Saturday, April 13, 2024

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.

Tuesday, April 09, 2024

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.

Monday, April 08, 2024

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.

Sunday, April 07, 2024

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.

Friday, April 05, 2024

How to take into account the gravitational interactions in the cosmic string model of spiral galaxy?

What has been neglected in the model is the presence of gravitational force.
  1. The thickened string in the galactic plane acts with the cosmic string transversal to the galactic plane and with the matter formed by the decay of the cosmic string in the galactic plane to ordinary matter and reducing its string tension. The first guess is that this gives rise to a gravitational force, which in the first approximation is sum of the force F1=d(G M(ρ)/ρ) and the force caused F2= GT/ρ by the cosmic string. The non-relativistic Newton's equation for a point particle in this force field is v2= ρ(F1+F2)= d(G M(ρ))+ GM(ρ)/ρ + TG . At short distances, the force caused by matter dominates and at long distances the force due to the long cosmic string dominates.

    One can however argue that if the mass M(r) is generated by the decay of the cosmic string in the galactic plane, one should approximate the galaxy as a single thickened string, at least in the primordial state as a cosmic string.

  2. If the planar cosmic string would consist of independent particles, it would decay very rapidly. String tension prevents this. One might however hope that in the first approximation string tension forces initial conditions preserving the identity of the string but that the points otherwise move independently. Note that by Equivalence Principle the decomposition to smaller masses does not depend on the size of the small mass.
  3. The intuitive guess is that ince the velocity of rotation increases towards the galactic nucleus, the gravitational force causes a differential rotation of the planar cosmic string. Since the velocity and therefore also angular velocity ω(ρ) increases towards the center of the galaxy, spiral structure is generated. At long distances the velocity of rotation is the same as for distant stars.
The system could be modelled by addition of the gravitational force to the equations of string world sheets as a minimum as an additional radial force. The model would generalize the ordinary Newtonian description of point-like particles in a gravitational field. The above model suggests that convenient coordinates for the string world sheet are (t,φ) and the dynamical variable is the radial coordinate ρ along the rotating string as a function of (t,φ). Numerical modelling along these lines would give partial differential equations. Also now conservation of energy and angular momentum can be used. Could one imagine any elegant solution to the problem.
  1. Physical intuition suggests that one should start from the solution without the gravitational force already considered since it looks realistic in some aspects. One should transform the static string to a string in a differential rotation determined by the gravitational forces and forcing only coherent initial conditions for the points of the string so that they all rotate with the velocity. One might even hope that Kepler's law can be used besides conservation laws.
  2. Equivalence Principle suggests how one might achieve this at least approximately. Gravitational force is in the Einsteinian description a coordinate force describable in terms of Christoffel symbols. In TGD this force is force in H which can be approximated with M4. Could one find a coordinate system of M4 in which this coordinate force vanishes? Could a differentially rotating system be the system in which this is the case. This would generalize Einstein's freely falling elevator argument.
Could one obtain this coordinate system by an analog of Lorentz boost in (t,φ) plane by a velocity β(ρ)=v(ρ)/c and leaving ρ and z invariant. This transformation looks like Lorentz transformation for a given ρ but is a transformation to an accelerating system (acceleration is radial).
  1. One could consider an infinitesimal variant of thef effective Lorentz boost and exponentiate it to get a flow restricting to the motion of the string defining the string world sheet. The infinitesimal boost would be

    dt= γ(dT- β ρ dΦ) , dφ= (1/ρ)γ(ρ dΦ-β dT) , γ=(1/(1-β2)1/2 .

    These equations define a flow in (T,φ) plane as an exponentiation of an infinitesimal Lorentz boost for a given value of radial coordinate ρ and one can solve (t,φ) as function of (T,Φ). The intuitive idea is that for ρ given by the static model but with (t,φ) replaced with (T,Φ) this flow reduces to the equations of the static string world sheet. This flow need not be integrable in the entire M4. The points (T,ρ) for which Φ differs by a multiple of 2π could correspond to different turns of the spiral rotating around the origin.

