (CVC) is part of this picture. This is not new: I have developed this picture earlier in an attempt to understand what the reported X boson with 17.5 MeV mass is in the TGD framework. Scaled down pion would be in question (see this).

4. What about masses? Since the flux loop would have considerably greater size than proton, the mass scale of udbar state would be smaller than say MeV, and the contribution to mass of proton would be small.
5. Why the asymmetry for anti-quarks of sea? The generation u-anti-d loop would increase the charge of the core region by two 2 units and transform it to Δ. This looksneither plausible nor probable. Proton would be a superposition consisting mostly of the proton of good old QCD and neutron plus flux loop with quantum numbers of a scaled down pion.
6. Also the presence of scaled down ρ meson loops can be considered. Their presence would turn the spin of the core part of the proton opposite for some fraction of time. One can wonder whether this could relate to the spin puzzle of proton.

For the TGD based model of X boson see the article "X boson as evidence for nuclear string model".

See the article a The asymmetry of antimatter in proton from TGD point of view.

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

Articles and other material related to TGD.

Is analysis as a cognitive process analogous to particle reaction?

The latest work with number theoretical aspects of M⁸-H duality (see this) was related to the question whether it allows and in fact implies Fourier analysis in number theoretical universal manner at the level of H= M⁴× CP₂.

The problem is that at the level of M⁸ analogous to momentum space polynomials define the space-time surfaces and number theoretically periodic functions are not a natural or even possible basis. At the level of H the space-time surfaces can be regarded orbits of 3-surfaces representing particles and are dynamical so that Fourier analysis is natural.

That this is the case, is suggested by the fact that M⁸-H duality maps normal spaces of space-time surface to points of CP₂. Normal space is essentially the velocity space for surface deformations normal to the surface, which define the dynamical degrees of freedom by general coordinate invariance. Therefore dynamics enters to the picture. It turns out that the conjecture finds support.

Consider now the topic of this posting. Number theoretic vision about TGD is forced by the need to to describe the correlates of cognition. It is not totally surprising that these considerations lead to new insights related to the notion of cognitive measurement involving a cascade of measurements in the group algebra of Galois group as a possible model for analysis as a cognitive process (see this, this and this).

1. The dimension n of the extension of rationals as the degree of the polynomial P=P_n1∘ P_n2∘ ... is the product of degrees of degrees n_i: n=∏_in_i and one has a hierarchy of Galois groups G_i associated with P_ni∘.... G_i+1 is a normal subgroup of G_i so that the coset space H_i=G_i/G_i+1 is a group of order n_i. The groups H_i are simple and do not have this kind of decomposition: simple finite groups appearing as building bricks of finite groups are classified. Simple groups are primes for finite groups.
2. The wave function in group algebra L(G) of Galois group G of P has a representation as an entangled state in the product of simple group algebras L(H_i). Since the Galois groups act on the space-time surfaces in M⁸ they do so also in H. One obtains wave functions in the space of space-time surfaces. G has decomposition to a product (not Cartesian in general) of simple groups. In the same manner, L(G) has a representation of entangled states assignable to L(H_i) (see this and this).

This picture leads to a model of cognitive processes as cascades of "small state function reductions" (SSFRs) analogous to "weak" measurements.

1. Cognitive measurement would reduce the entanglement between L(H₁) and L(H₂), the between L(H₂) and L(H₃) and so on. The outcome would be an unentangled product of wave functions in L(H_i) in the product L(H₁)× L(H₂)× .... This cascade of cognitive measurements has an interpretation as a quantum correlate for analysis as factorization of a Galois group to its prime factors defined by simple Galois groups. Similar interpretation applies in M⁴ degrees of freedom.
2. This decomposition could correspond to a replacement of P with a product ∏_i P_i of polynomials with degrees n= n₁n₂..., which is irreducible and defines a union of separate surfaces without any correlations. This process is very much analogous to analysis.
3. The analysis cannot occur for simple Galois groups associated with extensions having no decomposition to simpler extensions. They could be regarded as correlates for irreducible primal ideas. In Eastern philosophies the notion of state empty of thoughts could correspond to these cognitive states in which SSFRs cannot occur.
4. An analogous process should make sense also in the gravitational sector and would mean the splitting of K=n_A appearing as a factor n_gr=Kp to prime factors so that the sizes of CDs involved with the resulting structure would be reduced. Note that ep(1/K) is the root of e defining the trascdental infinite-D extension rationals which has finite dimension Kp for p-adic number field Q_p. This process would reduce to a simultaneous measurement cascade in hyperbolic and trigonometric Abelian extensions. The IR cutoffs having interpretation as coherence lengths would decrease in the process as expected. Nature would be performing ordinary prime factorization in the gravitational degrees of freedom.

