Still about the topology of elementary particles and hadrons

In its recent form TGD allows several options for the model of elementary particles (see this).

1. Euclidian wormhole contacts (having Euclidian signature of induced metric) modellable as deformed pieces of CP₂ type extremals connecting Minkowskian space-time sheets (representable as graphs of a map M⁴→ CP₂) are identified basic building bricks of elementary particles. Light-like wormhole throats are assumed to be carriers of elementary particle quantum numbers.
   
   
2. One can identify simplest wormhole contact as topological sum. Remove 3-D regions from both space-time sheets and connecting the topologically identical boundaries with a cylinder X²× D¹, where X² has the topology of the boundary characterized by genus. The assumption that X² is boundary requires that its projection to CP₂ is homologically trivial. This is not consistent with the assumption that the flux tube carries monopole flux. These wormhole contacts are unstable and must be distinguished from wormhole contacts mediating monopole flux. I have not however defined the notion precisely enough.
   
   
3. One can consider two situations in which homologically non-trivial wormhole contact appears.
   

   Option I: Assume the two Minkowskian space-time sheets are glued together along their boundaries to form a closed two sheeted surface and the throats of wormhole contact serve as magnetic charges creating opposite fluxes. One can say that the two throats have opposite homology charges and therefore form a homologically trivial 2-surface to which one can glued the wormhole contact along its boundaries. The flux at sheet B could be seen as return flux from sheet A and the throat could be seen as very short monopole flux tube.
   

   Option II: Assume no gluing for the two Minkowskian space-time sheets. In this case one must assume at least two wormhole contacts. At both space-time sheets the throats of the contacts with opposite homology charges would be connected by monopole fluxes flowing through the wormhole contacts identifiable as a very short monopole flux tube. This makes sese also for the Option I and might be required since is not clear whether space-time having boundaries carrying monopole flux can be glued together.
   
   

The proper identification of the model of elementary particles remains still open (see this and this). What relevance do these two options this picture have to the model of elementary particles?

1. For Option I leptons and gauge bosons could be identified as single wormhole contact carrying non-trivial homology flux. The size scale of the closed space-time sheet would correspond to the Compton wavelength of the particle. This model is the simplest one at the level of scattering diagrams and was re-considered in the article SUSY in TGD framework.
   

   Even Euclidian regions of single space-time sheet with vanishing homology charge can be considered as a model for leptons and gauge bosons. In this case it is however not clear how to understand how the size scale of the particle as Compton length could be understood at space-time level. This model was one of the first models. I have also considered the identification of the particle as boundary component of Minkowskian space-time surface.
   
   

2. Option II was assumed in the model following the original model for leptons and gauge bosons. It was also proposed that electroweak confinement as dual description of massivation takes place in the sense that the weak charges associated with the two wormhole contacts cancel each other. The size scale of flux tube at given sheet would correspond to the Compton length assignable to the particle. In this case scattering amplitudes are more complex topologically.
   
   

What about baryons?

1. The simplest model assumes that quarks do not differ from leptons and gauge bosons in any manner. The contribution of the quarks to masses of hadrons is very small fraction of total mass, which suggests that color flux tubes carrying also homology charge are present and give the dominating contribution.
   

   One can also consider a structure formed by color magnetic monopole flux tubes carrying most of the hadron mass with Minkowskian signature carrying flux of 2 units branching to two flux tubes carrying 1 unit each. The flux tubes would have length given by hadronic p-adic length scale. The ends of flux tubes would be wormhole throats connected by wormhole contacts to the mirror image of this structure. One can say that homology charges 2,-1,-1 assignable to the throats of single space-time sheet sum up to zero. This brings in mind color hypercharge. Could color confinement have vanishing of homology charge as classical space-time correlate?
   
   

2. In the proposal for the TGD based realization of space-time supersymmetry and the notion of super-space I considered two alternative identification of leptons. Leptons and quarks could correspond to the different chiralities of M⁴× CP₂ spinors and lepton and baryon numbers would be separately conserved. For second option leptons would b local 3-quark composites and therefore analogous to spartners of quarks: this option is possible only in TGD framework and the reason is that color is not spin-like quantum number in TGD framework. Baryon and lepton numbers would not be separately conserved.
   

