Anil Seth and his view of consciousness as controlled hallucinations

The neuroscientist and consciousness theoretician Anil Seth will speak in Helsinki University at Friday. The relevant data are here: 26 April at 16.00–18.00 EEST Place: University of Helsinki, Main building (Fabianinkatu 33, 2nd floor), Auditorium (F2044). Live stream can be found here.

I looked at the summary of AS:s book "Being You: A New Science of Consciousness" (see this).

1. Anil Seth (AS) is a materialist and therefore believes that the neurophysiological state of the brain completely determines the contents of consciousness. AS tries to answer the "real problem" that is why a particular sensory input gives rise to a particular conscious experience. AS admits however that the hard problem, that is why there is any experience associated with the perceptions, is real.
2. The usual view in which sensory input arrives the brain and is processed to produce sensory representations and then follows motor action as a reaction. The view of AS is in some sense opposite. Brain is continually making predictions for the future and they are realized as experiences, which can be sensory experiences and also emotions which relate to the state of the body. Sensory experience is not a summary of what was but a prediction of what it will be! We live in a continual hallucination which does its best to predict the future reliably. When it fails, we speak of hallucination instead of a real sensory experience.

From this brief description motor action is missing. What could it mean in this framework? I do not know what Seth's answer is. How does the view of AS relate to the TGD based view of consciousness? TGD view involves the following new elements.

1. Zero energy ontology (ZEO) replaces the standard ontology of quantum theory and solves the basic paradox of quantum measurement theory. The key point is that quantum state is replaced with a superposition of classical deterministic time evolutions of 3-surface, that is 4-surfaces of H=M⁴×CP₂, obeying holography meaning that 3-D initial data dictate the time evolution almost uniquely. The space-time surface is an analog of Bohr orbit for a particle represented by a 3-surface.

   These Bohr orbits reside inside a causal diamond CD, which has the intersection of future and past directed light-cones as its M⁴ projection. CDs form a scale hierarchy and CD defines the 4-D perceptive field of a conscious entity. The 4-dimensionality of the perceptive field conforms with the idea of AS that conscious experience is a prediction rather than a mere representation of what the world is in 3-D sense.

   The 4-surfaces as analogs of Bohr orbits and as classical time evolution correspond to the predictions of AS. Quantum prediction of the future is quantum state, that is a wave function in the set of Bohr orbits.

2. A new element is the existence of a hierarchy of phases of ordinary matter for which the number theoretically determined effective Planck constant can be arbitrarily large and therefore the scale of quantum coherence. These phases behave like dark matter and control ordinary matter since the h_eff as a measure of algebraic complexity is also a kind of IQ. In this framework, biosystems become quantum coherent systems in scales of the biological body and even in much longer scales corresponding to EEG wavelengths for instance.
3. The new view of space-time as a 4-D surface in M⁴xCP₂ predicts also a new view of Maxwell fields. Field bodies, in particular magnetic bodies consisting of monopole flux tubes as kinds of body parts in an abstract sense, are a basic prediction and central for biology. Field/magnetic bodies w carry dark matter as h_eff>h phases and receive information from biological bodies containing ordinary matter and control it. EEG relates to the communication between the field body and biological body. This view resonates with the view of Fadden.
4. The ZEO based quantum measurement generalizes ordinary measurement theory, which involves ordinary state function reductions (SFRs) and sequences of repeated measurements which do not affect the system at all (Zeno effect) and in a more general view suggested by quantum optics involve a small change.

   Ordinary SFRs become "big" SFRs (BSFRs) in the TGD framework and in these the arrow of geometric time changes. From the point of view of outsider the system loses consciousness/falls asleep/dies but actually in reincarnates and lives with opposite arrow of time so that signals sent by it go to geometric past and are not received by the system as it has reincarnated by making a second BSFR and therefore has the original arrow of time.

