tag:blogger.com,1999:blog-106143482020-09-21T17:17:49.427-07:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger1753125tag:blogger.com,1999:blog-10614348.post-25140869953169144662020-09-21T17:15:00.004-07:002020-09-21T17:17:49.230-07:00Expanding Earth model, Cambrian Explosion, and Pangaea supercontinentThis is a response to a comment of David Whitfield in a discussion related to the life on Mars and whether it might be a good idea to reserve a ticket to the next spacecraft going to Mars. The comment is about TGD based Expanding Earth model suggesting thatin Cambrian Explosion Earth experienced a rapid phase of expansion increasing it radius by a factor 2. The model is natural in TGD and forced by the assumption that cosmic expansion occurs in average sense also for astrophysical objects. Since no smooth expansion has been observed, the expansion must occur as rapid jerks.
</p><p>
The TGD based model is consistent with my knowledge about geological and climate evolution: I am of course not an expert and I know well that experts disagree in many aspects. I put my money on general arguments and empirical anomalies: cosmic expansion must take place also for the planets and stars and must occur in discrete steps since smooth expansion is not observed. Here testing is possible.
<OL>
<LI> Climate evolution: the snowball earth model has anomalies and it must be given up in TGD framework. The evolutionary history of magnetic fields could allow testing of the model: their behavior challenges the snowball earth model.
<LI> Biological evolution: the sudden emergence of a huge number of multicellulars as from nothing is the strongest argument in favor of the the burst of intraterrestrial life living in the underground ocean to the surface. The life forms in the start of the expansion lived in the world with a 6 hour long day instead of 24 hours. This might make itself visible in the biorhythms of animals living today as a kind of genetic memory. Could this biorhythm show itself somehow in the very early fossils? The expansion of Earth led to a weakening of the gravitational field: this explains the emergence of giant creatures, which lost the fight for survival: small animals with big brains were the winners.
<LI> Geological evolution: An interesting question related to the Pangaea supercontinent can be raised. Pangaea is thought to have emerged from continents about 335 million years ago: there would have been Pangaea and the Ocean. The Cambrian Explosion occurred roughly 500 million years. Did Pangaea form from separate continents or did the Cambrian Explosion create a single gradually expanding Ocean and plus one super continent which did not increase in size but was like an island. Can one think that the recent continents emerged from Pangaea. I have not considered this question.
</OL>
</p><p>
See <A HREF="http://tgdtheory.fi/public_html/articles/expearth.pdf">this</A> and <A HREF="http://tgdtheory.fi/public_html/articles/platoplate.pdf">this</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-6024504688723709772020-09-21T02:17:00.000-07:002020-09-21T02:17:00.288-07:00How dreams are transformed to realities?The question "<I>Why there is something rather than nothing</I>" was fashionable question years ago. I wrote with some irritation about the ill-posedness of the question an article to a journal edited by Huping Hu around 2012 and for some reason the article found numerous readers. Unfortunately I do not have the article at my homepage.
</p><p>
The emergence of a universe /sub-universe from nothing is prevented by he conservation law of energy in the standard ontology.
</p><p>
What about zero energy ontology (ZEO) behin TGD? In ZEO situation changes. The following assumptions are needed to avoid obvious contradictions with the existing views about time.
<OL>
<LI> Causal diamonds (CSa) define the 4-D perceptive fields of conscious entities.There seems to be hierarchy of CDs within CDs and CDs can overlap and define a kind of conscious atlas of perceptive fields in which chart pages as CDs form a fractal hierarchy. The notion of manifold would generalize to consciousness theory. The intersecting CDs would make possible selves having shared mental images.
<LI> The perceptive fields defined by CDs increase in size during each life cycle with passive boundary and states at it being stationary and second boundary active. In BSFR the roles of active and passive boundary would change and CD would shrink in size as passive boundary would shift to future and CD would start to increase in an opposite time direction. CDS would also shift towards the geometric future inside a bigger CD.
<LI> The center slice of a given CD - the largest one - would define the moment "Now" of a corresponding self and shifts towards the geometric future. The surprise is that also memories are mental images - smaller CDs - shift towards the geometric future of this slice. The roots of the polynomial defining CD would define special moments in the life of self as time slices at which SSFR could perhaps take place.
<LI> What happens outside a given CD: do the space-time sheets representing incoming particles continue outside its so that there would be the analog of incoming particles and outgoing particles as in particle reactions. This would be suggested by the belief in objective 4-D reality. My recent view is that for given self having subselves having... there is the largest CD beyond which it does not continue.
</OL>
</p><p>
After this sidetrack the question. Can realities - sub-universes represented by zero energy states inside CDs be created from nothing? Can CDs together with their contents pop up from nothing?
<OL>
<LI> ZEO would allow it but experimental physicists would shake his head: this is against the materialistic idea of single unchanging reality - and say something nasty about crazy theoreticians. My colleague William Shakespeare would have a different opinion but I am unable to put in englsh what he said about dreams as threads of the reality.
<LI> One can however transform the ZEO based proposal into a milder form. Could dreams pop up from nothing and then can transform to realities?
p-Adic physics describes intentions and cognition and M^8-H duality suggest that one could have space-time sheets defined by polynomials with coefficients which are piecewise constant rationals defined as functions of the light-like radial coordinate of CD. They cannot correspond to a real space-time surfaces but could correspond to p-adic ones.
<OL>
<LI>Could these space-time surfaces inside corresponding CDs be created from nothing? Could they in turn transform to real space-time surface with p-adic pseudo constants becoming genuine constants. Either in SSFRs - ("small" state function reductions happening when nothing would happen in standard ontology (Zeno effect in repeated measurements) or more probably in BSFR ("big" or ordinary SFRs). The outcome would be a real space-time surface and its p-adic cognitive variants providing its cognitive correlates: cognitive representation would be the intersection of reality and p-adities consisting of points if imbedding space in the extension of rationals defining the adele. Dream would have transformed to a reality.
<LI> Partial realization would select only a single pieces of piecewise continuous polynomial, that beginning from the tip of CD in the division of ligh-like radial coordinate axis to pieces. Hence only imagination instead of full realization.
</p><p>
Imagined percepts and motor actions as almost percepts and motor actions is one basic notion of TGD based quantum neuroscience. Could one learn something useful by regarding imagination as partial realizations of p-adic intentions and dreams?
</OL>
</OL>
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-27805672054558109982020-09-16T01:47:00.004-07:002020-09-16T01:47:44.660-07:00Binaural beat as a support for TGD view about brain
The phenomenon known as binaural beat see <A HREF="https://en.wikipedia.org/wiki/Beat_(acoustics)">this</A>) provides support for the TGD view about the brain. Binaural beat occurs when sound waves with slightly different frequencies arrive in both ears. The beat can be understood as interference due to the time-varying phase difference of the waves. What is heard is the difference frequency, even when it is below 20 Hz - for instance 10 Hz-, and therefore not audible. The amplitude modulation with 10 Hz would be perceived, not the 10 Hz frequency. Strangely, the binaural beat occurs also when the signals arrive only to separated ears so that interference is not possible. In the standard neuroscience binarual beat is a mystery.
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The TGD based explanation could be that the sound waves generate dark photon signals propagating along flux tubes and having classical em waves as correlates. The waves from different ears would interfere if the flux tubes meet at some point in the brain located at auditory areas perhaps. The first option is that this interference gives rise to the experience of the binaural beat and superposes with the sensory input assigned to ears (one cannot exclude the possibility that the sensory qualia are assigned to virtual sensory organs in the brain). Second option is that the virtual sensory input as feedback sent back to ears as dark photons superpose to the sensory input from ears.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-461722001732493342020-09-14T23:09:00.002-07:002020-09-16T19:49:25.566-07:00Halo model of dark matter meets further difficultiesWithin few days become aware of several interesting findings challenging the halo model of dark matter. Here is the brief summary of these findings with possible TGD based interpretations.
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<B>Dark matter seems to be more clumpy than predicted</B>
</p><p>
The following piece of text is from a popular article "Hubble Uncovers an Unexpected Discrepancy: An Ingredient Missing From Current Dark Matter Theories?" in <A HREF="https://scitechdaily.com/hubble-uncovers-an-unexpected-discrepancy-an-ingredient-missing-from-current-dark-matter-theories/">Scitechdaily</A>. The article tells about the observations by the NASA/ESA Hubble Space Telescope and the European Southern Observatory’s Very Large Telescope (VLT) in Chile. The original article “An excess of small-scale gravitational lenses observed in galaxy clusters” by Massimo Meneghette et al is published in 11 September 2020 in Science (see <A HREF="https://arxiv.org/abs/2009.04471">this</A>).
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<I>"The researchers then used the Universe simulator to build 25 simulated clusters and performed a similar analysis with the clusters. They did so in order to identify the sites of possible lensing and the locations that could create the greatest distortions. The two didn't match. There were significantly more areas that generated high distortion in the real-Universe galaxy than there were in the model. This would be the case if the distribution of dark matter were a bit more clumpy than the models would predict-the dark matter halos around galaxies were more compact than the models would predict."</I>
</p><p>
Cold matter scenario seems to be in grave difficulties. There are a lot of problems met already earlier but put under the rug. Probably an unavoidable outcome of over-specialization. During the years I have commented on these failures in articles, which can be found also at my homepage (see <A HREF="http://www.tgdtheory.fi/tgdarticlesall.html">this</A>).
</p><p>
The basic problem is that a continuous distribution of dark matter is assumed. Galaxies and other structures would be formed by the gravitational attraction of seeds producing filament like structures. Seeds would have emerged by fluctuations in mass density.
