Singularities and infinities from the TGD point of view

Gary Ehlenberg sent two links to Quantamagazine articles, which are very relevant (perhaps not by accident!) for what I have been working with recently.

The first link was to a very interesting article about the the role of singularities in physics. Already in twistor Grassmann approach, singularities of the scattering amplitudes turned out to be central as data determining them. Kind of holography was in question.

I have been just working with singularities of space-time surface and have made a breakthrough in the understanding of what graviton is but also in the understanding of what the fundamental vertices (actually vertex!) of the scattering amplitudes are in the TGD framework.

In holography=generalized holomorphy view space-time surfaces are minimal surfaces with generalized holomorphic imbedding to H=M⁴×CP₂ implying the minimal surface property.

1. The minimal surface property fails at lower-dimensional singularities taking the role of holographic data and the trace of the second fundamental form (SFF) analogous to a acceleration associated with the 4-D Bohr orbit of the particle as 3-surface has a delta function like singularity but vanishes elsewhere.
2. The minimal surface property expressess masslessness for both fields and particles as 3-surfaces. At the singularities masslessness property fails and singularities can be said to serve as sources which in QFTs define scattering amplitudes.
3. The singularities are analogs of poles and cuts for the 4-D generalization of the ordinary holomorphic functions. Also for the ordinary holomorphic functions the Laplace equation as analog massless field equation and expressing analyticity fails. Complex analysis generalizes to dimension 4.
4. The conditions at the singularity give a generalization of Newton's F=ma! I ended up where I started more than 50 years ago!
5. In dimension 4, and only there, there is an infinite number of exotics diff structures, which differ from ordinary ones at singularities of measure zero analogous to defects. These defects correspond naturally to the singularities. For the exotic diff structure one can say that there is no singularity. This means that complex analysis generalizes to dimension 4 and only to dimension 4.
6. Group theoretically the trace of the SFF can be regarded as a generalization of the Higgs field, which is non-vanishing only at the vertices and this is enough. Singularities take the role of generalized particle vertices and determine the scattering amplitudes. The second fundamental form contracted with the embedding space gamma matrices and slashed between the second quantized induced spinor field and its conjugate gives the universal vertex involving only fermions (bosons are bound states of fermions in TGD). It contains both gauge and gravitational contributions to the scattering amplitudes and there is a complete symmetry between gravitational and gauge interactions. Gravitational couplings come out correctly as the radius squared of CP₂ as also in the classical picture.

This generalized Higgs field characterizing singularities would dictate all scattering amplitudes! Generalized Higgs would be really the God particle! Its CP₂ part gives standard model interactions and M⁴ part gives gravitation.

Gary Ehlenberg sent another link to a Quantamagazine article (see this), which is very relevant to what I have been working on recently. I am not going to comment on the so called alien calculus discussed in the article as a proposal to get rid of the infinities of quantum field theories. Rather, I will explain how this problem is solved in the TGD framework (see https://tgdtheory.fi/public_html/articles/whatgravitons.pdf).

The problem of infinities is due to the assumption that the point-like nature of fundamental objects. In superstring models this problem was at least partially solved but superstrings were not the option chosen by Nature.

1. The basic discovery of TGD is that the generalization of complex structure is possible in dimension 4 of the space-time and corresponds to the existence of exotic diff structures (see https://tgdtheory.fi/public_html/articles/intsectform.pdf). Nature wants all that it can get and has chosen the option with the maximal structural richness.
2. In TGD particles become 3-D surfaces whose 4-D orbits are analogs of Bohr orbits with a finite non-determinism at which the minimal surface property fails. The mathematically ill-defined path integral reduces to a finite sum and only the well-defined functional integral over 3-surfaces remains. Divergences disappear completely.
3. Scattering amplitudes reduce to sums over contributions from the lower-D singularities of the minimal surfaces. Singularities are analogous to the poles of holomorphic functions in holography=holomorphy vision and generalized holomorphic maps define an infinite-D symmetry group analogous to holomorphic maps in string models.
4. The trace of the second fundamental form slashed between the induced free spinor fields of M^{42 gives the universal vertex and contains contributions of all basic interactions including gravitation. Induced spinor fields are second quantized spinor fields of H=M4×CP₂ and correlation functions for these free spinor fields determine the scattering amplitudes.}

See the article What gravitons are and could one detect them in the TGD Universe?) and the chapter the chapter About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

The symmetry between gravitational and gauge interactions

The beauty of the proposal is that implies a complete symmetry between gravitational and gauge interactions.

