Could taos hum and quantum gravitation relate to each other?

I have been tormented from time to time by an unpleasant sensation of sound. Always at night. Last night it came back after a long time and lasted for several hours and I had to think about what it was.

During my stay here in Karkkila, it has been a very frequent night experience from time to time, especially in the summer. The sound source does not move. As if someone were keeping the car idling or even screaming the car engine to drive his fellow men to the brink of rage. It's hard to think that anyone could continue this kind of bullying for very long. Even the option that someone would listen to, say, a video of formula race at night time year after year, seems unlikely already because of the reaction of the neighbors.

I had to think about these options too, because a few years ago my hometown was a victim of moped terrorists and speeders for a few summers until the police finally became active. Fortunately, that time has passed.

The option that the voices were hallucinations didn't seem likely. Another option was that they are sensory memories. Such are possible and can be induced by electrically stimulating the temporal lobes. For example, some previously experienced pain due to some real cause can be chronically repeated as a sensory memory.

Then at night I realized a possible explanation. When I was living in Hanko, I wrote about a strange phenomenon called taos hum (taos hum) (see this). For the TGD view of taos hum see this and this . While writing about taos hum, I realized that I had this syndrome myself!

1. An idling diesel engine is a good characterization for the sound. Here in Karkkila, the sound has been only more aggressive: as if deliberate gassing had been involved. Taos hum is not detected by microphones and does not create a normal sensation of hearing.
2. Taos hum cannot be connected to any device produced by technology. It starts after sunset and the initial cause seems to be biological. Interestingly, also animals and plants start producing electrostatic noise after sunset. In Karkkila, during the winter, there are no other options than trees.
3. Microwave hearing (Frey effect) could be involved. The series of microwave pulses can be modulated with low but audible frequencies, for example around 50 Hz. Microwave frequencies range is 3 decades: from 300 MHz to 300 GHz. They interact in the brain and produce an auditory experience. In which parts of the brain are not clear. The effect can also occur in the ears, but not in the normal way.

The carrier frequencies in the Frey effect are of the order of GHz. They are technologically significant (mobile phones for example) and this may explain why the effect has been reported for them. I am not aware of any reports regarding higher microwave frequencies that are not so technologically central. The piezoelectric effect, which converts electromagnetic radiation into sound and vice versa, could be essential to the effect.

Some people can sense the amplitude modulated frequency as a sound from radio masts, for example those used in radiotelephone connections.

Could also my unpleasant experience in Karkkila be the taos hum, which I already suffered in Hanko! Funnily enough, once I realized this connection, I stopped hearing anything! As if someone had worked hard to force me to realize this connection!

1. Connection with quantum gravitation?

Next, it occurred to me to ask what the frequency for the carrier wave of the taos hum could be.

1. In quantum biology based on TGD, quantum gravity is essential and here Nottale's hypothesis is generalized and assigns macroscopic and even astrophysical quantum coherence to classical gravitational fields created by astrophysical objects.

   In the Earth's gravitational field, the gravitational Compton wavelength is Λ_gr= GM_E/β₀, where the velocity parameter satisfies β₀= v₀/c<1. The corresponding frequency does not depend on the mass of the particle (Equivalence Principle). For β=1 one has Λ_gr = .45 cm. It corresponds to the microwave frequency f_gr=67 GHz. This would be some kind of universal clock frequency of quantum biology.

2. I have considered also the possibility that computers (see this, this, and this) could acquire some characteristics of a biological organism, if their clock frequency is higher than 67 GHz, because then the statistical determinism would no longer apply. In fact, the gravitional Compton wavelength associated with the Sun is half the radius of the Earth for β0≈ 2^-11 deduced from the orbital radii of inner planets identified as Bohr orbits and corresponds to the EEG frequency of 50 Hz, which inspires many questions.
3. For biomolecules, microwave frequencies play an essential role. Microwaves are associated with many strange effects such as ball lightning and light balls that have often been interpreted as UFOs. The creation of crop circles could be based on the same mechanisms as the explosion of a tomato in a microwave oven, which can be also used to produce this kind of light balls. There are also reports of lightballs in the act of building a crop circle.
4. Could the amplitude modulation of the radiation with gravitational Compton frequency produce the taos hum?! The modulating frequencies are in the EEG range and quite low (this brings in mind the gravitational magnetic body of the Sun). Why would this give the impression of an idling diesel engine? Could it correspond to some kind of random noise but what about the impression of deliberate gassing? The carrier frequencies would be microwave frequencies and by a factor of 67 higher than in the Frey effect, which has been associated with the microwave hearing.

There is also another important microwave frequency. The maximum for the frequency distribution of the cosmic microwave background is at the frequency 160 GHz and to wavelength .2 cm. This frequency is roughly 2 times twice the gravitational Compton frequency for Earth. This is close to the upper limit of microwave frequencies of 300 GHz. Is it a coincidence that these two frequencies are so near to each other?

2. Generalization of stochastic resonance as an explanation of Taos hum?

Stochastic resonance occurs in the brain and its quantum analog serves as a candidate for the mechanism behind the perception of taos hum.

Consider first the classical variant of the stochastic resonance, which I have considered here.

1. Classical stochastic resonance is an amplification mechanism for a signal represented as an amplitude modulation of a carrier wave with a basic frequency f acting as a harmonic perturbation of a bistable system, which is also subject to a white noise. In the recent case the message could correspond to the amplitude modulated signal with frequency f in the microwave range. f=f_gr is an interesting option. One might say that the system manages to extract the energy of the noise, which creates the question whether the mechanism conforms with the second law of thermodynamics.
2. In the resonance, the signal frequency f must be one half of the average frequency f(spont) for the jumps between two states of the bistable system: f= f(spont)/2. This condition has a simple physical interpretation: the height of the potential barrier separating the two potential wells varies periodically with a period which is half of the period defined by f, and the best opportunity to get to another potential well is to hop when the potential barrier is lowest possible.
3. For the mechanical analog system the rate f(spont)=r₀A is proportional to an "Arrhenius factor" A= exp(-Δ V/D), where Δ V is the height of the potential barrier and D characterizes the intensity of the white noise. f(spont) is also proportional to a factor r₀= ω ω_b/\gamma where ω is the frequency of small oscillations at either bottom of the symmetric potential well, ω_b is the analogous quantity at the top of the barrier (for harmonic oscillator potential one would have ω=ω_b), and \gamma characterizes the linear dissipative force (overcritical damping is assumed).
4. Thus, when the white noise has a correct intensity, a weak harmonic perturbation with a given frequency is amplified in the sense that the Fourier expansion of the system's time development regarded as jumps between the two states contains a peak at the multiples of the frequency of the amplitude modulated harmonic perturbation. Neuroscientists refer to this phenomenon as phase locking. The peaks for the higher multiples of the input frequency f are exponentially suppressed. The notion of stochastic resonance makes sense also in the quantum context: now quantum tunnelling would replace the jumps induced by the stochastic noise.

In stochastic resonance the system extracts energy from the environment to amplify the signal. Does this really conform with the second law of thermodynamics: it would seem that the second law temporarily fails but is true with an opposite arrow of time. The TGD view of stochastic resonance could be motivated by this question.

Could stochastic resonance generalize to a quantum situation but with the ordinary ontology of quantum theory replaced with the zero energy ontology (ZEO) of TGD (see this)? What would be new is the identification of the ordinary quantum jump as a "big" state function reduction (BSFR) in which the arrow of time changes. One can consider two interpretations.

1. Consider first the TGD analog of the standard interpretation. The jump between the potential wells corresponds to a quantum tunnelling as a transition of states with the same arrow of time and therefore involves two subsequent BSFRs. In stochastic resonance, the frequency f(spont) for these tunnellings should satisfy f=f_spont/2. Each period T= 1/f would correspond to two pairs of BSFRs. In the TGD framework, this interpretation looks too complicated.
2. For the second option, a single BSFR defines the counterpart for the hopping between two potential wells and 2 BSFRs define quantum tunnelling. Bistability has nothing to do with the details of the dynamics and is universal and corresponds to the two arrows of time. f(spont) is identified as the rate for BSFRs rather than their pairs and characterizes external perturbations.

   In the stochastic resonance, the rate f(spont)/2 for a pair of BSFRs would be equal to the carrier frequency f so that quantum tunnelling is in synchrony with the driving frequency f and each period corresponds to a quantum tunnelling. The intensity of the noise could be used to induce this synchrony.

   This synchronization mechanism applies to all transitions and to all frequencies f but f=f_gr,E would be in a special role since f_gr,E defines a universal gravitational Compton frequency of the Earth. For instance, EEG could involve this mechanism and the halves of the EEG period would correspond to different arrows of time as I have indeed proposed here) on basis of observations of brothers Fingelkurts (see this). As already noticed, the gravitational Compton frequency f_gr,S=50 Hz of Sun is EEG frequency and EEG frequencies appear as modulation frequencies in Taos hum.

See the article Taos hum, stochastic resonance, and sensory perception 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.

What happens in the transition to superconductivity?

I learned about very interesting discoveries related to the quantum phase transition between the ordinary and superconducting phase (see this).