   The sequences of repeated measurements of the same observables correspond to sequences of SSFRs and give rise to a continuous flow of consciousness. They would relate to sensory perceptions. BSFR would correspond to motor actions changing the arrow of time and the second BSFR would bring back the original arrow of time and correspond to wake-up and motor action.

   When the sensory input changes the set of commuting observables measured in SSFR, it becomes impossible to continue the peaceful life and BSFR must take place: self loses consciousness temporarily (dies) for a moment. This corresponds to motor action, which is missing from the view of AS as represented above.

   In the TGD framework sensory perception as a sequence of SSFRs yields continually updated quantum predictions and BSFR forced by the change of the measured observables so that it does not anymore commute with the earlier observables, gives rise to motor action as a reaction.

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

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

About Biefeld Brown effect

Biefeld Brown effect is one of the effects studied by "free energy" researchers. What happens that an asymmetry capacitor for which the electrodes are of different size starts to move in the direction of the smaller electrode. The so called emdrive (see this), which I have commented here and here, could be also based on this effect. The has been a lot of overhyping such as vehicles moving with light-velocity to Mars and the failure of momentum conservation by the Biefeld Brown effect is real.

The recent experiments carried out by Buhler's team using capacitors in vacuum chamber acieve a levitation in gravitational field of Earth (see this). If this is really the case, new physics is involved.

Standard physics based models for the effect are discussed here. The electric fields associated with the capacitors are about 30 kV/dm, which is about 10 per cent of the electric field 30 kV/cm causing dielectric breakdown in air. Note that the electric field of Earth 10-30 V/dm and therefore roughly by a factor 1/1000 weaker.

Brown makes several important statements, including:

1. The greatest force on the capacitor is created when the small electrode is positive.
2. The effect occurs in a dielectric medium (air).
3. The effect can be used for vehicle propulsion or as a pump of dielectric fluid.
4. Brown s suggeset that the effect involves ionic motion.
5. The detailed physics of the effect is not understood.

The models assume that the cm motion is due to the loss of energy and momentum to the environment and fail if the effect is possible in vacuum. The first model assumes ionic wind between the electrodes and predicts effect, which is 3 orders of magnitude too small. The model based on ionic drift is a rough order of magnitude model and predicts that the effect can have an order of magnitude consistent with the findings. The reason why the ionic wind predicts a smaller effect is that the absence of dissipation tends to reduce the effect since the ions arriving to the opposite electrode induce an opposite recoil.

The interview of Charles Buhler by Tim Ventura (see this) gives more details about what has been found in the experiments giving a thrust which is now around one g. Buhler's team has been developing the propellantless propulsion based on asymmetric capacitors understood in a very general sense, i.e. there are just two electrodes which are asymmetric. The work is completely independent of NASA and has been patented. From the interview I learned the following.

1. Electric field is more intense at the smaller electrode and is believed to make the effect larger.
2. The electrodes are cased which means that there is no leakage of charge between them. The claim is that this prevents all kinds of leakage currents between the electrodes. The system is also enclosed in high vacuum and this allows use of lower voltages. There are two types of charges involved. The free charge appearing in conductors and the bound charge appearing in insulators. The interpretation would be in terms of electrons. It is reported that at low voltage free charge dominates the effect and at higher voltages bound charge dominates. The interpretation could be in terms of ionization in high enough voltage in which bound charges go somewhere.
3. Mere charge and electric field are enough and there is no external energy feed. The mere existence of the electric field gives rise to the thrust. In the standard physics framework, this raises problems with the conservation laws of energy and momentum.

I have already earlier commented on the Biefeld Brown effect from the TGD point of view (see this, this and this).

1. In standard physics the center of mass of the system should remain at rest if the system is in vacuum and there is no charge leakage between the electrodes. The findings of Buhler's team demonstrate that there is a center of mass motion in vacuum. Therefore there should exist a momentum and energy exchange with some unidentified system. Charges and/or radiation should leave the capacitor to produce a recoil.

   If the charges leaving a given electrode return to the system, the only possibility is that they end up at the opposite electrode. This cannot take place via standard physics mechanisms in the experiments of Buhler's team since the electrodes are cased. The charges must go to some third system and possibly return back.

