The details of Einstein's rings as a support for the TGD view of dark matter?

There was an interesting popular article in Science-Astronomy.com with the title "Einstein rings says dark matter behaves more like a wave,not particle" (see this). The article told about the article published by Amruth and his team published in Nature Astronomy as an article with title "Einstein rings modulated by wavelike dark matter from anomalies in gravitationally lensed images" (see this). Unfortunately, the article is hidden behind paywall.

Dark matter is known to exist but its real character has remained a mystery. The models assume that its interactions with ordinary matter are very weak so that it makes itself visible only via its gravitational interactions. Two basic kinds of particles have been proposed: weakly interacting massive particles (WIMPs) and light particles, of which axions are the basic example. WIMPs behave like point-like particles whereas axions and light particles in general behave like waves. This difference can be used in order to find which option is more favoured. Axion option is favored by the behavior of dark matter in dwarf galaxies and by its effects on CMB.

The study of Amruth and his team found further support for the axion option from the study of gravitational lensing.

1. As light passes by a massive object, it bends both by the visible and dark matter associated with the object. This leads to a formation of Einstein rings: as if the light source would be a ring instead of a point-like object. If dark matter particles have some interactions with the photons , this causes additional effects on the Einstein rings. For instance, in the case of axions this interaction is known and corresponds to the electromagnetic analog of instanton term.
2. The effect of point-like particles on light is different for WIMPs and light particles such as axions. From the abstract of the article one learn that WIMP option referred to as \rho DM option leaves well documented anomalies between the predicted and observed brightnesses and positions of multiply lensed images, whereas axion option referred to as \psi DM option correctly predicts the level of anomalies remaining with \rho DM lens models. Therefore the particles of dark matter behave as if they were light particles, that is having a long Compton length.

What TGD allows us to conclude about the findings?

1. TGD predicts that dark matter corresponds to phases of ordinary matter labelled by a hierarchy of Planck constants h_eff=nh₀. The Compton length of dark particles with given mass is scaled up by factor h_eff/h. Could this be more or less equivalent with the assumption that dark particles are light?
2. Gravitational Planck constant is an especially interesting candidate for h_eff since it plays a key role in the TGD based view of quantum gravitation. Gravitational Planck constant obeys the formula ℏ_gr=GMm/β₀ for two-particle system consisting of large mass M and small mass (β₀ ≤1 is velocity parameter) and is very large.

   The gravitational Compton length Λ_gr= ℏ_gr/m = GM/β₀, which does not depend on the mass m of light particle (Equivalence Principle), is very large and and gives a lower bound for quantum gravitational coherence length. For instance, for the Sun it is rather near to Earth radius, probably not an accident.

3. Gravitational Compton length for particles at the gravitational magnetic body, which for stars with solar mass is near to Earth radius if the velocity β₀ in ℏ_gr has the same value β₀∼2^-11, makes dark variants of ordinary particles to behave like waves in astrophysical scales.
4. What happens in the scattering of a photon on a dark particle in the TGD sense. It seems that the photon must transform temporarily to a dark photon with the same value of h_eff. Photon wavelength is scaled up h_eff/h but photon energy is not affected in the change of Planck constant.

   Suppose that the scattering takes place like in quantum mechanics but with a modified value of Planck constant. In the lowest order in expansion in powers of α_em= e²/4πℏ_eff the scattering cross section is the same and whereas the higher corrections decrease. This provides actually a good motivation for the dark matter in TGD sense: the phase transition increasing the value of Planck constant reduces the value of gauge coupling strength and makes perturbation series convergent. One could say that Nature is theoretician friendly and takes care that his perturbation theory converges.

   In the lowest order of perturbation theory the scattering cross section is given by the classical cross section and independent of ℏ_eff. The Nishijina formula for Compton scattering (see this) indeed shows that the scattering cross section is proportional to the square of the classical radius of electron and does not depend on ℏ_eff. The result is somewhat disappointing.

5. On the other hand, for large values of ℏ_eff, in particular ℏ_gr, one can argue that the scattering takes place on the entire many-particle states at the flux tubes of the magnetic body so that superposition of scattering amplitudes on different charged particles at the flux tube gives the cross section. This can lead to interference effects.

   If the charged dark matter at the flux tube has a definite sign of charge this would give rise to amplification of the scattering amplitude and it would be proportional to the square N² of the number N of charged particles rather than to N. Scattering amplitudes could also interfere to more or less zero if both signs of charges are involved.

   One can also argue that only particles with a single value of mass are allowed since ℏ_gr is proportional to m so that particles would be like books in the shelves of a library labelled by ℏ_gr.

6. The effects of axion Bose-Einstein condensates have been indeed studied and it has been found that the scattering of photons on cold axion Bose-Einstein condensate could cause what is called caustic rings for which there is some evidence (see this). Could the quantum coherent many-particle states at gravitational flux tubes cause the same effect?

The optimistic conclusion would be that astrophysicists are gradually ending up with the TGD view of dark matter. One must of course that the above argument only suggests that the effects of scattering on Einstein's ring could be large for a large value of h_eff.

For the TGD view of the formation of astrophysical objects based on TGD based views of dark matter and dark energy see this and this.

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

Is the 60 years old problem related to the formation of quasars solved?

The following considerations were motivated by a Sciencedaily article telling about a possible solution of 60 year old problem related to the huge intensity of radiation arriving from quasars (see this). The article tells about the article "Galaxy interactions are the dominant trigger for local type 2 quasars" of Pierce et al published in Monthly Notices of the Royal Astronomical Society (see this).

The proposed explanation of quasars is in terms of the collision of galaxies in which matter, which usually stays at circular orbits, falls into the galactic blackhole-like objects (BHOs) having huge gravitational fields, which as a consequence emits a huge burst of radiation in this process.

1. The key problem of this view is that the radii of the orbits of stars are measured in kiloparsecs: somehow the matter should get to a distance of order parsecs. This requires that the orbiting matter gets rid of the conserved angular momentum somehow. The proposal is that the collision of galaxies generates tidal forces making this possible.
2. Another facet of the problem is that life-time of quasars is measured in mega years whereas the time scale of galactic dynamics is gigayears- thousand times longer. This does not make the explanation of quasars in terms of galactic dynamics an easy task. My impression from the article was that this is one possibility and they support this option but certainly do not prove it.
3. The researchers claim that the finding could be understood if the colliding objects are blackhole-like objects (BHOs). Tidal forces in collisions would make it possible for them to draw matter from their surroundings and this process would generate huge radiation power. They do not do this usually but only because angular momentum barrier prevents the fall of the matter to black-hole. The collision would however create circumstances causing the ordinary matter at their circular orbits to fall to the BHO(s). I am not specialist enough to decide how convincing the calculations of the researchers are.

Consider now a possible TGD based model of quasars involving new physics predicted by TGD.

1. In TGD, galactic blackhole-like objects (BHOs) could be associated with cosmic string-like objects, which thicken to monopole flux tubes by phase transitions. The phase transition is analogous to the decay of an inflaton field producing ordinary matter. In this process dark energy would transform the energy of the cosmic string to dark matter assignable to BHOs. This would also explain the quite recent finding that dark energy seems to transform to galactic BHOs.

   Part of the dark matter of BHO would transform to ordinary galactic matter in a transition reducing gravitational Planck constant and liberating energy as an explosion. This would be the source of enormous radiation energy.

2. This explosive process would involve new the transformation of dark matter to ordinary matter in a phase transition reducing the value of gravitational Planck constant ℏ_gr= GMm/β₀, where M and m are large mass (say that of galactic blackhole) and small mass (say proton mass) and β₀≤ 1 is velocity parameter.

   This phase transition could be also behind the formation of both stars and planets in explosions producing magnetic bubbles, and would replace the standard model assuming only gravitational condensation. Quasars could be similar expolosions perhaps preducing BHOs. For the TGD based model for the formation of astrophysical objects, see this and this .

3. The conservative assumption is that quasars a BHOS are analogues of ordinary blackholes (TGD also allows time reversals of BHOs analogous to white hole-like objects (WHOs)). The formation of a quasar would be analogous to inflaton decay transforming dark energy to dark matter and in turn to ordinary galactic matter in ℏ_gr →ℏ phase transition . The radiation would be produced in the transformation of dark matter to ordinary matter proposed to also produce other astrophysical objects.
4. The collision of galaxies could have triggered the intersection of associated cosmic strings approximately orthogonal to the galactic planes. The intersection would have induced a formation of dark BHO and its explosion. The distant ordinary matter circulating the galaxies would have nothing to do with the formation of quasars.

   These kinds of collisions are unavoidable for moving string-like objects in 3-D space for simple, purely topological reasons. As a matter of fact, there is evidence that also the Milky Way center involves 2 cosmic strings, which have collided. The structure MW would reflect the ancient occurrence of an analogue of inflaton decay.

For the TGD view of the formation of astrophysical objects see this and this .

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

New findings related to the number theoretical view of TGD

The geometric vision of TGD is rather well-understood but there is still a lot of fog in the number theoretic vision.