   One can ask what could be the simplest mechanism inducing the decay of baryon as 3-quark composite involving only 3 wormhole contacts and giving lepton as a local 3-quark composite plus something. Wormhole throats of 3 quarks carrying the quark quantum numbers should fuse together to form a leptonic wormhole throat, and the 3 quark lines representing boundaries of string world sheets should fuse to single line. If the sum of quark homology charges is vanishing, lepton must have a vanishing homology charge unless the reaction involves also a step taking care of the conservation of homology charge as a decay of the resulting wormhole contact with vanishing monopole flux to two wormhole contacts with opposite monopole fluxes. Already the first step of the decay process is quite complex, and one can hope that the rate for the reaction is slow enough.
   
   

See the article SUSY in TGD framework.

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

Articles and other material related to TGD.

Evidence for 3 different temperatures at Milky Way halo

The TGD based model for Milky Way suggests the presence of 3 cosmic strings thickened to flux tubes. Galactic disk has indeed 3 components with different thickness. There is support for the presence of 3 components also in the Milky Way halo (see this), thanks to Wes Johnson for the link) as gas at different temperatures, and perhaps assignable to 3 different cosmic strings.

The information was gained by studying X rays from a blazar, very active energetic core of a distant galaxy emitting intense beams of light. The blazar was at distance of 5 billion light years. The light passed through the galactic halo and the temperature of the halo was determined from the properties of light received at Earth.

The halo was expected to have single temperature in the range between 10⁴-10⁶ K. It was however found to contain 3 components at different temperatures, and the hottest component had temperature about 10⁷ K. The unexpectedly high temperature is proposed to be due to the winds emanating from the disc of stars of MW. It was also found that the halo contains besides hydrogen also significant amounts of heavier elements suggesting that the halo has received material created by certain stars during their lifetime and final stages.

In TGD framework "cold fusion" (see this) outside stellar interiors could have generated at least part of the heavier elements. "Cold fusion" proceeds by a formation of dark nuclei identifiable as dark nucleon sequences at magnetic flux tubes with h_eff/h≈ m_p/m_e∼ 2000 and having radius of electron Compton length. Nuclear binding energy is scaled down by a factor of about 1/2000 to keV range. Dark nuclei would have transformed to ordinary nuclei liberating practically all nuclear binding energy outside stellar nuclei. This process would serve as a kind of warm-up band in the pre-stellar evolution leading eventually to the ordinary fusion (see this).

See the article A model for galaxy formation or the chapter Cosmic string model for the formation of galaxies and stars.

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

Articles and other material related to TGD.

Direct astrophysical evidence for monopole flux tubes

Monopole flux is the key property of flux tubes proposed to be behind various astrophysical structures. Is there any direct evidence for this? Evidence has emerged for the existence of giant clouds with size about 100 AU in the vicinity of the supermassive GBHE of Milky Way (see this and this). These objects - called G objects - look like gas clouds but behave like stars. G objects stretch longer when nearer to GBHE but get their original shape when farther away. One would expect that they are torn apart by the enormous tidal forces created by GBHE.

The identification could be as visible matter assignable to a spaghetti like structure formed by monopole like flux tube, which could have also produced the visible matter in the thickening of the flux tube. By flux conservation the monopole flux prevents the flux tubes from splitting even in the huge gravitational field of supermassive GBHE. Without monopole flux tubes to which visible matter is gravitationally bound the structure would be torn to pieces. In Maxwellian world monopole flux tubes are not possible. In biology the behavior of gels (the contents of an egg is the basic example) could be based on monopole flux tubes connecting the cells together.

See the article A model for galaxy formation
or the chapter Cosmic string model for the formation of galaxies and stars.

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

Articles and other material related to TGD.

A model for the formation of galaxies

I have proposed a general vision about galaxy formation as formation of tangles on cosmic strings carrying monopole flux. The strings can be long and also short. In the case of long string the model explains flat velocity spectrum of distant stars automatically. For closed short strings the velocity spectrum is not flat. There is however no detailed model for the galaxy formation. In particular, the complex structure of spiral galaxies is poorly understood. Even the question whether there is single long cosmic string orthogonal to the galactic plane or cosmic string parallel to the spiral structure in galactic plane - as proposed decades ago in the original model - or both has remained open. In the sequel I make an attempt to collect the essential facts about elliptic and spiral galaxies and consider a qualitative model for the galaxy formation consistent with these facts. The goal is rather modest: just to develop an internally consistent view about the evolution of galaxies.

