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.