These kinds of findings are very valuable in the attempts to build a TGD based view of what exactly happens in the transition to super-conductivity. I have developed several models for high Tc superconductivity (see this, this and this) but there is no single model.

Certainly, the TGD based view of magnetic fields distinguishing them from their Maxwellian counterparts is bound to be central for the model. However, the view about what happens at the level of magnetic fields in the transition to superconductivity, has remained unclear.

Consider first the findings of the research group. The basic question of how two-dimensional superconductivity can be destroyed without raising the temperature. The ordinary phase transition to superconductivity is induced by thermal fluctuations. Now the temperature is very close to the absolute zero and the phase transition is quantum phase transition induced by quantum fluctuations.

1. The material under study was a bulk crystal of tungsten ditelluride (WTe2) classified as a layered semi-metal. The tungsten ditelluride was converted into a two-dimensional material consisting of a single atom-thin layer. This 2-D material behaves as a very strong insulator, which means its electrons have limited motion and hence cannot conduct electricity.
2. Surprisingly, the material exhibits a lot of novel quantum behaviors, in particular, a switching between insulating and superconducting phases. It was possible to control this switching behavior by building a device that functions like an "on and off" switch.
3. At the next step, the researchers cooled the tungsten ditelluride down to exceptionally low temperatures, roughly 50 milliKelvin (mK). Then the material was converted from an insulator into a superconductor by introducing some extra electrons to the material. It did not take much voltage to achieve the superconducting state. It turned out to be possible to precisely control the properties of superconductivity by adjusting the density of electrons in the material via the gate voltage.
4. At a critical electron density, the quantum vortices rapidly proliferated and destroyed the superconductivity. To detect the presence of these vortices, the researchers created a tiny temperature gradient on the sample, making one side of the tungsten ditelluride slightly warmer than the other. This generated a flow of vortices towards the cooler end. This flow generated a detectable voltage signal in a superconductor, which can be understood in terms of the integral form of Faraday's law. Voltage signals were in nano-volt scale.

Several surprising findings were made.

1. Vortices were highly stable and persisted to much higher temperatures and magnetic fields than expected. They survived at temperatures and fields well above the superconducting phase, in the resistive phase of the material.
2. The expectation was that the fluctuations perish below the critical electron density on the non-superconducting side, just as they do in ordinary thermal transition to superconductivity.

   In contrast to this, the vortex signal abruptly disappeared when the electron density was tuned just below the critical value of density at which the quantum phase transition of the superconducting state occurs. At this critical (quantum critical point (QCP) quantum fluctuations drive the phase transition.

What could be the interpretation of these findings in the TGD Universe and could they give hints for a more precise formulation of the TGD inspired model.

1. TGD leads to a rather detailed proposal for high Tc - and bio-superconductivity. There are reasons to think that this model might work also in the case of low temperature superconductivity, in particular in the proposed situation with one-atom-thick layer (see this, this, this and this).
2. The unique feature of the monopole flux tube is that its magnetic field needs no currents as a source. The cross section of the flux tube is not a disk, but a closed 2-surface. There is no boundary along which the current could flow and generate the magnetic field. In the absence of these ohmic boundary currents there is no dissipation and the natural interpretation is that electrons form Cooper pairs.

   These monopole flux tubes are central for TGD based physics in all length scales and explain numerous anomalies related to the Maxwellian view of magnetic fields. The stability of the Earth's magnetic field and the existence of magnetic fields in cosmic scales are two examples.

3. There are also ordinary flux tubes with disk-like cross sections for which current along the boundary creates the magnetic field just like in an inductance coil. The loss of superconductivity means generation of these disk-like magnetic vortices with quantized flux created by ordinary current at the boundaries of the disk-like flux quantum.

   The monopole flux has a cross sectional area twice that of disk-like flux tube so that one can see the monopole flux tube as being obtained by gluing two disk-like flux tubes along the boundaries. The signature of the monopole flux tube is that magnetic flux is twice that of ordinary flux tubes.

4. Whether the disk-like flux tubes are possible in the TGD Universe has remained uncertain. My latest view is that they are and I have written a detailed article about how boundary conditions could be satisfied at the boundaries (see this).

   The orbits of the disk-like boundaries would be light-like 3-surfaces. This is not in conflict with the fact that the boundaries look like static structure. The reason is that the metric of the space-time surface is induced from that of M⁴× CP₂ and the large CP₂ contribution to the induced 3-metric makes it light-like. One might say that the boundary is analogous to blackhole horizon.

This picture allows us to sketch what could happen at the quantum critical point.

1. Both monopole flux tubes and disk-like flux tubes are present at the critical point. Monopole flux tubes dominate above the critical electron density whereas disk-like flux tubes dominate above it. In the transition pairs of disk-like flux tubes fuse to form monopole flux tubes and electrons at the boundaries combine to Cooper pairs inside the monopole flux tube and form a supra current. The transition would be a topological phase transition at the level of the space-time topology and something totally new from the standard model perspective.
2. Cyclotron energy scale, determined by the monopole flux quantization and flux tube radius, is expected to characterize the situation. The difference of the cyclotron energies for the monopole flux tube with Cooper pair and for two disk-like flux tubes with one electron should correspond to the binding energy of the Cooper pair. If the thermal energy exceeds this energy, superconductivity is lost. The disk-like flux tubes can however remain stable.
3. The transition could involve the increase of the effective Planck constant h_eff but its value would remain rather small as compared to its value of high Tc superconductivity. The value of h_eff should be correlated with the transition temperature since the difference of total cyclotron energies would be proportional to h_eff.

This picture does not yet explain why the vortices suddenly disappear at the critical electron density. The intuitive guess is that the density of electrons is not high enough to generate the disk-like monopole flux tubes.

1. Suppose that these flux tubes have a constant radius and fill the 2-D system so that a lattice like system consistent with the underlying lattice structure is formed.
2. There must be at least 1 electron per flux tube to create the magnetic field inside it. The magnetic flux is quantized and if the boundary of the disk contains single electron, the number of electrons per flux tube area S is 1: the density of electrons is n=1/S. If the electron density is smaller than this, the formation of disk-like flux tubes is not possible as also the transition to superconductivity.

This proposal is not consistent with the earlier TGD based model for high Tc superconductivity (see this and this) In high Tc superconductivity there are two critical temperatures. At the higher critical temperature T_c1 something serving as a prerequisite for super-conductivity appears. Superconductivity however appears only at a lower critical temperature T_c.

1. The earlier TGD based proposal is that the superconductivity appears at T_c1> T_c in a short length scale so that no long scale supra currents are possible. The magnetic flux tubes would form short loops. At T_c the flux loops would reconnect to form long flux loops. The problem with this option is that it is difficult to understand the energetics.
2. The option suggested by the recent findings, is that disk-like half-monopole flux tubes carrying Ohmic currents at their boundaries are stabilized at T_c1. At T_c they would combine to form monopole flux tubes.
3. The difference Δ E_c of the cyclotron energies of the monopole- and non-monopole states would naturally correspond to T_c whereas the cyclotron energy scale E_c= ℏ_eff{eB/m of the non-monopole state would correspond to T_c1.
4. In the first approximation, the value of B is the same for the two states. For the non-monopole state the electrons reside at the boundary and the effective harmonic potential energy is maximal. For the monopole state Cooper pair resides in the interior so that the cyclotron energy is smaller in this case. This gives Δ E_c<0. The simplest interpretation is that the binding energy of the Cooper pair corresponds to this contribution.
5. If the value of h_eff is the same for the pair of half-monopole flux tubes and monopole tube states, both E_c and Δ E_c scale like h_eff/h. Also the critical temperatures T_c and T_c1 would scale like h_eff/h. High Tc superconductivity would therefore provide a direct support for the hierarchy of Planck constants.

See the article What happens in the transition to superconductivity? or the chapter TGD and condensed matter.

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 twistor space of H=M4× CP2 allows Lagrangian 6-surfaces: what does this mean physically?

This article was inspired by the article "A note on Lagrangian submanifolds of twistor spaces and their relation to superminimal surfaces" of Reinier Storm. For curiosity, I decided to look at Lagrangian surfaces in the twistor space of H=M⁴× CP₂. The 6-D Kähler action of the twistor space existing only for H=M⁴× CP₂ gives by a dimensional reduction rise to 6-D analog of twistor space assitable to a space-time surface. In the dimensional reduction the action reduces to 4-D Kähler action plus a volume term characterized by a dynamically determined cosmological constant Λ.

One can identify space-time surfaces, which are Lagrangian minimal surfaces and therefore have a vanishing Kähler action. If the Kähler structure of M⁴ is non-trivial as strongly suggested by the notion of twistor space, these vacuum extremals are products X²× Y² of Lagrangian string world sheet X² and 2-D Lagrangian surface Y² of CP₂, and are deterministic so that they allow holography. As minimal surfaces they allow a generalization of holography= holomorphy principle: now the holomorphy is not induced from that of H but by 2-D nature of X² and Y². Therefore holography=holomorphy principle generalizes.

Λ can vanish and in this case the dimensionally reduced action equals Kähler action. In this case, vacuum extremals are in question and symplectic transformations generate a huge number of these surfaces, which in general are not minimal surfaces. Holography= holomorphy principle is not however lost. Λ=0 sector contains however only classical vacua and also the modified gamma matrices appearing in the modified Dirac action vanish so that this sector contributes nothing to physics.

