Friday, April 28, 2023

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

There was an interesting popular article in 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 heff=nh0. The Compton length of dark particles with given mass is scaled up by factor heff/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 heff since it plays a key role in the TGD based view of quantum gravitation. Gravitational Planck constant obeys the formula ℏgr=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 Λgr= ℏgr/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 ℏgr 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 heff. Photon wavelength is scaled up heff/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 αem= e2/4πℏeff 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 ℏeff. 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 ℏeff. The result is somewhat disappointing.

  5. On the other hand, for large values of ℏeff, in particular ℏgr, 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 ℏgr is proportional to m so that particles would be like books in the shelves of a library labelled by ℏgr.

  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 heff.

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 ℏgr= 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 ℏgr →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.

Thursday, April 27, 2023

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 M8c 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 H3m⊂ 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.

Monday, April 10, 2023

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[-∫x1x2(2m(qV-E))1/2 dx/ℏeff] ,

    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 heff 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 ME, ℏgr(ME,mp) for a frequency of 10 Hz corresponds to an energy E= hgrf 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 heff=hgr(ME,mp) 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 Λgr= GME0 =.45× 10-2 m, if β0=1. The frequency Tgrgr/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 Λgr is only the lower bound for the length of gravitational flux tubes carrying massless radiation.
  2. For heff=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 heff must satisfy heff ≥ 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 heff=h, it would correspond to a period of .6× 10-10 s. Could the f= 1 GHz induce a resonance with dark photons with heff>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 heff would be rather small as compared to ℏgr(ME,mp) and the challenge is to identify a candidate for a system with this value of heff.

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 heff that the perturbation theory converges. Nottale formula generalized to electromagnetic interactions suggests that one has

    ℏ → ℏeff= ℏem= Z2e20 ,

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

    (Z2e2/4π ℏem)= 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 heff ≥ 3× 103h would suggests ℏem/hbar= Z2e20ℏ = 4π Z2αem ≥ 3× 103. This gives the estimate

    Z2≥(1/4παem)> × 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 H1.5O. 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 ℏgr(M,m) for some pair (M,m) of masses so that one has E=hgr(M,m)f> .03 eV for f=109 Hz.

  1. For instance, could one replace the masses ME and mp with identical masses M=m in hgr. One should have M/mPl2> 3× 103. This would give M/mPl >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 Tgr 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 Es= 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 VG controls the capacitance of the MOS.

    MOSFET size scale is around 10 nm. Gate voltage VG-VB 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 heff 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.

Sunday, April 02, 2023

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.