1. The simplest model for elliptic galaxy is as a closed string possibly reconnected as a loop from long string or as a tangle of a cosmic string having topology analogous to that of field lines of dipole magnetic field. Quasar would have preceded the formation of the tangle in which string would have thickened to flux tube and dark energy would have transformed to ordinary matter. Quasars would be time reversal of galactic blackhole like entity (GBHE).
   
   
2. In the case of spiral galaxies the existence of vast polar structures (VPOS) in the plane orthogonal to the galactic plane of spiral galaxy (see this) strongly suggest that two cosmic strings are involved and that the spiral structure believed to correspond to a standing wave analogous to traffic jam is associated with dark matter of a long cosmic string. This model conforms with the fact that the stars of spiral galaxies are older than those of elliptic galaxies except inside the bulge.
   

   The asymmetry between the two planes suggests that the spiral arms are formed when an elliptic galaxy identified as a tangle of a long string S_|| formed via a quasar stage in the galactic plane has collided with a cosmic string S_⊥ orthogonal to the galactic plane. These collisions are unavoidable for non-parallel strings and gravitational attraction causes the needed relative motion.
   

   The differential rotation of portion of S_|| around S_⊥ would have deformed S_|| to a spiral shape. S_|| would have also generated the visible spiral arm pair in the transformation of dark energy to ordinary matter. Galactic bulge would correspond to the elliptic galaxy and galactic blackhole like entity (GBHE) would have formed from the matter in bulge: this conforms with the fact that elliptic galaxies have always galactic blackhole. The galactic bar could be analogous to the dipole of dipole magnetic field. In principle also the string orthogonal to the galactic plane could produce ordinary matter by thickening.
   
   

One open question relates to the fact that TGD predicts two kinds of cosmic strings with closed transverse cross section and having vanishing induced Kähler field or non-vanishing induced Kähler form carrying monopole flux. The latter are stable against splitting by the conservation of the monopole flux and have no counterpart in Maxwellian electrodynamics. The monopole flux tubes could correspond to the cosmic strings giving rise to galaxies, stars, and even planets as tangles. Non-monopole flux tubes might serve as gravitational flux tubes mediating gravitational interactions. Presumably both kinds of flux tubes are involved but their precise roles are not well-understood.

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

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

Articles and other material related to TGD.

Lense effect as support for TGD view about galaxies

Cosmology an also other fields of physics with one exception - particle physics - produces fascinating results on daily basis. It is really a pity that particle physicists living in the jail of their reductionistic world view cannot pay any attention to these discoveries and continue moaning that there is no data so that it impossible to go beyond standard model. Bad philosophy can kill entire field of science. Having replaced Planck length scale reductionism by fractality I can enjoy swimming in the flood of anomalies.

The surprise of this morning was a popular article about a detection of dark matter lumps by Hubble telescope. The discovery is based on gravitational lense effect. The popular article tells about light coming distant quasars - distance is about 10 million light years. At the path of light coming to Earth there is foreground galaxy - distance is about 2 million light years. They are reported to give rise to four separate images of the galaxy by lense effect.

I am however wondering why one observes four images of each quasar by foreground galaxy. My naive expectaton would be a ring if dark matter halo gives rise to the lensing. Tell me if I am wrong.

It is also stated that the number of images depends on how many different dark matter particles there exists. I must admit that I do not understand. I would be happy for explanation.

What says TGD?

1. If galaxies are associated with long cosmic strings as tangles as in TGD Universe, flat velocity spectrum is automatically predicted without any other assumptions and velocity spectrum determines string tension. See http://tgdtheory.fi/public_html/articles/meco.pdf and http://tgdtheory.fi/public_html/articles/galaxystars.pdf .
   
   
2. Long cosmic string would give rise to two separate images in lensing effect rather than ring as halo would do. Two long foreground cosmic strings with different directions - say being nearly orthogonal - would give rise to four images. Two cosmic strings could be assigned with fusion of two galaxies associated with separate cosmic strings.
   