This cognitive process would also have a geometric description.

1. For the algebraic EQs, the geometric description would be as a decay of n-sheeted 4-surface with respect to M⁴ to a union of n_i-sheeted 4-surfaces by SSFRs. This would take place for flux tubes mediating all kinds of interactions.

   In gravitational degrees of freedom, that is for trascendental EQs, the states with n_gr=Kp having bundles of Kp flux tubes would deca to flux tubes bundles of n_gr,i=K_ip, where K_i is a prime dividing K. The quantity log(K) would be conserved in the process and is analogous to the corresponding conserved quantity in arithmetic quantum field theories and relates to the notion of infinite prime inspired by TGD \citeallbvisionc.

2. This picture leads to ask whether one could speak of cognitive analogs of particle reactions representing interactions of "thought bubbles" i.e. space-time surfaces as correlates of cognition. The incoming and outgoing states would correspond to a Cartesian product of simple subgroups: G=∏^×_i H_i. In this composition the order of factors does not matter and the situation is analogous to a many particle system without interactions. The non-commutativity in general case leads to ask whether quantum groups might provide a natural description of the situation.

See the article Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂? or the chapter Breakthrough in understanding of M⁸-H duality.

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

Articles and other material related to TGD. 


Is M8-H duality consistent with Fourier analysis at the level of M4× CP2?

Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂? M⁸-H duality predicts that space-time surfaces as algebraic surfaces in complexified M⁸ (complexified octonions) determined by polynomials can be mapped to H=M⁴× CP₂.

The proposal (see this) is that the strong form of M⁸-H duality in M⁴ degrees of freedom is realized by the inversion map p^k∈ M⁴→ ℏ_eff×p^k/p². This conforms with the Uncertainty Principle. However, the polynomials do not involve periodic functions typically associated with the minimal space-time surfaces in H. Since M⁸ is analogous to momentum space, the periodicity is not needed.

In contrast to this, the representation of the space-time surfaces in H obey dynamics and the H-images of X⁴⊂ M⁸ should involve periodic functions and Fourier analysis for CP₂ coordinates as functions of M⁴ coordinates.

Neper number, and therefore trigonometric and exponential functions are p-adically very special. In particular, e^p is a p-adic number so that roots of e define finite-D extensions of p-adic numbers. As a consequence, Fourier analysis extended to allow exponential functions required in the case of Minkowskian signatures is a number theoretically universal concept making sense also for p-adic number fields.

The map of the tangent space of the space-time surface X⁴⊂ M⁸ to CP₂ involves the analog velocity missing at the level of M⁸ and brings in the dynamics of minimal surfaces. Therefore the expectation is that the expansion of CP₂ coordinates as exponential and trigonometric functions of M⁴ coordinates emerges naturally.

The possible physical interpretation of this picture is considered. The proposal is that the dimension of extension of rationals (EQ) resp. the dimension of the transcendental extension defined by roots of Neper number correspond to relatively small values of h_eff assignable to gauge interactions resp. to very large value of gravitational Planck constant ℏ_gr originally introduced by Nottale.

Also the connections with the quantum model for cognitive processes as cascades of cognitive measurements in the group algebra of Galois group (see this and this) and its counterpart for the transcendental extension defined by the root of e are considered. The geometrical picture suggests the interpretation of cognitive process as an analog of particle reaction emerges.

See the article Is M⁸-H duality consistent with Fourier analysis at the level of M⁴× CP₂? or the chapter Breakthrough in understanding of M⁸-H duality.

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

Articles and other material related to TGD.