1. Weak interactions and gravitation couple to weak isospin and spin respectively. Color interactions couple to the isometry charges of CP₂ and gravitational interactions coupling to the isometry charges of M⁴. The extreme weakness of the gravitation can be understood as the presence of the CP₂ contribution to the induced metric in the gravitational vertices.

Does color confinement have any counterpart at the level of M⁴? The idea that physical states have vanishing four-momenta does not look attractive.

1. In ZEO, the finite-D space of causal diamonds (CDs) forms (see this) the backbone of WCW and Poincare invariance and Poincare quantum numbers can be assigned with wave functions in this space. For CD, the infinite-D unitary representations of SO(1,3) satisfying appropriate boundary conditions are a highly attractive identification for the counterparts of finite-D unitary representations associated with gauge multiplets. The basic objection against gravitation as SO(1,3) gauge theory would fail.

   One could replace the spinor fields of H with spinor fields restricted to CD with spinor fields for which M⁴ parts sinor nodes as plane waves are replaced with spinor modes in CD labelled by spin and its hyperbolic counterpart assignable to Lorentz boosts with respect to either tip of CD. One could also express these modes as superpositions of the plane wave modes defined in the entire H.

   The analog of color confinement would hold true for particles as unitary representations of SO(1,3) in CD. One could say that SO(1,3) appears as an internal isometry group of an observer's perceptive field represented by CD and Poincare group as an external symmetry group treating the observer as a physical object.

2. By separation of variables the spinor harmonics in CD factorize phases depending on the mass of the particle determined by CP₂ and spinor harmonic of hyperbolic 3-space H³=SO(1,3)/SO(3). SO(1,3) allows an extremely rich set of representations in the hyperbolic space H³ analogous to spherical harmonics. A given infinite discrete subgroup Γ⊂ SO(1,3) defines a fundamental domain of Γ as a double coset space Γ\SO(1,3)/SO(3). This fundamental domain is analogous to a lattice cell of condensed matter lattice defined by periodic boundary conditions. The graphics of Escher give an idea about these structures in the case of H². The products of wave functions defined in Γ⊂ SO(1,3) and of wave functions in Γ define a wave function basis analogous to the space states in condensed matter lattice.
3. TGD allows gravitational quantum coherence in arbitrarily long scales and I have proposed that the tessellations of H³ define the analogs of condensed matter lattices at the level of cosmology and astrophysics (see this). The unitary representations of SO(1,3) would be central for quantum gravitation at the level of gravitationally dark matter. They would closely relate to the unitary representations of the supersymplectic group of δ M⁴₊× CP₂ in M⁴ degrees of freedom and define their continuations to the entire CD.
4. There exists a completely unique tessellation known as icosa tetrahedral tessellation consisting of icosahedrons, tetrahedrons, and octahedrons glued along boundaries together. I have proposed that it gives rise to a universal realization of the genetic code of which biochemical realizations is only a particular example (see this and this). Also this supports a deep connection between biology and quantum gravitation emerging also in classical TGD (see this and this). Also electromagnetic long range classical fields are predicted to be involved with long length scale quantum coherence (see this).

The challenge is to understand the implications of this picture for M⁸-H duality (see this). The discretization of M⁸ identified as octonions O with the Minkowskian norm defined by Re(Im(o²)) is linear M⁸ coordinates natural for octonions. The discretization obtained by the requirement that the coordinates of the points of M⁸ (momenta) are algebraic integers in an algebraic extension of rationals would make sense also in p-adic number fields.

In the Robertson-Walker coordinates for the future light-cone M⁴₊ sliced by H³:s the coordinates define by mass (light-cone proper time in H), hyperbolic angle and spherical angles, the discretizations defined by the spaces Γ\SO(1,3)/SO(3) would define a discretization and one can define an infinite hierarchy of discretizations defined by the discrete subgroups of SO(1,3) with matrix elements belonging to an extension of rationals. This number theoretically universal discretization defines a natural alternative for the linear discretization. Maybe the linear resp. non-linear discretization could be assigned to the moduli space of CDs resp. CD.

See the article What gravitons are and could one detect them in the TGD Universe?) and the chapter the chapter About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe.

What modified Dirac action is and how it determines scattering amplitudes?