See the article The twistor space of H=M⁴× CP₂ allows Lagrangian 6-surfaces: what does this mean physically? or the chapter Symmetries and Geometry of the ”World of Classical Worlds” .

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.

Comments about Vopson's second law of infodynamics

I read an article Euronews article about Melvin Vopson's work claiming that the second law of this infodynamics gives support for the simulation hypothesis (see this). Thanks for Matti Vallin for informing me about Vopson's work.

First I want to drop from consideration what looks to me nonsense.

1. Our senses are only electrical signals that the brain encodes. We are just a biocomputers. This is the first fatal mistake, which, thank God, w are getting rid of as theories of consciousness develop.
2. The assumption that we are a simulation is non-sensical and explains nothing except maybe Vopson's second rule of infodynamics, which is most probably wrong as will be found. It however creates myriads of questions: for instance, who are those simulators and what physics do they obey?
3. Vopson's second law of infodynamics is motivated by facts: by the experience with computer codes and corona viruses. Interpretation of these facts does not howerve require Vopson's second law. The system's goal is to have just enough information, only the most significant bits, for it to cope with its tasks. This is because the maintenance of information requires (metabolic) energy and this must be saved.

   If an increase in information as an increase in complexity is followed by an increase in entropy then this would explain why entropy decreases as the genome develops and gets simpler. Complexity, the maintenance of which requires metabolic energy and its input is minimized subject to the constraint that the genome works. In computer science one speaks about compression.

Therefore there seems to be no need for the second main rule of Vopson's infodynamics.

Above I however made some assumptions: the increase of conscious information means increase of complexity accompanied by the increase of entropy and metabolic energy is needed to preserve complexity. How does TGD justify these assumptions and can it explain the findings.

1. One must explain why an increase of conscious information results in an increase of entropy. One must of course define first what conscious information is, and this cannot be achieved without the theory of consciousness, cognition and quantum biology. In TGD, number theory is an integral part of the physics of cognition.

   The first results of TGD-based cognition was the concept of p-adic entropy as a generalization of Shannon entropy. p-Adic entropies can be interpreted as measures of both algebraic complexity and the amount of conscious information, a universal IQ.

   Conscious information defined as the sum of p-adic entropies turns out to be greater than the usual entropy even though these two quantities are strongly correlated. This information tends to grow in the number theory evolution. Its increase also results in an increase of entropy. Jeremy England has postulated the same on basis of empirical findings, but in TGD it is predicted.

2. One must also understand why metabolic energy is necessary for the growth of information/complexity. Here, too, number-theoretic physics is needed. It predicts a hierarchy of Planck's constants h_eff which corresponds to the hierarchy of extensions of rational numbers. h_eff is proportional to the dimension of the extension and serves as a measure of the algebraic complexity of the extension. The deviation of h_eff from h means that the phase of ordinary matter in question behaves like dark matter, which would be an essential part of biosystems and would control ordinary biomatter.
3. The increase of h_eff requires energy, i.e. metabolic energy. h_eff tends to decrease spontaneously, so that the system remains complex/intelligent/aware only if it receives metabolic energy continually.

   The minimization metabolic energy feed forces the system to eliminate unnecessary complexity, to represent just the signification bits, and this explains the findings of Vopson and others.

All in all, this endless stream of increasingly bizarre proposals pouring out from the web reflects deep gaps in our understanding and underlying wrong assumoptions. Our view of dark matter is completely wrong, and quantum biology and quantum theories of consciousness and cognition do not exist, and we have completely missed number theory as basic aspect of physics and cognition. There is not even an understanding of what would serve a measure of conscious information!

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.

About Lagrangian surfaces in the twistor space of M4×CP2

I received from Tuomas Sorakivi a link to the article "A note on Lagrangian submanifolds of twistor spaces and their relation to superminimal surfaces" (see this). The author of the article is Reinier Storm from Belgium.

The abstract of the article tells roughly what it is about.

In this paper a bijective correspondence between superminimal surfaces of an oriented Riemannian 4-manifold and particular Lagrangian submanifolds of the twistor space over the 4-manifold is proven. More explicitly, for every superminimal surface a submanifold of the twistor space is constructed which is Lagrangian for all the natural almost Hermitian structures on the twistor space. The twistor fibration restricted to the constructed Lagrangian gives a circle bundle over the superminimal surface. Conversely, if a submanifold of the twistor space is Lagrangian for all the natural almost Hermitian structures, then the Lagrangian projects to a superminimal surface and is contained in the Lagrangian constructed from this surface. In particular this produces many Lagrangian submanifolds of the twistor spaces and with respect to both the Kähler structure as well as the nearly Kähler structure. Moreover, it is shown that these Lagrangian submanifolds are minimal submanifolds.

The article examines 2-D minimal surfaces X² in the 4-D space X⁴ assumed to have twistor space. From superminimality which looks somewhat peculiar assumption, it follows that in the twistor space of X⁴ (assuming that it exists) there is a Lagrangian surface, which is also a minimal surface. Superminimality means that the normal spaces of the 2-surface form a 1-D curve in the space of all normal spaces, which for the Euclidian signature is the 4-D Grassmannian SO(4)/SO(2)× SO(2)= S²× S² (SO(1,3)/SO(1,1)× SO(2) for M⁴). Superminimal surface is therefore highly flattened. Of course, already the minimal surface property favours flatness.

Why the result is interesting from the TGD point of view?

It is interesting to examine the generalization of the result to TGD because the interpretation for Lagrangian surfaces, which are vacuum extremals for the Kähler action with a vanishing induced symplectic form, has remained open. Certainly, if M⁴Käher form vanishes, they do not fulfill the holomorphy=holography assumption, i.e. they are not surfaces for which the generalized complex structure in H induces a corresponding structure at 4-surface.

Superminimal surfaces look like the opposite of holomorphic minimal surfaces (this expectation turned tou to be wrong!). If M⁴Käher form vanishes, their counterparts give a huge vacuum degeneracy and non-determinism for the pure Kähler action, which turned out to be mathematically undesirable. The cosmological constant, which follows from twistoralization, was believed to correct the situation.

I had not noticed that the Kähler action, whose existence for T(H)=T(M⁴)× T(CP₂) fixes the choice of H, gives a huge number of 6-D Lagrangian manifolds! Are they consistent with dimensional reduction, so that they could be interpreted as induced twistor structures? Can a complex structure be attached to them? Certainly not as an induced complex structure. Does the Lagrangian problem of Kähler action make a comeback? Furthermore, could one extend the very promising looking holography=holomorphy picture by allowing also Lagrangian 6-surfaces T(H)?

Do they have a physical interpretation, most naturally as vacuums? The volume term of the 4-D action characterized by the cosmological constant Λ does not allow vacuum extremals unless Λ vanishes. But Λ is dynamic for the twistor lift and can vanish! Do Lagrangian surfaces in twistor space correspond to 4-D minimal surfaces in H, which are vacuums and have a vanishing cosmological constant? Could even the original formulation of TGD using only Kähler action be an exact part of the theory and not just a long-length-scale limit? And does one really avoid the original problem due to huge non-determinism of vacuum extremals!? And what about the Lagrangian minimal surfaces possibly obtained when Λ is non-vanising?

The question is whether the result presented in the article could generalize to the TGD framework even though the super-minimality assumption does not seem physically natural at first.

Lagrangian surfaces in H=M⁴× CP₂ and its twistor space

So let's consider the 12-D twistor space T(H)=T(M⁴)× T(CP₂) and its 6-D Lagrangian surfaces having a local decomposition X⁶=X⁴× S². Assume a twistor lift with Kähler action on T(H). It exists only for H=M⁴× CP₂.

Let us for a moment forget the requirement that these Lagrangian surfaces correspond to minimal surfaces in H. Let us first consider the situation in which there is no generalized Kähler and symplectic structure for M⁴.

One can actually identify Lagrangian surfaces in 12-D twistor space T(H).

1. Since X⁶=X⁴× S² is Lagrangian, the induced symplectic form of the for it must vanish. This is also true in S². Fibers S² together with T(M⁴) and T(CP₂) are identified by an orientation-changing isometry. The induced Kähler form S² in the subset X⁶=X⁴× S² is zero as the sum of these two contributions of different signs. If this sum appears in the 6-D Kähler action, its contribution to the 6-D Kähler action vanishes. The cosmological constant is zero because the S² contribution to the 4-D action vanishes.
2. The 6-D Kähler action reduces in X⁴ to the 4-D Kähler action, which was the original guess for the 4-D action. The problem is that in its original form, involving only CP₂ Kähler form, it involves a huge vacuum degeneracy. The CP₂ projection is a Lagrangian surface or its subset but the dynamics of M⁴ projection is essentially arbitrary, in particular with respect to time. One obtains a huge number of different solutions. Since the time evolution is non-deterministic, the holography, and of course holography=holomorphy principle, is lost. This option is not physically acceptable.

How the situation changes when also M⁴ has a generalized Kähler form that the twistor space picture strongly suggests, and actually requires.