Can one regard leptons as effectively local 3-quark composites?

The idea about leptons as local composites of 3 quarks (see this) is strongly suggested by the mathematical structure of TGD. Later it was realized that it is enough that leptons look like local composites  in scales longer than CP₂ scale defining the scale of the partonic 2-surface assignable to the particle.   

The proposal has profound consequences. One might say that SUSY  in the TGD sense has been   below our nose  for more than a century. The proposal could also solve matter-antimatter asymmetry since the twistor-lift of TGD predicts the analog of Kähler structure for Minkowski space and a small CP breaking,  which could make possible   a cosmological evolution in which quarks prefer to form baryons and antiquarks to form leptons. 

The basic objection is that the leptonic analog of Δ might emerge. One must explain why this state is at least experimentally absent and also develop a detailed model. In the article Can one regard leptons as effectively local 3-quark composites?  the construction of leptons as effectively local 3 quark states allowing effective description in terms of the   modes of leptonic spinor field in H=M⁴× CP₂ having H-chirality opposite to quark spinors is discussed in detail.

See the article Can one regard leptons as effectively local 3-quark composites? and the chapter The Recent View about SUSY in TGD Universe.

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

Articles and other material related to TGD. 


Quantum asymmetry between space and time

I received a link to a popular article about a test the proposal of Joan Vaccaro that if time reversal symmetry T were exact, our Universe would be radically different (thanks for Reza Rastmanesh and Gary Ehlenberg) For instance, wave functions would be wave packets in 4-D sense and conservation laws would be lost. Breaking of T would however come in rescue and give rise to the world in which we live. This proposal does not make sense in standard quantum theory but JV proposes a modification of path integral for single particle wave mechanism leading to the result.

I found that I could not understand anything about the popular article. I however found the article "Quantum asymmetry between space and time" by Joan Vaccaro. I tried to get grasp about the formula jungle of the article but became only confused. I expected clear logical arguments but I found none.

My comments are based mostly on the abstract of the article.

Asymmetry between time and space

[JV] An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental, is represented by equations of motion and conservation laws that operate differently over time and space.

My comments:

1. One might argue like JV does if one does not keep in mind that Lorentz invariance allows to distinguish between timelike and space-like directions and base the notion of causality on their properties.

   In Euclidian geometry there would be no such special choice of time coordinate. But also now field equations would define slicing of space-time to 3-D slices since initial values at them would fix the time solution. Now however the slices could be chosen in very manner manners - for instance 3-spheres rather than hyperplanes as in Minkowski space.

2. JV argues that there is an asymmetry in the quantum description of space and time in conventional quantum theory. The spatial coordinates of particle are treated as operators but time is not represented as an operator.

   The first mis-understanding is that the position of operator of particle is not space-time coordinate but specifies position of point-like particle in space time.

   The second mis-understanding is to think that the configuration space of the particle would be 4-D space-time. The configuration space of particle in non-relativistic wave mechanics is 3-space and time is the evolution parameter for unitary time evolution, not space-time coordinate. In the relativistic picture it could correspond to proper time along a world line.

   In quantum field theory (QFT) the spatial and temporal coordinates are in completely symmetric position. Wave mechanics is an approximation in which one considers only singlenon-relativistic particle. One should start from QFT or some more advanced to see whether the idea makes sense.

3. JV identifies subjective and geometric time as practically all colleagues do. In geometric time time evolution is determined by field equations and conservation laws. In TGD zero energy ontology (ZEO) does not identify these times and resolves the problems caused by identification of these two times. The counterpart of time evolution with respect to subjective time is sequence of small state function reductions.
4. The asymmetry between the two time directions appears in two manners.
   1. There is the thermo-dynamical arrow of time usually assumed to be the same always. In TGD both arrows are possible and the arrow changes in "big" (ordinary) state function reduction (BSFR). Subjective time correlates with geometric time but is not identical with it is closely related to the thermo-dynamical breaking of time reversal.
   2. The field equations (geometric time) have slightly broken time reflection symmetry T. This breaking is quite different from the generation of the thermo-dynamical arrow of time.

Could we give up the conservation laws and unitary time evolution and could the breaking of time reversal symmetry bring them back?