</p><p>
In the TGD framework the situation is exactly opposite: the seeds for the formation of galaxies are present from the very beginning as what I call cosmic strings. The model explains galactic velocity distribution, providing a model for the formation of galaxies,stars, and planets, and for the linear structures formed by galaxies.
<OL>
<LI>Cosmic string-like objects carrying dark matter and energy - not possible in GRT space-time - thicken to flux tubes and generate ordinary matter much like the decay of the inflaton field. There is no need to explain how cold dark matter generates clumps, cosmic strings as clumps are there from the very beginning. Galaxies and other visible structures - also filaments - are generated along cosmic strings and flat velocity spectrum for stars rotating around the galaxy is an automatic prediction.
<LI> Also the invisible portions of cosmic strings not net decayed to dark matter induce a lense effect. The simulation of the presence of cosmic strings requires in halo models the distribution of the dark matter to be more lumpy and that requires too compact dark matter halos.
<LI> The observed lense effect can be even 10 times stronger than predicted by the halo model. TGD explanation could be in terms of cosmic strings whose thickening to flux tubes at tangles liberates energy as ordinary matter forming the galaxies and string tension lowers leading to a smaller lense effect. The portions of the flux tube still thin and with higher string tension can explain the anomalously large lense effect.
</OL>
</p><p>
<B>Universe seems too thin and two large clumps of dark matter are required to explain the distribution of galaxies in clusters </B>
</p><p>
It has been found that the observerved clumping of the dark matter is 10 per cent smaller than the clumping required by LambdaCDM scenario to make possible the formation of galaxies. The Universe seems to be also thinner than expected. This what one learns from <A HREF="https://www.quantamagazine.org/a-new-cosmic-tension-the-universe-might-be-too-thin-20200908/">Quantamagazine</A> telling about the findings of the Kilod-Degree Survey (KiDS) published in the article "KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics" (see <A HREF="https://arxiv.org/abs/2007.15633">this</A>). The group studied about 31 million galaxies from up to 10 billion light-years away.
</p><p>
Could the TGD view about dark matter and energy provide understanding? Dark matter and energy would be associated with long flux tubes emerging as cosmic string-like objects thicken and liberate energy transforming to matter. Dark matter and energy are associated with effectively string-like objects. Could this help to understand these findings?
</p><p>
The dark energy and matter assigned to string-like entities would generate the ordinary matter around themselves and serves as seeds possibly attracting more matter also created in this manner. How would the clumping in the TGD Universe differ from the clumping in the LambdaCDM scenario?
</p><p>
In LambdaCDM clumps are necessary for the formation of galaxies and other structures. In the TGD framework they are not needed, one-dimensional string-like networks present from the beginning and create galaxies by decaying to ordinary matter. In long enough scales the average density would be constant and there would be no clumps at all.
</p><p>
Can one understand why the Universe is too thin? Could it be the energy and mass of all cosmic strings have not been taken into account. Long cosmic strings have galaxies and other structures as tangles decaying to ordinary matter. What about the straight portions. Have they been taken into account in the survey?
</p><p>
For the TGD view about the formation of galaxies and start see for instance <a HREF= "http://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-56849953140583867002020-09-14T21:08:00.038-07:002020-09-20T01:29:18.957-07:00Life in Venus? What says TGD?Evidence for life in a rather unexpected place - Venus - has emerged (see <A HREF="https://www.scientificamerican.com/article/venus-might-host-life-new-discovery-suggests/">this</A>). The atmosphere of Venus shows signs of phophine, which cannot be produced by inorganic processes. There are small amounts of phosphine in the Earth's atmosphere and has an organic origin. Same might be true in the case of Venus. Perhaps simple bacterial life is in question. Is it in the atmosphere or somewhere deeper is an open question - at least to me.
</p><p>
<B>1. The first impressions</B>
</p><p>
One can find from Wikipedia that phosphine has the chemical formula PH<sub>3</sub>. In inorganic chemistry it is very difficult to form phosphine from phosphate (PO<sub>4</sub>)<sup>-3</sup> which is central in living matter. Somehow reduction must occur: the double valence bonds O=P of phosphates must in the final situation ordinary valence bonds in PH<sub>3</sub>.
</p><p>
TGD predicts that all planets have life in their interior. This would solve the Fermi paradox. Also Earth's life would have evolved in the interior and emerged to the surface in the Cambrian Explosion when a large number of multicellulars emerged as if nowhere. The reason would have been a rather fast increase of Earth radius by factor 2: in TGD cosmology continuous expansion for astrophysical objects is replaced by a sequence of fast expansions followed by steady non-expanding states (see <A HREF="http://tgdtheory.fi/public_html/articles/expearth.pdf">this</A> and <A HREF="http://tgdtheory.fi/public_html/articles/platoplate.pdf">this</A>). Whether the phosphine could emerge from the interior of Venus is an interesting question.
</p><p>
TGD also predicts a new kind of chemistry involving the notions of magnetic body (MB) carrying dark matter identified as phases of ordinary matter with effective Planck constant h<sub>eff</sub>=nh<sub>0</sub> (h=6h<sub>0</sub>), which can have very large values. Also the notions of acid resp. base and reduction and oxidation would involve dark protons resp. Dark valence electrons but in biosystems these notions would become fundamental. For instance, in Pollack effect exclusion zones as regions in which every fourth proton goes to a magnetic flux tube as a dark proton would be formed. For pH = 7 the fraction 10<sup>-7</sup> of protons would be dark! In biology dark protons, electrons, and also dark ions would be fundamental.
</p><p>
MB would be the "boss" controlling the ordinary biomatter using dark cyclotron photon signals and resonance as a control tool. This new chemistry relying on what I call number theoretical (or adelic) physics would be central for the basic biomolecules such as DNA, RNA, tRNA, and amino acids having dark analogs accompanying them. The phosphates of DNA nucleotides with negative charges would be neutralized by dark protons and dark proton triplets would define a fundamental realization of the genetic code. Also amino-acids would be accompanied by dark proton (actually dark hydrogen) triplets.
</p><p>
Transforming protons to dark protons in Pollack effect requires an energy feed: IR photons do the job best. This means that dark protons carry metabolic energy and in ATP there could be 3 dark protons neutralizing the negative charges of phosphates. Together with dark electrons associated with valence bonds this would explain the questionable notion of high energy phosphate bond. ATP→ ADP would transform one dark proton to ordinary one and break a valence bond, which for a dark electron has an abnormally high energy. Both of them would give energy.
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If it is life, I expect that both these new phenomena predicted by TGD are involved.
</p><p>
<B>2. Could there be sulfuric life in Venus?</B>
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There is an article about the chemistry involved with phosphine (see <A HREF="https://arxiv.org/pdf/1910.05224.pdf">this</A>). Not only there exists no known in-organic manners to produce phosphine in Venusian atmosphere but also the biological pathways for the production of phosphine in the Earth's atmosphere by bacteria are unknown. Note that these bacteria are non-aerobial: I do not know whether S replaces O in their metabolism.
</p><p>
Could the new chemistry predicted by TGD and based on dark protons and dark electrons be involved? Dark protons carry metabolic energy - Pollack effect producing dark protons indeed requires energy feed - and the transformation of one of 3 dark protons in ATP → ADP would liberate metabolic energy. Could an alog of this metabolic mechanism help formation of phosphine?
</p><p>
<B>2.1 Basic fact about Venus and Venusian atmosphere</B>
</p><p>
One learns from Wikipedia (see <A HREF="https://en.wikipedia.org/wiki/Venus">this</A>) basic facts about Venus.
<OL>
<LI> Venus is one of the four terrestrial planets meaning that it has a rocky body like Earth. Surface gravity is .904 g, surface pressure is 91 atm, and surface temperature corresponding to .0740 eV (eV = 10<sup>4</sup> K), which happens to be rather near to cell membrane potential.
</p><p>
In clouds at heights 50-60 km from Venusian surface, the temperature is between 0 and 50 C. The assumption that these regions contain the PH<sub>3</sub> is theoretically justified if the life in question is similar to that at Earth.
<LI>Venusian atmosphere (see <A HREF="https://en.wikipedia.org/wiki/Atmosphere_of_Venus">this</A>) has 95 per cent CO<sub>2</sub>, 3.5 per cent N, 150 ppm SO<sub>2</sub>, 70 ppm Ar, 20 ppm water vapor, 17 ppm CO<sub>2</sub>, 12 ppm He, 7 ppm Ne, .1-.6 ppm HCl, and 0.01 - 0.05 HF.
</OL>
</p><p>
<B>2.2 Some data items about the role of sulfur in terrestrial biology</B>
</p><p>
There is a nice article "Sulfur: Fountainhead of life in the Universe?" by Benton Clark at the page of Nasa (see <A HREF="https://cutt.ly/qfGsIST">this</A>) giving a summary about sulfur and - as the title suggests - implicitly proposing that sulfur based life might have preceded the recent life.
<OL>
<LI>Table 1 gives an overview about the cosmochemisty of sulfur. Note that in Sun S/Si ratio is .5.
</p><p>
<B> Remark</B>: Even Sun has been proposed as a possible seat of life. The general vision about dark matter as a master controlling ordinary matter and dark proton sequences at magnetic flux tubes providing a universal realization of genetic code allows to consider the possibility of life at temperatures much higher than at Earth.
<LI>The role of sulfur in planetary evolution is discussed. The abundance of S is as high as 15 per cent in the Earth's core. Earth's crust contains 500 ppm of S and volcanic emissions are rich in sulphur. Sea water is rich in sulfate (SO<sub>4</sub>) ions. Table 2 two lists various sulfur compounds in volcanic emissions.