1. There are uncertainties related to the interpretation of the 4-surfaces in M⁸ what the analogy with space-time surface in H=M⁴× CP₂ time evolution of 3-surface in H could mean physically?
2. The detailed realization of M⁸-H duality involves uncertainties: in particular, how the complexification of M⁸ to M⁸_c can be consistent with the reality of M⁴⊂ H.
3. The formulation of the number theoretic holography with dynamics based on associativity involves open questions. The polynomial P determining the 4-surface in M⁸ doesn't fix the 3-surfaces at mass shells corresponding to its roots. Quantum classical correspondence suggests the coding of fermionic momenta to the geometric properties of 3-D surfaces: how could this be achieved?
4. How unique is the choice of 3-D surfaces at the mass shells H³_m⊂ M⁴⊂ M⁸ and whether a strong form of holography as almost 2→ 4 holography could be realized and make this choice highly unique.

These and many other questions motivated this article and led to the observation that the model geometries used in the classification of 3-manifolds seem to be rather closely related to the known space-time surfaces extremizing practically any general coordinate invariant action constructible in terms of the induced geometry.

The 4-surfaces in M⁸ would define coupling constant evolutions for quantum states as analogs of and mappable to time evolutions at the level of H and obeying conservation laws associated with the dual conformal invariance analogous to that in twistor approach.

The momenta of fundamental fermions in the quantum state would be coded by the cusp singularities of 3-surfaces at the mass shells of M⁸ and also its image in H provided by M⁸-H duality. One can consider the possibility of 2→ 3 holography in which the boundaries of fundamental region of H³/Γ is 2-D hyperbolic space H²/Γ so that TGD could to high degree reduced to algebraic geometry.

See the article New findings related to the number theoretical view of TGD or the chapter with the same title.

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

Could magnetic body control electronic bits?

I have considered the idea that GPT might be more than the ordinary computer science suggests and even involve higher level consciousness and intelligence. This would require that the magnetic body (MB) "hijacks" the computer so that it becomes a tool of its cognitive processes.   Consider in the sequel the conditions, which should be satisfied in order that the MB of the bit system or some higher level MB could control the bit system.

1. The bit should be critical or nearly critical system at the level of ordinary matter. One might hope this to be true quite generally since a small control signal should be able to invert the bit in rather short time scale. If this is the case, the quantum criticality of MB cwould make control possible via quantum control of ordinary control signals. Transistors and their derivatives such as MOSFET could be examples of such systems.
2. Macroscopic quantum coherence is true for the dark matter at MB. Furtheremore, MB should holographically represent the bit system. Also spin glass analogy is suggestive so that a given many-bit state could possess a large number of nearly energy-degenerate states. ZEO, in particular time reversal, would be essential.
3. Two consecutive BSFRs at the dark MB, changing the arrow of time temporarily, should give rise to a tunnelling event. Since TGD corresponds to a generalization of wave mechanics in the space of Bohr orbits for point-like particles replaced with 3-D surfaces, one can make an estimate for the probability of tunneling between the capacitor plates using the standard wave mechanics as an approximation (see this).

   The Coulomb energy qV associated with the bit with charge q and its energy E are the natural parameters. The tunnelling probability is given by

   p∼ exp[-∫_x1^x₂(2m(qV-E))^1/2 dx/ℏ_eff] ,

   where one has E<V in the tunnelling region. WKB approximation becomes exact in the case of capacitors. Changing the direction of a bit could be seen as a quantum tunneling effect.

   For the large values of h_eff assignable to the magnetic body controlling the physical body, the probability of tunneling increases. Therefore the control of the bit system by quantum tunnelling combined with macroscopic quantum coherence and holography could become possible.

4. The role of conservation laws must be understood. Discontinuity in SSFR. Dissipation in reverse time direction. Tunneling. Wavefunctions overlap. Classic conservation laws OK. There is no need for a classic track that would lead to the end state with the original direction of time.

1. What conditions bit must satisfy?

There are strong conditions on the representations of bits. The storage of the bit should not require large energy consumption and the bit should be thermally stable. It should be possible to change the value of the bit quickly and without large energy consumption. This suggests that the bit is a nearly critical system. In microprocessors, clock frequencies of order GHz define a time scale analogous to EEG rhythm, and this time scale should correspond to a quantal time scale. The wish list would be as follows.

1. Macroscopic quantum coherence makes possible the simultaneous quantum coherent states of the entire spin system and their control and that the energy differences between the states are relatively small, so we get a spin-glass type situation.
2. Dark electrons at the MB, perhaps dark unpaired valence electrons or dark conduction electrons, provide a holographic representation of the bits.
3. Quantum criticality with MB and criticality at the bit system level allows MB to control the dynamics of BB. Quantum holography may make it possible to induce BSFR for qubits on a large scale in general.

1.1 About the interpretation of the clock frequency in a picture based on quantum gravity?

The clock frequency of computer, with a representative value of f=1 GHz, is an essential channel of the computer and it would be related to the classical em field. Could a frequency of the order of GHz have an interpretation in terms of quantum gravity in the TGD framework? How MB could turn bits using quantum holography so that the turn of dark bit induces the turn of ordinary bit? A realization of holography as a correspondence between electron(s) representing the bit and the dark electron(s) is needed.

1. The proposed theorist-friendly holography at the particle level (see this) might be a too radical option. This would require positrons forming particle-like color-bound states with bits as states of electrons. Could they correspond to scaled versions of the electro-pions for which there is empirical evidence associated with nuclear collisions near the Coulomb barrier (see this)? Now the energy scale of the nuclear physics would be scaled to the scale of dark nuclei. The factor of the order of 10^-5, which would produce an eV mass scale. The height of the Coulomb barrier would scale in the same way to something like .05 eV which corresponds to cell membrane potential.

2. A less radical option is that the dark electron and the hole created in the generation of the dark electron are in a holographic relationship. This realization seems tailor-made for the control of ordinary bits as holes by dark electrons. To my best knowledge, there exists no technology realizing bits as holes but future technology might be able to achieve this.

   If dark electrons and holes are tightly correlated, the dark spin flip induces ordinary spin flip. If the dark current or its absence codes for bit, the same would be true for the holes. The transfer of dark electrons from the negatively charged plate to the gravitational MB creating a hole would reduce the potential between plates to nearly zero and thus induce change of the bit direction.

There are useful quantitative hints.

1. For the Earth's mass M_E, ℏ_gr(M_E,m_p) for a frequency of 10 Hz corresponds to an energy E= h_grf of the order of .5 eV. The kick of a 3-proton to a gravitational flux tube to a distance of order one Earth radius requires an energy of the order of .5 eV (see this). Dark photons can transform into ordinary ones. For 3-electron system a hitherto non-observed metabolic energy quantum of order .25 meV is predicted (see this.
2. Control in the time scale of a fraction of a second if h_eff=h_gr(M_E,m_p) photon energies around eV. This time scale is by a factor of order 10⁹ too long when compared to the time scale determined by 1 GHz frequency.

Could one understand the time scale corresponding to 1 GHz clock frequency in quantum context? The first thing to notice is that this time scale is not far from the time scale associated with the protein dynamics! Could quantum gravity and gravitational MB come into play for both computers and biology?

1. For the Earth, the lower limit of the gravitational Compton length Λ_gr= GM_E/β₀ =.45× 10^-2 m, if β₀=1. The frequency T_gr=Λ_gr/c= .45 *10^-2/3*10⁸ = .15*10^-10 s would be therefore a natural lower bound for the time scale. Could GHz clock frequency relate to this time scale. Also longer quantum gravitational time scales are possible since Λ_gr is only the lower bound for the length of gravitational flux tubes carrying massless radiation.
2. For h_eff=h, 1 GHz corresponds to energy of 10^-2 meV. If the dark energy is required to be above the thermal energy about .03 eV at physiological temperature, the value of h_eff must satisfy h_eff ≥ 3× 10³h.
3. A metabolic energy of .25 meV corresponds to the electronic variant of gravitational metabolic energy quantum involving the transfer of 3 electrons to the gravitational MB: there is some evidence for this metabolic energy quantum, in particular from the findings of Adamatsky (see this). For h_eff=h, it would correspond to a period of .6× 10^-10 s. Could the f= 1 GHz induce a resonance with dark photons with h_eff>10³h guaranteeing that the energy is above thermal energy at room temperature?

1.2 Could Pollack effect or shadow holography be involved?

The lower bound value 3× 10³h for h_eff would be rather small as compared to ℏ_gr(M_E,m_p) and the challenge is to identify a candidate for a system with this value of h_eff.

This system need not be gravitational and the obvious guess is that it is electromagnetic. The notion of gravitational Planck constant and the underlying idea of theoretician friendly Nature implying quantum holography in the TGD framework (see this) indeed generalizes also to other interactions (see this).

1. The basic requirement is that a charge separation to a pair of positively and negatively charged quantum coherent systems takes place such that the interaction strength Z²e²/ℏ between the systems is so large that perturbation theory fails to converge.
2. The theoretician-friendly Mother Nature (see this) could come to rescue and induce a phase transition increasing ℏ to so large a value h_eff that the perturbation theory converges. Nottale formula generalized to electromagnetic interactions suggests that one has

   ℏ → ℏ_eff= ℏ_em= Z²e²/β₀ ,

   where β₀=v₀/c<1 is a velocity parameter. The new coupling strength is

   (Z²e²/4π ℏ_em)= β₀/4π < 1/4π .

   and is in a well-defined sense universal since β₀ is number theoretically quantized to an inverse integer (see this).