    This flow should be integrable in order that the flow lines have interpretation as coordinate lines. It should be possible to write the infinitesimal generator of the Lorentz boosts in (t,φ) plane for a given ρ as a product of scalar function and gradient: j= Ψ dΦ giving dΦ=j/Ψ so that Φ serves as a coordinate. Is it enough to satisfy this condition at the string world sheet at which the condition ρ=ρ(Φ,T) mildens it?

  2. It is easy to find how this pseudo Lorentz boost affects the expression of M4 metric ds2=dt2-dz2-dρ222 by writing the differentials dt, dφ and dρ explicitly:

    ds2=dt2-dz2-dρ222 =(γ(dT- β ρ dΦ)2- (γ(ρ dΦ-β dT)2 -dρ2 -dz2 .

    Here ρ(Φ,T) corresponds to the orbits of the point of the string and must satisfy the field equations. Here dρ2 expressed in terms of dΦ and dT gives additional contribution to the induced metric.

  3. If only the gravitational force of the long cosmic string is taken into account one has β= constant and the analogy with Lorentz books is even stronger.
The wishful conjecture is that these equation satisfy integrability conditions on string world sheet and that the gravitational force disappears from field equations using coordinates (T,Φ) when the velocity parameter corresponds to the expected solution in the external field in coordinate (t,φ).

See article About the recent TGD based view concerning cosmology and astrophysics or the 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.

Wednesday, April 03, 2024

Can one define the analogs of Mandelbrot and Julia sets in TGD framework?

The stimulus to this contribution came from the question related to possible higher-dimensional analogs of Mandelbrot and Julia sets (see this). The notion complex analyticity play a key role in the definition of these notions and it is not all clear whether one can define these analogs.

I have already earlier considered the iteration of polynomials in the TGD framework (see this) suggesting the TGD counterparts of these notions. These considerations however rely on a view of M8-H duality which is replaced with dramatically simpler variant and utilizing the holography=holomorphy principle(see this) so that it is time to update these ideas.

This principle states that space-time surfaces are analogous to Bohr orbits for particles which are 3-D surfaces rather than point-like particles. Holography is realized in terms of space-time surfaces which can be regarded as complex surfaces in H=M4× CP2 in the generalized sense. This means that one can give H 4 generalized complex coordinates and 3 such generalized complex coordinates can be used for the 4-surface. These surfaces are always minimal surfaces irrespective of the action defining them as its extermals and the action makes itself visible only at the singularities of the space-time surface.

Ordinary Mandelbrot and Julia sets

Consider first the ordinary Mandelbrot and Julia sets.

  1. The simplest example of the situation is the map f:z→ z2+c. One can consider the iteration of f by starting from a selected point z and look for various values of complex parameter c whether the iteration converges or diverges to infinity. The interface between the sets of the complex c-plane is 1-D Mandelbrot set and is a fractal. One can generalize the iteration to an arbitrary rational function f, in particular polynomials.
  2. For polynomials of degree n also consider n-1 parameters ci, i=1,...,n, to obtain n-1 complex-dimensional analog of Mandelbrot set as boundaries of between regions where the iteration lead or does not lead to infinity. For n=2 one obtains a 4-D set.
  3. One can also fix the parameter c and consider the iteration of f. Now the complex z-plane decomposes to two a finite region with a finite number of components and its complement, Fatou set. The iteration does not lead out from the finite region but diverges in the complement. The 1-D fractal boundary between these regions is the Julia set.
Holography= holomorphy principle

The generalization to the TGD framework relies heavily on holography=holomorphy principle.

  1. In the recent formulation of TGD, holography required by the realization of General Coordinate Invariance is realized in terms of two functions f1,f2 of 4 analogs of generalized complex coordinates, one of them corresponds to the light-like (hypercomplex) M4 coordinate for a surface X2⊂ M4 and the 3 complex coordinates to those of Y2 orthogonal to X2 and the two complex coordinates of CP2.

    Space-time surfaces are defined by requiring the vanishing of these two functions: (f1,f2)=(0,0). They are minimal surfaces irrespective of the action as long it is general coordinate invariant and constructible in terms of the induced geometry.

  2. In the number theoretic vision of TGD, M8-H-duality (see this) maps the space-time as a holomorphic surface X4⊂ H is mapped to an associative 4-surface Y4⊂ M8. The condition for holography in M8 is that the normal space of Y4 is quaternionic.