<LI>Sulfur compounds are discussed. Sulfur can have several valence states including oxidation numbers -2,0+2,+4,+6 and sulfur can appear in compounds with several valence numbers. By this transversality sulphur could have an important role in autotrophic metabolism involving only chemical energy sources.
</p><p>
<B> Remark</B>: The valence of given atom in molecule (see <A HREF="https://cutt.ly/QfGhaCL">this</A>) is the number of valence electrons, which the atom has. For instance, the double bond corresponds to 2 units of valence. Atomic valences characterize the topology of the valence bond network assigned with the molecule. Oxidation state, which can be negative, is a more precise measure telling how many valence electrons the atom has gained or lost. In the TGD framework the valence bond network would correspond to a flux tube network.
<LI>The role of sulfur in biochemistry is central. Sulfur plays major roles in energy transduction, enzyme action, and as a necessary constituent in certain biochemicals. The latter include important vitamins (biotin, thiamine), cofactors (CoA, CoM, glutathione), and hormones. Table 4 given also here summarizes the biological utilization of sulfur compounds.
<UL>
<LI>Energy source (sulfate reduction, sulfide oxidation)
<LI>Photosynthesis (non-O2 -evolving)
<LI>Amino acids (met, cys):
<LI>Protein conformation (disulfide bridges)
<LI>Energy storage (APS, PAPS)
</p><p>
These are analogous to AMP and ADP. Could one think of generalization of the TGD view for ATP → ADP to PAPS → APS as a basic metabolic mechanism? It might be that APS and PAPS do not survive in the Venusian atmosphere.
<LI>Enzyme Prosthetic group, (Fe-S proteins)
<LI>Unique biochemicals (CoA, CoM, glutathione, biotin, thiamine, thiocyanate, penicillin, vasopressin, insulin).
</UL>
<LI>The role of sulfur in the biogeochemical cycle is illustrated in Figure 1. In autotrophic energy metabolism, which does not have organic compounds as sources of energy, sulfur compounds are involved. One can distinguish between sulfur bacteria, sulfate reducers, and sulfur oxidizers. For sulfur bacteria the photosynthesis proceeds - not by splitting H<sub>2</sub>O as in the case of green plants and algae - but by splitting H<sub>2</sub>S to obtain H atoms: H<sub>2</sub>S replaces water.
</p><p>
Sulfate (SO<sub>4</sub>) reducers liberate energy by increasing the oxidation numbers of S and O (Na<sub>2</sub>SO<sub>4</sub> → Na<sub>2</sub>S+4H<sub>2</sub>O). Sulfur oxidizers (H<sub>2</sub>S +2(O2)<sub>2</sub> → H<sub>2</sub>SO<sub>4</sub>)) reduce the oxidation number of S.
<LI>SH-group is important for the catalytic function of many enzymes. -S-S link stabilizing systeine is important in establishing the tertiary structure of proteins. Fe-S appear as a prosthetic group (non-peptide group) in enzymes known as iron-sulfur proteins.
<LI>The presence ecosystems at the mouths of active hydrothermal submarine vents not depending on photosynthesis suggests a chemosynthetic energy source. These communities however require oxides and thus photosynthesis in the surface layers. Table 6 lists sulfur based energy sources for biological systems.
</OL>
</p><p>
<B> 2.3 The minimal option for a sulphur based life in Venus</B>
</p><p>
Before speculating it is good to summarize the basic facts. Venus has a lot of H<sub>2</sub>S - analog of water H<sub>2</sub>O in its atmosphere. Also CO<sub>2</sub> is present as also nitrogen N. There is a could layer rich in H<sub>2</sub>S and having temperature and pressure very much like at Earth. The environment is extremely acidic and this is a real challenge for terrestrial life forms. There exists however extreme terrestrial extremal acidophiles. They are bacteria.
</p><p>
The idea is to replace O with S in some basic molecules of life and processes to overcome the acidity problem. What are these molecules and processes?
<OL>
<LI> Could other biomolecules remain as such and could the cell membrane shield the DNA and proteins inside it against sulphur acid? The outer ends of lipids are hydrophobic: could they be also H<sub>2</sub>S-phobic?
<LI> Could H<sub>2</sub>S replace water in some sense in Venusian life? Could water as an environment of the cell be replaced with H<sub>2</sub>S?
</OL>
What could the replacement of the water environment with H<sub>2</sub>S mean?
<OL>
<LI> Could photosynthesis rely on the splitting of H<sub>2</sub>S rather than H<sub>2</sub>O? Ordinary photosynthesis takes place inside the cell interior and involves ordinary proteins in enzymes and sugars as products. This would however require the presence of H<sub>2</sub>S is in the cell interior. This does not look a plausible option without a profound change of the chemistry inside the cell replacing perhaps O with S in basic biomolecules such as DNA, RNA and proteins? This suggests that the photosynthesis inside Venusian bacterial cells occurs in the usual manner.
<LI> The TGD based quantum biology also involves the notion of magnetic body (MB) as a controller of the biological body. Could H<sub>2</sub>S have the same role in Venusian prebiotic life as H<sub>2</sub>O in the terrestrial prebiotic life?
</p><p>
In the terrestrial life according to the TGD magnetic body (MB) of the water with hydrogen bonds is accompanied by flux tubes appearing with various values of h<sub>eff</sub>> h for dark protons. This would make water a multiphase system providing water with its very special thermo-dynamical properties at the temperature range 0-100 C.
</p><p>
The flux tubes carrying dark protons sequences generated in the Pollack effect creating negatively charged exclusion zones (EZs) would realize the dark analog of genetic code: the negatively charged cell is an example of this kind of EZ.
</p><p>
Water memory and the entire immune system would basically rely on these flux tube structures. DNA would be accompanied by parallel dark analog and the same would be true for RNA, tRNA, and amino acids. Water would be living even before the emergence of the chemical life and MB would control the chemical life.
</p><p>
Could also H<sub>2</sub>S allow dark hydrogen bonds and Pollack effect? Could the basic difference with respect to terrestrial life be that cells live in H<sub>2</sub>S rather than in H<sub>2</sub>O?
</OL>
What could the replacement of the water environment with H<sub>2</sub>S mean?
<OL>
<LI> Could photosynthesis rely on the splitting of H<sub>2</sub>S rather than H<sub>2</sub>O? Ordinary photosynthesis takes place inside the cell interior and involves ordinary proteins in enzymes and sugars as products. This would however require the presence of H<sub>2</sub>S is in the cell interior. This does not look a plausible option without a profound change of the chemistry inside the cell replacing perhaps O with S in basic biomolecules such as DNA, RNA and proteins? This suggests that the photosynthesis inside Venusian bacterial cells occurs in the usual manner.
<LI> The TGD based quantum biology also involves the notion of magnetic body (MB) as a controller of the biological body. Could H<sub>2</sub>S have the same role in Venusian prebiotic life as H<sub>2</sub>O in the terrestrial prebiotic life?
</p><p>
In the terrestrial life according to the TGD magnetic body (MB) of the water with hydrogen bonds is accompanied by flux tubes appearing with various values of h<sub>eff</sub>> h for dark protons. This would make water a multiphase system providing water with its very special thermo-dynamical properties at the temperature range 0-100 C.
</p><p>
The flux tubes carrying dark protons sequences generated in the Pollack effect creating negatively charged exclusion zones (EZs) would realize the dark analog of genetic code: the negatively charged cell is an example of this kind of EZ.
</p><p>
Water memory and the entire immune system would basically rely on these flux tube structures. DNA would be accompanied by parallel dark analog and the same would be true for RNA, tRNA, and amino acids. Water would be living even before the emergence of the chemical life and MB would control the chemical life.
</p><p>
Could also H<sub>2</sub>S allow dark hydrogen bonds and Pollack effect? Could the basic difference with respect to terrestrial life be that cells live in H<sub>2</sub>S rather than in H<sub>2</sub>O?
</OL>
The separation of O <I> resp.</I> S to protocell interior <I> resp.</I> exterior is required for the most conservative option. This requires a formation of lipid membrane like structures consisting of hydrocarbons isolating the interior from exterior and taking care of the separation. This requires charge separation by Pollack effect and solar radiation could provide this energy. H<sub>2</sub>S must be replaced with H<sub>2</sub>O in the protocell interior. As a physicist I can only speculate about the possible chemistry of the process. For sulfur and its chemistry see the Wikipedia article (see <A HREF="https://en.wikipedia.org/wiki/Sulfur">this</A>).
<OL>
<LI>How the double lipid layer of the protocell membrane separating S- and O-worlds could have formed? The formation of hydrocarbons of form C<sub>n</sub>H<sub>2n</sub> appearing as building blocks of lipids had to take place - perhaps only from CO<sub>2</sub> and H<sub>2</sub>S. Note that that SO<sub>2</sub> is the third most significant atmospheric gas in Venus and could have been be produced in this process and participate it. SO<sub>2</sub> has been detected also in volcanoes and one can consider the possibility that the mono-cellular life in volcanoes could have evolved by the same mechanism as in Venus clouds.
</p><p>
Did something like CO<sub>2</sub> +H<sub>2</sub>S → CH<sub>2</sub> + SO<sub>2</sub> necessarily accompanied by a polymerization of CH<sub>2</sub> to C<sub>n</sub>H<sub>2n</sub> occur? Also in the protocell interior hydrocarbons could have formed by this mechanism. The consumption of CO<sub>2</sub> in the protocell interior would have induced a further flow of CO<sub>2</sub> from the protocell exterior and generated more SO<sub>2</sub> which could have flown out or been used for other processes.