[JV] If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time.

In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrdinger equation) and conservation laws apply. This suggests that the timespace asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution.

My comments:

1. JV is ready to give up symmetries and conservation laws altogether in the new definition of path integral but of course brings them implicitly in by choice of Hamiltonian and by using the basic concepts like momentum and energy which are lost if one does not have Poincare symmetry.

   What remains is an attempt to repair the horrible damage done. The hope is that the tiny breaking of T invariance would be capable of this feat.

2. Author uses a lot of formulas to show that T breaking can save the world. There are however ad hoc assumptions such as coarse graining and assumptions about the difference between Hamiltonian and time reversed Hamiltonian argued to lead to the basic formulas of standard quantum theory.

   The proposed formulas are based on single particle wave mechanics and do not generalize to the level of QFT. If one is really ready to throw away the basic conservation laws and therefore corresponding symmetries also the basic starting point formulas become non-sensible.

   Holistic mathematical thinking would help enormously the recent day theoretical physicists but it is given the label "philosophical" having the same emotional effect as "homeopathic" to the average colleague. What my colleague called formula disease has been the basic problem of theoretical physics for more than half century.

3. This modification of path integral formula looks rather implausible to me.
   1. Giving up the arrow of time in the sum over paths formalism breaks the interpretation as a representation for Hamiltonian time evolution (path integral is mathematically actually not well-defined and is meant to represent just Schroedinger equation).

      If there were no asymmetry between time and space, quantum states would be wave packets in 4-D sense rather in 3-D sense. This is of course complete nonsense and in conflict with conservation laws: an entire galaxy could appear from nothing and disappear. Author notices this but does not seem to worry about consequences. By the way, in TGD inspired theory of consciousnessthe mental image of the galaxy can do this but this does not mean the disappearance of the galaxy!

      The use of the wave mechanics which is not Lorentz invariant, hides the loss of Lorentz invariance implied by the formalism whereas ordinary Schrödinger equation as non-relativistic approximation of Dirac equation does not break Lorentz invariance in non-relativistic approximation.

   2. It is optimistically assumed that the tiny breaking of T symmetry could change the situation completely so that the predictions of the standard quantum theory would emerge. Somehow the extremely small breaking of T would bring back arrow of time and save conservation laws and unitary time evolution and we could be confident that our galaxy exists also to-morrow.

      Why the contributions to modified path integral for which time arrow is not fixed would magically interfere to zero by a tiny breaking of T invariance?

      The proposal seems to be in conflict with elementary particle physics. The view is that neutral kaon is a superposition of a state and its T mirror image and this means tiny T breaking. Neutrinos also break T symmetry slightly. In this framework all other particles would represent complete T breaking. Usually the interpretation is just the opposite. This does not make sense to me.

   3. The test for proposal would be based on the idea that neutrino from nuclear reaction defined flux diminishing as 1/r², r the distance from the reactor. This should somehow cause an effect on clocks proportional to 1/r² due to the incomplete destructive interference of the contributions breaking the ordinary picture. I do not understand the details for how this was thought to take place.

      The small T violation of neutrinos would affect the maximal T violation in environment and somehow affect the local physics and be visible as a modification of clock time - maybe by modification of the Hamiltonian modelling the clock. This is really confusing since just the small T violation is assumed to induce the selection of the arrow of time meaning maximal T violation!

To sum up, I am confused.

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

Articles and other material related to TGD.

A test for the quantum character of gravity as a test for quantum TGD

The following represents comments to a popular article describing a proposed experiment possibly conforming the quantum character of gravity. Thanks for the link to Gary Ehlenberg.

The proposal in idealized form is following.

1. One has two diamonds which are originally in superposition of two opposite spin directions.
2. One applies magnetic field with gradient. We know that in external magnetic field which is not constant, particle with spin is deflected to a direction which is opposite for opposite sping directions. If one has a superposition of spins then one would obtain superposition of deflected spin states with different spatial positions. The diamond can be said to be at two positions simultaneously. This is the key effect and leads to the question about whether and how it could be described in general relativity.

Consider now the situation in various approaches to quantum gravity.