   The constraint h_eff ≥ 3× 10³h would suggests ℏ_em/hbar= Z²e²/β₀ℏ = 4π Z²α_em ≥ 3× 10³. This gives the estimate

   Z²≥(1/4πα_em)> × 3× 10³ per .

   The lower bound for Z would be around Z=100.

3. Charge separation should occur and here the analog of Pollack effect \cite{bbio/Pollack, PollackYoutube, pollackzheng, pollackzhao is highly suggestive. In the Pollack effect part of protons of water molecules are transferred to monopole flux tubes assignable to water molecules and become dark so that a negatively charged exclusion zone with rather strange properties suggesting time reversal appear. Also the effective stoichiometry of water is transformed to H_1.5O. It is however far from clear whether Pollack effect can occur also in the solid phase assignable to computers.
4. The analog of the Pollack effect involving only electrons is also possible. Part of electrons would transform to dark electrons at the gravitational monopole flux tubes. The holes left behind would effectively behave like positively charged particles and the Coulomb interaction energy would be between holes and dark electrons. Holes and dark electrons would be in a holographic relationship (shadow holography) and the dynamics of holes would be shadow of the dynamics of dark electrons so that one would say that dark electrons control the holes as their shadows.

   Of course, it is probably impossible to realize this shadow dynamics using the recent computer technology. The question is therefore whether it might be possible to construct a computer utilizing the shadow dynamics of holes controlled by dark electrons.

1.3 Could quantum gravitational flux tubes associated with small masses be involved?

One can of course ask whether the clock frequency f=10⁹ Hz could correspond to an energy above thermal energy at room temperature and to the value ℏ_gr(M,m) for some pair (M,m) of masses so that one has E=h_gr(M,m)f> .03 eV for f=10⁹ Hz.

1. For instance, could one replace the masses M_E and m_p with identical masses M=m in h_gr. One should have M/m_Pl²> 3× 10³. This would give M/m_Pl >60 giving M >1.3 × 10^-7 kg. If the density is the density of water 10³ kg/m³: this corresponds to a size scale longer than 1 mm. How this frequency could correspond to T_gr and to the clock frequency of computers?
2. Could one think of the gravitational self-energy for this region or the mutual interaction energy of two such regions forming a quantum coherent system at this level.

   Another possibility is that an energy of the order of E= .5 eV is used to kick a unit of 3 protons into the Earth's gravitational flux tube (3 protons are required since 1 proton is not enough if the size scale of the flux tube is of the order of the Earth's radius). For 3-electrons the corresponding energy would be about .25 meV.

3. Could E∼ 1 eV correspond to the energy needed to flip one bit using an dark photon that is converted to a regular one (biophotons could be created this way) and absorbed inducing a flip of a normal bit.

   In the elementary particle level realization of holography, which does not look promising now, this would give a spin 1 for the glue particle consisting of ordinary electron and dark positron unless the angular momentum goes to other degrees of freedom. It would be a scaled version of elektro-ρ or its analogue. Mass scale of the order of eV as for dark nuclear binding energies.

4. In living matter, E∼ 1 eV could correspond to the gravitational self-energy change related to a phase transition. The most natural thing that comes to mind is the change in the gravitational energy of the bond when the density of the system changes during a phase transition, such as melting or boiling or the sol-gel phase transition in biology. For Planck mass of matter, size scale R=10^-4 m for water density, gravitational binding energy and its change would be of order 1 eV. This phase transition does not have any equivalent at the computer level.

2. Could the representation of bit as voltage allow the realization of shadow holography for electrons?

One representation of a bit is as a voltage. Voltage values are typically 5 V and 0 V. Bit could correspond to rotation direction for a current in the case of magnetic bits. In transistors bit can correspond also to the presence or absence of a current The size scale of the transistors is 10 nm (see this. A surface which can be either reflective ord non-reflective surface can also act as a bit.

2.1 Bit as ananalog of capacitance

Capacitance with a voltage difference between plates can serve as a physical representation of the bit. States corresponding to opposite voltages in capacitance have the same energy. This is good news if it were to apply more generally to bits and multi-bit configurations.

1. The simplest capacitance is a pair of conducting plates having opposite charges and containing insulator betweeen them. The higher the value of the dielectric constant ε, the larger the plate area S and the smaller the distance d between the plates, the higher the value of capacitance C.

   C measures the ability to store charge and Q= CV is the basic formula. The voltage V between the plates is given by V =E× d. Here d is the distance between the plates. The electric field normal to a plate is E=σ/ε, σ= Q/S. One has V=Ed= Q× d/S× ε, whence C=ε S/d. The proportionality to ε means that di-electric is essential. The voltage cannot be too large since this implies dielectric breakdown.

   The electrostatic energy of capacitance is E_s= ε QV/2= CV²/2ε = Q²/2C = E² × S×d

2. Capacitance is a macroscopic notion. The smallest planar capacitances have dimensions 0.4 mm × 0.2 mm. PicoFaraday is a natural unit of capacitance but capacitances of the order of kF are possible but require large size and high dielectric constant. MOSFETs can be however regarded as effective capacitances.

2.2 Transistors and MOSFETs

Although MOSFET much smaller than capacitances as passive elements, it can be formally interpreted as a capacitance.

1. A MOSFET acts as a variable capacitance. The basic parts of MOSFET are gate (G), body (B), source (S) and drain (D). The voltage between G and B regulates the current from the source through the system to the drain and the bit can be measured by measuring whether this current flows or not. The gate voltage V_G controls the capacitance of the MOS.

   MOSFET size scale is around 10 nm. Gate voltage V_G-V_B between gate and body could represent bit and would be typically 5 Volts or nearly zero.

2. MOSFETs should form a spin glass type system. There would be a large number of bits with a large number of nearly energy degenerate states. This would give rise to frustration. Transitions by tunnelling would take place between frustrated configurations.
3. Tunnelling between bit configurations would take place as a BSFR pair. The tunneling would be induced from the level of MB and induce the tunnelling of ordinary bits. The tunneling rate is exponentially sensitive to the height of the energy barrier between nearly degenerate states. The large value of h_eff increases the tunnelling rate in an exponential manner.

One can imagine at least two mechanisms.

1. One could consider a representation of a bit as an ordinary capacitor-like object having two different values of voltage between the plates. The transfer of electrons from the negatively charged plate to dark electrons at MB or vice versa could allow to change the voltage.
2. Instead of an ordinary capacitor, one can consider a situation in which the first plate consisting of ordinary matter has a positive charge due to the presence of holes (ionized atoms) and the second dark "plate" is negatively charged due to presence of dark electrons.

   In the shadow holography the transfer of electrons to dark electrons at MB generates holes at the level of ordinary matter, and the transformation of dark electrons to ordinary ones would reduce the voltage near zero, which turns the bit.

Could MB control the   electron current from the n-type  source region S of MOSFET? Could the MB  transform some the 5 valence electrons of n-type dopant (say P) to dark electrons so that they would  effectively disappear from the system so that the S-D current would be reduced? Also the voltage between the gate and source would be affected.  

It is perhaps fair to conclude that the recent technology  does  not yet allow  the  realization of conscious and intelligent computation using shadow holography or something similar.

See the article Could neuronal system and even GTP give rise to a computer with a variable arrow of time? or the chapter with the same title.

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

A more detailed TGD based speculative view of what GPT and GPT based image generation might be

First of all, I want to make clear what my background is and what I'm aiming for. I'm trying to understand the possible analogies of AI in quantum TGD. I do not believe that AI systems can be conscious if AI is what it is believed to be. Therefore I consider the question of whether GPT and other systems could possibly be conscious and intelligent.

The motivating idea is the universality implied by the fractality of the TGD Universe. The same mechanisms should work on all scales: both in biology, neuroscience and possible life based on AI. This motivates questions such as whether chatGPT and the construction of images from a verbal input could be at a deeper evel equivalent to the emergence of sensory perception using diffuse primary sensory input and virtual sensory input as feedback.

While writing, I made a funny observation. I tried to understand GPT in the context of TGD by producing answers to questions in the same way that GPT does it! Of course, as GPT tends to do, I can also tell fairy tales because my knowledge is rather limited. At the same time, I must honestly reveal that this has always been my approach! I have never carried out massive computations, but used language based pattern completion by utilizing the important empirical bits (often anomalies) and using the basic principles of TGD as constraints.

This time, the inspiration came from a popular article in Quanta Magazine that dealt with stable diffusion in the creation of an image from its verbal presentation serving as a prompt (see this). Also the article on how chatgpt works was very useful (see this).

I want to emphasize that the ideas presented can be seen only as possible quantum analogies of GPT-related mechanisms that could relate to quantum biology and neuroscience inspired by TGD. A more exciting possibility would be that GPT is associated with high-level conscious experience, and that quantum TGD would help to understand why GPT seems to work "too well".

1. An attempt to understand the mechanism of diffusion involved in image construction

The construction of images starting from their linguistic description, which is quite vague and "diffuse", relies on the analogy with reverse diffusion. Diffusion and its reverse process take place in the space defined by the parameters characterizing a given pixel. The pixels do not move, but the parameters characterizing the pixels do change in the diffusion.