Holography=generalized holomorphy property means that minimal surface field equations are true outside singularities for any general coordinate invariant action constructible in terms of the induced geometry. However, the twistor lift of TGD suggests that 6-D Kähler action is the fundamental action. It reduces to 4-D Kähler action plus volume term in the dimensional reduction guaranteeing that the 6-surface can be regarded as a generalization of twistor space having space-time surface as a base-space and 2-sphere.

One can express the induced spinor field obtained as a restriction of the second quantized H spinor field to the space-time surface and it satisfies modified Dirac equation (see this).

Modified Dirac action L_D is defined for the induced spinor fields.

1. It is fixed by the condition of hermiticity stating that the canonical momentum currents appearing in it have a vanishing divergence. If the modified gamma matrices Γ^α are defined by an action S_B defining the space-time surface itself, they are indeed divergenceless by field equations. This implies a generalization of conformal symmetry to the 4-D situation (see this) and the modes of the modified Dirac equation define super-symplectic and generalized conformal charges defining the gamma matrices of WCW (see this).
2. Generalized holomorphy implies that S_B could be chosen to correspond to modified gamma matrices defined by the sum of L_K+L_V or even by L_V defining induced gamma matrices. Which option is more plausible?
3. An attractive guiding physical idea is that the singularities are not actually singularities if exotic diffeo structure is inducted. Field equations hold true but with S_K+S_V. The singularities would cancel. One would avoid problems with the conservation laws by using exotic diffeo structure.
4. At the short distance limit for which α_K is expected to diverge as a U(1) coupling, the action reduces to S_V and the defects would be absent. Only closed cosmic strings and monopole flux tubes would be present but wormhole contacts and string world sheets identifiable as defects are absent: this would be the situation in the primordial cosmology (see this). Only dark energy as classical energy of the cosmic strings and monopole flux tubes would be present and there would be no elementary particles and elementary particle scattering at this limit.

One can consider several options assuming that the singularities are not actually present for the exotic diffeo structures.

Option 1: The first option relies on the assumption that the exponential of the modified Dirac action is imaginary and analogous to the phase defined by the action in QFTs. This is enough in TGD since fermions are the only fundamental particles and bosonic action is a purely classical notion.

1. Volume action is in a very special role in that it represents both the classical dynamics of particles as 3-D surfaces as analogs of geodesic lines, the classical geometrized dynamics of massless fields, and generalizes the Laplace equations of complex analysis.

   This motivates the proposal that only induced the gamma matrices Γ^αg^αβh^k_βγ_k (no contribution from L_K) corresponding to S_V appear in L_D and the bosonic action S_B=S_K+S_V+S_I, where S_I is real, is defined by the twistor lift of TGD. The field equations are satisfied also at the singularities so that the contributions from S_K+S_I and S_V cancel each other at the singularity in accordance with the idea that an exotic diffeo structure is in question. Both S_K and S_I contributions would have an imaginary phase.

2. Therefore L_V, which involves cosmological constant Λ, disappears from the scattering amplitudes by the field equations for L_B although it is implicitly present. The number theoretic evolution of the S_K+S_I makes itself visible in the scattering vertices. Outside the singularities both terms vanish separately but at singularities this is not the case. Only lower-D singularities contribute to the scattering amplitudes.

   The number theoretical parameters of the bosonic action determined by the hierarchy of extensions of rationals would parametrize different exotic diffeo structures and make themselves visible in the quantum dynamics in this way. S_I would contribute to classical charges and its M⁴ part would contribute to the Poincare charges.

3. An objection against this proposal is that the divergence of the modified gamma matrices defined by the S_K+S_I need not be well-defined. It should be proportional to a lower-dimensional delta function located at the singularity.

   For 3-D light-like light-partonic orbits, the contravariant induced metric appearing in the trace of the second fundamental form has diverging components but it is not clear whether the trace of the second fundamental form can give rise to a 3-D delta function at this limit. Chern-Simons action at the light-like partonic orbit coming from the instanton term is well-defined and field equations should not give rise to a singularity except at partonic 2-surfaces, which have been identified as analogs of vertices at which the partonic 2-surface X² splits to two.

   At X² the trace of the second fundamental form can be well-defined and proportional to a 2-D delta function at X² since the 4-metric metric has one light-like direction at X² and has a vanishing determinant and is therefore is effectively 2-D (the light-like components of g_uv =g_vu of the 4-metric vanish). Therefore vertices would naturally correspond to partonic 2-surfaces, which split to two at the vertex. This is indeed the original proposal.