1. Now the Lagrangian surfaces would be products X²× Y², where X² and Y² are the Lagrangian surfaces of M⁴ and CP₂. The M⁴ projections of these objects look like string world sheets and in their ground state are vacuums.

   Furthermore, the situation is deterministic! The point is that X² is Lagrangian and fixed as such. In the previous case much more general surface M⁴ projection, even 4-D, was Lagrangian. There is no loss of holography! Holography = holomorphy principle is however lost. Holography would be replaced with the Lagrangian property.

2. The symplectic transformations of H produce new Lagrangian vacuum surfaces. If they are allowed, one might talk of symplectic phase. The second phase would be the holomorphic phase. The two major symmetry groups of physics would both be involved. For Λ= 0 these Lagrangian surfaces are classical vacua and also fermionic vacua because the modified gamma matrices appearing in the modified Dirac action vanish identically. Therefore Λ=0 sector does not contribute to physics at all. For non-vanishing Λ one has only minimal Lagrangian surfaces, which are string like entities and they contribute to physics.

   It should be however made clear that the symplectic transformations are not isometries so that minimal surface property is not preserved. Minimal surface property would reduce the vacuum symmetries to isometries.

3. In this phase induced Kähler form and induced color gauge fields vanish and it would not involve monopole fluxes. This phase might be called Maxwell phase for nonvanishing Λ. Could it correspond to the Coulomb phase as the perturbative phase of the gauge theories, while the monopole flux tubes (large h_eff and dark matter) would correspond to the non-perturbative phase in which magnetic monopole fluxes are present. If so, there would be an analogy with the electric-magnetic duality of gauge theories although the two phases does not look like two equivalent descriptions of one and the same thing unless one restricts the consideration to fermions.

Can Lagrangian surfaces be minimal surfaces?

I have not yet considered the question whether the Lagrangian surfaces can be minimal surfaces as they should be for a non-vanishing Λ. In the theorem the minimal Lagrangian surfaces were superminimal surfaces.

1. For super-minimal surfaces, a unit vector in the normal direction defines a 1-D very specific curve in normal space. It should be noted that for minimal surfaces, however, the second fundamental form disappears and cannot be used to define the normal vector. Lagrangian surfaces in twistor space also turned out to be minimal surfaces.
2. The field equations for the Kähler action do not force the Lagrangian surfaces to be minimal surfaces. However, there exists a lot of minimal Lagrangian surfaces.
   1. In CP₂, a homologically trivial geodesic sphere is a minimal surface. Note that the geodesic spheres obtained by isometries are regarded here as equivalent. Also g=1 minimal Lagrangian surface in CP₂ is known. There are many other minimal Lagrangian surfaces and second order differential equations for these surfaces are known (see this).
   2. In M⁴, the plane M² is an example of a minimal surface, which is a Lagrangian surface. Are there others? Could Hamilton-Jacobi structures (see this) that also involve the symplectic form and generalized Kähler structure (more precisely, their generalizations) define Lagrangian surfaces in M⁴? There is a general construction for Lagrangian minimal surfaces in M⁴ allowing to construct them from the solutions of a massless Dirac equation.
   As found, minimal surface property requires additional assumptions that could correspond to the somewhat strange-looking super-minimality assumption of the theorem. Could super-minimalism be another way to state these assumptions?
3. In the case considered now, the Lagrangian surfaces in H would be products X² × Y². Interestingly, in the 2-D case the induced metric always defines a holomorphic structure. Now, however, this holomorphic structure would not be the same as the one related to the holomorphic ansatz for which it is induced from H.

So What?

These findings raise several questions related to the detailed understanding of TGD. Should one allow only non-vanishing values of Λ? This would allow minimal Langrangian surfaces X²× Y² besides the holomorphic ansatz. The holomorphic structure due to the 2-dimensionality of X² and Y² means that holography=holomorphy principle generalizes.

If one allows Λ=0, all Lagrangian surfaces X²× Y² are allowed but also would have a holomorphic structure due to the 2-dimensionality of X² and Y² so that holography=holomorphy principle would generalize also now! Minimal surface property is obtained as a special case. Classically the extremals correspond to a vacuum sector and also in the fermionic sector modified Dirac equation is trivial. Therefore there is no physics involved.

Minimal Lagrangian surfaces are favored by the physical interpretation in terms of a geometric analog of the field particle duality. The orbit of a particle as a geodesic line (minimal 1-surface) generalizes to a minimal 4-surface and the field equations inside this surface generalizes massless field equations.

See the article The twistor space of H=M⁴× CP₂ allows Lagrangian 6-surfaces: what does this mean physically? or the chapter Symmetries and Geometry of the "World of Classical Worlds" .

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.

About mathematical cognition in TGD Universe

When one ponders about consciousness, one sooner or later realizes that the emergence of mathematical consciousness has meant an enormous evolutionary leap. Something completely exceptional seems to have occurred when the apple fell down about 382 years ago. Of course, also the emergence of our species was this kind of event? And there are my heros of science. This raises questions. What really happens in this kind of giant leaps of mathematical consciousness or cognitive consciousness in general. What does being or becoming conscious of a mathematical concept mean? Could one see this kind of event as an emergence of a new reflective level of consciousness? One cannot answer these questions unless one can identify the physical correlates of cognition, in particular mathematical cognition. In the sequel these questions are considered in the TGD framework in which the number theoretic and geometric views of physics are dual to each other.

This raises questions. What really happens in this kind of giant leaps of mathematical consciousness or cognitive consciousness in general. Is our species even in principle able to answer this kind of questions?

What does being or becoming conscious of a mathematical concept mean? Could one see this kind of event as an emergence of a new reflective level of consciousness? But how to describe this kind of hierarchy of levels of consciousness? What kind of phenomenon, bringing in mind phase transition, took place when humankind became conscious of differential and integral calculus, number theory, algebra, logic? Or did already the emergence of our civilization lead to this even?

One can imagine a more modest goal. What could be the physical correlates of these kinds of cognition. The easy solution of the problem would be that deterministic computations are conscious and one can formally regard any time deterministic time evolution as a computer program. This hypothesis does not however explain anything and is untestable.

Even the understanding of how the basic notions and algorithms are realized consciously at the level of cognitive consciousness seems very difficult in the framework of the recent day physics which has hitherto refused to say anything about conscious experience. Is the existing view of physics enough to meet the challenge?

These challenges look formidable but one can try! Maybe one could say at least something about cognition and mathematical cognition?

1. What are the physical correlates of cognition? Cognition is discrete and finite and cognition represents. Could one identify cognitive representations as a discretization of the sensory world. TGD leads to a number theoretic vision about physics dual to the geometric vision and provides a theory of cognition.

   p-Adic topologies seems to be very natural candidates for the topology of cognition. p-Adic number fields fusing together with reals to what is called adele. One can also defined entire hierarchy of adeles induced by algebraic extensions of rationals. There is also a second adele-like structure defined by the union of the p-adic number fields. Two p-adic number fields are glued together at interfaces formed by numbers, which have an expansion in powers of an integer divisible by both primes.

2. Concepts, in particular mathematical concepts, are a key element of cognition. What could be the quantum description of concepts and their emergence. Here standard quantum theory suggests an answer. Classically the field of concept is the set of its instances. In quantum theory wave functions in the set could define the instances of the concept.
3. What gives a concious meaning to the concept? Category theoretical thinking suggests that "arrows" as entanglements between concept and other concepts provide the meaning as state function reduction selecting one particular instance of the rule representd by entanglement. In physics this means quantum measurements.
4. What are the quantum physical correlates for Boolean logic? The Fock states define a Boolean algebra and in TGD framework these states span an infinite-D state space. In zero energy ontology (ZEO) \cite{allb/ZEO} \cite{btar/zeoquestions} of TGD this leads to a natural realization of Boolean algebras and zero energy state defines a quantum version of Boolean map \cite{allb/intsysc}.
5. We learn in school mathematics as associations such as "1+2"$\rightarrow$ "3" and the recent successes of GPT have demonstrated how powerful tool associations are. I have consider the possible quantum aspects of AI and GPT in \cite{btart/GPT,tgdcomp}) Could associative rules be represented by using quantum entanglement? This could reduce the development of mathematical understanding to the emergence of entangled states representing correlations as rules.
6. What conscious computation could mean? This requires a theory of consciousness and here TGD inspired theory of consciousness provides an approach. Could state function reduction reducing the entanglement defining associative rule give rise to a conscious experience associated with the association? Could one also imagine some kind of quantum hardware of mathematical consciousness perhaps representing the basic arithmetical operations?

Returning to the motivating question about the emergence of new reflective levels of consciousness and cognition, humans are distinguished from the other species by a highly evolved social organizations and in the TGD Universe the emergence of higher levels of consciousness assignable to social structures could be a central element. Single human viz. society would be like a single neuron viz. the entire brain. Here the hierarchy of magnetic bodies (MBs) is highly suggestive. The emergence of revolutionary ideas certainly requires a highly developed society with a large and complex MB. MBs involve an onion-like hierarchy of extensions of rationals and their dimension measuring their complexity serves as a kind of IQ. Could the emergence of a new level in this hierarchy give rise to these kinds of revolutionary events?