    In the number theoretic vision, the functions fi are naturally rational functions or polynomials of the 4 generalized complex coordinates. I have proposed that the coefficients of polynomials are rationals or even integers, which in the most stringent approach are smaller than the degree of the polynomial. In the most general situation one could have analytic functions with rational Taylor coefficients.

    The polynomials fi=Pi form a hierarchy with respect to the degree of Pi, and the iteration defined is analogous to that appearing in the 2-D situation. The iteration of Pi gives a hierarchy of algebraic extensions, which are central in the TGD view of evolution as an increase of algebraic complexity. The iteratikon would also give a hierarchy of increasingly complex space-time surface and the approach to chaos at the level of space-time would correspond to approach of Mandelbrot or Julia set.

  3. In the TGD context, there are 4-complex coordinates instead of 1 complex coordinate z. The iteration occurs in H and the vanishing conditions for the iterates define a sequence of 4-surfaces. The initial surface is defined by the conditions (f1,f2)=0. This set is analogous to the set f(z)=0 for ordinary Julia sets.

    One could consider the iteration as (f1,f2)→ (f1• f1,f2• f2) continued indefinitely. One could also iterate only f1 or f2. Each step defines by the vanishing conditions a 4-D surface, which would be analogous to the image of the z=0 in the 2-D iteration. The iterates form a sequence of 4-surfaces of H analogous to a sequence of iterates of z in the complex plane.

    The sequence of 4-surfaces also defines a sequence of points in the "world of classical worlds" (WCW) analogous to the sequence of points z,f(z),.... This conforms with the idea that 3-surface is a generalization of point-like particles, which by holography can be replaced by a Bohr orbit-like 4-surface.

  4. Also in this case, one can see whether the iteration converges to a finite result or not. In the zero energy ontology (ZEO), convergence could mean that the iterates of X4 stay within a causal diamond CD having a finite volume.
The counterparts of Mandelbrot and Julia sets at the level of WCW

What the WCW analogy of the Mandelbrot and Julia sets could look like?

  • Consider first the Mandelbrot set. One could start from a set of roots of (f1,f2)= (c1,c2) equivalent with the roots of (f1-c1, f2-c2) =(0,0). Here c1 and c2 define complex parameters analogous to the parameter c of the Mandelbrot sent. One can iterate the two functions for all pairs (c1,c2). One can look whether the iteration converges or not and identify the Mandelbrot set as the critical set of parameters (c1,c2). The naive expectation is that this set is 3-D dimensional fractal.
  • The definition of Julia set requires a complex plane as possible initial points of the iteration. Now the iteration of (f1,f2)=0 fixes the starting point (not necessarily uniquely since 3-D surface does not fix the Bohr orbit uniquely: this is the basic motivation for ZEO). The analogy with the initial point of iteration suggests that we can assume (f1,f2)=(c1,c2) but this leads to the analog of the Mandelbrot set. The notions coincide at the level of WCW.
  • Mandelbrot and Julia sets and their generalizations are critical in a well-defined sense. Whether iteration could be relevant for quantum dynamics is of course an open question. Certainly it could correspond to number theoretic evolution in which the dimension of the algebraic extension rapidly increases. For instance, one could one consider a WCW spinor field as a wave function in the set of converging iterates. Quantum criticality would correspond to WCW spinor fields restricted to the Mandelbrot or Julia sets. Could the 3-D analogs of Mandelbrot and Julia sets correspond to the light-like partonic orbits defining boundaries between Euclidean and Minkowskian regions of the space-time surface and space-time boundaries? Can the extremely complex fractal structure as sub-manifold be consistent with the differentiability essential for the induced geometry? Could light-likeness help here.

    Do the analogs of Mandelbrot and Julia sets exist at the level of space-time?

    Could one identify the 3-D analogs of Mandelbrot and Julia sets for a given space-time surface? There are two approaches.