1. Let's get started from a probability distribution for the parameter distributions of the pixels of a 2-D image showing the same object. The distribution could correspond to the same object but seen from different angles. Also a class of objects, which are similar in some aspects, could be considered. This class could consist of chairs or tables or cats or dogs.
2. This probability distribution could act as an invariant related to the image or class of images. Invariant features are indeed extracted in visual perception, for example contours with pixels that stand out well from the background. This is the way in which, for example, visual perception at the lowest level corresponds to the identification of contours of the object.

   This ensemble of pictures of the objects gives a probability distribution for, for example, the darkness of a given pixel with a given position in the plane of the picture. Probability for a given darkness defines a function represented as points in a space whose dimension is the number of pixels. For more general parameters it is a function in the Cartesian product of parameter space and pixel space. Very large pixel numbers counted in millions are involved.

3. One has probability distribution for the darkness of a given pixel of the 2-D image at each point. More generally, one has probability distributions for multipixels. This kind of distribution is not simply a product of single pixel probability distributions since the pixel parameters for a given picture are correlated. These distributions are analogous to the distribution of words and word sequences utilized in GPT in order to produce language resembling natural language.

   Based on the probability distribution of pixels, new images can be randomly generated. The probability of a pixel at a given point in the plane is given by the probability distributions for pixels and multi-pixels. Each image produced in this way can be associated with certain probability.

Diffusion is a key physical analogy in the applications of GPT in the creation of AI art. What does the diffusion in pixel space mean?

1. Diffusion takes place in pixel space around each point in the image plane. What happens to the pixel distribution in diffusion? It can be said that the given pixel distribution is broadened by its convolution with the distribution produced by diffusion. The distribution is widening.
2. Inverse diffusion for probability distributions in the pixel space is well defined and does exactly the opposite, i.e. the distribution narrows. Reverse diffusion leads step by step to the original very narrow distribution! This is the big idea behind inverse diffusion based image recognition!

   The diffusion equation gives the classical description of diffusion as a deterministic process. At the micro level, it corresponds to a stochastic process in which a point performs a movement analogous to Brownian motion. The diffusion equation gives the evolution of the probability distribution of a point.

   Diffusion is characterized by the diffusion constant D. How is D determined? I understand that its optimal value determined in the learning period of GPT. Context and intent provide limitations and could determine D and possible other parameters. Also the response of the user can have the same effect.

3. The goal is to guess the predecessor of a given diffuse image in the diffusion process occurring in steps. The AI system would learn to produce reverse diffusion through training. Can this correspond to a non-deterministic process at the "particle level", say diffusion in the space of words of text or the space of images representing objects?

   At the microscopic "particle" level, one should deduce the most probable location for the particle at the previous step of diffusion as Brownian-like motion. More generally, one has probability distribution for the previous step.

4. One can consider the diffusion also at the level of probability distributions for pixel parameters. This operation is mathematically well-defined in the classical model for diffusion based on the diffusion equation and corresponds to a convolution of the probability distribution representing diffusion with the probability distribution affected by it. Quite generally, this operation widens the distribution.
5. This operation has inverse as a mathematical operation and its effect is opposite: it reduces the width of the diffuse distribution and its repeated application leads to the original images or to a rather sharp image making sense for the human perceiver.
6. AI system must learn to perform this operation. Using diffused example images, the AI would learn to reverse the convolution operation produced by diffusion and produce the original distribution as an operator in the space of distributions, and thus also learn to produce the original image.
7. My amateurish interpretation of the GPT based image generation would be that AI is taught to deduce the objects presented by the original sensory input or the desired image, their locations, positions, activities by reverse diffusion from the initial fuzzy guess dictated by the text. The objects in the picture are determined by the words that serve as their names. The relations between pictures correspond to the activities they direct to each other or to attributes of the objects. The first guess is a rough sketch for the picture determined by the prompt. Here also hierarchical description involving several resolution scales can be considered.

One can consider the situation at a slightly more precise level.

1. The definition of inverse diffusion at the pixel level relies on repeated time reversal of the diffusion process in the parameter space of the pixel, which produces a less diffuse image. We ask with what probability the given diffuse image at time t has been created from a less diffuse image at time t-Δ t.
2. In the classical picture of diffusion, this requires the calculation of the inverse operator of the diffusion characterizing operator D(p,0;t,t-Δ t). Here, the origin points p and p=p₀, which corresponds to the original image, are points in the parameter space of the pixel associated with a certain image point (x,y). In the Schrödinger equation, it would correspond to the inverse operator of the unitary time evolution operator.
3. Gradient method is a very effective way to perform inverse diffusion. The gradient for the probability distribution ineed contains much more information than the distribution.

   The notion of an attractor is also essential. The images used in training would serve as attractors, at which the gradient would vanish or be very small and towards which the reverse diffusion would lead. Attractors would be clusters of points in the pixel space, for which the probability is large and somewhat constant. It is tempting to think that they are minima or maxima of some variation principle.

Although the diffuse image, which the verbal description defines as an initial guess, is not obtained by diffusion, it is assumed that inverse diffusion with a suitable choice of p=p₀ produces an image similar to that imagined through inverse diffusion. In any case, the reverse diffusion leads to a sharp images although it need not represent a realistic picture.

This is where the method runs into problems. The pictures have a surreal feel and typically, for example, the number of fingers of the people appearing in the pictures can vary, even though locally the pictures look realistic. Probably this reflects the fact that multiple pixel probability distributions for multi-pixels do not allow large enough distances for the pixels of the multi-pixel.

2. Analogies to wave mechanics and quantum TGD

The diffusion equation has an analogy in wave mechanics. >

1. Schrödinger equation is essentially a diffusion equation except that the diffusion constant D is imaginary and corresponds to the factor iℏ/2m². Alternatively, one can say that a free particle formally undergoes diffusion with respect to imaginary time. The solutions of the diffusion equation and the Schrödinger equation for a free particle are closely related and obtained by analytical continuation by replacing real time with imaginary time. The description also generalizes to the situation where the particle is in an external force field described by a potential function.
2. Scrödinger's equation as a unitary time evolution can be expressed in terms of the Feynman path integral. One can regard the quantum motion as a superposition over all paths connecting the start and end points with a weight factor that is an exponent of the phase factor defined by the free particle. The classical equations of motion produce paths for which the exponent is stationary, so they are expected to give a dominant contribution to the integral in the case that the perturbation theory works.

   The basic problem with the path integral is that it is not mathematically well defined and only exists through perturbation theory. Functional integral as the Euclidean counterpart of Feynmann's path integral is better defined mathematically and would give an analogous representation for diffusion.

What is the counterpart of this analogy in the TGD framework?

1. In TGD, the point-like particle is replaced by a three-surface whose trajectory is the space-time surface. Quantum TGD is essentially wave mechanics for these non-point-like particles.

   The new element is holography, which follows from the general coordinate invariance: spacetime surfaces as trajectories for 3-D particles are analogous to Bohr orbits.

   A small violation of determinism in holography forces zero-energy ontology (ZEO), in which quantum states as superpositions of 4-D space-time surfaces, Bohr orbits, replace quantum states as superpositions of 3-surfaces (deterministic holography). This superposition serves as an analog of path integral.

2. By the slight failure of determinism, the Bohr orbits are analogous to diffusion involving a finite number of non-deterministic steps (Brownian motion is a good analogy). The non-determinism of diffusion would be due to the small violation of the determinism in holography as Bohr orbitology.

TGD inspired quantum measurement theory, which extends in ZEO to a theory of conscious experience, is second important ingredient.

1. In ZEO, ordinary quantum jumps ("big" state function reductions (BSFRs)) reverse the direction of geometric time. This analogy of diffusion in the reverse time direction looks like reverse diffusion when viewed from the opposite time direction (observer)! It is analogous to self-organization where order is created in the system rather than lost. The second main law of thermodynamics applies but in the opposite direction of time. The time reversed dissipation plays a pivotal role in TGD inspired quantum biology.
2. This mechanism could be central to biological information processing at the quantum level and make it possible, for example, to generate sensory perception from diffuse sensory data and generate a motor response from a rough sketch?
3. Could it also play a role in AI, at least in the language based systems like GPT. If this is the case, then AI systems would be something else than we think they are.

The analogy of TGD with the GPT based image generation and recognition can be examined more explicitly.