See the article About mathematical cognition 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.

About long range electromagnetic quantum coherence in TGD Universe

The focus of TGD inspired quantum biology has been hitherto in long range quantum gravitational coherence characterized by quantum gravitational Planck constant introduced by Nottale. The notion of gravitational Planck constant however generalizes also to other classical fields, in particular electric fields and one can define electromagnetic Planck constant. DNA, cells, and the Earth's surface carry negative charge. In this article, the possible presence of the long range quantum coherence in these systems is considered. Also a model for the interaction between living matter and computers is discussed.

See the article About long range electromagnetic quantum coherence in TGD Universe 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.

A possible mechanism of radiative energy transfer from the Earth's core to underground oceans near the surface of Earth

The recent observations (see this) strongly suggest that there is an ancient seabed on top of the Earth's core, and there are also mountains with a height of about 10 km. The proposed model, in which convection moves the sea floor to the region above the mantle, is probably correct.

This finding combined with the discovery of the so-called superionic ice (see this), which could exist above the Earth's core, allows to develop a proposal for a mechanism of metabolic energy transfer from the Earth's core to the underground oceans near the surface of Earth. This would make possible the development of photosynthesizing life forms in underground oceans. The generalization of the Pollack effect (see this and this) would play a key role in the mechanism.

Ultralow velocity zones

The following abstract of the article (see this) published by a group led by Dr. Samantha Hansen gives an overall view of what has been observed.

Ultralow velocity zones (ULVZs) are the most anomalous structures within the Earth s interior; however, given the wide range of associated characteristics (thickness and composition) reported by previous studies, the origins of ULVZs have been debated for decades. Using a recently developed seismic analysis approach, we find widespread, variable ULVZs along the core-mantle boundary (CMB) beneath a largely unsampled portion of the Southern Hemisphere. Our study region is not beneath current or recent subduction zones, but our mantle convection simulations demonstrate how heterogeneous accumulations of previously subducted materials could form on the CMB and explain our seismic observations. We further show that subducted materials can be globally distributed throughout the lowermost mantle with variable concentrations. These subducted materials, advected along the CMB, can provide an explanation for the distribution and range of reported ULVZ properties.

The so called S waves (see this) are transversal acoustic waves caused by the shear force parallel to the propagation. This force is proportional to viscosity and is negligible in liquids but much larger in solid phase waves reflected at mantle-core boundary. The core of Earth is in a liquid phase. Therefore sound waves from the surface of Earth are reflected back at the mantle-core boundary.

This makes it possible to deduce information from the structure of the mantle-core boundary and it has turned out that it has a highly complex structure. First of all, these waves propagate very slowly. This allows us to conclude that there is a relatively thin layer with a high density, which could consist of the same material as the seabed. This layer contains mountains with heights of order 10 km.

The TGD inspired view of the evolution life, inspired by the Cambrian Explosion and TGD based view of cosmology, is that photosynthesizing life evolved in underground oceans and that the expansion of the Earth radius by about factor 2 bursted these oceans to the surface of Earth in Cambrian Explosion (see this, this,this,this, and this).

The existence of an underground ocean immediately above the mantle is impossible due to the high pressure and temperature so that the convection remains the natural explanation for the presence of seabed.

The second objection is that life in the underground oceans is not possible because solar energy needed by photosynthesis is not available. How could photosynthesis have developed in the underground oceans? The key observation is that energies of the photons of thermal radiation coming from the core are of the same order as the metabolic energy currency with nominal value of .5 eV: could this radiation have served as a source of metabolic energy.

How would this energy be transferred? The Pollack effect (see this and this) and its reversal, whose TGD based understanding (see this, this, this,this, and this) has increased considerably during this year, could provide a fast energy transfer mechanism, but in its standard form the Pollack effect requires liquid water. Could the so-called superionic ice (see this and this), which has been speculated to be found even near the mantle of Earth, make possible the analogy of the Pollack effect?

Ordinary water cannot survive near mantle

Although it is obvious that ordinary liquid water cannot exist at temperatures and pressures prevailing near the mantle, it is useful to look at the situation more quantitatively.

In mechanical equilibrium, pressure gradient and the gravitational force, expressible in terms of the gradient of gravitational potential, cancel each other in good approximation. One can estimate the change of pressure as Δ p = ρ Δ Φ_gr= ρ GMΔ (1/R). The equation of state allows an estimate for Δ T.

Pressure is estimated to increase from 100 MPa at the surface of the Earth to 139 GPa above the mantle, that is by a factor 1000. Temperature, converted to thermal energy E=kT, is estimated to increase from .03 eV→ to 0.42 eV. The increase is by a factor of 10. Ordinary water cannot survive in this kind of environment so that underground water is possible only sufficiently near to the surface of Earth.

Could one imagine a phase of water allowing the analog of Pollack effect so that the transformation of protons to dark protons at the gravitational MB could make it possible to transfer metabolic energy to the higher heights, where underground liquid water can exist. This would have made possible the development of photosynthesizing life and would also solve the "faint Sun" paradox (see this) meaning that the solar energy feed was not enough for the metabolic needs of life at the surface of Earth.

Pollack effect for superionic water and metabolic energy feed from the core of Earth

Superionic ice (see this and this) existing at extreme pressures. The density of superionic ice is slightly less than 4 times the density of ordinary ice. In superionic ice O^2- ions form a lattice whereas H⁺ ions float freely. This phase is conductor with H⁺ ions serving as charge carriers. Superionic ice is proposed to appear in the mantles of giant planets such as Uranus and Neptune and I have proposed the possibility that it could occur in the Earth's mantle (see this and this).

Could water appear as superionic ice above the Earth's core and allow Pollack effect and its reversal so that gravitational flux tubes would carry dark protons? Could dark photons emitted in the reverse Polack effect transfer the energy along gravitational flux tubes to the underground oceans near the surface of the Earth?

Let's assume that there exists superionic ice above the mantle.

1. Could the radiation from the core kick part of the protons of the superionic water to the gravitational magnetic body? The gravitational binding energy of protons at the surface of Earth is about .5 eV and now roughly by a factor 4 larger, that is 2 eV, at the top of the mantle. At the gravitational magnetic flux tubes the reduction of gravitational binding energy is therefore below 2 eV. The temperature of the core corresponds to the metabolic energy currency of about .4 eV so that the radiation could have played the same role as the solar radiation in photosynthesis.
2. If the reverse Pollack effect occurs, dark photons are emitted and they propagate to the MBs of water volumes near the surface of Earth and could provide energy for photosynthesis. Also time reversal can occur for the water near the surface of Earth and the proton can gain the energy required by darkness by emitting a negative energy dark photon propagating to the MB near the mantle. I have called this mechanism remote metabolism or quantum credict card and asked whether it could play a key role also in the ordinary biology.
3. If the temperatures of the lower part of the mantle and the core are the same, the energy input from the core could feed protons to gravitational MB, maintain the superionic water phase and compensate for the energy loss due to the reverse Pollack effect. The transfer of energy near the earth's surface would take place at the speed of light and dissipation would be very small.
4. The number of ordinary-to-dark transitions of protons per unit time determines the energy flow to the MB and the energy flow to the uppermost layers of the mantle. In a steady state, this flow must be the same as the radiative heat flow from the core. This transfer rate is determined by the rate for the photon absorptions kicking protons to the MB. The energy flow of energy coming as radiation is proportional to T⁴.

See the article A possible mechanism of radiative energy transfer from the Earth’s core to underground oceans near the surface of Earth or the chapter Expanding Earth Hypothesis and Pre-Cambrian Earth.

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."https://tgdtheory.fi/tgdmaterials/curri.html">this.

Pollack Effect, Lightnings and Ball Lightnings

A TGD inspired model  for the ball lightning-like structures in silicon and for the real ball lightnings is developed. The model  relies on following assumptions. The TGD view  of space-time predicting fractality and inspiring the hypothesis that   biosphere could be regarded as a system analogous to neuronal membrane and that lightnings could be analogous to nerve pulses; the identification of  dark matter as phases with non-standard value of Planck constant allowing quantum coherence in arbitrarily long scales; the TGD view of quantum gravitation and its role in quantum biology; and the TGD inspired model of nerve pulse.

See the article Pollack Effect, Lightnings and Ball Lightnings or the chapter EEG and the structure of magnetosphere .

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.

Virtual touching of a virtual body part generates a real sensation of touching

This post was inspired by a highly interesting finding related to an experiment in which the subject person creates a virtual sensory input to a virtual hand that represents her own hand. The popular article is here and the original article "Phantom touch illusion, an unexpected phenomenological effect of tactile gating in the absence of tactile stimulation" of Pilacinski et al can be found here.

It was found that the virtual touching of the virtual hand creates a sensation in the corresponding body part of the subject person, say forearm. This occurs even if the person does not see the corresponding virtual body part. This suggests that more than visual cues are needed.

Consider first the TGD inspired view of sensory perception (see for instance this and a HREF= "https://tgdtheory.fi/pdfpool/emotions.pdf">this).