4. The divergence of g^μνh^k_ν vertex as the trace of the second fundamental form D_αh^k_β defined by the covariant derivatives of coordinate gradients, appears in the vertex. The second fundamental form is orthogonal to the space-time surface and can be written as

   g^μνD_ν∂_μh^k= P^k_lH^l , P^k_l = h^k_l- g^μνh^k_μh_lrh^r_ν ,

   H^k= g^αβ (∂_α+B^k_α)g^αβh^k_β , B^k_α= B^k_lmh^m_α .

   P^k_l projects to the normal space of the space-time surface. H^k is covariant derivative of h^k_α and B^k_α= B^k_lmh^m_α is the projection of the Riemann connection of H to the space-time surface.

5. This allows a very elegant physical interpretation. In linear Minkowski coordinates for M⁴, one has B^k_α=0 but the presence of the CP₂ contribution coming from the orthonormal projection implies that the covariant divergence is non-vanishing and proportional to the radius squared of 2. Vertex is proportional to the trace of the second fundamental form, whose CP₂ part is analogous to the Higgs field of the standard model. This field is vanishing in the interior by the minimal surface property in analogy with the generalized Equivalence Principle.

   The trace of the second fundamental form is a generalization of acceleration from 1-D case to 4-D situation so that the interaction vertices are lower-dimensional regions of the space-time surface which experience acceleration. The regions outside the vertices represent massless fields geometrically. At the singularities the Higgs-like field is non-vanishing so that there is mass present. The analog of Higgs vacuum expectation is non-vanishing only at the defects.

   It seems that a circle is closing. I started more than half a century ago from Newton's "F=ma" and now I discover it in the interaction vertex, which is the core of quantum field theories! I almost see Newton nodding and smiling and saying "What I said!".

Option 2: Modified gamma matrices are defined by S_K+S_V +iS_I and the real part of the singularity vanishes. The imaginary part cannot vanish simultaneously.

1. The exponent of Kähler function defines a real vacuum functional and K is determined by S_K+S_V whereas the action exponential of QFTs of QFTs defines a phase. In topological QFTs, the contribution of the instanton term S_D,I is naturally purely imaginary and could define "imaginary part of the Kähler function K, which does not contribute to the Kähler metric of WCW.

   One can argue that this must be the case also for S_D. Hence the contribution of S_K+S_V to S_D would be real and differ by a multiplication with i from that in QFTs whereas the contribution of iS_I would be imaginary. One must admit that this is not quite logical. Also the contribution to the Noether charges would be imaginary. This does not look physically plausible.

2. One cannot require the vanishing of both the real part and imaginary part of the divergence of the modified gamma matrices at the singularity. The contribution of L_C-S-K at the singularity would be non-vanishing and determine scattering amplitudes and imply their universality.

   For the representations of Kac-Moody algebras the coefficient of Chern-Simons action is k/4π and allows an interpretation as quantization of α_K as α_K= 1/k. Scattering vertices would be universal and determined by an almost topological field theory. Almost comes from the fact that the exponent of S_B defines the vacuum functional.

3. The real exponential exp(K) of the real Kähler function defined by S_K+S_V would be visible in the WCW vacuum functional and bring in an additional dependence on the α_K and cosmological constant Λ, whose number theoretic evolution would fix the evolution of the other coupling strengths. Note that the induced spinor connection corresponds in gauge theories to gauge potentials for which the gauge coupling is absorbed as a multiplicative factor.

There are therefore two options. For both cases 1/α_K=1/k appears in the action.

1. For Option 1 only iS_V appears in S_D and iS_K+ iS_C-S-K determines the scattering amplitudes for option 2). Exponent of the modified Dirac action defines the analog of the imaginary action exponential of QFTs.
2. For Option 2 for which the entire action defines the modified gamma matrices the iS_C-S-K defines the scattering amplitudes and one has an analog of topological QFT. This picture would conform with an old proposal that in some sense TGD is a topological quantum field theory. One can however argue that the treatment of S_K+S_V and S_I in different ways does not conform with QFT treatment and also the Noether charges are a problem.

Some technical remarks are in order.

1. The spinor connection does not disappear from the dynamics at the singularities. It is transformed to components of projected Riemann connection of H appearing in the divergence D_αTα_kC-S-K.

2. The modified Dirac action must be dimensionless so that the scaling dimension of the induced spinors should be d=-3/2 and therefore same as the scaling dimension of M⁴ spinors. This looks natural since CP₂ is compact.