1. The situation is problematic from the point of view of classical GRT since the gravitational fields created by the different spin components of superposition would have different distribution of mass. Classical GRT space-time determined by Einstein's equations would not be unique. In order to avoidthis one could argue that state function reduction (SFR) occurs immediatelyso that the spin is well-defined and space-time is unique. This looks very ugly but to my surprise Dyson takes this possibility seriously.
2. In quantum gravity based on GRTview it seems that one should allow superposition of space-times or at least of 3-spaces. The superposition of 3-geometries would conform with Wheelerian superspace view but leads to the problems with time and conservationlaws quite generally. Wheeler's superspace did not work mathematically.
3. In the description in terms of quantum gravitons one would give up the GRT picture altogether and string model view is something akin to this. Unfortunately, the attemptsto formulate quantum gravitation as a field theory in empty Minkowski space using Einstein's action fail. The divergences are horrible and renormalization is not possible. String models in turn try to get space-time by spontaneous compactification but this led to the landscape misery.

TGD based picture avoids the problems of these approaches.

1. In zero energy ontology (ZEO) the quantum states are superpositions of space-time surfaces : not superpositions of general 4-geometries making even not sense in standard QM or of 3-surfaces as they would be in generalization of Wheeler's superspace approach. The space-time surfaces would be preferred extremals of the action defining the theory and one obtains holography from general coordinate invariance: 3-surface determines space-time surface just as the point of Bohr orbit defines the Bohr orbit.
2. In this picture superposition of states with position of particle depending on spin direction corresponds to superposition of different space-time surfaces. Also the entanglement between various components of the state involving two spin superposed states of the two diamonds involved, is possible and generated in the time evolution. Entanglementwould have as a correlate magnetic flux tubes connecting the diamonds. One would have superposition of space-time surfaces corresponding to different flux tube lengths connecting spin states at various positions. Thereisno reason to expect that entanglement would not be generated. The expected positive outcome of the experiment could be seen as a proof of not only quantum character of gravitations but evidences for the superposition of space-time surfaces and ZEO.
3. Diamonds are rather large objects and the small value of Planck constant is the trouble in the standard approach. It might be possible to overcome this problem in TGD. TGD predicts that dark matter corresponds to phases of ordinary matter with arbitrarily large values of h_eff at MB glux tubes would have macroscopic quantum coherence in the scale of flux tube and could induce coherence of ordinary matter (diamonds) at their end as controllers of the ordinary matter. This would not be quantum coherence but would make visible the quantum coherence at the level of MB.

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

Articles and other material related to TGD. 


Oumuamua and TGD

The strange object known as Oumuamua (briefly O in the sequel) has gained a lot of attention. I have not had time to seriously check why O is so strange that Harward's top astronomer Avi Loeb regards it as evidence for alien life. Now I decided to do this and read a popular article describing the basic features of O. Wikipedia contains a more technical article about O.

O indeed has several strange features.

1. O had no tail as comets have: the tail is due to evaporation caused by the solar radiation. Artistic vision about O is as a long cylinder looking like rock. This vision is misleading since what was actually seen was a point-like object.
2. The reflectivity was highly varying and could be more than 10 times higher than for an average comet. From this it was deduced that O must have a shape of a cigar or a thin pancake. The spinning motion of O would be a tumbling characteristic for a rotor which rotates around a non-principal axis. This motion could explain the variations in reflectivity witha period of 7 hours.
3. O experiences a non-gravitational acceleration near Sun driving O away from Sun. Solar radiation pressure has been proposed as a reason. This would however suggest that solar light evaporates part of O:s mass and this causes a formation of a tail. No tail was observed.

   Could O have used an analog of a solar sail? The surface of the solar sail could have absorbed or perhaps even reflected the solar radiation and provided the momentum as a recoil to O. If the solar sail had a suitable shape, it perhaps prevented the radiation from reaching O itself and the formation of tail by evaporation. This shield mechanism would be somewhat similar to how the Earth's magnetic field shields life at the surface of Earth from the effects of cosmic rays and solar wind.