<LI>How was the H<sub>2</sub>S inside the protocell membrane replaced with H<sub>2</sub>O? Sulphur dioxide SO<sub>2</sub> was generated in the formation of hydrocarbons. Is the reaction SO<sub>2</sub>+ 2H<sub>2</sub>S → 2H<sub>2</sub>O+2S a plausible option?
</p><p>
The reaction 2S+ CO<sub>2</sub> → CS<sub>2</sub>+O<sub>2</sub> could have generated molecular oxygen O<sub>2</sub> in the protocell interior and CS<sub>2</sub> would have flown to cell exterior and created the analog of CO<sub>2</sub> there.
</OL>
The O-S separation would drive CO<sub>2</sub> from the exterior to interior and bring it back as CS<sub>2</sub> and replace S with O in the interior. Proto cell membrane would emerge before the standard chemical realisation of the genetic code. The usual hen-egg problem - which came first, cell membrane or genes - is avoided since the dark variant of the genetic code would be represented using sequences of dark proton triplets representing the analogs of DNA, RNA, tRNA, and amino acids. The fact that the lipids of the cell membrane involve phosphates with negative charge suggests that they are accompanied by dark protons and genetic code has a 2-D variant assignable to the lipid lattice as 2-D dark proton lattice and decomposing to 1-D sequences. The ordinary chemical genetic code would emerge later than this realisation after the emergence of basic biomolecules in the protocell interior.
</p><p>
<B>2.4 More radical options for sulfuric life at Venus</B>
</p><p>
There are also other options based on a radical modification of the chemistry of the ordinary life. They looks less realistic from TGD point of view (which has been changing on daily basis during this week!).
<OL>
<LI> Venus receives a lot of sunlight but one can ask whether photosynthesis be replaced with chemisynthesis? Chemical energy would be liberated in cycles involving sulphur containing compounds with varying degrees of oxidation of sulphur would liberate chemical energy as metabolic energy. At the bottoms of terrestrial oceans there are lifeforms around volcanoes, which might have this kind of metabolism.
</p><p>
<LI> <B>Option I</B> below: The extreme adicity of the Venusian atmosphere is the basic problem and the data about the composition of Venusian atmosphere suggest that O should be replaced with S in basic bio-molecules and water should be replaced with hydrogen sulfide H<sub>2</sub>S (about bacteria producing H<sub>2</sub>S see <A HREF="https://cutt.ly/CfD0t0d">this</A>), which is a gas smelling like rotten egg and produced in the decay of organic matter. Note however that CO<sub>2</sub> dominates in the Venusian atmosphere so that the replacement of O with S can be criticized. Carbon compounds can survive in the cloud to which PH<sub>3</sub> is assigned. The atmosphere contains also N.
</p><p>
<LI> <B>Option II</B> below: This option is radical and probably non-realistic but as a mathematician I cannot resist its formal beauty. Could Venusian life be obtained by shifting terrestrial life one row downwards along the right end of the Periodic Table so that basic elements O, N, P of terrestrial life would be replaced with their chemical analogs S, P, As?
</p><p>
<B> Remark</B>: Phosphine PH<sub>3</sub> reported to smell like rotten fish would be the counterpart of ammonia NH<sub>3</sub> giving pee its aroma and would have a similar role for Option II.
</p><p>
Si has boiling point .1687 eV to be compared with the surface temperature .0740 eV - note however that also carbon is solid up to very high temperature and also many hydrocarbons are solids physiological temperatures. Arsenic (As) is fused by some bacteria as a metabolite and one might think that the analog of the higher energy phosphate bond obtained by replacement (O,P) → (S,As). The basic objection is that the Venusian atmosphere contains a lot of C and in CO<sub>2</sub> and N so that Option I seems to be enough. PH<sub>3</sub> is produced also by the terrestrial bacteria.
</OL>
</p><p>
<B>2.5 Comparing the two radical options</B>
</p><p>
It is interesting to look explicitly for the modifications of the basic biomolecules for the proposed radical options although the look to me unrealistic.
<OL>
<LI>Consider first amino-acids (see <A HREF="https://en.wikipedia.org/wiki/Amino_acid">thi</A>). The replacements would be O → S for Option I and (O → S, N → P, P → As) for Option II.This would allow a realization of analogs of nucleotides and amino-acids providing representations for their dark analogs realized in terms of dark proton sequences.
</p><p>
Amino acid has the structure X-(Y-R)-Z, X= NH<sub>2</sub>, Y=C-H, Z= O=C-OH. R is the varying amino-acid residue and X,Y,Z define the constant part. The replacements would be
</p><p>
<B>Option I</B>: Z=O=C-OH → S=C-SH
</p><p>
<B>Option II</B>: X=C=NH<sub>2</sub> → PH<sub>2</sub>, Y= C-H→ Si-H. Z= O=C-OH → S=Si-SH.
</p><p>
In the formation of peptide one has replacement X= → C-N-H and Z→ O=C-O-C. This would give replacements of replacements:
</p><p>
<B>Option I</B>: (Z→ O=C-O-C ) →(Z→ S=C-S -C).
</p><p>
<B>Option II</B>: (X= → C-N-H) →( X→Si-P-H) and (Z→ O=C-O-C Z)→ (Z→ S=Si-S-Si) for Option II.
</p><p>
In the TGD framework amino-acids would be accompanied by dark proteins with sulfuric analogs of amino-acids pairing with dark proton triplets: the dark amino-acid would be same and couple with amino-acids having the residues for with energy resonance coupling is possible.
</p><p>
Cyclotron excitation of dark proton triplet and excitation of R would couple resonantly: the transition of dark photon triplet would generate dark photon triplet transforming to ordinary photon and exciting the R to excited state. This would select the possible residues.
</p><p>
The first guess is that they are obtained by the proposed replacement too. The dark protons coming from NH<sub>2</sub> and one dark proton coming from C-N-H would do so also for the Option I. Amino-acid residues contain as a rule OH and O= and would be replaced with SH and S=. Note that for methionine is the only amino-acid containing S.
</p><p>
For Option II dark protons would come from PH<sub>2</sub> and Si-P-H for option II and would be neutralized by dark electrons to give rise to dark hydrogens.
<LI>For DNA (see <A HREF="https://en.wikipedia.org/wiki/DNA">this</A>) the replacements would be following
</p><p>
<B>Option I</B>: O → S in sugar 5-ring and in nucleotides
</p><p>
<B>Option II</B>: (C, O, N) → (Si, S, P) in sugar 5-ring and nucleotides and PO<sub>4</sub> → AsS<sub>4</sub>.
<LI>Similar replacements would be carried in metabolic energy currencies AXP, X= M,D,T and GXP having also role as storages of metabolic energy. Saccharides like C<sub>6</sub>H<sub>12</sub>O<sub>6</sub> as chemical energy storages would have analogs obtained by replacement</p><p><B>Option I</B>: O → S</p><p><B>Option II</B>: (C,O,N) → (Si, S, P).
<LI>In the lipids of cell membrane there would be no changes for Option I and for Option II one would have (C → Si, PO<sub>4</sub> → AsS<sub>4</sub>).
</OL>
</p><p>
Option I is clearly favored over Option II if the Venusian life resides in clouds at height of 50-60 km, in particular by the possibility of having cell membrane identical that for the terrestrial life. However, in the TGD framework the most plausible option does not involve any changes in the basic biochemistry of life. The only change is the replacement of water with H<sub>2</sub>S as the environment of the bacterial cells. Dark protons and dark photons make possible communications between bacterial cells even in the acidic environment.The empirical test is whether the Pollack effect is possible also for H<sub>2</sub>S.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-57841641650987980002020-08-28T21:44:00.004-07:002020-08-28T21:44:52.326-07:00Summary of TGD (a lot of figures!)I wrote an article summarizing the recent situation in TGD. Without Reza Rastmanesh's encouragement and help this article would not have been written. I particular, the help of Reza in preparing figures making it easier to grasp the general structure of TGD was irreplaceable. As usual, the boring duty of writing about things already done transformed to a creative process and several new mathematical and physical results about TGD emerged.
</p><p>
Reza even persuaded me to send the article to Nature. That the editors do not even bother to send it to the proposed referees, was not a surprise, but I managed to overcome the deep professorphobia induced during the painful 42 years by academic arrogance and stupidity. Thanks to the therapeutical efforts of Reza, I even sent the article to big names like Witten, Maldacena, Susskind, Penrose, Arkani-Hamed, etc... I received a message about receival from Susskind and Penrose only. Probably the secretaries insulate most names into their academic bubble and probably they also want to live in the bubbles they have created.
</p><p>
I added the article "Summary of Topological Geometrodynamics" to both <A HREF="https://www.researchgate.net/publication/343601105_Summary_of_Topological_Geometrodynamics">Research Gate</A> and my <A REF="http://tgdtheory.fi/public_html/articles/articleTGD.pdf">homepage</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-53462419588761857922020-08-26T22:23:00.014-07:002020-08-28T21:10:37.037-07:00What MIP*= RE could mean in TGD Universe?
The MIP*=RE means that quantum entanglement has a crucial role in quantum computation. One the other hand, HFFs would not allow to use quantum entanglement to quantum computational purposes. This looks at first a bad news from the TGD point of view, where HFFs are highly suggestive. One must be however very careful with the basic definitions.
</p><p>
<B>1. The notion of finite measurement resolution in TGD</B>
</p><p>
Measurement resolution is one of the basic notions of TGD.
<OL>
<LI>There are intuitive physicist's arguments demonstrating that in TGD the operator algebras involved with TGD are HFFs provides a description of finite measurement resolution. The inclusion of HFFs defines the notion of resolution: included factor represents the degrees of freedom not seen in the resolution used (see <A HREF="http://tgdtheoryd.fi/pfpool/vNeumann.pdf">this</A>) and <A HREF="http://tgdtheoryd.fi/pfpool/vNeumannnew.pdf">this</A>).