   The volume term included in the definition of the induced gamma matrices must be normalized by 1/L_p⁴. L_p is a p-adic length scale and is roughly of order of a biological scale L_p≈ 10^-4 meters if the scale dependent cosmological constant Λ corresponds to the inverse squared for the horizon radius. One has 1/L_p⁴= 3Λ/8π G. This guarantees the expected rather slow coupling constant evolution induced by that of α_K diverging in short scales.

See the article What gravitons are and could one detect them in the TGD Universe?) and the chapter the chapter About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Common solution of 4 killer problems of TGD

Towards the end of the last year, I made considerable progress in understanding particle vertices (see this). The question however remained, what exactly is a graviton and what is the vertex corresponding to graviton emission.

The help came from condensed matter physics. There is evidence for a chiral graviton in systems exhibiting quantum Hall effect (see this). Chiral graviton is not a true graviton. However, the article inspired a rethinking of the problem.

The result was a beautiful picture that combined the previously identified big problems for which a common solution was already found.

1. Quantum gravity in TGD can be understood as a gauge theory where the gauge group is the Lorentz group SO(1,3). The whole point is that this group is an isometry group related to the other half of the causal diamond. The necessary infinite-dimensional unitary representations of SO(1,3), which are a disaster in standard gauge theory, have a beautiful interpretation in zero-energy ontology because SO(1,3) acts as isometries of the causal diamond. The unitary irreps of SO(1,3) take the role of the unitary representations of the Poincare group. Poincare invariance is in turn realized in the moduli space of causal diamonds (CDs) forming the backbone of the "world of classical worlds" (WCW) (see see this)).

   Here, surprisingly, a connection with Weinstein's work emerges. Weinstein's analogous attempt fails for many reasons, also because the unitary representations of SO(1,3) are infinite-dimensional and the usual measure theory does not work. I even wrote an article about this (see this). Thanks to Marko and others for directing attention to Weinstein, and to myself for taking Weinstein's stuff so seriously that SO(1,3) was bothered.

2. A spinor connection for M⁴ would induce a gauge potential of the gravitational field. Spin would take the role of gauge charge. The description of gravity and dimensional interactions would be exactly the same on a formal level. For both, the analogy of the classical energy-impulse tensor would occur at the vertices through modified gammas, and both would be gauge theories in a certain sense.

However, there are 4 problems that seem to destroy this vision, of which problems b,c,d were already solved towards the end of the last year .

1. The spinor connection can be dimensionally transformed to zero by a general coordinate transformation: no gravity at all!
2. In dimension D=4 for space-time, an infinite number of diffeo structures can be found and they differ from the normal s.e. it involves lower-dimensional defects. This is a catastrophe from the perspective of general relativity.
3. Fermion and antifermion numbers are separately conserved unless fermion pairs can be created in a vacuum. Fermion pair creation must be possible.
4. Furthermore, the modified Dirac effect which should give the vertices is exactly zero based on the Dirac equation. Could Dirac's equation break down in the defects and in this way produce the vertices looking like QFT vertices?

There is a common solution for all these four problems (see this)!

1. In Dirac's picture, the creation of a pair means that the fermion line reverses in time. This point would be exactly a defect for a standard diffeo structure when it is interpreted as an exotic for a diff structure! In that case, Dirac's equation does not apply at the defect and there is a delta function singularity that gives the vertex.
2. The creation of the pair is possible in dimension D=4 and only in dimension D=4!
3. The induced spinor connection can be converted to zero everywhere by a generalö coordinate transformation except in these diffeo-defects!! Gravitation can therefore be effectively eliminated by a general coordinate transformation, but not completely. This generalizes Einstein's elevator argument to the quantum level. This is nothing but the quantum version of the Equivalence Principle!

See the article What gravitons are and could one detect them in the TGD Universe?) and the chapter the chapter About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

What gravitons are and could one detect them in TGD Universe?

What gravitons are in the TGD framework? This question has teased me for decades. It is easy to understand gravitation at the classical level in the TGD framework but the identification of gravitons has been far from obvious. Second question is whether the new physics provided by TGD could make the detection of gravitons possible?

The stimulus, which led to the ideas related to the TGD based identification of gravitons, to be discussed in the sequel, came from condensed matter physics. There was a highly interesting popular article telling about the work of Liang et al with the title "Evidence for chiral graviton modes in fractional quantum Hall liquids" published in Nature.