In the TGD framework the natural question is whether the magnetic body (MB) of O - having much larger size than O itself - could have served as a highly effective solar sail. Did the solar photons from the Sun give their energy and momentum to the MB of O? Did MB absorbthe photons and transform them to dark photons providing their energy for dark Bose-Einstein condensate of ions at the MB of O making it a primitive intelligent life form? Did solar light push MB away from the Sun and did O follow it?

A connection with the rotating magnet system studied by Godin and Roschin is suggestive. This system had strange features.

1. The system was accompanied by thin cylindrical magnetic walls in the direction of rotation axis.
2. As the rotation frequency approached 10 Hz (alpha frequency), the rotation started to accelerate and the system's effective weight either increased or decreased depending on the direction of rotation.
3. Also the air around the system was ionized and was cooled by a few degrees. This is not in accordance with thermodynamics.

In the TGD based model (see this) the system is regarded as a primitive life form.

1. The magnetic walls would correspond to the magnetic body (MB) of the system containing dark ions in TGD sense, in particular iron ions having very high value of h_eff=nh₀ and defining giving rise to cyclotron Bose-Einstein condensate to which the energy of the motor driving the system would have been stored. MB would have gained part of the energy feeded by the motor as analog of metabolic energy.
2. Eventually the system made a macroscopic state function reduction ("big" state function reduction (BSFR)). In TGD based theory of consciousness BSFR means what might be called death and reincarnation with an opposite arrow of time - this in a completely universal sense.
3. The time reversed dissipation by transformation of dark photons to ordinary photons looked for outsiders with the standard arrow of time like absorbing energy from the environment and causing the cooling. The energy and momentum of the photons would have caused effective loss of weight and accelerated rotation.

Could O be an analogous system? Elongated cigar shape would favor MB consisting of thin magnetic walls forming an ideal solar sail gathering the energy and momentum of solar photons by transforming them to dark photons of BE condensate. MB would have shielded O just like it shields life forms at Earth so that it O have avoided evaporation.

Is O a product of an advanced engineering or a primitive life form? It might be that the latter option is correct. As astronomer Avi Loeb suggests the interstellar space might be teeming these entities. If so, primitive life would populate the interstellar space.

See the article Time reversal and the anomalies of rotating magnetic systems or the chapter About Strange Effects Related to Rotating Magnetic Systems .

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

Articles and other material related to TGD.

How could the higher levels of MB use the brain to realize their free will?

The model proposed why predictions of events known to occur are better than those believed to be fictive (see this) assumes that the experienced long terms goals (in the recent case the goal of experimenter to perform the experiment) correspond to state function reductions (SFRs) that have already (with respect to subjective time) occurred at some higher layer of MB controlling the brain but that this subjective time corresponds to geometric time in the future of the participants and experimeters.

Neuroscience supports the view that frontal lobes are responsible for long term planning and decision making. They are involved also with the self model. This suggests that the highest layers of MB control frontal lobes. There would be a hierarchy of layers of MB having frontal lobes at the bottom.

Model for the coupling of MB with frontal lobes in terms of cognitive entanglement

A natural assumption is that the control of biological body by MB involves entanglement. Since frontal lobes are associated with high level cognition, this entanglement could be cognitive entanglement discussed in (see this). Cognitive entanglement is a hierarchical entanglemen between wave functions in hierarchy of sub-groups in the factorization of Galois group to a product G₁G₂...G_n of sub-groups reflecting directly the representation of extension as extension of extensions of .... of rationals.

What is special is that entanglement is directed like attention and hierarchical just like for the slaving hierarchy. The entanglement between states in group algebras of G₁ and G₂...G_n is directed from boss G₁ to slave G₂..G_n. Cognitive SFRs are cascades proceeding downwards and reducing entanglement. Negentropy Maximization Principle can however prevent the cognitive measurement cascade from proceeding down to G_n (see this) if it does not give rise to negentropy gain.

Long term goals could involve this kind of cognitive entanglement assignable to directed attention and motor actions as BSFRs at this layer of MB would produce what is experienced by the levels of the hierarchy with the standard arrow of time as a behavior with long termgoals. This would produce what could be regarded as analog of precognition (see this and identifiable as sensory perception of signals propagating to non-standard direction of time. Precognitive dreams would be an example of this.