    1. The parameter space (c1,c2) for a given initial point h of H for iterations of f1-c1,f2-c2) defines a 4-D complex subspace of WCW. Could one identify this subset as a space-time surface and interpret the coordinates of H as parameters? If so, there would be a duality, which would represent the complement of the Fatou set (the thick Julia set) defined as a subset of WCW as a space-time surface!
    2. One could also consider fixed points of iteration for which iteration defines a holomorphic map of space-time surface to itself. One can consider generalized holomorphic transformations of H leaving X4 invariant locally. If they are 1-1 maps they have interpretation as general coordinate transformations. Otherwise they have a non-trivial physical effect so that the analog of the Julia set has a physical meaning. For these transformations one can indeed find the 3-D analog of Julia set as a subset of the space-time surface. This set could define singular surface or boundary of the space-time surface.
    Could Mandelbrot and Julia sets have 2-D analogs in TGD?

    What about the 2-D analogs of the ordinary Julia sets? Could one identify the counterparts of the 2-D complex plane (coordinate z) and parameter space (coordinate c).

    1. Hamilton-Jacobi structure defines what the generalized complex structure is (see this) and defines a slicing of M4 in terms of integrable distributions of string world sheets and partonic 2-surfaces transversal or even orthogonal to each other. Partonic 2-surface could play the role of complex plane and string world sheet the role of the parameter space or vice versa.

      Partonic 2-surfaces resp. and string world sheet having complex resp. hyper-complex structures would therefore be in a key role. M8-H duality maps these surfaces to complex resp. co-complex surfaces of octonions having Minkowskian norm defined as number theoretically as Re(o2).

    2. In the case of Julia sets, one could consider generalized holomorphic transformations of H mapping X4 to itself as a 4-surface but not reducing to 1-1 maps. If f2 (f1) acts trivially at the partonic 2-surface Y2 (string world sheet X2), the iteration reduces to that for f1 (f2). Within string world sheets and partonic 2-surfaces the iteration defines Julia set and its hyperbolic analog in the standard way. One can argue that string world sheets and partonic 2-surfaces should correspond to singularities in some sense. Singularity could mean this fixed point property.

      The natural proposal is that the light-like 3-surfaces defining boundaries between Euclidean and Minkowskian regions of the space-time surface define light-like orbits of the partonic 2-surface. And string world sheets are minimal surfaces having light-like 1-D boundaries at the partonic 2-surface having physical interpretation as world-lines of fermions.

      One could also iterate only f1 or f2 allow the parameter c of the initial value of f1 to vary. This would give the analog of Mandelbrot set as a set of 2-D surfaces of H and it might have dual representation as a 2-surface.

    3. The 2-D analog of the Mandelbrot set could correspond to a set of 2-surfaces obtained by fixing a point of the string world sheet X2. Also now one could consider holomorphic maps leaving the space-time surface locally but not acting 1-1 way. The points of Y2 would define the values of the complex parameter c remaining invariant under these maps. The convergence of the iteration of f1 in the same sense as for the Mandelbrot fractal would define the Mandelbrot set as a critical set. For the dual of the Mandelbrot set X2 and Y2 would change their roles.
    See the article Can one define the analogs of Mandelbrot and Julia sets in the TGD framework? or the chapter Could quantum randomness have something to do with classical chaos?.

    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.

  • Tuesday, April 02, 2024

    About new energy technologies and TGD

    The motivation for summarizing a general vision of future energy technologies based on dark matter in the TGD sense came from the video of Sabine Hossenfelder titles "Sulfur Better than Hydrogen for Energy Storage, Engineers Find" (see this).

    TGD view of dark matter briefly

    Number theoretic view of TGD predicts a hierarchy of phases of ordinary matter labelled by the value of effective Planck constant heff=nh0. The simplest assumption is that n is the dimension of algebraic extension of rationals. For a more complex option it is a product of dimensions of two algebraic extensions.

    These phases behave like dark matter and would be located at monopole magnetic flux tubes and also electric flux tubes. They would not be galactic dark matter but correspond to the missing baryonic matter whose fraction has been increasing during the cosmological evolution. Galactic dark matter would correspond to the energy of cosmic strings (space-time surfaces with 2-D M4 and CP2 projections). The unavoidable mumber theoretical evolution implies the increase of the number theoretical complexity and therefore increase of n. The larger the value of n the longer the quantum coherence scale of the system.