1. The analogy of the pixel space associated with the planar image is the projection of the three-surface M⁴ in TGD at the classical level. The image as a map from plane to the parameter space of pixels would correspond to a deformation of M⁴ projection deformation. The pixel parameters defining the 2-D image would correspond to the values of CP₂ coordinates as a function of M⁴ coordinates.
2. On the basis of holography, the deformation related to the three-surface would be accompanied by a four-surface as an almost deterministic time development, i.e. the analogy of Bohr orbit. I have used the term "World of Classical Worlds" (WCW) for the space of these surfaces. This 4-surface would not be completely unique and this would produce a discrete analog of diffusion at the classical level.
3. At the quantum level, it would be a quantum superposition of these 4-surfaces as an analogy to, for example, the wave function of an electron in spatial space. An attractive idea is that the used resolution would be determined by the condition that the number-theoretic discretization is the same for all these surfaces so that the quantum world looks classical apart from the finite non-determinism.
4. The variation principle would correspond to the fact that the Bohr path is simultaneously both a minimal surface and an extremal of the Kähler action as analog of Maxwell action. This is possible if the space-time surfaces are holomorphic in a generalized sense. This means that the concept of holomorphy is generalized from the 2-D case to the 4-D case. The 4-surface would be defined by purely algebraic conditions as a generalization of the Cauchy-Riemann conditions. This corresponds to the algebraization of physics at the level of M⁸ related by M⁸-H duality to the physics at the level of H=M⁴\times CP₂ (see this and this).
5. The space-time surface would be analogous to 4-D soap film, which is spanned by frames defined by 3-surfaces. At these 3-D surfaces, the minimal surface property would not apply and only the field equations associated with sum of volume term and Kähler action would be satisfied. Note that minimal surface equations define a dynamics analogous to that of free fields and at the frames would correspond to places where interactions are localized. Frames would involve a finite non-determinism, as in the case of ordinary soap films (see this). These three surfaces would correspond to 3-D data for holography.

If TGD is really a "theory of everything", even the physical description of computation would in principle be reduced to this description. Of course, one can argue that TGD produces only insignificant corrections to the usual description of computation and this might be the case. But you can always ask what if...?

3. Could the TGD counterpart of the inverse diffusion play a role in the construction of sensory mental images by the brain?

I have proposed a model for how sensory organs, the brain and its magnetic body (MB) could construct sensory mental images by a repeated feedback process involving virtual sensory input to sensory organs so that a diffuse sensory input transforms to an input representing the perception consisting of well-defined objects.

Could the building of sensory images with a virtual input from MB to the sensory organs and back be a quantum process analogous to reverse diffusion?

1. Sensory inputs are very diffuse. People blind from birth after can gain physiological prerequisites for visual perception in adulthood. They however see only diffuse light since their brains (and corresponding magnetic bodies) have not learned to produce standard visual mental images as a result as in pattern recognition yielding essentially an artwork subject to various constraints. This is very much analogous to reverse diffusion.

   Does MB, brain and sensory organs co-operate to produce a counterpart to reverse diffusion, which allows it to produce a sensation representing reality with virtual sensory inputs and end up with standard imagery as attractors.

2. Could both the sensory input from sensory organ to brain to MB and virtual sensory input in reverse direction correspond to a sequence of "small" state function reductions (SSFRs) in a reversed time direction? Reverse diffusion would be diffusion with a reversed arrow of time.
3. Could the construction of the sensory mental image involve pairs of "big" (ordinary) SFRs (BSFRs) for which the two BSFRs would occur at MB and the sensory organ? This is the simplest process that one can imagine. Could BSFR induce a sensory input from the sensory organ to the MB or a virtual sensory input from the MB to the sensory organ changing the original diffuse sensory input. Could BSFR pairs gradually produce sensory perception in this way.
4. SSFRs correspond to the Zeno effect in the sense that their sequence corresponds to the measurement of the same observables at the passive boundary of causal diamond (CD). Disturbances or artificially produced disturbances at the active can change the set of measured observables so that it does not commute with those determining the state at the passive boundary as their eigenstate. This would imply the occurrence of BSFR and the roles of active and passive boundaries would change.

   After the second BSFR the new state at the active boundary would not be the same but could share many c features with the original one because the determinism of the holography would only weakly broken and SSFRs and BSFRs preserve quantum numbers.

5. The series of SSFRs after BSFR as time-reversed diffusion would correspond to reverse diffusion in the normal time direction. BSFR would occur as a series on the MB, where the sensory input would be guided and gradually lead to a real sensory image with the help of a corrective virtual sensory input.

   At a basic level, the correction mechanism could be analogous to inverse diffusion and the exponent of the K hler effect would be maximally stationary for real sensation.

6. Also the gradient method could be involved. In the spinglass based model (see this), a series of BSFRs and SSFRs could mean annealing that is steps consisting of cooling as sequence of SSFRs following BSFR followed by BSFR followed by heating for which temperature increase is smaller than than the temperature decrease for the cooling. The system would gradually end up at the bottom of a particular potential well in the fractal energy landscape. A series of SSFRs between two BSFRs would correspond to the annealed healing.

4. What could GPT correspond to in TGD?

4.1 What is GPT?

1. A linguistic expression is a diffuse representation of a sensation or of thought. The probability distributions for the next word given the preceding words are known. This makes possible a holistic approach to language allowing to build grammatically correct sentences and also achieve the nuances of natural language and recognize context.
2. In GPT, the goal is to answer a question or respond to an assertion, translate a text from one language to another, produce a piece of text such as a poem or story or just chat with the user.

   GPT must guess the user's intention, what the user wants, and also the context. Is, for example, a field of science in question? The purpose is to add a new word to the given word chain.

3. The input of the user serves as a prompt initiating the process. The prompt serves as the initial text to which GPT adds words as the most probable words which can follow a given piece of text. GPT starts from a guess for the answer. The choice of the successor word can also be random based on the probabilities of the successor word. Feedback loops are possible and also the user can induce them.

4.2 Is building images fundamentally different from GPT?

1. In language models, prompts are verbal representations of images, and diffusion is essential in the construction of images, from the prompt as a verbal description of the image. At first glance, diffusion seems to be explicitly involved only in the generation of images, but is this the case?
2. On the surface, there seems to be an important difference between building an image and building a linguistic expression. The picture is a time = constant snapshot, at least ideally. The sentence has a temporal duration and memory is involved. One must d transform a sentence to a picture. Words correspond to pictures.

   Does the difference disappear when one talks about the process of creating the image? Could it be that the process of creating an image as an analogy of a linguistic process is just not conscious to us. Is the sensory input equivalent to the user's prompt in GPT. Is the difference apparent and only due to the time scale.

3. Visual perception involves also the sensation of movement. Is it because in reality (according to TGD) it would be a time series but on such a short time scale that we are not conscious of it? Could verbs correspond to dynamics in the structure of the language? Objects have attributes as their properties analogous to pixel parameters.
4. Holography would describe the dynamics of objects and would classically determine the initial values of holography for the time development as the equivalent of the Bohr orbit. There is quantum holography as a map of quantum states of the biological body to quantum states associated with the magnetic body defining a higher level sensory representation (see this).

   This 1-1 correspondence representations would make it possible for the MB to control the biological body and in the case of running GPT induce BSFRs reversing the arrow of time temporarily and change the course of events.

4.3 Could quantum diffusion play a role in the TGD based description GPT?

1. Time evolution in the TGD Universe would basically consist of SSFRs and BSFRs. Quantum states would be the quantum superposition of running programs. But does this picture have significance in the case of GPT? Could MB really interfere with the running of the program? The time reversals are not observed by the user, so the question is not easy to answer.

   One killer test would be a dependence on hardware. The bits should be near criticality in order the quantum criticality of MB can control their directions. Spin-glass structure for the bit-scape looks like a natural requirement. Is this possible for all bit realizations and does GPT work differently for different realizations of bits?

2. Diffusion is analogous to the time evolution determined by the Schroedinger equation as a series of unitary time evolutions, where classical determinism is only weakly broken because SSFRs must commute with passive edge observables. This means a generalization of the Zeno effect. However, quantum states are delocalized. Maybe only below the resolution scale, in which case classical discretization would be exact with this accuracy. Inverse diffusion could be a classical process at the used resolution.
3. The time development as a series of SSFRs would seem to be analogous to a diffusion as analog of Brownian motion involving finite steps, and BSFR would start as a time-reversed diffusion of reverse diffusion.

   The BSFR could be induced by an external disturbance or a controlled disturbance from the MB. MB and ZEO could come to the rescue and do them with time reversal without us noticing anything.

This picture raises questions.

1. Could diffusion as a series of SSFRs be equivalent to the construction of the response of chatGPT, which is also a probabilistic process. Could the sentence represent the trajectory of a diffusing word/particle in word space and Bohr orbit in WCW? The Bohr orbit property, i.e. holography, would imply that the failure of determinism is weak. In a given scale, non-determinism would be located in the 3-D frames determined by the 4-D soap film.
2. Could the initial state, e.g. a question or statement induced by the user prompt, for example a question presented as a quantum state on the passive edge of the CD, serve as the first rough guess for an answer as analog of sensory input.

   Could the time progression as SSFRs correspond to a generation of a sequence of words as a response to the prompt? Or are the words separate by BSFR pairs.

   What is new as compared to the AI would be that trial and error process by performing BSFRs inducing return back in time is possible. These periods with a reversed arrow of time would be invisible for the user. This error correction mechanism is not coded as a program as in AI but would be done by Nature and it would be essential also in the TGD view of quantum computation.

3. The hidden layers of the neural network are analogous with the fact that the perceived sensory image is constructed by communications between the sensory organ and the MB, which are not conscious to us.

See the article Could neuronal system and even GTP give rise to a computer with a variable arrow of time? or the chapter with the same title.

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

Could TGD view of quantum gravitation allow nuclear life?