What happens when frontal lobes are damaged?

This vision conforms with what happens when frontal lobes are damaged. Although intellectual abilities are not lost, long term planning is not possible and the patient loses the ability to initiate actions. Damage can also lead to idiot savant phenomenon. Although the person seems to lack conceptual thinking completely, he/she can possess miraculous looking mathematical skills (see this) or artistic gifts (see this). In some poorly understood sense idiot savants can be extremely intelligent.

Is the character of the cognitive entanglement changed or replaced with something totally different in these situations? TGD predicts two kinds of information related to two different representations of genetic code which relate to each other like function represented by its local values to its Fourier transform as a non-local and holistic representation (see this and this). The local representation of the genetic code is in terms of bits and using sequences of genetic codons as units of 6 bits. The second representation is in terms of 3-chords of light defining the allowed chords of a bio-harmony. Music expresses and induces emotions and bio-harmony would characterize a mood. Emotional intelligence would relate to this representation. Could it be that for idiot savants non-verbal emotional intelligence dominates.

The duality of these two representations of genetic code is highly analogous to the duality of momenta and position coordinates in wave mechanics. In quantum TGD this duality has as an analog M⁸-H duality (see this and this ) stating that space-time surfaces can be regarded as 4-surfaces in H=M⁴× CP₂ or in M⁸. M⁸-H duality relates these representations. H corresponds to ordinary differential geometric space-time representation involving also the notion of field. M⁸ identifiable as 8-D momentum space corresponds to non-local algebraic and number theoretic representation, which is non-local and holistic since the momenta are analogous to frequencies. Scattering amplitudes in particle physics provide an example of this representation.

Both representations can be used and it depends on the situation which representation is more appropriate. Could it be that for ordinary resp. emotional intelligence H resp. M⁸ representation is more appropriate? Could one exaggerate and say that not only idiot savants but also people in timeless meditative state and experiencing no separations (produced by cognitive SFRs), and maybe also children "live" in M⁸ whereas the ordinary people with their tight time schedules and busily performing comparisons "live" in H? Momentum eigenstates are delocalized.

Are meditative states labelled by finite simple groups?

What could be the counterpart of meditative state without cognition be at the level of cognitive representations? Could it correspond to a situation in which it is not possible to create separations as decompositions to unentangled system pairs by reducing the entanglement between the factors of the Galois group G?

This is certainly the case if G is simple, that is does not allow this factorization at all. Simple finite groups are the basic building bricks of finite groups: the classification theory for simple groups (see this) states that simple finite groups is cyclic and of prime order, alternating group consisting of even permutations of n objects, group of Lie type or one of the 26 sporadic groups or Tits group. The meditative states of pure consciousness would correspond to finite simple groups!

A question about possible classification of meditative states definitely raises eyebrows. But the power of mathematics is miraculous: if one agrees that thinking means SFRs (thought generates separations and comparisons) and that in meditative states thinking ceases, this is the conclusion.

Rather paradoxically, the "idiot savant state" would be cognitively irreducible in the same sense as the states of Hilbert space with prime dimension do not allow a representation as entangled states. They would represent elementary particles of cognition - fundamental ideas - from which more complexthoughts are composed by performing repeated extensions. The basic advice of meditative practices is to stop thinking: maybe this is indeed the manner to achieve the state of understanding.

See the article Why the outcome of an event would be more predictable if it is known to occur? (with Reza Rastmanesh) or the chapter About the nature of time.

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

Articles and other material related to TGD.

Why the outcome of an event would be more predictable if it is known to occur?

The experiments of Armor and Sackett demonstrate that the reliability of future predictions for events is better for real than for hypothetical events. This strange finding, if real, would be an anomaly analogous to Libet's findings about active aspects of consciousness challenging the notion of free will.

In this article it is argued that it is difficult to explain the finding in the physicalistic framework, and that the allowance of free will seems only to worsen the situation since precognition of acts of free will does not make sense. In the framework of Topological Geometrodynamics (TGD) zero energy ontology (ZEO) replaces the standard ontology of quantum theory. ZEO predicts that in "big" (ordinary) state function reductions (BSFRs) the arrow of time changes and that the identification of acts of free will identified as BSFRS is not in conflict with the determinism of classical physics as an exact part of quantum TGD. Also Libet's findings can be understood.