</p><p>
Hyperfinite factors involve new structures like quantum groups and quantum algebras reflecting the presence of additional symmetries: actually the "world of classical worlds" (WCW) as the space of space-time surfaces as maximal group of isometries and this group has a fractal hierarchy of isomorphic groups imply inclusion hierarchies of HFFs. By the analogs of gauge conditions this infinite-D group reduces to a hierarchy of effectively finite-D groups. For quantum groups the infinite number of irreps of the corresponding compact group effectively reduces to a finite number of them, which conforms with the notion of hyper-finiteness.
</p><p>
It looks that the reduction of the most general quantum theory to TGD-like theory relying on HFFs is not possible. This would not be surprising taking into account gigantic symmetries responsible for the cancellation of infinities in TGD framework and the very existence of WCW geometry.
<LI>Second TGD based approach to finite resolution is purely number theoretic (see <A HREF="http://tgdtheory.fi/public_html/articles/adelephysics.pdf">this</A>) and involves adelic physics as a fusion of the real physics with various p-adic physics as correlates of cognition. Cognitive representations are purely number theoretic and unique discretizations of space-time surfaces defined by a given extension of rationals forming an evolutionary hierarchy: the coordinates for the points of space-time as a 4-surface of the imbedding space H=M<sup>4</sup>× CP<sub>2</sub> or of its dual M<sup>8</sup> are in the extension of rationals defining the adele. In the case of M<sup>8</sup> the preferred coordinates are unique apart from time translation. These two views would define descriptions of the finite resolution at the level of space-time and Hilbert space. In particular, the hierarchies of extensions of rationals should define hierarchies of inclusions of HFFs.
</OL>
For hyperfinite factors the analog of MIP*=RE cannot hold true. Doesn't the TGD Universe allow a solution of all the problems solvable by Turing Computer? There is however a loophole in this argument
<OL>
<LI>The point is that for the hierarchy of extensions of rationals also Hilbert spaces have as a coefficient field the extension of rationals!. Unitary transformations are restricted to matrices with elements in the extension. In general it is not possible to realize the unitary transformation mapping the entangled situation to an un-entangled one! The weakening of the theorem would hold true for the hierarchy of adeles and entanglement would give something genuinely new for quantum computation!
<LI>A second deep implication is that the density matrix characterizing the entanglement between two systems cannot in general be diagonalized such that all diagonal elements identifiable as probabilities would be in the extension considered. One would have stable or partially stable entanglement (could the projection make sense for the states or subspaces with entanglement probability in the extension). For these bound states the binding mechanism is purely number theoretical. For a given extension of p-adic numbers one can assign to algebraic entanglement also information measure as a generalization of Shannon entropy as a p-adic entanglement entropy (real valued). This entropy can be negative and the possible interpretation is that the entanglement carries conscious information.
</OL>
</p><p>
<B>2. What about the situation for the continuum version of TGD?</B>
</p><p>
At least the cognitively finitely representable physics would have the HFF property with coefficient field of Hilbert spaces replaced by an extension of rationals. Number theoretical universality would suggest that HFF property characterizes also the physics of continuum TGD. This leads to a series of questions.
<OL>
<LI>Does the new theorem imply that in the continuum version of TGD all quantum computations allowed by the Turing paradigm for real coefficients field for quantum states are not possible: MIP*⊂ RE? The hierarchy of extensions of rationals allows utilization of entanglement, and one can even wonder whether one could have MIP*= RE at the limit of algebraic numbers.
<LI> Could the number theoretic vision force change also the view about quantum computation? What does RE actually mean in this framework? Can one really assume complex entanglement coefficients in computation. Does the computational paradigm makes sense at all in the continuum picture?
</p><p>
Are both real and p-adic continuum theories unreachable by computation giving rise to cognitive representations in the algebraic intersection of the sensory and cognitive worlds? I have indeed identified real continuum physics as a correlate for sensory experience and various p-adic physics as correlates of cognition in TGD: They would represent the computionally unreachable parts of existence.
</p><p>
Continuum physics involves transcendentals and in mathematics this brings in analytic formulas and partial differential equations. At least at the level of mathematical consciousness the emergence of the notion of continuum means a gigantic step. Also this suggests that transcendentality is something very real and that computation cannot catch all of it.
<LI>Adelic theorem allows to express the norm of a rational number as a product of inverses of its p-adic norms. Very probably this representation holds true also for the analogs of rationals formed from algebraic integeres. Reals can be approximated by rationals. Could extensions of all p-adic numbers fields restricted to the extension of rationals say about real physics only what can be expressed using language?
</OL>
Also fermions are highly interesting in the recent context. In TGD spinor structure can be seen as a square root of Kähler geometry, in particular for the "world of classical worlds" (WCW). Fermions are identified as correlates of Boolean cognition. The continuum case for fermions does not follow as a naive limit of algebraic picture.
<OL>
<LI>The quantization of the induced spinors in TGD looks different in discrete and continuum cases. Discrete case is very simple since equal-time anticommutators give discrete Kronecker deltas. In the continuum case one has delta functions possibly causing infinite vacuum energy like divergences in conserved Noether charges (Dirac sea).
<LI> I have proposed (see <A HREF="https://cutt.ly/zfftoK6">this</A>) how these problems could be avoided by avoiding anticommutators giving delta-function. The proposed solution is based on zero energy ontology and TGD based view about space-time. One also obtains a long-sought-for concrete realization for the idea that second quantized induce spinor fields are obtained as restrictions of second quantized free spinor fields in H=M<sup>4</sup>× CP<sub>2</sub> to space-time surface. The fermionic variant of M<sup>8</sup>-H-duality (see <A HREF="http://tgdtheory.fi/public_html/articles/M8Hfermion.pdf">this</A>) provides further insights and gives a very concrete picture about the dynamics of fermions in TGD.
</OL>
These considerations relate in an interesting manner to consciousness. Quantum entanglement makes in the TGD framework possible telepathic sharing of mental images represented by sub-selves of self. For the series of discretizations of physics by HFFs and cognitive representations associated with extensions of rationals, the result indeed means something new.
</p><p>
<B>3. What about transcendental extensions?</B>
</p><p>
During the writing of this article an interesting question popped up.
<OL>
<LI> Also transcendental extensions of rationals are possible, and one can consider the generalization of the computationalism by also allowing functions in transcendental extensions. Could the hierarchy of algebraic extensions could continue with transcendental extensions? Could one even play with the idea that the discovery of transcendentals meant a quantum leap leading to an extension involving for instance e and π as basic transcendentals? Could one generalize the notion of polynomial root to a root of a function allowing Taylor expansion f(x)= ∑ q<sub>n</sub> x<sup>n</sup> with rational coefficients so that the roots of f(x)=0 could be used define transcendental extensions of rationals?
<LI>Powers of e or its root define and infinite-D extensions having the special property that they are finite-D for p-adic number fields because e<sup>p</sup> is ordinary p-adic number. In the p-adic context e can be defined as a root of the equation x<sup>p</sup>-∑ p<sup>n</sup>/n!=0 making sense also for rationals. The numbers log(p<sub>i</sub>) such that p<sub>i</sub> appears a factor for integers smaller than p define infinite-D extension of both rationals and p-adic numbers. They are obtained as roots of e<sup>x</sup>-p<sub>i</sub>=0.
<LI>The numbers (2n+1)π (2nπ) can be defined as roots of sin(x)=0 (cos(x)=0. The extension by π is infinite-dimensional and the conditions defining it would serve as consistency conditions when the extension contains roots of unity and effectively replaces them.
<LI>What about other transcendentals appearing in mathematical physics? The values ζ(n) of Riemann Zeta appearing in scattering amplitudes are for even values of n given by ζ(2n)= (-1)<sup>n+1</sup> B<sub>2n</sub> (2π)<sup>2n</sup>/2(2n+1)!. This follows from the functional identity for Riemann zeta and from the expression ζ(-n)= (-1)<sup>n</sup> B<sub>n+1</sub>/(n+1) ( (B(-1/2)=-1/2) (see <A HREF="https://cutt.ly/dfgtgmw">this</A>). The Bernoulli numbers B<sub>n</sub> are rational and vanish for odd values of n. An open question is whether also the odd values are proportional to π<sup>n</sup> with a rational coefficient or whether they represent "new" transcendentals.
</OL>
</p><p>
<B>4. What does one mean with quantum computation in TGD Universe?</B>
</p><p>
The TGD approach raises some questions about computation.
<OL>
<LI> The ordinary computational paradigm is formulated for Turing machines manipulating natural numbers by recursive algorithms. Programs would essentially represent a recursive function n→ f(n). What happens to this paradigm when extensions of rationals define cognitive representations as unique space-time discretizations with algebraic numbers as the limit giving rise to a dense in the set of reals.
</p><p>
The usual picture would be that since reals can be approximated by rationals, the situation is not changed. TGD however suggests that one should replace at least the quantum version of the Turing paradigm by considering functions mapping algebraic integers (algebraic rational) to algebraic integers.
</p><p>
Quite concretely, one can manipulate algebraic numbers without approximation as a rational and only at the end perform this approximation and computations would construct recursive functions in this manner. This would raise entanglement to an active role even if one has HFFs and even if classical computations could still look very much like ordinary computation using integers.
<LI> ZEO brings in also time reversal occurring in "big" (ordinary) quantum jumps and this modifies the views about quantum computation. In ZEO based conscious quantum computation halting means "death" and "reincarnation" of conscious entity, self? How the processes involving series of haltings in this sense differs from ordinary quantum computation: could one shorten the computation time by going forth and back in time.