2. The findings suggest that the charges involved are conduction electrons at low voltages and bound electrons at high voltages and that the bound electrons increase the thrust dramatically. In the latter case an ionization of atoms is required.

   If the electronic charge is lost from a negatively charged electron, a current is needed to preserve the charges of the electrode. If only the negatively charged electrode emits electronic charge, the system develops a positive charge. The system would experience a force in the electric field of Earth. This cannot explain the effect. Since the Earth is negatively charged, the force would tend to decrease the thrust. The generation of net positive charge could however be relevant for the effect.

3. If negative charge is lost and there is no energy and momentum feed from outside, the electrostatic energy of the system must decrease. The rate of energy loss must be rather slow since the thrust is reported to continue for a rather long time.

   Part of the electrostatic energy should go to the cm motion of the system. Where does the momentum and energy leaving the system responsible for thrust as the recoil effect go? In the experiments of Buhler's team it cannot go to the environment as it is understood in the standard physics.

What could TGD say about the situation? TGD predicts that besides classical gravitational fields of the Sun, Earth and other planets are responsible for very large values of effective Planck constant h_eff for ordinary particles located at the gravitational monopole flux tubes. The generalization of this proposal for electric fields is discussed here. Examples are electric fields of DNA, cell, ionospheres of the Earth and Sun, and also of large capacitor-like systems.

1. Are the charged particles transferred to electric or magnetic flux tubes of the field body (FB) as dark charges as in the Pollack effect (see this)? Can one locate the relevant part of the FB to the interior or exterior of the electrodes? Could the charge transfer via the FB take place by an analog of the Pollack effect and its reversal? Why would the charge transfer be for electrons?

   Is there a fast charge transfer only between the electrodes via FB or is there an accumulation of positive and negative charges at the FB? It is reported that the thrust continues also in absence of a current feed so that there could be accumulation of charges from both electrodes to the FB. Also the electric body of the Earth could be involved.

   Also mere radiation to the FB could produce a recoil effect but would not produce charge transfer. The required force would be between FB and the capacitor system. The force is known to be directed to the smaller electrode on the smaller electrode, especially so if it has a positive charge.

2. If the charge transfer occurs between the electrodes via the FB and no charge remains at the FB, center of mass motion requires that part of the energy is dissipated, perhaps as dark photons at the magnetic or electric body or as ordinary photons.

   Suppose that the net momentum transferred to a given flux tube is parallel to it. The net momentum, which is transferred is the sum of the momenta and in the case of parallel plates of infinite size directed towards another plate. The recoil is in the opposite direction. The deviation of the distribution of flux tubes from spherical symmetry favors transfers of momenta directed towards the opposite electrode so that recoil is away from it. Why should the smaller electrode get a larger recoil momentum? Why should the smaller area favor this?

Could macroscopic quantum coherence predicted by TGD explain why the smaller electrode gets a larger recoil momentum?

1. TGD predicts large scale quantum coherence and this could be highly relevant for the Biefeld Brown effect (see this). The electric Planck constant for a pair of charged particle with charge e and for charged system with charge is h_eff= h_em= Qe/β₀, where β₀= v₀/c≤ 1 is a velocity parameter. For the pair of capacitor plates would be given by h_em= Q²/β₀. h_em would characterize charged particles at the electric body of the system consisting of electric flux tubes, which can be also magnetic since electric flux tubes can obtained as small deformations of the magnetic monopole tubes!

   Note that one cannot exclude the possibility of Maxwellian half-monopole flux tubes having boundary, which I have proposed to be important in the temperature region above the transition temperature in the case of high Tc superconductors (see this).