The generalized Kähler structure for M⁴ ⊂ M⁴\times CP₂ leads to together with holography=generalized holomorphy hypothesis to the question whether the spinor connection of M⁴ could have interpretation as gauge potentials with spin taking the role of the gauge charge. The objection is that the induced M⁴ spinor connection has a vanishing spinor curvature. If only holomorphies preserving the generalized complex structure are allowed one cannot transform this gauge potential to zero everywhere. This argument can be strengthened by assigning the fundamental vertices with the splitting of closed string-like flux tubes representing elementary particles. The vertices would correspond to the defects of 4-D diffeo structure making possible a theory allowing a creation of fermion pairs. The induced M⁴ spinor connection could not be eliminated by a general coordinate transformation at the defects.

One could have an analog of topological field theory and the Equivalence Principle at quantum level would state that locally the M⁴ spinor connection can be transformed to zero but not globally. Gravitons and gauge bosons would be in a completely similar role as far as vertices of generalized Feynman diagrams are considered.

The second question is whether gravitons could be detected in the TGD Universe. It turns out that the FQHE type systems do not allow this but dark protons at the monopole flux tube condensates give rise to a mild optimism.

See the article What gravitons are and could one detect them in TGD Universe? or the chapter About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Neutrons form bound states with nanocrystals: how?

A very interesting observation is described in MIT News. The original article telling about the discovery can be found here. What has been found that neutrons form bound states with nanocrystals of size about 13 nm and are located outside the crystals.

In wave mechanics, the de Broglie wavelength for a neutron gives an idea of its quantum coherence scale, which should be on the order of 10 nanometers for quantum dots. The energy of the neutron must be above the thermal energy. The temperature must be at most milli Kelvin for this condition to be fulfilled.

The range of strong interactions is of order 10^-14 -10^-15 meters and extremely short as compared to the 10 nanometer scale of nanocrystals. I don't really understand how strong interactions could produce these states. Another strange feature is that neutrons are outside these quantum dots. Why not inside, if nuclear power is involved somehow?

Contrary to what the finnish popular article where I found this news first (see this) claims, neutrons interact electromagnetically. They have no charge but have a magnetic moment related to the neutron's spin so that they interact with the magnetic fields. How is this option ruled out? Is it really excluded?

In the TGD Universe, the new view of space-time implies that the magnetic fields of Maxwell's theory are replaced by magnetic flux quanta, typically flux tubes. Also monopole flux tubes are possible and explain quite a large number of anomalies related to the magnetic fields. The monopole flux tubes are actually basic objects in all scales.

Could one think that the neutrons reside at the monopole flux tubes associated with the nanocrystal? Could the neutrons be bound to the magnetic fields of the magnetic flux tubes and form cyclotron states? If so, the de Broglie wavelength would be related to the free motion in the direction of the necessarily closed monopole flux tube.

More generally, neutrons could have an effective Planck constant larger than the ordinary Planck constant and behave like dark matter. In the TGD based model of biomatter, phases of protons with very large effective Planck constant behaving like dark matter are in an essential role.

See the article TGD and condensed matter or the chapter with the same title.

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

Sleeping neurons and TGD

I learned of a very interesting finding related to cerebellar neurons associated with so-called climbing fibers and Purkinje cells. (see this). The popular article tells about the findings described in an article by N.T. Silva et al published in Nature (see this).

Climbing fibers and Purkinje cells are involved with the receival information from the external world and with the conditioning to external stimuli. Mice were studied and the external stimulus was light and produced eye blink as a response. It was possible to produce conditioning by using preceding cues. It was found that even a subtle reduction of the signalling using light-sensitive protein ChR2 made the neurons in question "zombies", which were not able to receive information from the external world.

Can one understand the zombi neurons in the TGD framework? The TGD based view of consciousness as a generalization of quantum measurement theory relies on zero energy ontology (ZEO), which solves the quantum measurement problem (see this, this and this).

1. The first prediction is a hierarchy of Planck constant, meaning the possibility of quantum coherence in arbitrarily long scales: the phases of ordinary matter with this property behave like dark matter.
2. Second prediction is that quantum physics dominates in all scales but in zero energy ontology we do not see this since quantum jumps occur between superpositions of Bohr-orbit like space-time surfaces and there is no violation of classical determinism!
3. The third prediction is that in ordinary "big" state function reductions (BSFRs) the arrow of time changes. This is analogous to death or following sleep and means reincarnation with an opposite arrow of time. Quantum tunnelling means to such states function reduction and return to the original arrow of time.