<LI>There are many interesting questions to be considered. M<sup>8</sup>-H duality gives justifications for the vision about algebraic physics. TGD leads also to the notion of infinite prime and I have considered the possibility that infinite primes could give a precise meaning for the dimension of infinite-D Hilbert space. Could the number-theoretic view about infinite be considerably richer than the idea about infinity as limit would suggest (see <A HREF="http://tgdtheory.fi/pdfpool/visionc.pdf">this</A>).
The construction of infinite primes is analogous to a repeated second quantization of arithmetic supersymmetric quantum field theory allowing also bound states at each level and a concrete correspondence with the hierarchy of space-time sheets is suggestive. For the infinite primes at the lowest level of the hierarchy single particle states correspond to rationals and bound states to polynomials and therefore to the sets of their roots. This strongly suggests a connection with M<sup>8</sup> picture.
</OL>
</p><p>
See the article <a HREF= "http://tgdtheory.fi/public_html/articles/deeptheorem.pdf">MIP*= RE: What could this mean physically?</A> or the chapter <a HREF= "http://tgdtheory.fi/pdfpool/vNeumannnew.pdf">Evolution of Ideas about Hyper-finite Factors in TGD</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-19137244834351229072020-08-26T03:52:00.009-07:002020-08-28T21:09:04.285-07:00MIP*=RE: What it could possibly mean?I received a very interesting link to a popular article (see <A HREF="https://cutt.ly/sfd5UQF">this</A>) explaining a recently discovered deep result in mathematics having implications also in physics. The article (see <A HREF="https://arxiv.org/abs/2001.04383">this</A>) by Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen has a rather concise title "<B> MIP*=RE</B>". In the following I try to express the impressions of a (non-mainstream) physicist about the result. In the first posting I discuss the finding and the basic implications from the physics point of view. In the second posting the highly interesting implications of the finding in the TGD framework are discussed.
</p><p>
The result expressed can be expressed by using the concepts of computer science about which I know very little at the hard technical level. The results are however told to state something highly non-trivial about physics.
<OL>
<LI>RE (recursively enumerable languages) denotes all problems solvable by computer. P denotes the problems solvable in a polynomial time. NP does not refer to a non-polynomial time but to "non-deterministic polynomial acceptable problems" - I hope this helps the reader- I am a little bit confused! It is not known whether P = NP is true.
<LI>IP problems (P is now for "prover" that can be solved by a collaboration of an interrogator and prover who tries to convince the interrogator that her proof is convincing with high enough probability. MIP involves multiple l provers treated as criminals trying to prove that they are innocent and being not allowed to communicate. MIP* is the class of solvable problems in which the provers are allowed to entangle.
</OL>
The finding, which is characterized as shocking, is that <I> all</I> problems solvable by a Turing computer belong to this class: RE= MIP*. All problems solvable by computer would reduce to problems in the class MIP*! Quantum computation would indeed add something genuinely new to the classical computation.
</p><p>
<B> Two physically interesting applications</B>
</p><p>
There are two physically interesting applications of the theorem which are interesting also from the TGD point of view and force to make explicit the assumptions involved.
</p><p>
<B>1. About the quantum physical interpretation of MIP*</B>
</p><p>
To proceed one must clarify the quantum physical interpretation of MIP*.
<OL>
<LI>Quantum measurement requires entanglement of the observer O with the measured system M. What is basically measured is the density matrix of M (or equivalently that of O). State function reduction gives as an outcome a state, which corresponds to an eigenvalue of the density matrix. Note that this state can be an entangled state if the density matrix has degenerate eigenvalues.
<LI>Quantum measurement can be regarded as a question to the measured system: "What are the values of given commuting observables?". The final state of quantum measurement provides an eigenstate of the observables as the answer to this question. M would be in the role of the prover and O<sub>i</sub> would serve as interrogators.
</p><p>
In the first case multiple interrogators measurements would entangle M with unentangled states of the tensor product H<sub>1</sub>⊗ H<sub>2</sub> for O followed by a state function reduction splitting the state of M to un-entangled state in the tensor product M<sub>1</sub>⊗ M<sub>2</sub>.
</p><p>
In the second case the entire M would be interrogated using entanglement of M with entangled states of H<sub>1</sub>⊗ H<sub>2</sub> using measurements of several commuting observables. The theorem would state that interrogation in this manner is more efficient in infinite-D case unless HFFs are involved.
<LI> This interpretation differs from the interpretation in terms of computational problem solving in which one would have several provers and one interrogator. Could these interpretations be dual as the complete symmetry of the quantum measurement with respect to O and M suggests? In the case of multiple provers (analogous to accused criminals) it is advantageous to isolate them. In the case of multiple interrogators the best result is obtained if the interrogator does not effectively split itself into several ones.
</OL>
</p><p>
<B>2. Connes embedding problem and the notion of finite measurement/cognitive resolution</B>
</p><p>
Alain Connes formulated what has become known as Connes embedding problem. The question is whether infinite matrices forming factor of type II<sub>1</sub> can be <I> always</I> approximated by finite-D matrices that is imbedded in a <I> hyperfinite</I> factor of type II<sub>1</sub> (HFF). Factors of type II and their HFFs are special classes of von Neumann algebras possibly relevant for quantum theory.
</p><p>
This result means that if one has measured of a complete set of for a product of commuting observables acting in the full space, one can find in the finite-dimensional case a unitary transformation transforming the observables to tensor products of observables associated with the factors of a tensor product. In the infinite-D case this is not true.
</p><p>
What seems to put alarms ringing is that in TGD there are excellent arguments suggesting that the state space has HFFs as building bricks. Does the result mean that entanglement cannot help in quantum computation in TGD Universe? I do not want to live in this kind of Universe!
</p><p>
<B>2. Tsirelson problem</B>
</p><p>
Tsirelson problem (see <A HREF="https://arxiv.org/abs/0812.4305">this</A>) is another problem mentioned in the popular article as a physically interesting application. The problem relates to the mathematical description of quantum measurement.
</p><p>
Three systems are considered. There are two systems O<sub>1</sub> and O<sub>2</sub> representing observers and the third representing the measured system M. The measurement reducing the entanglement between M and O<sub>1</sub> or O<sub>2</sub> can regarded as producing correspondence between state of M and O<sub>1</sub> or O<sub>2</sub>, and one can think that O<sub>1</sub> or O<sub>2</sub> measures only obserservables in its own state space as a kind of image of M. There are two manners to see the situation. The provers correspond now to the observers and the two situations correspond to provers without and with entanglement.
</p><p>
Consider first a situation in which one has single Hilbert space H and single observer O. This situation is analogous to IP.
<OL>
<LI> The state of the system is described statistically by a density matrix - not necessarily pure state -, whose diagonal elements have interpretation as reduction probabilities of states in this bases. The measurement situation fixes the state basis used. Assume an ensemble of identical copies of the system in this state. Assume that one has a complete set of commuting observables.
<LI>By measuring all observables for the members of the ensemble one obtains the probabilities as diagonal elements of the density matrix. If the observable is the density matrix having no- degenerate eigenvalues, the situation is simplified dramatically. It is enough to use the density matrix as an observable. TGD based quantum measurement theory assumes that the density matrix describing the entanglement between two subsystems is in a universal observable measure in state function reductions reducing their entanglement.
<LI>Can one deduce also the state of M as a superposition of states in the basic chosen by the observer? This basis need not be the same as the basis defined by - say density matrix if the system has interacted with some system and this ineraction has led to an eigenstate of the density matrix. Assume that one can prepare the latter basis by a physical process such as this kind of interaction.
</p><p>
The coefficients of the state form a set of N<sup>2</sup> complex numbers defining a unitary N× N matrix. Unitarity conditions give N conditions telling that the complex rows and unit vectors: these numbers are given by the measurement of all observables. There are also N(N-1) conditions telling that the rows are orthogonal. Together these N+N(N-1)=N<sup>2</sup> numbers fix the elements of the unitary matrix and therefore the complex coefficients of the state basis of the system can be deduced from a complete set of measurements for all elements of the basis.
</OL>
Consider now the analog of the MIP* involving more than one observer. For simplicity consider two observers.
<OL>
<LI>Assume that the state space H of M decomposes to a tensor product H=H<sub>1</sub>⊗ H<sub>2</sub> of state spaces H<sub>1</sub> and H<sub>2</sub> such that O<sub>1</sub> measures observables X<sub>1</sub> in H<sub>1</sub> and O<sub>2</sub> measuresobservables X<sub>2</sub> in H<sub>2</sub>. The observables X<sub>1</sub> and X<sub>2</sub> commute since they act in different tensor factors. The absence of interaction between the factors corresponds to the inability of the provers to communicate. As in the previous case, one can deduce the probabilities for the various outcomes of the joint measurements interpreted as measurements of a complete set of observables X<sub>1</sub> ⊗ X<sub>2</sub>.
<LI>One can also think that the two systems form a single system O so that O<sub>1</sub> and O<sub>2</sub> can entangle. This corresponds to a situation in which entanglement between the provers is allowed. Now X<sub>1</sub> and X<sub>2</sub> are not in general independent but also now they must commute. One can deduce the probabilities for various outcomes as eigenstates of observables X<sub>1</sub> X<sub>2</sub> and deduce the diagonal elements of the density matrix as probabilities.
</OL>
Are these manners to see the situation equivalent? Tsirelson demonstrated that this is the case for finite-dimensional Hilbert spaces, which can indeed be decomposed to a tensor product of factors associated with O<sub>1</sub> and O<sub>2</sub>. This means that one finds a unitary transformation transforming the entangled situation to an unentangled one and to tensor product observables.