This suggests a model for the anomaly. The experiment would have already happened as BSFR ("already" is with respect to subjective time to be distinguished from geometric time) for a quantum system associated with the experimenters and participants. The knowledge that the event is actual inspires unconsciously the attempt to "remember" the personal performance in the experiment instead of only imagining it and this would explain the improved future predictions.

See the article Why the outcome of an event would be more predictable if it is known to occur? (with Reza Rastmanesh) or the chapter About the nature of time.

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

Articles and other material related to TGD. 


Time reversal and the anomalies of rotating magnetic systems

Free energy phenomena can be  defined as phenomena exhibiting   thermo-dynamical anomalies such as generation of gradients  rather than their disappearance. Concentration gradients can develop, electric fields as potential gradients can emerge  due to generation of  charge separations,   and  temperature gradients can be created.  The failure of  the second law in its standard form   also  manifests  itself as over-unity energy production,  cooling of the environment, and generation of structures rather than their decay characterizing self-organization.  

  The  general explanation of  these phenomena   would rely on the  change of the arrow of time in  ordinary ("big") state function reduction (BSFR) reversing the arrow of time  in the quantum measurement theory based on zero energy ontology (ZEO). This implies a new view about self-organization and also an explanation for self-organized (quantum) criticality.  BSFR would take place at the level of  the magnetic body (MB) carrying dark matter as h_eff=nh₀ phases and controlling ordinary matter, and BSFR would be macroscopic for large values of h_eff. 

In this article the anomalies in rotating magnetic systems  (RMSs)  discovered by Russian researchers Godin and Roschin are  discussed as  a particular free energy phenomenon. The time evolution of a rotating magnetic system (RMS) could be seen as an emergence  of a very simple life form receiving  and storing metabolic energy from the    motor driving the RMS, and liberating it at the moment of "death" as dark photons transformed to ordinary photons, whose counterparts in ordinary living matter are biophotons.  

See the article Time reversal and the anomalies of rotating magnetic systems or the chapter About Strange Effects Related to Rotating Magnetic Systems .

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

Articles and other material related to TGD. 


Aging from TGD point of view

The article "Aging from TGD point of view" written together with Reza Rastmanesh was inspired by the book "Lifespan" by Sinclair and LaPlante. The books proposed that aging is basically  caused by the approach to epigenetic  chaos. The book also proposesthat bio-information is not only associated with DNA and genetic code but the  conformational  degrees of DNA and these are crucial in epigenesis. This vision  serves as the starting point of   TGD (Topological Geometrodynamics) inspired view. 

Negentropy Maximization principle replacing in adelic physics second law but implying it for ordinary matter is the first key notion. Magnetic body (MB )carrying dark matter as h_eff=nh₀ phases of ordinary matter  implying quantum coherence in the scale characterized by h_eff represents the second key notion. MB is the controller of the dynamics and its quantum coherence induces the coherence  of ordinary biomatter as forced coherence rather than quantum coherence.  

 Zero energy ontology (ZEO) predicting the occurrence of time reversal in "big" (ordinary) state function reductions is the third key notion.   Time reversal forces generalization of thermodynamics and dissipation of a subsystem with a reversed arrow of time looks like self-organization from the point of view of the system. Also self-organized quantum criticality difficult to understand in ordinary thermodynamics becomes possible.

The basic idea is that at birth  the  MBs of information molecules are at very low temperature and gradually approach the  physiological temperature, which is near to Hagedorn temperature defining the maximal temperature of MB. This thermalization leads to epigenetic chaos implying that the flux tubes carrying dark DNA and therefore also  DNA become loopy. Also the control of methylation and other modifications and their reversals   crucial for epigenesis is lost. In particular, demethylation fails  and leads to hyper-methylation of the  promoter regions of genes. This leads to the failure of the control of genes coding for housekeeping  proteins and eventually the system suffers a crash down.

See the article Aging from TGD point of view or the chapter chapter with the same title.

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

Articles and other material related to TGD.