   Sleep would initiate a life with an opposite arrow of time. Life would be a universal phenomenon appearing in all scales. The most dramatic example is provided by stars and galaxies older than the universe. The evolutionary age of a galaxy living forth and back in geometric time is much longer than according to the ordinary view of time.

The zombie neurons would be sleeping! During the sleep period they would not receive information from the environment and would not learn. The dose of Chr would induce a BSFR. How?

1. TGD inspired quantum measurement theory predicts also a second kind of SFR, "small" SFR. In SSFR the state of the system changes but not much and the arrow of time is preserved. SSFRs are the TGD counterparts of repeated measurements of the same observables, which, according to the standard quantum theory (Zeno effect), have no effect on the state. In the TGD Universe, SSFRs give rise to the flow of subjective time and their sequence defines a conscious entity, which "dies" or falls asleep in BSFR.
2. SSFRs correspond to a measurement of a set of observables. The external perturbation can change this set such that it does not commute with the set measured in the previous SSFRs. This forces the occurrence of a BSFR changing the arrow of time. How this happens, requires a more detailed view of ZEO (see this and this). In the recent situation this would mean that the neuron falls asleep and does not receive sensory input from the external world.
3. This falling asleep phenomenon would be universal (see for instance (see this)and apply also to other neurons: BSFR could be induced by inhibitory neurotransmitters whereas excitatory neurotransmitters would help to wake up. A short sleep period of about 1 ms could take place also during the nerve pulse (see this).

Sleep would also have other functions than causing a sensory decoupling from the external world. Sleep is essential for healing and learning. These analogs of sleep states are encountered also at the level of biomolecules. BSFRs make it possible to learn by trial and error. When the system makes a mistake it falls asleep and wakes up after the next BSFR. We would be doing this all the time since our flow of consciousness is full of gaps. External noise males possible this learning by changing the set of observables measured in SSRS.

Interestingly, this learning mechanism has obvious parallels with how large language systems learn in presence of noise (see this, this, and this). TGD predicts the possibility of quantum coherence in arbitrarily long scales and this allows us to consider the possibility that computers are actually conscious entities when the quantum coherence time is longer than the clock period. This artificially induced noise could induce conscious learning. This could help to explain why large language systems seem to work "too well".

See the article Some new aspects of the TGD inspired model of the nerve pulse or the chapter chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Standard view of dark energy could be wrong

The basic assumption of standard cosmology is that dark energy is constant. It has turned out that this need  not be the case: there are indications that dark energy evolves with time (see this).

This is almost what TGD  predicts. In the TGD Universe, dark energy however evolves with   scale rather than with Minkowski time. Due to the extended conformal  the time evolution is replaced by scale evolution invariance at the fundamental level. This is the case also in string models (see this).  

The twistor lift of TGD predicts that the counterpart of the  dark energy in the TGD Universe is the sum of two contributions in the action whose extremals space-times of M⁴× CP²  as minimal surfaces satisfying holography  are. The contributions come from Kähler action and volume term. The coefficient of the volume term corresponds to cosmological constant Λ  depending on p-adic scale and approaches zero at infinite scale. Number theoretical physics dual of geometrized physics is needed to understand the origin of p-adic length scales. In standard physics one cannot assign scale to a physical system. In TGD this is possible and led already around 1995 to very precise predictions for elementary particle masses involving only p-adic primes characterizing the p-adic scale of the particle besides the quantum numbers of the particle.

In short scales Λ is huge  as the standard cosmology predicts but in long length scales Λgoes to zero like the inverse of the p-adic length scale squared. This solves the problem of cosmological constant and in standard cosmology one also gets rid of the predicted catastrophic  ripping of 3-space to pieces. In TGD the 3-space consists of disjoint pieces although the space-time surface  as a quantum coherence region is connected.

An  alternative way to see the length scale dependence  is in terms of decay of cosmic strings to ordinary matter as  the TGD counterpart of inflation. Cosmic strings are 4-D space-time surfaces having 2-D M⁴ projection and are critical  against thickening to monopole magnetic flux tubes. In this process their energy identified as dark energy is reduced and transformed to ordinary matter.  The reductions of string tension can take place also for the flux tubes as phase transitions and correspond to periods of accelerated expansion.

See for intance this .

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.