</p><p>
For the infinite-dimensional case the situation remained open. According to the article, the new result implies that this is not the case. For hyperfinite factors the situation can be approximated with a finite-D Hilbert space so that the situations are equivalent in arbitrary precise approximation.
</p><p>
See the article <a HREF= "http://tgdtheory.fi/public_html/articles/deeptheorem.pdf">MIP*= RE: What could this mean physically?</A> or the chapter <a HREF= "http://tgdtheory.fi/pdfpool/vNeumannnew.pdf">Evolution of Ideas about Hyper-finite Factors in TGD</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-91260488327678176652020-08-11T22:12:00.002-07:002020-08-11T22:12:21.299-07:00Why not publish a book about TGD?I was asked why I do not publish a book about TGD. Some people also ask why I have not considered the idea of applying TGD to some real problem in physics. I glue below the reply which should explain why not.
</p><p>
Some people have also informed me that Einstein said that any big idea must be so simple that even a child can understand. Why I do not publish a picture book for children about TGD explaining the big idea using a couple of pictures? My answer could be the following: Einstein made only a single big blunder in his life. It was not the proposal of the cosmological constant but the above statement: fools around the world really take it literally. I appreciate people writing for children but I am a different kind of writer.
</p><p>
So: why don't I publish a book for adult readers or even colleagues about TGD? I actually have 24 online books almost ready for printing. Basic theory and lots of applications covering all branches of physics and also biology and neuroscience, which the people making these questions have not noticed since just seeing a link to my homepage - no time for more than this - does not give any idea about what TGD really is. These books can be published posthumously as collected works when the time is ripe for this. The reasons are many-fold.
</p><p>
There are overlapping topics and colleagues would not lose the opportunity to blame me for self-plagiarism as happened with the previous book about TGD. There was some ridiculous counting of words mechanism used to reveal my criminal character. For two years I spent a lot of useful working time with totally irrelevant activities having very little to do with the contents of the book. The compensation is so small that bank costs would make me the net payer. No one reads books nowadays and no-one even considers buying a book by non-name.
</p><p>
I do not have too many years left and I want to use them to develop TGD. This is for purely selfish reasons: it marvellous to live in full swing still at this age and do history of science.
</p><p>
I have also given up the hopes of explaining TGD understandably: 42 years distance to colleagues is so long that I feel myself being on a mountain top covered by clouds. They refuse even to believe that there is some-one there. 24 books as a climbing guide telling also about all wrong tracks is too much for anyone, and it is not inspiring to passively follow the instructions. It is much more motivational for them to rediscover TGD by themselves.
</p><p>
I have hoped that I could help them in this process and perhaps shorten 42 years to a decade. I have explained again and again what the deep problems are and what would be the TGD solution to them hoping that it would be more motivational to use their own brain to solve the key problems. They are not interested even in this option. They prefer to follow the wrong paths shown by names and repeat the mistakes already made. Or alternatively, to build totally non-sensible one-line theory based on mere pictures. So: let them discover all by themselves. Trial and error is the most effective manner to learn.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.</p><p><A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com1tag:blogger.com,1999:blog-10614348.post-10689747036639265172020-08-10T06:01:00.020-07:002020-08-28T21:15:18.016-07:00Fast Radiowave bursts in TGD framework
I encountered a highly interesting popular article (thanks for my friend Asta for the link) with title "Mysterious 'fast radio burst' detected closer to Earth than ever before" (<A HREF="https://cutt.ly/QdNX5Xc">this</A>).
</p><p>
Fast radio wave bursts (FRBs) arrive from a distance of hundreds of millions of light years - the scale of a large void. If the energy of FRBs is radiated isotropically in all directions - an assumption to be challenged below - the total energy is of the same order of magnitude that the energy of the Sun produced during a century. There are FRBs repeating with a period of 16 days located to a distance of 500 million light years from Earth.
</p><p>
The latest bursts arrive from a distance of only about 30 thousand light years from our own galaxy Milky Way described in the popular article can be assigned with magnetar (see <A HREF="https://cutt.ly/udNMKRF">this</A>) which is a remnant of neutron start and has extremely strong magnetic field of about 10<sup>11</sup> Tesla.
</p><p>
Below is the abstract of the article (<A HREF="https://cutt.ly/sdNX69z">this</A>) reporting the discovery.
</p><p>
<I> We report on International Gamma-Ray Astrophysics Laboratory (INTEGRAL) observations of the soft γ ray repeater SGR 1935+2154 performed between 2020 April 28 and May 3. Several short bursts with fluence of ∼ 10<sup>-7</sup>-10<sup>-6</sup> erg cm<sup>-2</sup> were detected by the Imager on-board INTEGRAL (IBIS) instrument in the 20-200 keV range. The burst with the hardest spectrum, discovered and localized in real time by the INTEGRAL Burst Alert System, was spatially and temporally coincident with a short and very bright radio burst detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and Survey for Transient Astronomical Radio Emission 2 (STARE2) radio telescopes at 400-800 MHz and 1.4 GHz, respectively.
</p><p>
Its lightcurve shows three narrow peaks separated by ∼ 29 ms time intervals, superimposed on a broad pulse lasting ∼ 0.6 s. The brightest peak had a delay of 6.5 +/- 1.0 ms with respect to the 1.4 GHz radio pulse (that coincides with the second and brightest component seen at lower frequencies). The burst spectrum, an exponentially cutoff power law with photon index Γ =0.7<sub>-0.2</sub><sup>+0.4</sup> and peak energy E<sub>p</sub>=65+/- 5 keV, is harder than those of the bursts usually observed from this and other magnetars.
</p><p>
By the analysis of an expanding dust-scattering ring seen in X-rays with the Neil Gehrels Swift Observatory X-ray
Telescope (XRT) instrument, we derived a distance of 4.4<sub>-1.3</sub><sup>+2.8</sup> kpc for SGR 1935+2154, independent of its possible association with the supernova remnant G57.2+0.8. At this distance, the burst 20-200 keV fluence of (6.1+/- 0.3)× 10<sup>-7</sup> erg cm<sup>-2</sup> corresponds to an isotropic emitted energy of ∼ 1.4× 10</sub><sup>39</sup> erg. This is the first burst with a radio counterpart observed from a soft γ ray repeater and it strongly supports models based on magnetars that have been proposed for extragalactic fast radio bursts.</I>
</p><p>
What could be the interpretation of the finding in the TGD framework? The weirdest feature of the FRB is its gigantic total energy assuming that the radiation is isotropic during the burst. This assumption can be challenged in the TGD framework, where the stellar systems are connected to a monopole flux tube network and radiation flows along flux tubes, which can also branch. This brings strongly in mind the analog of a nervous system in cosmic scales and this analogy is used in what follows.
<OL>
<LI>The duration of pulses is few milliseconds: the duration of nerve pulses is the same. Is this a wink-wink to the Poirots of astrophysics?
<LI>Bursts can arrive regularly for instance with a period of T=16.35 days (see <A HREF="https://cutt.ly/xdNMjQK">this</A>). This brings in the mind of astro-Poirot biorhythm, in particular EEG rhythms. This would not be the only such rhythms: also the period of T<sub>alpha</sub>=160 minutes, for which have proposed an interpretation as a cosmic analog of alpha rhythm is known (see <A HREF= "http://tgdtheory.fi/public_html/articles/cosmoalpha.pdf">this</A>). The ratio T/T<sub>α</sub>=147.15 would give for the analogous brain rhythm the value of 14.7 seconds.
<LI>Let us assume that stellar systems indeed form an analog of neural network connected by flux and assume that the topology of this network is analogous to that defined by axons. In TGD framework neural communications between neurons occur actually by using dark photons with effective Planck constant h<sub>eff</sub>=nh<sub>0</sub> along the flux tubes with the velocity of light so that feedback from brain and even from the magnetic body of brain back to sensory organs as a virtual sensory input becomes possible. The function of nerve pulses is to connect the outgoing branch of the flux tube associated with the axon and those associated with dendrites of the post-synaptic neuron toa longer flux tubes by using neurotransmitters as relays.
<LI>The stellar object as an analog of a neuron would send its dark photon signals along the flux tube assignable to a single axon. Axon would later branch to dendrites arriving to other stellar systems and eventually perhaps to planets as analogs of synaptic contacts. An interesting question is whether also the analogs of nerve pulses and neurotransmitters acting as relays in the synaptic contacts defined by planets could make sense. What could nerve pulses propagating along the flux tube correspond to?
</p><p>
<B> Remark</B>: In the TGD based model of brain there would be also flux tube network analogous to the meridian system of Eastern medicine and responsible for the holistic and spatial aspects of consciousness since more than one flux tube can emanate from a given node making possibly non-linear networks (see <A HREF= "http://tgdtheory.fi/public_html/articles/dmtpineal.pdf">this</A>). Nervous system with tree- like structure would be responsible for the linear and temporal aspects of conscious experience. Tree-like structure would be crucial for the understanding of Alzheimer disease (see <A HREF= "http://tgdtheory.fi/public_html/articles/Alzheimer.pdf"> this</A>). Meridian system would be a predecessor of the neural system.
<LI>The distances of FRBs are of the order of large voids having galaxies at their boundaries and forming lattice-like networks possibly assignable to the tesselations of 3-D hyperbolic space defining cosmic time= constant surfaces. This kind of tesselations could accompany also brain (see <A HREF = "http://tgdtheory.fi/public_html/articles/hyperbolicbrain.pdf"> this</A>). In the fractal Universe of TGD one can wonder whether these voids are analogs of cells or even neurons and form cosmic biological organisms with flux tubes forming a network allowing communications.