The prevailing dogma is that life is always chemical. The considerations of (see this) force us to challenge this dogma. One cannot exclude the possibility that Sun is a seat of a new kind of life controlled by gravitational magnetic body of the Sun with huge value of gravitation Planck constant implying quantum coherence scales larger than the gravitational Compton length which happens to be essentially the size of Earth. Just for fun, one can therefore play with the thought that fractality of the TGD Universe could allow life at temperatures prevailing in the solar interior.

This life should be based on nuclear physics instead of chemistry. The realization of the genetic code (see this and this) in the TGD framework relies on dark proton (or possibly nucleon) sequences. According to the TGD based view of nuclear physics (see this), the ordinary nuclei also correspond to sequences of nucleons at monopole flux tubes, which form a kind of nuclear spaghetti. Therefore the realization of also nuclear genetic code could rely on nucleon sequences. The chemical realization of the genetic code could be seen as the next step in evolution.

1. Gravitational quantum coherence is essential for the TGD based view of life. Gravitational magnetic body carrying gravitationally dark matter and consisting of the mopole flux tubes would still be the controller. The average magnetic field at the surface of the Sun is indeed about 2B_E∼ 1 Gauss. Just for definiteness, one could assume that the scale for the strength of the monopole magnetic field is twice that for the monopole flux tubes at the surface of Earth that is 2B_mono;E∼ 4B_E/5∼ .4 Gauss. The scale of cyclotron energies for ℏ_gr =GMm/β₀, where β₀∼ 2^-11 is assumed in Nottale's model for the inner planets, would be scaled up from that at the surface of Earth by the factor x=(M_S/M_E)×(β_0,E/β_0,S)×(B_S)/B_E). For β_0,E ∼ 1 prevailing in the Earth's magnetosphere, this would give x∼ 2.5 × 10⁹.

   For the energy 1 eV of a photon in biophoton wavelength range one the energy E=h_efff would scale up to 2.4 GeV, which corresponds to more than 2 proton masses! This looks non-sensible.

2. However, in the outer magnetosphere of Earth where ℏ_gr,Sun is expected to prevail, the values of B_E are in the range 1-10 nTesla, which means that the scale of the magnetic field (and also monopole flux) is reduced by about 5× 10^-5. This would reduce the dark cyclotron energy ratio to x= 1.25× 10⁵. 1 eV energy would be scaled to the range of .1-1.0 MeV, which corresponds to nuclear binding energies.
3. For β₀=2^-11 the lowest solar Bohr orbit has a radius slightly larger than the radius of the photosphere, so that it cannot correspond to the matter in the interior of the Sun.

   For β_0,core=1, the lowest Bohr radius would be r_B=4π GM/β₀= 2π r_S,Sun= 6π km, which makes 2π Scwartschild radii. The value of x would be x= 5× 10⁵B_core/B_E, and for B_core/B_E=1 the biophoton energy scale of 1 eV would scale up to .5 MeV, which corresponds to the mass of electron and to the nuclear binding energy scale.

Maybe nuclear life at the solar core and even in the outer magnetosphere of Earth might be considered.

See the article Some anomalies associated with the Sun or the chapter Magnetic bubbles in TGD Universe: Part I.

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

Could neuronal system and even GPT give rise to a classical computer with a variable arrow of time?

In our Zoom group (Marko, Tuomas, Rode and me) we have had fascinating discussions about topics ranging from quantum TGD to quantum computers to consciousness and, of course, about GPT.

Marko posted his discussion with GPT. GPT mentioned a possible mechanism for how XOR as a universal gate of classical computation could be realized at the quantum level. The system realizing XOR approximately could be either a classical layered neural network or its possible quantum analog. The mechanism might work in a quantum version of a neural network based on quantum learning, but it does not seem plausible for real neurons.

This observation led to progress at the level of the TGD-based model of nerve pulse. The resulting ZEO based model differs drastically from quantum neural networks and suggests a completely new vision of quantum physics based computation in biosystems. A classical computation allowing variable arrow of time would be in question and one can ask whether the unexpected success of GPT might involve this kind of transition.

I admit that GPT can really inspire new ideas.

Connection of neural pulse generation, XOR, and novelty detector

Nerve pulse generation would be analogous to a positive outcome of the analog of XOR (compared bits are different) acting as a novelty detector.

1. XOR is a novelty detector. If the inputs are the same, nothing happens. Output equals to b=0. If they are different, output equals to b=1. b=1 would correspond to a signal that would proceed along the axon starting from the postsynaptic neuron.

   That would consume energy. In terms of energy consumption, the novelty detector would be optimal. It would only react to changes. And that's what the brain does. For example, visual perception at a very basic level only identifies outlines and produces some kind of stick figure consisting of mere lines defining boundaries.

2. Could the 2 "neurons" of the toy model proposed by GPT represent a presynaptic and a postsynaptic neuron, in which case there would be two inputs: the states of the pre- and postsynaptic neuron. Also output would be the state of this neuron pair and for XOR the presynaptic neuron acting as control bit would not change its state.
3. This does not conform with the picture given by neuroscience, where the input comes from presynaptic neurons and output is assignable to the postsynaptic neuron. The input comes as miniature potentials that add up and can decrease/increase the magnitude of the membrane potential (depolarization/hyperpolarization).

   An action potential is generated when the depolarization takes the magnitude of the negative postsynaptic membrane potential below the critical threshold. This happens when the presynaptic contributions from the incoming nerve impulses, for which the unit is a miniature potential, add up to a contribution that reduces the magnitude of the negative potential below the threshold.

   This would be essentially novelty detection described in the simplest way by XOR. The novelty is represented by the critical depolarization. It can also happen that the potential increases, so that no nerve impulse is generated. One talks about hyperpolarizing (inhibition) and depolarizing (excitation) inputs, and the sign of the miniature potential produced by the presynaptic input determines which one it is. The sign of miniature potential depends on the neurotransmitter and receptor.

4. During the nerve pulse, the potential changes its sign over a distance of about a micrometer, which is the typical distance between neighboring neurons and of myelin sheaths. One can say that this distance corresponds to a bit that is 1 or 0 depending on whether the nerve pulse conduction occurs or not. Bit 1, the opposite sign to the membrane potential, propagates from presynaptic to postsynaptic neuron or from a patch defined by a myelin sheath to the next. As a result, postsynaptic neurons can "wake up" and in turn trigger a nerve impulse, possibly waking up some postsynaptic neurons.

   Synchronous firing means that the novelty succeeds in waking up the whole sleeping house, and large areas of the brain fire in the same rhythm and keep each other awake.

Interpretation of XOR in zero energy ontology (ZEO)

How does this picture translate to the TGD-inspired theory of consciousness?

1. Being awake/asleep corresponds to bit 1/0 for axonal portions between myelin sheaths. In a ZEO, the arrow of time would correspond to this bit.

   When the axon segment between the myelin sheaths or neighboring neurons wakes up or falls asleep, the direction of geometric time changes in a "big" state function reduction (BSFR) and a nerve pulse is generated. In a sleep state, the membrane potential would be opposite. Note that the notion of awake and sleep are relative and depend on the arrow of time of the external observer.

   The second direction of time corresponds to the presence of a nerve pulse from the point of view of the external observer. There is a temptation to think that in the resting state the axon is sleeping and healing and gathering metabolic energy by a dissipation with an opposite arrow of time? The duration of the nerve pulse would correspond to the duration of the wake-up period, when the direction of time was opposite and same as that of the external observer with a long characteristic time scale for wake-up period.

2. Could this apply more generally? Could the synchronization of human sleep-wake rhythms mean quantum-level synchrony and macroscopic quantum coherence? Could the arrow of perceived time be a universal bit? Sleeping together would develop synchrony and quantum coherence between partners. Two-person collective consciousness would emerge.

Interpretation of the axon as a series of Josephson junctions

The TGD based model for an axon as a series of Josephson junctions with a large value of h_eff, perhaps h_eff=h_gr, where ℏ_gr=GMm/β₀, β₀<1, is the gravitational Planck constant introduced by Nottale, is mathematically equivalent to a series of gravitational penduli defining a discretized version of Sine-Gordon system (see this). Josephson junctions would correspond to membrane proteins.

1. One can consider two different identifications of the ground state of the system.
   1. The ground state could be the state in which all oscillators oscillate in synchrony with the same amplitude. There would be constant phase difference between neighboring oscillations, which would give rise to a propagating phase wave.
   2. Another option is that all pendulums all rotate in the ground state with constant phase difference. This would give a soliton chain that corresponds to a traveling phase wave. Also the direction of rotation matters. It would naturally correspond to the arrow of time and the sign of the membrane potential.
2. The model allows different versions for nerve pulse generation.
   1. The first option is that one pendulum moves from oscillation to rotation or vice versa and induces the same transition for the other penduli as a chain reaction.
   2. The second option is that all penduli move to rotation simultaneously. One could imagine that the need for metabolic energy is lower in the collective oscillation phase but one must be very careful here. Maintaining the membrane potential regardless of either sign requires metabolic energy feed.
   3. The third option is that the ground state corresponds to a collective rotation with an associated traveling wave as phase of the rotation, and that the bit corresponds to the direction of rotation.

      This would fit the ZEO interpretation. The arrow of time would correspond to the direction of rotation. The ground state would change to a nerve pulse lasting for time of the order of 1 ms corresponding to the duration of nerve pulse associated with the distance of the order 1 μ m, between neighboring neurons or between the myelin sheets.