2. Electric field strength rather than voltage is relevant for the effect. The charge Q of the capacitor as the electric flux Q= ∫ E• dS/ε₀ is indeed proportional to the electric field and this suggests that macroscopic quantum coherence might be important (see this). The effect could become large for strong field strengths suggesting that the transfer of charges to the electric body is a collective quantum effect proportional to the square N² of the number N of charges transferred. If the increase of voltage has been done by keeping the size constant in the experiments of Buhler's team, the dramatic increase of the thrust can be understood in this way.
3. For a particle of mass m, the electric Compton length Λ _em= h_em/m= Qe/β₀m serves as a good guess for the lower bound for the quantum coherence length and is for proton by a factor 1/2000 smaller than for electron. The first guess for the thickness d of the electric flux tube is as d=Λ_em= 2π Qe/β₀m. Here m would refer to electron mass. This would explain why the transfer of electrons is what matters in the experiments. Hitherto its assumed that only valence electrons can become dark having h_eff> h. These findings would require that also bound electrons could become dark.
4. Can one assume that the entire electrodes form quantum coherent systems or should one assume that only the flux tubes are such systems? Suppose that the latter option is realized. A natural first guess is that the flux tube radius d is equal to the electric Compton length so that one would have d= 2πQe/β₀m. The entire electrodes need not be quantum coherent systems.

   For instance, if the smaller electrode corresponds to a single flux tube, it decompose to smaller flux tubes near the larger electrode giving rise to smaller quantum coherent units with charge Q_large/Q_small= S_small/S_large and having therefore also a smaller values of electric flux and of Maxwellian electric field. Quite generally, the flux tubes from the smaller electrode would decompose in this way at the larger electrode.

5. The geometric asymmetry of the electrodes, or more precisely the convergence of flux tubes at the smaller electrodes, is believed to somehow explain the thrust towards the smaller electrode.

   Suppose that the flux tubes correspond to bundles of electric field lines as predicted by Maxwell's theory. Suppose that the flux tube acts as a quantum coherent unit. The charges Q(tube) of the flux tubes near the small resp. large electrode are in the ratio S_small/S_large of their areas. By quantum coherence the rate for the momentum transfer is proportional to Q²(tube) and is therefore larger near the smaller electrode. The transfer rates are proportional to the square of the charge per flux tube and in the ratio (S_small/S_large)². This predicts that the rate of momentum transfer is higher at the smaller electrode.

6. The thrust is reported to be larger when the smaller electrode has a positive charge: I do not know whether this is the case in the experiments of Buhler's team. This does not seem to fit the proposed picture. If only electrons are transferred to the electric body, one would expect that the rate is larger at the negatively charged electrode.

See the article About long range electromagnetic quantum coherence in TGD Universe or the chapter with the same title.

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

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

Disappearing stars: one further explanation

One of the numerous anomalies of the recent cosmology are the disappearing stars (see for instance this and this) The latter popular article tells that a group of astronomers has discovered around 100 stars, which have disappeared from view in the last 70 years - and they don't know why. For instance, astronomers remain baffled by what appeared to be a trio of stars disappearing 'within 50 minutes' in 1952. The first article gives a list of explanations. The prosaic explanations are as follows:

1. Instrumentation Errors: Some of the vanishings could be due to errors or malfunctions in the astronomical instruments used to observe these stars.
2. Data Processing Errors: Errors in the processing of astronomical data could mistakenly categorize a visible star as having vanished.

There is a long list of less prosaic explanations.

1. Gravitational Lensing: The gravitational field of a massive object, like a black hole, can bend the light from a star, making it appear to vanish. This phenomenon is known as gravitational lensing. The lense effect caused by an object between the observer and star would create a ring which is too weak to be visible.
2. Transient Light Phenomena: Events like gamma-ray bursts or other short-lived luminous events might cause a star to temporarily flare up before disappearing.
3. Natural Dimming: Stars may naturally dim over time due to changes in their life cycle, although this usually doesn’t result in a complete disappearance.
4. Obstruction by Cosmic Objects: The light from a star could be blocked by interstellar objects like dust clouds or newly formed celestial bodies, causing the star to appear as if it vanished.
5. Supernova Events: One explanation for a star’s disappearance could be a supernova, an event marking the explosive death of a star. However, supernovae leave behind distinct signatures, often observable as a bright burst before the star’s remnants fade away. In cases of disappearing stars, such signatures are notably absent.
6. Black Hole Consumption: Another hypothesis is that these stars could be consumed by black holes. This would theoretically happen without the typical bursts of energy associated with such events, leading to a sudden disappearance.
7. Dyson Spheres: This is a speculative theory suggesting advanced civilizations could build massive structures around stars to harness their energy, potentially causing the stars to disappear from our view.