1. Sensory data at sensory organs is very fuzzy and the building up of sensory experience by pattern completion and recognition is almost a miracle. The process building sensory perception consisting of standard mental images must involve virtual sensory input to sensory organs, in particular eyes.
2. The sensory input would be communivated from sensory organ to cortex as dark photons (decaying to biophotons) with light velocity along flux tubes parallel to axons. From the cortex a signal to the MB would be sent. After that MB would make a guess about the final sensory perception very different from the actual sensory input. This guess must generate at sensory organs a diffuse sensory signal and must be compared with the diffuse sensory input.
3. This is achieved if the first guess generates a virtual sensory signal with a reversed arrow of time propagating to the sensory organs and becoming a diffuse sensory input at the sensory organs. The usual sensory processing in the brain would take place but in the opposite time direction. When the difference between virtual and real signal is small enough, the process stops.

   Note that the original model assumed that the virtual signal corresponds to the final percept but this is not the case for this variant of the model and ZEO becomes an absolutely essential element of the model.

4. At the next step, the virtual sensory signal would be compared with the real sensory input from the external world and the difference would be signalled via the cortex to MB. MB would make an improved guess. The iteration of this process would lead to sensory percept consisting of standardized mental images as pieces.
5. Dreams would be generated by a mere virtual sensory input coming from MB. Also imagination would rely on this process. Now the signals from the MB would not propagate to sensory organs but would stop at some higher level of hierarchy so that no real sensory experience would be generated.

It is known that intentional stimulation of (say) the skin by person himself creates a considerably weaker sensory signal than the simulation by an external input.

1. The reason for this would be savings in metabolic energy. There is no need to build intense sensory mental images if the stimulus is already known to be there. This would be achieved by sensing a virtual sensory input from the MB to the sensory organ, which would tend to cancel the real sensory input.
2. This happens also when one swims in a windy sea. When one returns to the beach, one experiences the sensation of being in the windy sea and the sensation can continue for quite a long time. The explanation is that the virtual sensory input from MB continues but is not cancelled by the real sensory input. Magnetic body would generate a compensating virtual sensory input tending to cancel the sensory input caused by the motion of biological body.
3. Correlational opponent processing seems to be a more general concept inspired by this phenomenon. Ron Blue has proposed in his correlational opponent-processing theory (see this) that the right and left hemisphere form opponents for each other creating opposite reactions. Magnetic body would tend to generate compensating effect cancelling the effect caused by the motion of biological body with respect to the MB to minimize metabolism. This would in general lead to a habituation.

Consider in this framework the situation in which a person induces virtual sensory input to a virtual body part. The mere intention about producing this virtual sensory input progates to MB which however believes that the sensory input is real (why this is the case?) and sends the compensating sensory input to the real body part. The situation is very much like swimming in a windy sea.

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.

Chronic pain as a sensory memory of pain

There was an interesting popular article related to the phenomenon of chronic pain as phantom pain. The article has title "Understanding that chronic back pain originates from within the brain could lead to quicker recovery, a new study finds". The original article "Reattribution to Mind-Brain Processes and Recovery From Chronic Back Pain A Secondary Analysis of a Randomized Clinical Trial" of Ashar et al can be found here.

It is known that for patients a chronic pain in the back, without actual problems in the back anymore, continues although the physiological reason for the pain is not present anymore. The proposal is that this pain originates in the brain.

The TGD interpretation is the same as in the case of phantom limb. The pain would not be imagined but would be real pain as a sensory memory of the pain, just as in the case of phantom limb. We indeed have sensory memories: long ago it was learned that the stimulation of parietal regions of the brain created sensory memories as direct experiences. The memory feats of some idiot savants are very probably based on sensory memories. Instead of a verbal representation, they have a direct sensory experience about say landscape or a music piece.

The view about memories provided by zero energy ontology is that they are in space-time where the original painful event occurred and involve a communication with the brain and body of the geometric past. This is essentially seeing in the direction of geometric time: time reflection takes place from an appropriate region of the brain or MB. Therapy might allow us to get rid of these sensorily painful memories in the same way as it allows us to get rid of psychologically painful memories.

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.

Quantitative support for the model of blackhole-like object as flux tube spaghetti

The TGD based model for blackhole-like object is as monopole flux tube spaghetti (see this) containing one proton per proton Compton length and filling the entire volume. There is no need to emphasize that the model means giving up the standard view of blackhole-like objects and that the model does not differ very much from the model for neutron stars.

Consider now the estimation of the total mass of the flux tube spaghetti.

1. Assuming additivity and neglecting self-gravitation, the total mass in units of m_p is M/m_p (here m_p≈ m_n is proton mass, the star would consist of neutrons).
2. Self gravitation for a spherically symmetric mass constant distribution inside sphere of radius R and given as ρ= M/Vol(R) created by the flux tube spaghetti gives to the stationary metric the deviation of g_tt from flat Minkowski metric is given by Δ g_tt = - Φ_gr, where one has

   Φ_gr (r)= 2G(2M(r)/r= (8π/3)×(GM/Vol(R)) r²= 2GM(r²/R³) .

   The gravitational potential energy of the mass distribution is in the Newtonian appproximation given by

   E_gr= -∫ρ(r)Φ_gr (r)dV=-6GM²/5R .

   For R= r_S= 2GM this gives

   E_gr=- 6GM²/10GM = -(3/5)M .

   Therefore the observed mass M_obs using m_p as a unit is given by

   M_obs=E_tot/m=(2/5) (M/m_p) .

3. Suppose that the flux radius of thickness R contains a single proton per length zR so that one proton fills the volume π× zR³. Suppose R corresponds to the proton Compton length L_p = h/m_p.

   Assume that h_eff ≠ h is possible so that L_p is scaled by y= h_eff/h. One would have

   L_p(h_eff)= y L_p .

4. The total mass M using m_p as unit and neglecting gravitational potential energy is given by the ratio of the volume V of the blackhole regarded as region of Minkowski space to the volume V_p taken by a single proton:

   M/m_p= V/V_p= (4/3z) × (r_S/L_p)³) y^{-3 .}

   Taking into account gravitational potential energy, one obtains

   M_obs/m= (2/5)(V/V_p)=(8/15z) × (r_S/L_p)³ y^{-3 .}

One can test the model for the Sun. One has M_S=2× 10³⁰ kg and r_S= 3 km. Proton has mass m_p= 1.6× 10^-27 kg and Compton length L_p= 1.3× 10^-15 m. Substituting the values to the above formula, one obtains (y,z)= (1,.992)≈ (1,1).

In the above formula M_obs/m on r.h.s decreases slightly in m_p→ m_n and 1/L_p³ on l.h.s increases slightly in m_p→ m_n. The changes of l.h.s and r.h.s are proportional to -ε × l.h.s and 3ε × r.h.s, where one has ε= (m_n-mp)/m_p&asymp: 1.811× 10^-3. This requires Δ (1/z) ≈-4ε (1/z) so that z=.992 is replaced with z_new=z(1+ 4ε)≈ .9992, which deviates from unity by -8× 10^-4.

The conclusion is that the simple flux tube model for h_eff=h and neutron taking a volume of Compton length, which is definitely different from the general relatistic model, is surprisingly realistic.

See the article Cosmic string model for the formation of galaxies and stars 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.

Ajatuksia sanasta jota on vaikea lausua

Rakkaus on sana, jota nykyisessä materialistisen tieteen hallitsemassa maailmassa on vaikea sanoa. Se tuntuu vain,... nololta. Ei se kuulu reaalimaailmaan, jossa taseet ovat töissä ja bisnes on bisnestä.

Rakkaus ei sovi nykytieteen, tai tarkemmin sanoen, kahdeksannentoista vuosisadan tieteen, maailmankuvaan, jossa maailman on deterministinen kone eikä ole sijaa tietoisuudella, vapaalle tahdolle eikä rakkaudelle.

Tässä vanhentuneessa maailmankuvassa me kuitenkin elämme, ainakin yhteiskunnan jäseninä, ja uskottelemme olevamme tämän determinismin täysin avuttomia uhreja. Yhteiskuntamme on tässä maailmankuvassa rakkaudeton kone ja meidän on alistuminen sen pieneksi rattaaksi. Ei voisi olla parempaa ilmaisua tälle uskolle kuin pääministerimme pakkomielteen omainen toistelu "On pakko!". Verohelpotukset rikkaille ja köyhät kyykkyyn. Perusteluksi on keksitty velka: sen lyhentäminen edellyttää tämän kaiken ja tämä kaikki on tietysti määrätty tapahtumaan jo alkuräjähdyksessä joten köyhän turha pullikoida.

Maailmankuvassamme on kuitenkin edellisen kanssa täysin ristiriitainen elementti: vulgaari-darwinimismi. Elämä nähdään armottomana olemassaolon taisteluna, jossa vahvempi voittaa, nopeat syövät hitaat, ja kaverille ei jätetä. Mutta eikötässä olekin ristiriita: miten ihmeessä tämä on mahdollista, jos yhteiskunta on tiedoton kone ja me sen mukana? Onko meillä sittenkin vapaa tahto, jos ei muuta niin ainakin jättää kaveri ilman?