   
3. The two cosmic strings could be assigned with fusion of two galaxies associated with separate cosmic strings. One can consider the possibility that visible galaxies are formed as two cosmic strings collide: this would give rise to instability initiating the thickening of the 2-D M4 projection of cosmic string and formation of tangles associated with both cosmic strings. Magnetic energy would be liberated and transform to ordinary matter giving rise to the visible matter of galaxy. For instance, could the 4 spiral arms of Milky way could relate to the second cosmic string in the plane of Milky way tangled around the second cosmic string orthogonal to the plane of Milky Way?
   

   One can consider also a situation in which there is no foreground galaxy but just two cosmic strings and this might provide a test for TGD view.
   
   

See the article Two interesting findings related to dark energy and galactic dark matter or the chapter Cosmic string model for the formation of galaxies and stars .

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

Articles and other material related to TGD.

Comparing Gisin's intuitionistic mathematics with adelic physics

Nikolina Benedikovic had an interesting posting commenting the work of physicist Nicolas Gisin. Gisin makes several strange looking statements.

1. Gisin states that physicists apply classical physics, which is deterministic. This is of course true. They however apply also quantum physics, which involves non-deterministic state function reduction in conflict with the determinism of Schrödinger equation but is necessary for the interpretation of experiments. Statistical determinism is assumed but requires the notion of ensemble.
   
   
2. Gisin claims and numbers with infinite number of decimals involve infinite number of information. This is not the case in general. For instance, if the decimals obey some formula the information is finite. Also rationals have infinite number of decimals but the the sequence of decimals is periodic so that the information content can be said to be finite.
   
   
3. Gisin claims that the world is finite. Presumably he means that world is discrete and consists of finite number of points. This picture leads to insurmountable difficulties in practice.
   

   I believe that it is not world which is discrete but the cognitive representations about it. They are always discrete and in computer science based on the use of finite rational numbers reducing to pairs of integers. What is wrong with recent day physics is that cognition together with consciousness is kept out from consideration. Finite measurement resolution is described in ad hoc manner.
   
   

4. Intuitionistic mathematics is the proposal of Gisin in which everything is finite. Finite number of decimals brings in indeterminism and Gisin argues that this number increases with time - kind of evolution.
   
   

It is interesting to compare this with TGD view.

1. Finite measurement resolution instead of finite world looks to me a more realistic option. Classical realities - say space-time surfaces in TGD - are continua but our observations are always discrete because of finite observational and cognitive resolution.
   
   
2. Gisin's approach excludes algebraic numbers. In TGD also algebraic numbers are allowed - essentially as roots of polynomials and are represented geometrically - say sqrt(2) as the length of the diagonal of square. Geometric representations complete the linear representations of numbers based on sequences of digits. This corresponds to the reductionistic-holistic dichotomy or left brain-right brain dichotomy.
   
   
3. Cognition has as correlates p-adic numbers and their extensions induced by those of rationals- one can speak of -p-adic variants of space-time surfaces. This leads to what I call adelic physics (see also this). Cognitive representations correspond to points of space-time surface common to both real and p-adic space-time surfaces with preferred imbedding space coordinates (by symmetries) having values in extension of rationals and making sense in all number fields involved. They are essentially unique for given extension and the representation is in generic case discrete and even finite. These unique discretizations in the intersection of reality and various p-adicities are the TGD counterpart for intuitionism.
   
   Remark: Interestingly, the extension of rationals by powers of Neper number e or its root induces finite-D extension of p-adic numbers. So that also roots of e could be allowed by cognitive representations with finite resolution just like roots of unity. They would be very exceptional transcendentals.
   
   
4. In TGD framework cognitive resolution is characterized by the n and the number N(p) of pinary digits and to the integer n. The mathematics of cognition is discrete and analogous to intuitionistic mathematics. n measures algebraic complexity and is kind IQ. n actually corresponds to effective Planck constant h_eff =nh_0 and measures quantum coherence scale in TGD framework so that a direct connecting with quantum physics allowing dark matter in TGD sense emerges.
   
   
5. Gisin compares the increase of decimals as a process analogous to evolution. In TGD evolution would reduce to an unavoidable increase of n and N(p).
   