TGD adds one possible item to this list.

1. TGD predicts a hierarchy of effective Planck constants having arbitrarily large values. This implies quantum coherence in arbitrarily long scales. Ordinary matter, when in phases characterized by h_eff different from h, behaves like dark matter but does not correspond to the galactic dark matter. It however explains the increasing fraction of missing baryons as a transformation of ordinary baryons to their large h_eff counterparts predicted by the TGD view. In biology these dark baryons and also electrons could play a key role. In the TGD Universe galactic dark matter would consist mostly of dark energy assignable to the space-time surfaces that I call cosmic strings. They can thicken to monopole flux tubes. This process, which is analogous to inflation, transforms the dark energy to ordinary matter.
2. Zero energy ontology (ZEO) is the second key element of TGD and solves the basic paradox of the quantum measurement theory and extends it to a theory of consciousness. There are two kinds of state function reductions (SFRs).

   The sequence of "small" SFRs (SSFRs) is the TGD counterpart for the repeated measurements of the same observables and gived rise to the flow of consciousness.

   "Big" SFRs (BSFRs) are the counterpart of ordinary SFRs and involve the change of the arrow of time. In the time reversed state the classical signals sent by the system travel to non-standard direction of time so that this kind of system cannot be detected by classical means. If falling asleep corresponds to BSFR, one can understand why we do not remember anything about the period of deep sleep.

3. TGD predicts an hierarchy of values of h_eff and therefore hierarchy of quantum coherence scales. Magnetic/field bodies of physical systems like stars would carry these phases with a very large value of h_eff. They would also emit radiation which has a large value of h_eff and can be observed only if it transforms to ordinary radiation.

   Could one understand the disappearing stars in terms of BSFRs occurring in astrophysical scales at the level of the magnetic body of an astrophysical system? This would require that most of the observed classical radiation from the star arrives from the magnetic body of the system as a dark radiation. This is because for ordinary matter the period of phases with a reversed arrow of time are very short so that effectively there is no arrow of time.

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

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

Leading astronomers meet at London's Royal Society to examine the basic assumptions of the recent cosmology

The leading astronomers will have a conference at London's Royal Society to examine the basic assumptions of the recent cosmology . The conference is organized by Subir Sarkar (see this).

I am happy to hear that also leading cosmologists are aware of what is happening. In contrast to this, in my own country Finland, the local leading cosmologist appearing in the media became completely silent when JWST began to produce its findings.

The TGD view based on the new view of space-time and quantum is consistent with these findings. The following comments include the TGD based reaction on some points represented in the popular article.

The basic new elements brought by TGD to the cosmology are the new view of space-times as 4-surfaces in H=M⁴× CP₂, a generalization of quantum theory based on number theoretical view of physics complementary to the geometric view, and zero energy ontology (ZEO) solving the basic problem of quantum measurement theory and predicting that the arrow of time changes in ordinary state function reductions.

1. A number of researchers have found evidence that the universe may be expanding more quickly in some areas compared to others, raising the tantalizing possibility that megastructures could be influencing the universe's growth in significant ways.

   Comment: The basic prediction of TGD inspired cosmology is the existence of 4-D space-time surfaces that I call cosmic strings. They are unstable against thickening to monopole flux tubes, liberating huge energy transformed to ordinary matter. This would be the TGD counterpart for inflation. These objects can have length scales which are cosmological and can affect the rate of cosmic expansion.