Nyt mieleen tulee luvaton ajatus. Olisiko niin, että jotkut, ne jotka hallitsevat, tajuavat tämän ristiriidan aivan mainiosti. Mikä onkaan parempi tapa hallita kuin uskotella hallittaville että heillä ei lainkaan vapaata tahtoa: että he ovat vain pieniä rattaita isossa koneistossa. Toisaalta voi vapautua omantunnon vaivoista kun voi todeta olevansa vain pieni ratas suuressa koneistossa.

Ja tässä tullaankin persuihin. Hallituksessa on monia uusnatseja ja natsismin perusidea on että vahvoilla on oikeus ja jopa velvollisuus käyttää hyväkseen heikkoja. Tämän Nietche muotoili niin karskiksi filosofiaksi, ettei edes hänen oma mielenterveytensäkään ei sitä kestänyt. Empatiat pois politiikasta niinkuin Riikka Purra asian ilmaisee! Hallituksen irtisanoutuminen rasismista ja uusnatsismista oli puhdasta poliittista kosmetiikkaa. Koko hallitusohjelma on konkreettista yli-ihmis-ideologian toteuttamista. Enkä epäile, etteikö taustalla olisi tietoinen ajatus siitä että vahvemmmilla oikeus on nujertaa heikommat. Sitä ei tietysti voi ääneen sanoa, joten on kätevää vedota taloudelliseen determinismiin.

Mutta miten sitten rakkaus voisi auttaa tässä? Tiedämme, että rakkaus saa kirjaimellisesti ihmeitä aikaan. Se voi antaa uuden suunnan kokonaiselle ihmiselämälle. Ja voidaanko esimerkiksi yhteiskuntien käsittämättömän nopea toipuminen sotien tuottamasta täydellisestä hävityksestä ymmärtää materialistisessa kuvassa? Voisiko rakkaus olla todellinen vaikuttaja?

Nykyistä talouselämää luonnehtii rakkaudettomuus: kaikkialla vallitsee raaka kilpailu jossa vastustaja pyritään nujertamaan. Ei ole ystäviä, on vain liittolaisia. Luomme yhä uusia teknologiasia innovaatioita ja lopputuloksena on vain uusia ongelmia. Voisiko rakkaus auttaa?

Maailman uskontojen takana on oivallus rakkauden ainutlaatuisesta voimasta. Tieteessä esimerkiksi Einstein näki sen mysteerinä, jota emme ymmärrä. Mutta materialistinen nykytieteemme, joka on yhteiskuntafilosofiamme perusta ei halua rakkaudesta puhua, se vain sotkisi finanssi-teollisuuden yhtälöt. Ekonomistisessa maailmankuvassa on mahdotonta kuvitella, että rakkaus, joka rikkoisi tekisi mahdottoman mahdolliseksi rikkomalla determinismin pakkopaidan, voisi ratkaista yhteiskunnallisia ongelmia ja jopa pelastaa ihmiskunnan umpikujastaan johon materialistinen filosofia yhdistettynä vulgaaridarwinismiin on sen ajanut.

Kun esittää ekonomistille tai tieteentekijälle väitteen, että rakkaus voisi pelastaa sivilisaatiomme, on esitettävä myös tieteelliset perustelut. On kerrottava jotain oleellista siitä mitä rakkaus on tieteen näkökulmasta ja miten se kykenee vapauttamaan meidät determinismin. Tämä varmastikin vaatii tietoisuuden teorian ja sellainen on paraikaa kehittymässä: tosin YLEn uutiset eivät siitä ole kertoneet sanallakaan.

Ensimmäinen lohdullinen havainto on, että kvanttimekaniikka korvasi klassisen fysiikan determinismin tilastollisella determinismillä jo vuosisata sitten. Toinen lohdullinen havainto on että tilastollinen determinismi pätee vain tietyin edellytyksin. Skaaloissa, joissa kvanttikoherenssi vallitsee, ei tilastollinen determinismi pädekään ja maailma ei olekaan enää tiedoton kone vaan ennemminkin elävä ja tietoinen organismi.

Edelleen, kokeelliset havainnot jopa astrofysikaalisissa skaaloissa sekä kehittyvät tietoisuuden teoriat pakottavat kysymään onko kvanttikoherenssi vain atomaaristen systeemien ominaisuus vain onko se mahdollinen jopa elävän aineen tasolla?

Tekisikö kvanttikoherenssi mahdolliseksi elävälle aineelle uudelleen-luoda itseään ja ympärillä olevaa maailmaa? Jos vapaa tahto olisi jotain todellista niin myös etiikka ja moraali löytäisivät paikan maailmankuvassamme. Tietoiset olennot joutuisivat tällaisessa maailmankuvassa valitsemaan hyvän ja pahan välillä. Hyvät teot kasvattavat kvanttikoherenssia ja maailman ymmärrystä itsestään, pahat pienentävät sitä. Hyvät teot lisäävät rakkautta ja ne tehdään rakkauden motivoimina.

Voisiko siis rakkauden ohjaama vapaa tahto vaikuttaa jopa yhteiskuntamme tasolla? Kysymys saattaa kuulostaa maallikon korvissa hassulta: ilmeiseltähän tämä tuntuu. On kuitenkin muistettava, että tieteentekijä on dogmiensa vanki ja kykenee kyseenalaistamaan ne vain kun on ehdoton pakko (ja urakehitys ei vaarannu). Näyttää siltä, että tieteentekijät, joilla on papiston rooli nykymaailmassa, ovat avainasemassa. Jos haluamme pelastaa pallomme, on heidän pakko muuttaa dogmejaan. Pidetään siis peukkuja, aikaa ei ole paljon.

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.

Dirac and Bohr orbits

I received from Baba Ilya lyo Azza the following piece of text from Dirac. Since "Bohr orbit" appears in the text and I have used this word to  describe holography as  it is realized in TGD, I could not resist  the temptation to comment since Bohr orbit is such a word that colleagues cannot resist the temptation to label TGD as a childish  attempt to do theoretical physics by using some ancient notion.

“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.

As an example of a philosophical idea without a precise mathematical basis I would like to mention Mach's principle. Einstein has stated that he was indebted to this principle in his line of thought which led him to general relativity. But I do not see how this could be. I do not see how the principle can be formulated in a sufficiently definite way to be of any value in the search for a precise physical theory.

One should keep the need for a sound mathematical basis dominating one's search for a new theory. Any physical or philosophical ideas that one has must be adjusted to fit the mathematics. Not the other way around.

The need for putting the mathematics first comes from its more rigid nature. One can tinker with one's physical or philosophical ideas to adapt them to fit the mathematics. But the mathematics cannot be tinkered with. It is subject to completely rigid rules and is harshly restricted by strict logic.

The reason I feel so strongly about the views expressed above is because of the success I have had with them in the past. My early research work, in the early 1920's, was based on Bohr orbits, and was completely unsuccessful. I was taking the Bohr orbits as physically real and trying to build up a mathematics for them. I worked hard on this problem…

One sees now how futile such work was. Heisenberg showed that one needed a completely new mathematics, involving non-commutative algebra. The Bohr orbits were an unsound physical concept and should not be used as the basis for a theory.

I learnt my lesson then. I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting an interesting mathematics.”

Paul Dirac  Mathematical Foundations of Quantum Theory (1978).

My comment:

Bohr orbit was a brilliant physical  idea but was not of course mathematically sound. The mistake  was to give up this notion instead of trying to develop it further.  The price paid was the basic paradox of quantum measurement theory which is still with us. Wave functions in the space of Bohr orbits generalize the  standard notion of wave function, give precise connection with the classical theory,  and  lead to zero energy ontology. The classical determinism is consistent with the quantum jumps since they occur between these wave functions.  The experiments of Minev et al provide direct experimental evidence for the zero energy ontology. Quantum jumps correspond to smooth classical developments leading to the final state of quantum jump.   Second big mistake was the neglect of the fact that the conservation laws are lost in general relativity.

The notion of Bohr orbit,  in the sense that I use  it in TGD,  realizes holography. In   TGD  holography is forced by 4-D general coordinate invariance. Otherwise one would  have path integral over all space-time surfaces,  plagued by horrible infinities. This is  certainly consistent with the idea of sound mathematics as a basis of theoretical physics.

TGD provides a concrete realization of holography as a   4-D generalization of holomorphy in  terms of combination of 2-D complex and hypercomplex structures   as analogs of complex structures.   I call these structures Hamilton-Jacobi structures.  An explicit general solution of field equations is in question so that TGD is an exactly solvable theory. See this and this .

Irrespective of the  action principle, Bohr orbits are minimal surfaces locally if    the action is a general coordinate invariant constructed in terms of induced geometry. Only the singularities such as light-like boundaries and   interfaces of Minkowskian and Euclidean regions, and string world sheets depend on action. This reflects the universality of quantum criticality. Kahler action plus volume term is the action implied by the twistor lift of TGD.

The  holomorphic ansatz works also in the case of string models based on area action. In TGD the conformal and Kac-Moody symmetries of string model are replaced by an  infinite algebra of a  4-D generalization of conformal symmetries in terms of Noether currents and act as isometries of ther "world of classical worlds". Remarkably,  the action is *not* invariant under these symmetries as the naive expectation would be. Also symplectic symmetries assignable to the orbits of partonic symmetries and satisfying field equations for Chern-Simons-Kahler action are symmetries of the theory and act as isometries of WCW.