   

To sum up, the indeterminism about which Gisin talks would thus correspond to finite measurement and cognitive resolution in TGD framework. This indeterminism is in certain sense a correlate also for quantum non-determinism. For instance, geometric time order of "small" state function reductions (weak measurements) in events in zero energy ontology can vary and this variation corresponds classically to the lack of well-ordering for p-adic numbers.

Indeed, as one types text one often finds that the experienced order of digits as sequence of small state function reductions is different from that for the outcome representing corresponding sequence of moments of geometric time: you experience typing "outcome" but the result is "outocme"! Neuroscientist would of course invent other explanations.

See this and this .

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

Articles and other material related to TGD.

A model for protocell based on Pollack effect

I learned about extremely interesting Quanta Magazine article telling about findings related to water droplets as protocells able to perform chemical metabolism as a transfer of molecules to exterior and back.

The work is doen by David Zwicker and collaborators at the Max Planck Institute for the Physics of Complex Systems and the Max Planck Institute of Molecular Cell Biology and Genetics, both in Dresden. The work is published in Nature Physics.

In a simplified model for the droplets (P-granules in C-elegans cell is the real life example) the proteins in droplet can be in two states: in state A the stay in droplet and do not get out but can enter to the droplet from outside. In state B they can get out from droplet. To get into state B energy such as sunlight would be required.

The model has real life realization!

1. The exclusion zones (EZs) discovered by Pollack (see this) behave just like this. For TGD based model see this. The formation of EZs requires water bounded by a gel phase and they are negatively charged. Their really strange feature is that they throw out impurities just like state B in the model: this seems to defy second law telling that gradients tend to disappear. This makes possible primitive chemical metabolism involving exchange of chemicals between droplet and exterior. Light signal initiating the transfer by providing the metabolic energy needed. Transfer would stop as light signal stops.
   
   In TGD inspired quantum biology EZs are in crucial role. For instance, cell is negatively charged as also DNA double strand. Interpretation as EZs is natural.
   
   
2. The explanation for the negative charge of EZ is that part of protons and possibly other ions go to magnetic flux tubes forming the magnetic body (MB) of the system (see this). Dark ions form phases with nonstandard value h_eff=n×h₀>h of effective Planck constant as cyclotron Bose-Einstein condensates. This system has long length scale quantum coherence and serves as a master controlling bio-chemistry, which is in the role of slave. This forces the mysterious coherence of the ordinary bio-matter impossible in life-as-mere-chemistry approach.
   
   
3. MB could control chemical metabolism of the droplet by sending dark photons to the droplet transforming to bio-photons and generating EZ state in the droplet and initiating transfer of molecules to the outside. The transition reducing the value of h_eff at MB would bring protons back to EZ droplet and it would become normal again. Secpnd law would force the molecules from outside to diffuse back to the droplet.
   
   
4. There is still one hard problem to be solved. What causes the mysterious removal of impurities from EZ challenging second law? Here zero energy ontology (ZEO) comes in rescue (see this). In ZEO macroscopic quantum jump corresponding to ordinary state function reduction changes the arrow of time . This would occur to MB as EZ is formed. Second law holds still true but in reverse time direction. MB is the boss and forces time reversal also at the level of ordinary bio-matter. The usual diffusion of molecules to cell occurs but with reverse arrow of time and explains the mysterious removal of impurities observed by Pollack for EZs.
   
   

All biological self-assembly processes would use this mechanism. In fact, self-organization quite generally would be dissipation in reverse direction of time: this would explain self-assembly aspect of self-organization. The big quantum jumps would inducing change of the arrow of time would tend to increase of h_eff in statistical sense (h_eff is identifiable number theoretically essentially as dimension of extension of rationals and bound to increase). This would correspond to the evolutionary aspect of self-organization. The increase of h_eff requires energy since the energy of state increases with h_eff with other parameters kept constant. Energy feed is therefore needed.

See the article A model of protocell based on Pollack effect, the article Some applications of TGD inspired quantum biology: bio-chemistry, metabolism, replication, or the chapter Getting philosophical: some comments about the problems of physics, neuroscience, and biology.

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

Articles and other material related to TGD.