   Number theoretic view of TGD predicts that these cosmic strings are characterized by p-adic length scale characterizing their thickness and length and also by effective Planck constant h_eff which is essentially the dimension of an algebraic extension of rationals assignable to the space-time surface that they correspond. The quantum coherence scale of the cosmic string is proportional to h_eff. The quantum coherent phases characterized by h_eff reside at the monopole flux tubes and behave like dark matter.

   Quantum coherence is possible in arbitrarily long scales and completely changes the views of what quantum gravitation is. For instance, classical gravitational fields of astrophysical objects like the Sun and Earth would play a key role in biology.

   For primordial cosmic strings h_eff is its minimal value smaller than h, but increases during cosmological evolution. The portion of ordinary matter with h_eff=h is reduced during cosmological evolution and this corresponds to the increasing portion of missing baryons. Galactic dark rather would correspond to the energy of cosmic strings consisting of magnetic and volume energy and thus dark energy plus a possible, probably small, contribution of h_eff> h phases. The model explains the flat velocity spectrum of distant stars around galaxies.

2. Sarkar and his colleagues, for instance, are suggesting that the universe is "lopsided" after studying over a million quasars, which are the active nuclei of galaxies where gas and dust are being gobbled up by a supermassive black hole.

   The team found that one hemisphere actually hosted slightly more of these quasars, suggesting one area of the night sky was more massive than the other, undermining our conception of dark energy, a hypothetical form of energy used to explain why the universe is expanding at an accelerated rate.

   Other researchers have suggested that the cosmological constant, which has been used for decades as a way to denote the rate of the universe's expansion, actually varies across space, which would contradict the standard model of physics.

   Comments:

   1. In the TGD framework quasars as active nuclei would be cosmic strings which have just started to decay to ordinary matter and to feed energy and mass to the environment. They are not blackholes, which would "eat" matter from the environment, and are blackhole-like objects in their exterior. They feed energy to their environment and this is the TGD counterpart of inflation. Whitehole might be a better metaphor.
   2. In the TGD framework the fluctuations of the value of h_eff explain density fluctuations inducing CMB temperature fluctuation. The local especially large fluctuation of h_eff could solve the problem of two Hubble constants.
   3. In the fractal cosmology associated with the many-sheeted space-time of the TGD Universe fluctuations of h_eff appear in arbitrary long scales and could also explain the lopsidedness.
   4. Vacuum energy density depends on the value of the Hubble constant, which depends on h_eff and its fluctuations would make average vacuum energy density dependent on position.
3. Stars and galaxies older than the Universe is one paradoxical discovery made already before JWST but not mentioned in the popular article. The zero energy ontology (ZEO) forces by TGD changes profoundly the view about the relationship between experienced time and the geometric time of physics. Ordinary, "big" state function reductions change the arrow of geometric time so that the system can live forth and back in geometric time. This implies that the evolutionary age of a system can be longer than its usual age. One estimate gives an age which is roughly 2 times longer and it has been indeed suggested that the age of the universe explaining the findings could be this.

See for instance https://tgdtheory.fi/public_html/articles/3pieces.pdf .

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

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

What singularities can correspond to vertices for fermion pair creation?

It is far from clear whether all singularities have an interpretation in terms of exotic smooth structures. The physical criterion would be that the creation of a fermion pair takes place at the defect and that the minimal surface property fails. Fermions can correspond to induced spinor fields and fermion pairs could be created at surfaces of dimension d<4.