TGD also leads to a very detailed new  geometric and topological view of atoms, nuclei and hadrons and the relationship between strong and electroweak interactions relying strongly on the topology of the space-time surfaces representing the system and making strong and testable predictions. In particular, a  problem in the standard atomic theory is discovered: the atoms with many electrons are not classically stable and the TGD view provides stability.    See this and this .

So sum up, theoreticians must always start from the requirement that the theory is free of logical contradictions. Quantum measurement theory gave up this requirement and this stopped the progress.

TGD involves of course extremely beautiful mathematical structures: WCW as a mathematical construct  based on Bohr orbitology and making physics unique from its mere mathematical existence, physics as geometry and physics as number theory as  the basic approaches dual to each other,   M^8-H duality generalizing momentum position duality and strongly suggesting a connection with Langlands duality, number theoretic vision predicting standard model symmetries and giving rise to   possible correlates of cognition, hyperfinite factors and their inclusions,...

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 Notion of Generalized Integer

The inspiration for this contribution came from the article "Space Element Reduction Duplication (SERD) model produces photon-like information packets and light-like cosmological horizons" by Thomas L. Wood. published in Metodologia IV B:  Journal of International and Finnish Methodology, expressess the basic assumptions of the SERD approach very coherently and in a systematic way so that it easy easy to criticize them and compare with other views, in my case the TGD view.

My criticism is based on a different interpretation of the discreteness. It would be assignable to cognitive representations based on p-adic numbers fields involving extensions of rationals. Bringing in also the continuous number fields (reals, complex numbers, quaternions, octonions) brings in real space-time as sensory representation and one ends up to a generalization of the standard model proving a number theoretic interpretation for its symmetries.

The approach of Thomas looks to me essentially topological: for instance, the information propagating in the hypergraph is assumed to be topological. In TGD, discrete structures analogs define cognitive representations of the continuous sensory world and are basically number theoretic. The description of the sensory world involves both topology and geometry.

The articulation of this view led to the main result of this article, which is a generalization of the number concept as a fusion of all p-adic number fields and rationals to a single structure that I call generalized integers. Besides being useful in TGD, this framework could be very useful in the modelling of spin glass-like systems.

See the article The Notion of Generalized Integer or the chapter Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole

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.

Doubly magic mystery for nuclei

Recently I learned of a nuclear physics finding, which is interesting from the point of view of TGD based model for nuclei in terms nuclear strings that I managed to develop to a rather detailed form quite recently \cite{btart}{nuclatomplato}. This model extends to a model of both atoms and hadrons based on the same general basic ideas and makes rather non-trivial and testable predictions.

1. The first basic notion is nuclear string identifiable as a monopole flux tube. The nucleus would consist of one or more nuclear strings and they would define Hamiltonian cycle going through all vertices of the Platonic solid assignable to j-shell with angular momentum j=l +/- 1/2 and number of states N_-=2l or N₊=2l+2.
2. The fact that flux tubes involve also Coulomb flux does not allow closed Hamiltonian cycles: these are possible only for electromagnetically neutral systems.

   One can however eliminate one edge from the cycle. This kind of quasicycle for which the flux tube arrives point A from another Platonic solid and flows through all the remaining points of the cycle and returns to a neighboring point B and continues to a neighboring Platonic solid. This kind of quasicycles can be generated when the flux tube portions defining edges of closed cycles form reconnections: in this case however both the incoming and outgoing flux tube would correspond to missing edges. This would also allow degenerate quasi cycles with 2 vertices required by the model.

   One can ask whether one should one allow Hamiltonian paths in which incoming and outgoing fluxes are not associated with neighboring vertices. Their number is obviously larger than the number of cycles.

3. Both the harmonic oscillator potential used in the simplest nuclear model and Coulombic potential used in the model of atoms are characterized by a principal quantum number n such that l=1,2,..,n orbital angular momenta are realized for it.

   This motivates the idea of nucleus-atom holography meaning that the protonic states of the nucleus correspond to the states of electrons of the atom. This also leads to a speculative question whether neutrinos could play the role of neutrons in atoms.

One can imagine two options for how the particles are assigned to Hamiltonian cycles.

1. For the first option the particles could be assigned to V vertices of the platonic solid or to the V edges of the Hamilton cycle: if the quasi-Hamilton cycles are allowed, then only the vertices are allowed. The numbers of vertices are given by V= 4,6,8,12,20 for T,O,C,I,D.

   It is interesting to look in detail at the assignments of states at different n-shells.

   1. n=0: l=0. There are 2 states. Degenerate Platonic solid as diametrically opposite points of the sphere.
   2. n=1: l=0,1. There are 2+2+4 states. 2 degenerate Platonic solids + T
   3. n=2: l=0,1,2: 4+6 additional states to n=1-shell. Additional T and O.
   4. n=3: 6+8 additional states to n=2-shell. Additional O and C.
   5. n=6: 8+10 additional states to n=3 shell. 6 corresponds to C. 10 has no counterpart as a single platonic solid. 10 → T +O.
   6. n=6: 10 +12 states: 12 corresponds to I. 10→ T+O.

2. For the second option one assigns particles at the centers of complementary edges which by definition do not belong to the Hamiltonian cycle. There are F-2 complementary edges.

   One has F-2\in {2,6,4,18,10} for T,O,C,D,O.

   1. n=0: The 2 states correspond to T.
   2. n=1: The 2+4=6 additional states correspond to T+C:
   3. n=2: l=0,1,2: The 4+6=10 additional states correspond to C+O.
   4. n=3: There are 6+8 additional states. 6 corresponds to O but 8 corresponding to j=3+1/2 is missing. T+O would give 2+6=8 and C+C would give 4+4=8. j=3+1/2 cannot therefore correspond to a single platonic solid.
   One could worry about the fact that the magic number N=20 does not find an explanation in this picture. Rather, N=18 would correspond to 3 full shells. As if l=0 doublet would stabilize N=18 state. Why should this be the case? Interestingly, N=18 is atomic magic number.

   Energy shell can be defined in terms of an energy gap to the next state with a higher energy and this suggests that the discrepancy relates to the fact that l=0 state of n=3 shell are near to the energy of the highest state of the n=2.

   Spin-orbit interaction comes first into mind since it distinguishes between the energies for a given value of n and comes first to mind. L•S term is vanishing and its spin-orbit interaction is therefore expected to be smallest for l=0 state. In the case of atom, the interaction energy is nonvanishing since it involves expectation value of 1/2dV/dr, where V is in the atomic case Coulomb potential, in l=0 state and gives a term proportional to 1/l which at the limit l→ 0 gives a non-vanishing net result. In the case of a nucleus, the harmonic oscillator potential would give vanishing interaction energy.

   The F-2 option does not require the somewhat questionable degenerate Platonic solid but the V option works also for n=3.

3. One can ask whether the notion of n-shell could allow a description in terms of Platonic solids? In atoms l=0 and l=1 shells for n=1 shells give 2+2+4 =8 states, which could be assigned to the 8 vertices of the cube. F-2=8 is not satisfied by any Platonic solid.

   l=0,1,2 shells for the n=2-shell correspond to 2+ 2+4+4+6= 8+10=18 states assignable to the n=2 shell. These 18 states cannot be assigned to the vertices of a single Platonic solid. These states can be however assigned with the complementary edges of the icosahedron with F-2 =18. It would look however strange to assign the n=2 shell to complementary edges of the icosahedron and n=1 shell to the vertices of the cube.

With this background one can try to answer the question whether the recent findings, suggested to involve new nuclear physics, could help to test and even fix the details of the TGD based model.

1. ²⁸O nucleus has 8 protons and 20 neutrons and is doubly magic and should be therefore stable. It has 12 surplus halo neutrons and decays to a state with 8 surplus neutrons plus 4 neutrons with a life-time about 10^-21 seconds. The 12 surplus neutrons in the halo cannot correspond to a full shell. This could explain the short life-time.
2. ²⁸O decays by emitting 4 neurons to ²⁴O with 8 surplus neutrons. This state should be rather stable.

What could TGD say about this?

1. The reason why one cannot apply the magic nucleus rule could be that halo neutrons are different from the core neurons and must be treated separately. A possible reason is that the halo neutrons correspond to a non-standard value of h_eff=nh₀>h. This can occur also for the valence electrons of rare earth metals.
2. The 12 surplus neutrons in the halo do not correspond to a full n-shell. Both V and F-2 options are doomed to fail if the stability corresponds to a full n-shell.

   The ordinary 8 neutrons of ¹⁶O could correspond to a full n=1 shell. 8+4=12 halo neutrons would naturally correspond to a partially filled n=2 shell having 8+4+6=18 neutrons. This does not depend on whether one has V or F-2 option.

3. The 8 halo neutrons have the same quantum numbers as the full n=1 shell, which suggests stability. This conforms with the experimental findings. 4 neutrons, which correspond to j=3/2-plet could be assigned with the complementary edges of the cube but cannot form a full shell since the 6 j= 5/2-plet is missing.

See the article About Platonization of Nuclear String Model and of Model of Atoms 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.