    1. The predicted huge values of heff assignable to classical gravitational and electric fields of astrophysical objects (see this) mean that weak interactions become as strong as em interactions below the scale up Compton length of weak bosons, which, being proportional to heff, can be as large as cell size.
    2. Large heff phases behave like dark matter: they do not however explain the galactic dark matter, which in the TGD framework is dark energy assignable to cosmic strings (no halo and an automatic prediction of the flat velocity spectrum). Instead, large heff phases solve the missing baryon problem. The density of baryons has decreased in cosmic evolution (having biological evolution as a particular aspect) and the explanation is that evolution as unavoidable increase of algebraic complexity measured by heff has transformed them to heff> h phases at the magnetic bodies (thickened cosmic string world sheets, 4-D objects), in particular those involved with living matter.
    3. The large value of heff has besides number theoretical interpretation (see this) also a geometric interpretation. Space-time surface can be regarded as many-sheeted over both M4 and CP2. In the first case the CP2 coordinates are many-valued functions of M4 coordinates. In the latter case M4 coordinates are many-valued functions of CP2 coordinates so that QFT type description fails. This case is highly interesting in the case of quantum biology. Since a connected space-time surface defines the quantum coherence region, an ensemble of, say, monopole flux tubes can define a quantum coherent region in the latter case: one simply has an analog of Bose-Einstein condensate of monopole flux tubes.
    Why dark matter is so excellent for energy storage?

    The basic observation is that the energies of quantum states as a function of heff increase. For instance, cyclotron energies are proportional to ℏeff and atomic binding energies are proportional to 1/ℏeff2.

    This suggests that the transformation of ordinary particles, say protons or electrons, to their dark variants at the magnetic body (MB) of the system allows to store energy and also information at MB. Due to the large value of heff the dissipation would be slow.

    One can imagine a practically endless variety of ways to achieve this.

    1. In the Pollack effect the solar radiation would kick part of the protons of the water molecules to the gravitational MB of Earth. Pollack effect creates negatively charged exclusion zones (EZs) with strange properties suggesting time reversal which is indeed predicted to occur in the TGD Universe if its TGD counterpart corresponds to an ordinary state function reduction.

      In the case of protons the scale of the reduction of the gravitational energy is of order .5 eV if the flux tubes have the scale of Earth radius. For reasonably small heff these flux tubes could be long hydrogen bonds carrying protons. The flux tubes can also carry several protons and one ends up to a proposal for the genetic codes in terms of dark proton triplets. These dark DNA molecules would be paired with ordinary DNA. Same could be true for other basic information molecules.

    2. Dark cyclotron states with energy proportional to ℏgr or ℏeff assignable to long range gravitational fields of Sun and planets and electric fields of Sun and Earth and also smaller systems such as cell and DNA would allow the storage of energy to the energy of dark particles.
    3. Pollack effect generalizes in the TGD framework. Also electrons could be kicked to the gravitational MB: in this case the energy scale would be meV scale (see this and this). Both protonic and electronic energy scales appear in cell biology. Especially interesting systems are charged conductors: their electric bodies could consist of flux tubes which are deformed gravitational magnetic flux tubes carrying dark electrons.

      The proposed realization of genetic code for dark protons generalizes to the case of dark electrons and suggests that genetic code realized in terms of a completely exceptional icosa tetrahedral tessellation of H3 and theref also life is much more general phenomenon than thought hitherto. Therefore both energy and information storage without the problems caused by dissipation would be in question.

    4. In principle, the energy needed to kick the protons to the MB could come from practically any source. For instance, the formation of atomic or molecular bound states would liberate energy stored as energy of dark particles at the MB. This energy would be liberated when dark protons transform to ordinary protons but the system need not transform back to the original energy so that the liberated energy could be used.

      The molecular energy storage in living matter to proteins could rely on this mechanism and could use relatively small values of heff assignable to valence bonds. High energy phosphate bonds could correspond to short term storage, perhaps at the gravitational magnetic body.

    "Cold fusion" and energy storage

    TGD leads also to a second proposal for energy storage based on another key aspect of number theoretical physics. The polynomials associated with a given extension of rationals are characterized by ramified primes whose spectrum depends on the polynomials. These ramified primes define preferred p-adic number fields characterizing the cognitive aspects of these systems. The p-adic length scale characterizes the mass/energy scale of the system and the prediction is that a given system can appear in several p-adic length scales with different mass/energy scales. TGD suggests the existence of p-adically scaled variants of hadron physics, nuclear physics and even atomic and molecular physics.