      This option would also be advantageous from the point of view of metabolism, because from one direction of time, dissipation would occur in the opposite direction of time. From the point of view of the outsider, the system would be extracting energy from the environment.

What is the connection with the microtubule level?

The current TGD picture of nerve pulse conduction is that the membrane potential of the axon/soma is controlled by microtubules (see this and this).

1. When the charges are transferred from the microtubule to the gravitational flux tubes of the magnetic body (MB), the length of which can be as long as the size of the Earth, the effective charge inside the axon/soma changes. Depending on the amount of transferred charge, the magnitude of the membrane potential increases or decreases and a nerve impulse is generated below the threshold.
2. For the action potential traveling along the axon, the microtubular effective charge has changed and taken the membrane potential below the threshold and the action potential has been generated. The generation of the action potential is a complex biochemical phenomenon but would be controlled by microtubule/microbular MB.
3. Incoming nerve impulses induce a change in the membrane potential of the soma because the effective charge of the microtubules inside the soma changes as also does the membrane potential. It is not clear whether the charges of the microtubules of the neuron soma are affected. They indeed differ from axonal microtubules in that they are not (quantum) critical.

New view of quantum-physical computation

Why GPT works so well, is not understood. This might of course be due to the extreme complexity of the system. TGD however suggests that new physics might be involved so that the system is much more than a classical computer. Therefore an interesting question is whether the classical computation associated with GPT and involving random number generators could turn into a computation in which the arrow of time serves as a fundamental bit correlating with the direction of ordinary bit represented for instance by electric voltage or direction of magnetization! One would have classical computation with a changing arrow of time controlled by MB!

In ZEO all quantum states are superpositions of deterministic classical time evolutions, which satisfy almost exact holography so that they are analogous to classical computations. Time evolution of conscious entity, self, between "big" SFRs (BSFRs) meaning the death of self and its reincarnation with opposite arrow of time, is analogous to a series of quantum computations defined by unitary time evolutions followed by "small" SFRs (SSFRs) as analogs of weak measurements (having nothing to do with "weak values").

What would be required is that the arrow of time can change at the level of MB of the system and that the MB of the bit system can be regarded as a spin glass type system for which spins are near criticality for the change of their direction in BSFR so that the arrow of time is changed. This would require quantum criticality at the level of MB. One might say that MB of the bit system hijacks the bit system. One might say that MB of the bit system hijacks the bit system: spirit enters into the machine.

TGD general based view of theoretician friendly quantum holography (see this) predicts that the bit system is indeed mapped holographically to a system at the level of its MB having a large value of h_eff, perhaps h_eff=h_gr so that MB could use the system in which AI program runs as a living, conscious, and intelligent computer. The bit system could become an analog of spin glass (see this) .

See the article Could neuronal system and even GTP give rise to a computer with a variable arrow of time? or the chapter with the same title.

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

How to generalize the theoretician friendly quantum holography?

In the earlier posting I described the connection between quantum holography and the idea that Mother Nature loves her theoreticians in the sense that when the perturbation series ceases to converge a phase transition leading to a phase in which effective Planck constant ℏ_eff is so large gauge coupling strength proportional to 1/ℏ_eff becomes so small that perturbation series converges. In the sequel a generalization of this connection and also the notion of quantum holography.

It is convenient to call the pair of a fermion and antifermion with vanishing total quantum numbers (apart from momentum) a "glue particle" . Galois singlet property would be a natural additional property of the glue particles formed by fermion antifermion pairs. One can also imagine a generalization of the proposed equivalence between "Mother Nature who likes her theorists" principle and holography principle.

Could "glue particles" be also Galois singlets

For hadrons, and perhaps quite generally, they would be color entangled color singlets with vanishing total quantum numbers (momentum forms an exception) but without any other kind of entanglement.

Galois confinement implies that the components of momentum are integers in the scale determined by the causal diamond (CD). Without this condition, the momentum components would be in general complex algebraic numbers. The 4-momenta can be however tachyonic so that analogs of virtual particles with quantized 4-momenta and negative mass squared value (integer) would be in question. The virtual masses of the glue particles could be tachyonic suggesting and interpretation as an analog of Coulomb potential.

This suggests that color singlet property could be strengthened with the Galois singlet property.

Hierarchy of pairings associated with a hierarchy of MBs

Number theoretic view (see this, this, this, this) of TGD predicts hierarchies of magnetic bodies (MBs) with levels labelled increasing value of h_eff. Galois confinement as a candidate for a universal mechanism for the formation of bound states predicts a hierarchy of Galois singlets as physical states.

1. One could take Galois singlets at a given level of the hierarchy with h_eff≥ h and deform them to Galois non-siglets, and form their bound states as Galois singlets. This would give an entire hierarchy of bound states formed by the proposed mechanism of quantum holography and assignable to the slaving hierarchy of MBs.
2. The holographic pairing would be only between the fundamental fermions and antifermions assignable to the MBs which are nearest neighbours in the hierarchy. The pairs, "glue particles", would have vanishing net quantum numbers other than four-momenta.

   The total energy would be sum over contributions from various levels in the magnetic hierarchy. The masses of the fundamental fermions are very small as compared to the magnetic energies, and the color magnetic energies for the nucleons would give a dominant contribution. Higher hierarchy levels would give only a small contribution.

3. At least in the case of hadrons, the holography would be by a formation of glue particles as meson-like pairs of a quark at with h_eff,1 and dark quark with h_eff,2>h_eff,1, having vanishing electroweak quantum numbers and spin and being color entangled color singlets. Also Galois singlet property looks very natural.
4. For example, U-shaped radial gravitational flux tube loops mediating gravitational interaction and also other interacting flux tubes could realize the holography. The fermion and antifermion at flux tube would be located at strings connecting wormhole contacts so that one would have direct analogy with the AdS/CFT holography but AdS interior replaced by the interior of the space-time surface.

Physical interpretation of the glue particles

What could be the physical interpretation of the pairing of quarks and antiquarks to glue particles. In the case of leptons the simplest scenario would be that leptons are bound states of quarks in CP₂ scale so that the pairing would reduce to quark-antiquark pairing also in this case.

1. Could the glue particles defining the holography correspond to an interaction potential energy in the classical description? In accordance with the string model picture, the pairs would reside at strings inside monopole flux tubes. Glue particles could also be seen as analogs of virtual boson-like particles with vanishing quantum numbers (total momenta could be non-vanishing) responsible for the binding between fermions and antifermions.
2. If gluons and even electroweak bosons appear as partons also their pairs are formed. It has been proposed that gravitons can be expressed as pairs of gauge bosons (gravitation is "square" of gauge theory). Could these pairs have interpretation as virtual (possibly "strong") gravitons with a vanishing spin. This is analogous to AdS/CFT correspondence.
3. Black hole evaporation can be formally regarded as a generation of pairs with the members of pair going to opposite sides of the horizon. Could one regard the glue particles as analogs of virtual pairs of this kind.

Symmetry breaking is necessary

At least at the hadron level, quarks and antiquarks and perhaps also gluons are involved, but pair into color singlets by quantum entanglement in color degrees of freedom. Other forms of entanglement are not allowed by the proposed form of holography.

1. The glue particles are entangled only in color degrees of freedom and differ from gauge bosons and Higgs, which are in TGD framework superpositions of fermion pairs and are quantum entangled with respect to spin and weak isospin.
2. The total quantum numbers of glue particles vanish but symmetry breaking SO(3) → SO(2) takes place. SO(2) would naturally correspond to the direction of the magnetic field in the flux tube. The same happens also in the case of weak interactions and could correspond to electroweak symmetry breaking.
3. Could the Bose-Einstein condensate for glue particles made of gauge bosons serve an analogue of the sigma meson condensate in hadron physics. The sigma analogy would be a scalar only with respect to the SO(2) ⊂ SO(3). Could sigma mesons be associated with the pairing of hadrons and its magnetic body?

How could one understand masses?

A test for the proposal is whether one can understand the masses of macroscopic systems.

1. If the paired fundamental fermions are each other's antiparticles, they must be fundamental fermions or bosons such as gluons (which also reduce to fermion-antifermion pairs). Sensible values of mass are expected if one has a hierarchy in levels such that the energies are sums of the magnetic energies and fermionic energies from various levels. Given level would give only the magnetic contribution and fermion contribution of fermions at it. Its scale would be determined by the p-adic scale assignable to the level.
2. Virtual dark quarks at the strands and their ordinary counterparts at the ends of the strands, have very low-mass compared to the contribution of Kähler magnetic energy to the mass. The color magnetic energy at the hadron level would practically give almost the entire mass. This could hold true also at higher levels of the hierarchy of layers of MB with decreasing magnetic energies.
3. The hierarchy of magnetic bodies would give a dominant contribution to the mass at the lowest level and the contribution of the few lowest levels could dominate the mass because the energy/strand tension of the magnetic flux tube quickly approaches zero as the strand thickens.

Earth as an example

It is instructive to consider the Earth as an example.