Findings challenging the notion of dark energy

Nikolina Benedikovic gave a very interesting link to a popular article describing a finding challenging the notion of dark energy.

This finding is very interesting since twistor lift of TGD predicts length scale dependent cosmological constant.

I try to collect the basic facts first.

1. Standard candle property is essential assumption leading to dark energy hypothesis. It states that the distance corrected luminosity of SN Ia supernovae does not evolve with redshift that it is it depends only on distance. See https://en.wikipedia.org/wiki/Type_Ia_supernova .
   
   
2. Observation: The luminosity of SN Ia supernova correlates strongly with the population age of the host galaxy. The luminosity thus depends on the environment provided by the host galaxy.
   
   
3. This is in conflict with the standard candle property if the population age of the host galaxy decreases with distance. This is obvious in standard cosmology. But is this true in TGD Universe obeying zero energy ontology (ZEO)?
   
   

In ZEO the situation might be different. ZEO provides a quantum measurement theory solving the basic paradox of standard quantum measurement theory and leads to a theory of consciousness.

1. The first prediction is that geometric time and experienced time identified as sequence of "small" state function reductions (SSFRs as counterparts of weak measurements) are not same. This is of course an empirical fact - thermodynamical time is irreversible unlike geometric time, etc... but in standard ontology these times are identified. See http://tgdtheory.f/public_html/articles/zeoquestions.pdf .
   
   
2. In small state function reductions (SSFRs) as counterparts of weak measurements) arrow of time does not change and their sequence defines self as conscious entity. In big (ordinary) state function reductions (BSFRs) the system "dies" and reincarnates with opposite arrow of time. The experiments of Minev et all provide direct support for ZEO in atomic systems. Libet's findings support this in neuroscience. See http://tgdtheory.f/public_html/articles/Bohrdead.pdf .
   
   
3. Assume that the size of the causal diamond (CD) decreases in "reincarnation" that is self experiences "childhood". If so the size of CD can remain bounded. Irrespective of this assumption the temporal center of mass position of CD in imbedding space H=M^4xCP_2 remains the same during the sequence of reincarnations.
   

   !!Most importantly: the steady motion towards future assumed in standard ontology with single arrow of time is replaced with forth-and-back motion in time with constant cm position of CD in H.
   
   

4. ZEO explains several time anomalies such stars older than the universe and the observation that the nuclear abundances of very distance stars seem to have nearly their modern values supporting the view that the population age of galaxy does not depend significantly on distance (see this) .
   

   In particular, the age distribution for the populations of galaxies would not depend significantly on distance - standard candle hypothesis would be saved!
   

See the article Cosmic string model for the formation of galaxies and stars or the chapter with the same title.

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

Articles and other material related to TGD.

Musings on the Current Status of HEP

Peter Woit had a posting titled "Musings on the Current Status of HEP" commenting the article of particle physicist Misha Shifman having the same title. Shifman's conclusion is that HEP represents a dead branch in the tree of science. There is no doubt that Shifman will have followers since most particle physicists and also those in other fields know the situation and telling the the ugly truth is not so dangerous anymore.

I remember when the first superstring revolution took place 1984. Sheldon Glashow, who shared with Salam and Weinberg Nobel from the development of standard model - was one of those who realized from the beginning what might be the consequences. I had published my thesis 1982 and was convinced that it would not take more than a couple of years before strings would be replaced with 3-D surfaces. I was wrong.

One of the comments made by Glashow later was "...you may call it a tumor, if you will..." . It was indeed a tumor, which spread almost instantaneously. 10 years later when it had already become clear that superstrings did not provide the unique theory of everything. M-theory emerged. At this time censorship was established in arXiv as also I had to painfully learn. This made impossible communication of ideas and turned out to be lethal for HEP: science cannot make progress under censorship.

Eventually the original vision about unique theory was replaced with its opposite. Landscape as set of solutions to the cosmological constant problem around 1997, and meant that there is in practice no hope for a theory able to predict anything. Two decades ago it became clear that there is actually no landscape, the desired solutions simply do not exist. Now Swampland is the fashion. The sad outcome of this Odysseia lasting for a quarter of century was the death of HEP.

It would be important to analyze carefully the sociology of super-string revolution to avoid similar catastrophes in future.

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

Articles and other material related to TGD.