    The so-called "cold fusion" could rely on dark fusion, as the formation of p-adically scaled atomic nuclei from dark protons which can also transform to dark neutrons by emission of dark weak bosons. This process could produce, not only energy, but also basic elements (see this and this). One would avoid the kicking of nuclei from the bottom of the nuclear energy valley by nuclear collisions requiring high energies.

    The dark proton sequences at monopole flux tubes defining dark DNA could be seen as dark nuclei. Their binding energies would scale down and they could form even at low temperatures and in living matter (biofusion for which there is evidence). They could spontaneously transform to ordinary nuclei and liberate practically all ordinary nuclear binding energy. This process could give rise to prestellar evolution heating the system to the ignition temperature of ordinary nuclear fusion. This process could produce elements with atomic numbers even higher than that of iron. Usually supernova explosions are believed to be responsible for this.

    Here I have not discussed the possible role of zero energy ontology concerning the transfer of energy: the basic idea is that the change of the arrow of time in the TGD counterpart of ordinary state function reduction makes possible for the system to get energy by emitting negative energy received by the source of energy in an excited state. Analog of population reverted laser would be in question. 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.

    Monday, April 01, 2024

    Flux tube condensates as a basic deviation between TGD from QFT descriptions and phases, which are not Fermi liquids

    The large value of heff has besides number theoretical interpretation (see this) also a geometric interpretation. Space-time surface can be regarded as many-sheeted over both M4 and CP2. In the first case the CP2 coordinates are many-valued functions of M4 coordinates. In the latter case M4 coordinates are many-valued functions of CP2 coordinates so that QFT type description fails. This case is highly interesting in the case of quantum biology. Since a connected space-time surface defines the quantum coherence region, an ensemble of, say, monopole flux tubes can define a quantum coherent region in the latter case: one simply has an analog of Bose-Einstein condensate of monopole flux tubes.

    The flux tube condensate as a covering of CP2 means a dramatic deviation from the QFT picture and is a central notion in the applications of quantum TGD to biology. Therefore some examples are in order.

    1. Fermi liquid description of electrons relies on the notion of a quasiparticle as an electron plus excitations of various kinds created by its propagation in the lattice. In some systems this description fails and these systems would. have a natural description in terms of space-time surfaces which are multiple coverings of CP2, say flux tube condensates.
    2. In high Tc superconductors and bio-superconductors (see this and this) the space-time surface could correspond to this kind of flux tube condensates and Cooper pairs would be fermion pairs with members at separate flux tubes. The connectedness of the space-time surface having about heff/h=n flux tubes would correlate the fermions.
    3. Bogoliubov quasiparticles related to superconductors are regarded as superpositions of electron excitation and hole. The problem is that they have an ill-defined fermion number. In TGD, they would correspond to superpositions of a dark electron accompanied by a hole which it has left behind and therefore having a well-defined fermion number. Bogoliubov quasiparticle is indeed what can be seen using the existing experimental tools and physical understanding.
    4. Strange metals would be an example of a system having no description using quasiparticles, as the linear dependence of the resistance at low temperatures demonstrates. I have considered a description of them in terms of Cooper pairs at short closed flux tubes (see this and this: this would however suggest a vanishing resistance in an ideal situation. Something seems to go wrong.

      An alternative description could be in terms of superpositions of dark electrons and holes assignable to the flux tube condensate. Strange metal is between Fermi liquid and superconductor: this conforms with the fact that strange metals are quantum critical systems. The transition to high Tc superconductivity is preceded by a transition to a phase in which something resembling Cooper pairs is present.

      A natural looking interpretation would be in terms of a flux tube condensate and pairs of dark and ordinary electrons. Also now the flux tubes could be short. In the article Comparing the Berry phase model of super-conductivity with the TGD based model), I have considered the possibility that high Tc superconductors could be this kind of "half-superconductors" but this option seems to be wrong.

      The phase transitions between "half-superconductivity" and superconductivity could play a central role also in living matter.

    See the article New findings related to the chiral selection or the chapter Quantum Mind, Magnetic Body, and Biological Body.

    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.