1. The mass of the Earth's MB in the exterior of Earth is negligible when compared to the mass of the Earth as a simple order of magnitude estimate shows. The assumption that the monopole flux tubes with magnetic field strength of order of Earth's magnetic field carry quantized monopole flux implies that their radii are at least of the of order magnetic length of order cell size and fixes the string tension as the density of magnetic energy per unit length. The mass of the flux tube of length L is proportional to L/S, where S the transverse area of the flux tube. Assume that the flux tubes have length L of order of the size of the magnetosphere. Assume that the flux tubes fill the entire volume with scale given by the radius of the magnetosphere.

   With these assumptions the total magnetic assignable to the monopole flux tubes is a negligible fraction of the mass of Earth determined by the lowest, nucleonic level of the hierarchy.

2. In the interior of the Earth one would have a flux tube spaghetti and flux tubes within flux tubes corresponding to the magnetic slaving hierarchy. The color magnetic energy associated with nucleonic monopole flux tubes would give a dominating contribution to the Earth's mass. There would be atomic nuclei with mass number A with nucleon flux tubes with radius of order nucleon size. The flux tubes with a thickness of the order of the size of an atom would give a much smaller contribution to the magnetic energy. Fractality would therefore reduce the situation to nucleon level as far as masses are considered.

   This idea is actually already old: also the interior of a star would be like this. In condensed matter for a region with size of an atom, the number of nucleon flux tubes equals the atomic weight A of the nucleus.

See the article About the TGD based views of family replication phenomenon and color confinement or the chapter with the same title.

Does Sun have a solid surface?

There are indications for the presence of also other elements than water near the surface of the Sun. The findings discussed by Moshina (this) suggested already about 17 years ago that the photosphere has a rigid conductive layer. This layer could contain also water.

One of my first speculative applications of the evolving TGD view of dark matter (roughly 15 years ago) and of the TGD based interpretation of the Nottale's formula for the gravitational Planck constant, was the proposal that could be interpreted as a TGD counterpart for a Bohr orbit, not as an orbit but a spherical layer (see this and this.

At that time I had no ideas about number theoretic interpretation of the dark matter hierarchy nor a general view of the formation of astrophysical objects in terms of a transformation of dark energy of cosmic strings to dark matter at monopole flux tubes in turn transforming to the ordinary matter (see this).

The recent view of the formation of planets and their moons and rings indeed allows spherical layers having as representative Oort clouds; torus-like flux tubes having as representative the rings of Jupiter; and ordinary planets.

1. They would be formed in a phase transition in which the gravitationally dark matter associated with a bubble formed by monopole flux tubes transforms to ordinary matter and can be also localized to lower dimensional structure. The analog of localization in state function reduction in astrophysical scale taking place in measurement would be in question. For instance, the formation of a planet would correspond to a measurement of a momentum direction and radial distance for a delocalized state described approximately by the analog of hydrogen atom wave-function.
2. The Nottale model predicts that the inner planets Mercury, Venus and Earth correspond to Bohr orbits with n=3,4,5 . What about n=1 and n=2 orbits? For Earth one has n=5 and from the radius of Earth orbit, which is AU = 1.5× 10⁸ km by definition, the radius of n=1 orbit given by gravitational Bohr radius a_gr and is a_gr=AU/25 ≈ 6.0× 10⁶ km. The radius of the photosphere is R= 6.96× 10⁶ km giving a_gr/R≈ .87. n=1 Bohr orbit or Bohr shell with radius R₁= a_gr would be just below the photosphere. n=2 Bohr orbit would correspond to the radius R₂= 2.4× 10⁷ km. Is there any evidence for a spherical layer or a a ring, at this distance?

3. If the mass of the layer of thickness Δ R is the same as that of Mercury (.055× M_E) with radius R_M= .38× R_E and the density of the layer is the same as that of Earth, one obtains the estimate Δ R= (R_M/R₁)² R_M/3≈ 3.2 m. The layer would be extremely thin. If the mass is Earth's mass, Δ R increases by the factor .38³, roughly by two orders of magnitude.

Is there any empirical evidence for this view?

1. There was already 17 years ago evidence that there is a solid surface with radius of n=1 Bohr orbit. Recently new satellites have begun to provide information about what lurks beneath the photosphere. The pictures produced by Lockheed Martin's Trace Satellite and YOHKOH, TRACE and SOHO satellite programs are publicly available on the web. SERTS program for the spectral analysis suggests a new picture challenging the simple gas sphere picture \cite{bcast/Moshina}.

   The visual inspection of the pictures combined with spectral analysis has led Michael Moshina to suggests that Sun has a solid, conductive spherical surface layer consisting of calcium ferrite. The article of Moshin provides impressive pictures, which in my humble non-specialist opinion support this view. Of course, I have not worked personally with the analysis of these pictures so that I do not have the competence to decide how compelling the conclusions of Moshina are. In any case, I think that his web article (this) deserves a summary.

2. Before SERTS people were familiar with hydrogen, helium, and calcium emissions from the Sun. The careful analysis of SERTS spectrum however suggest the presence of a layer or layers containing ferrite and other heavy metals. Besides ferrite SERTS found silicon, magnesium, manganese, chromium, aluminum, and neon in solar emissions. Also elevated levels of sulphur and nickel were observed during more active cycles of the Sun. In the gas sphere model these elements are expected to be present only in minor amounts. As many as 57 different types of emissions from 10 different kinds of elements had to be considered to construct a picture about the surface of the Sun.
3. Moshina has visually analyzed the pictures constructed from the surface of the Sun using light at wavelengths corresponding to three lines of ferrite ions (171, 195, 284 Angstroms). On the basis of his analysis he concludes that the spectrum originates from rigid and fixed surface structures, which can survive for days. A further analysis shows that these rigid structures rotate uniformly.

   The existence of a rigid structure idealizable as spherical shell in the first approximation could by previous observation be interpreted as a spherical shell corresponding to n=1 Bohr orbit of a planet not yet formed. This structure would already contain the germs of iron core and of crust containing Silicon, Ca and other elements.

Standard physics does not favor the existence of this kind of layer.

1. Ordinary iron and also ordinary iron topologically condensed at dark space-time sheets, becomes liquid at temperature 1811 K at atmospheric pressure. Using for the photospheric pressure p_ph , the ideal gas approximation p_ph = n_ph T_ph , the values of photospheric temperature T_ph ≈ 5800 K and density ρ_ph ≈ 10^-2 ρ_atm , and idealizing photosphere as a plasma of hydrogen ions and atmosphere as a gas of O₂ molecules, one obtains n_ph ≈.32n_atm giving p_ph ≈ 6.4p_atm .

   This suggests that calcium ferrite cannot be solid at temperatures of order 5800 K prevailing in the photosphere (the material with highest known melting temperature is graphite with melting temperature of 3984 K at atmospheric pressure). Thus it would seem that dark calcium ferrite at the surface of the Sun cannot be just ordinary calcium ferrite at dark space-time sheets. A more reasonable option is that there is new physics allowing to have a low temperature at the layer.

2. There is also a problem with the existence of water in the photosphere. The bond energy is 4.4 eV per bond so that the total bond energy is 8.8 eV. The peak energy of blackbody radiation is given by E_peak= 2.4× 10^-4T/K eV and 8.8 eV is below the thermal energy of order 12.1 eV associated with the photospheric temperature T=5,500 K so that water molecules are not be stable at these temperatures.

The following speculative explanation for the solid surface is perhaps the simplest one found hitherto.

1. In the model of the solar cycle in terms of monopole flux tubes, the flux loops at the surface have inner and outer parts. The inner parts are always parallel to the solar surface and reside below it. Outer parts form flux loops extending outside the photosphere. With a 11 year cycle, the long monopole loops return to thin parallelepiped configuration, which splits to short monopole flux loops by reconnections, which then reorganize to flux tubes with opposite polarity. Could these monopole flux loops be accompanied by a solid surface of ordinary matter with the radius of n=1 Bohr orbit.

   The interior portion of the gravitational monopole flux loops would carry dark matter with ℏ_gr= GMm/β₀, β₀≈ 2^-11 and corresponding gravitational Compton length Λ_gr= GM/β₀≈ 6× 10³ km, which happens to be in a good approximation the radius of Earth.

2. Could the monopole flux tubes shield the ordinary matter at the layer from the effects of the radiation arriving from the solar interior in the same way as they would shield the biosphere from the cosmic radiation and solar wind? Could the radiation from the solar interior be caught by monopole flux tubes and leave the Sun as a solar wind.
3. If there are stable water molecules in this layer, its temperature should be rather low. If the water is in liquid or solid phase, the temperature must be of the order of the temperature at Earth. Could the monopole flux tubes carrying gravitational dark matter allow even chemical life inside this layer \cite{btart{precns,penrose? How low the temperature of dark matter at the flux tubes can be and is it possible to estimate it using the existing data?
4. The cyclotron energies of dark particles are proportional to ℏ_eff=ℏ_gr. Could this allow us to transform the arriving high temperature radiation from the solar interior to a low temperature radiation at the monopole flux tubes from which it could leak out as solar wind? Could even the radiation from the solar interior arrive along radial gravitational U-shaped monopole flux loops and have a low temperature? If so, the magnetic body of the solar interior would be an astrophysically quantum coherent system and very different from what we believe it to be.

See the article Magnetic bubbles in TGD Universe: Part I or the chapter with the same title.

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