1. For closed two-sheeted cosmic strings and monopole flux tubes, which split by reconnection, the interpretation makes sense and means a generalization of the basic vertex for closed strings. These objects can be 2-sheeted as elementary particles in which case the reconnection would occur in the direction of CP₂. If they are single sheeted, the reconnection would occur in the direction of M⁴.
2. 3-D light-like light-partonic orbits appearing as interfaces between Euclidean and Minkowskian space-time regions and as boundaries of space-time surfaces are singularities (see this). Boundary conditions state that the possible flows of conserved charges from the interior go to the partonic orbit so that the divergence of the Chern-Simons-Kähler canonical momentum current coming from instanton term equals to the sum of the normal components of the canonical currents associated with Kähler action and volume term.
   1. Chern-Simons action at the light-like partonic orbit coming from the instanton term is well-defined and finite and field equations should not give rise to a singularity except at partonic 2-surfaces, which have been identified as analogs of vertices at which the partonic 2-surface X² splits to two.
   2. At the light-like partonic orbit 4-metric has a vanishing determinant and is therefore effectively 2-D (the light-like components of g_uv=g_vu of the 4-metric vanish). As a consequence, g₄^1/2 vanishes like L² at the partonic orbit unless some coordinate gradients diverge.

      The canonical momentum currents for the volume action are proportional to the contravariant induced metric appearing in the trace of the second fundamental form diverging like 1/L² and to g₄^1/2 so that they remain finite.

   3. Kähler action contains the contravariant metric twice and is proportional to g₄^1/2. This can give rise to a divergence of type 1/L² unless the boundary conditions make it finite. I have proposed long ago that the electric-magnetic self-duality at the partonic orbit can transform the Kähler action to an instanton term giving Chern-Simons Kähler term. In this case, a separate instanton term would not be needed. In this case everything would be finite at the partonic orbit. Minimal surface property fails in a smooth manner.

      The intuitive picture is that the contributions from the normal currents at the partonic orbit and the Chern-Simons term cancel each other and the partonic orbit cannot play a role of a vertex.

   4. The possible presence of 1/L² divergence could however give rise to a 2-D defect and genuine vertex. If it is identified as a creation of a pair of partonic 2-surfaces, the interpretation in terms of a creation of a fermion pair is possible and could be assigned to the splitting of a monopole flux tube.

      In accordance with the QFT picture, I have considered the possibility that the 2-D vertex could correspond to a branching of a partonic orbit. In the recent picture it would be accompanied by a creation of a fermion pair. The stringy view however suggests that pair creation occurs in the creation of partonic orbits in the splitting of monopole flux tubes. The stringy view is more attractive.

3. I have also proposed that 1-D singularities identifiable as boundaries of string world sheets and identifiable as fermion lines at the partonic orbits are important. The creation of a pair of fermion lines would give rise to the analogs of gauge theory vertices as 0-D singularities. It is however far from clear whether the stringy singularities are actually present and whether they could correspond to exotic smooth structures. One can imagine two options.
   1. There are no string world sheets. Monopole flux tubes can be regarded as deformations of cosmic strings. Instead of strings several monopole flux tubes can emerge from a wormhole contact. For the minimal option, monopole flux tubes, CP₂ type extremals, and massless extremals as counterparts of radiation fields are the basic extremals and the splitting of monopole flux tubes gives rise to vertices as defects of the ordinary smooth structure.
   2. String world sheets appear as singularities of the monopole flux tubes or even more general 4-surfaces and are analogous to wormhole contacts as blow-ups in which a point of X⁴ explodes to CP₂ type extremal. I have indeed proposed that a blow-up at which the points of the string world sheet as surface X²⊂ X⁴ are replaced with a homologically non-trivial 2-surface Y²⊂ CP₂ takes place. Y² could connect two parallel space-time sheets. Could these singularities correspond to defects of exotic smooth structures such that the ends of the string carry fermion number? The vertex for the creation of a pair of fermion and antifermion lines would correspond to a diffeo defect. Note that also these defects could reduce to a splitting of a monopole flux tube so that TGD would generalize the stringy picture.

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

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

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

Singularities and infinities from the TGD point of view

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

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

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

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

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

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

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

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

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

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

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

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

The symmetry between gravitational and gauge interactions

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

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

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

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

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

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

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

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

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

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Some technical remarks are in order.

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

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

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

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

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

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

Common solution of 4 killer problems of TGD

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

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

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

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

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

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

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

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

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

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

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

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

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