</OL>
The basic implication is that the energy of the emitted radiation could be dramatically smaller than that predicted by an isotropic radiation burst. It is interesting to look whether the proposed picture survives quantitative modelling.
<OL>
<LI>The reduction factor r for the total emitted energy would be essentially r= S/A, where S is the area of the "axonal" flux tube and A=4π R<sup>2</sup> is the surface area of the magnetar. One must estimate the value of r.
<LI>Flux quantization for a single sheet of the many-sheeted magnetic flux tube involved would give eBS= hbar<sub>0</sub> h=6h<sub>0</sub> (see <A HREF ="http://tgdtheory.fi/public_html/articles/Millsagain.pdf"> this</A> and <A HREF="http://tgdtheory.fi/public_html/articles/colorvision.pdf">this</A>). The general order of magnitude estimate is eB ∼ hbar<sub>0</sub>/S. If each sheet carries out the same energy, the number of sheets is n=h<sub>eff</sub>/h<sub>0</sub> and the effective area of a flux tube is S= hbar<sub>0</sub>/eB. Does the magnetic field assigned with magnetar correspond to a single sheet or to all sheets? If the field is measured from cyclotron energies assuming h<sub>eff</sub>=h it would correspond to all sheets and the measured magnetic field would be the effective magnetic field B<sub>eff</sub>= nB/6 for h= 6h<sub>0</sub>.
<LI>The branching of the flux tube could correspond to the splitting of the many-sheeted flux tube to tubes with smaller number of sheets and involve reduction of h<sub>eff</sub>. This would give the estimate r= hbar<sub>0</sub>/eBA. Magnetic field of 1 Tesla corresponds to a unit flux quantum with radius - magnetic length . about 2.6× 10<sup>-8</sup> meters. Assuming magnetar radius R=20 km one has r∼ 10<sup>-25</sup>/6.
<LI>The estimate for the total emitted energy assuming isotropic radiation is the energy radiated by the Sun during a century. Sun transforms roughly E<sub>100</sub>=1.3× 10<sup>19</sup> kg of mass to radiation during a century. This gives for the energy emitted in FRB the estimate E= r E<sub>100</sub>∼ 10<sup>-6</sup>/6 kg which is roughly 7.5 Planck masses m<sub>Pl</sub>≈ 2.2× 10<sup>-8</sup> kg. The order of magnitude is Planck mass. The estimate is of course extremely rough.
</p><p>
In any case, the idea that pulses could have mass of order few Planck masses is attractive. Note that a large neuron with radius about 10<sup>-4</sup> meters has a mass of order Planck mass (see <A HREF ="http://tgdtheory.fi/public_html/articles/waterbridge.pdf">this</A>).
<LI>From the total detected energy dE/dS= 6.1× 10<sup>-7</sup> erg m<sup>-2</sup>= 3.8× 10<sup>9</sup> eVm<sup>-2</sup> and total radiated energy E= 7.5 m<sub>Pl</sub> one can estimate the total area S covered by the branched energy flux if it covers the entire area with a shape of disk of radius R. This gives some idea about how wide the branching is. The total energy is E =(dE/dS)× π R<sup>2</sup> giving R= [E/π (dE/dS)]<sup>1/2</sup>∼ .9× 10<sup>9</sup> m. The equitoral radius of the Sun is R<sub>Sun</sub>= .7× 10<sup>9</sup> m. R<sub>Sun</sub>∼ .78 R. This conforms with the idea that the radiation arrives along the axon-like flux tube connecting Sun and the magnetar branching so that it covers the entire Sun.
</OL>
The ratio h<sub>eff</sub>/h should be of the same order of magnitude as the ratio X=E/E<sub>rad</sub>, where E<sub>rad</sub> is the energy of the radio wave photon with frequency 1.4 GHz for h<sub>eff</sub>=h: X∼ h<sub>eff</sub>/h. The ratio Y= X/(h<sub>eff</sub>/h) should satisfy Y∼ 1.
<OL>
<LI>To proceed further, one can use the TGD variant of Nottale's hypothesis. The hypothesis states that one can assign to gravitational flux tubes gravitational Planck constant hbar<sub>gr</sub>. The original hypothesis was ℏ<sub>eff</sub>=ℏ<sub>gr</sub> and the more recent form inspired by the adelic vision states that h<sub>gr</sub> corresponds to a large integer factor of h<sub>eff</sub>. One has ℏ<sub>gr</sub>= GMm/v<sub>0</sub>= r<sub>S</sub>m/2v<sub>0</sub>. Here M is the mass of the large object - now that of magnetar. m is the mass of the smaller quantum coherent object in contact with the gravitational flux tube mediating gravitational interaction as dark graviton exchanges.
</p><p>
v<sub>0</sub> is a velocity parameter. For Sun would have β<sub>0,S</sub>=v<sub>0</sub>/c≈ 2<sup>-11</sup> from the model for the inner planets as Bohr orbits (see <A HREF="http://tgdtheory.fi/pdfpool/astro.pdf">this</A>).
<LI> The Planckian educated guess is m∼ m<sub>Pl</sub> so that one would have hbar<sub>gr</sub>/hbar= r<sub>S</sub>(M)/(2L<sub>Pl</sub>β<sub>0</sub>), where L<sub>Pl</sub> is Planck length and r<sub>S</sub>(M) is the Schwartshild radius of magnetar. This would give Y= X/(ℏ<sub>gr</sub>/ℏ)= .4 if one has r<sub>S</sub>=3 km as for the Sun. r<sub>S</sub> is probably large but smaller than magnetar radius about 20 km. The masses of the magnetars are in the range 1-2 solar masses. For M= 2M<sub>S</sub> one obtains Y=.8.
</p><p>
The rough estimate is not far from Y=1 and suggests that the interacting quantum units at the receiving end have mass of order Planck mass. Interestingly, the mass of a large neuron with radius 10<sup>-4</sup> m is about Planck mass (see <A HREF= "http://tgdtheory.fi/public_html/articles/waterbridge.pdf">this</A>), which supports the view that quantum gravitation in the TGD sense is fundamental for life - even in the cosmic scales.
</OL>
The physical interpretation of the velocity parameter v<sub>0</sub> is one of the key challenges.
<OL>
<LI> The order of magnitude of v<sub>0</sub> is the same as for the rotational velocities in the solar system. I have considered a geometry based interpretation (see <A HREF="http://tgdtheory.fi/public_html/articles/vzero.pdf">this</A> and <A HREF="http://tgdtheory.fi/pdfpool/vzerovariableG.pdf">this</A>).
<LI> The analogy with the neural system encourages the question whether v<sub>0</sub> could have a concrete interpretation as the analog of the nerve pulse conduction velocity assignable to the dark magnetic flux tubes connecting distant systems.
</p><p>
In TGD framework nerve pulses (see <A HREF="http://tgdtheory.fi/pdfpool/pulse.pdf">this</A>) are proposed to be induced by the perturbations of Sine-Gordon soliton sequences for the generalized Josephson junctions assignable to the cell membrane and identifiable as transversal flux tubes assignable to various membrane proteins such as ion channels and pumps. The dark variants of the biologically important ions would give rise to the supra currents.
</p><p>
Could the gravitational flux tubes analogous to axons have this kind of structure and give rise to generalized Josephson junctions with ions serving also in this case as current carriers?
</OL>
To sum up, the proposed interpretation as cosmic neural networks conforms with the basic assumptions of TGD. Most importantly, quantitative predictions are correct. The picture is of course not deduce from axioms: this is pattern recognition with basic principles predicting a lot of new physics.
</p><p>I encountered a highly interesting popular article (thanks for my friend Asta for the link) with title "Mysterious 'fast radio burst' detected closer to Earth than ever before" (<A HREF="https://cutt.ly/QdNX5Xc">this</A>).
</p><p>
Fast radio wave bursts (FRBs) arrive from a distance of hundreds of millions of light years - the scale of a large void. If the energy of FRBs is radiated isotropically in all directions - an assumption to be challenged below - the total energy is of the same order of magnitude that the energy of the Sun produced during a century. There are FRBs repeating with a period of 16 days located to a distance of 500 million light years from Earth.
</p><p>
The latest bursts arrive from a distance of only about 30 thousand light years from our own galaxy Milky Way described in the popular article can be assigned with magnetar (see <A HREF="https://cutt.ly/udNMKRF">this</A>) which is a remnant of neutron start and has extremely strong magnetic field of about 10<sup>11</sup> Tesla.
</p><p>
Below is the abstract of the article (<A HREF="https://cutt.ly/sdNX69z">this</A>) reporting the discovery.
</p><p>
<I> We report on International Gamma-Ray Astrophysics Laboratory (INTEGRAL) observations of the soft γ ray repeater SGR 1935+2154 performed between 2020 April 28 and May 3. Several short bursts with fluence of ∼ 10<sup>-7</sup>-10<sup>-6</sup> erg cm<sup>-2</sup> were detected by the Imager on-board INTEGRAL (IBIS) instrument in the 20-200 keV range. The burst with the hardest spectrum, discovered and localized in real time by the INTEGRAL Burst Alert System, was spatially and temporally coincident with a short and very bright radio burst detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and Survey for Transient Astronomical Radio Emission 2 (STARE2) radio telescopes at 400-800 MHz and 1.4 GHz, respectively.
</p><p>
Its lightcurve shows three narrow peaks separated by ∼ 29 ms time intervals, superimposed on a broad pulse lasting ∼ 0.6 s. The brightest peak had a delay of 6.5 +/- 1.0 ms with respect to the 1.4 GHz radio pulse (that coincides with the second and brightest component seen at lower frequencies). The burst spectrum, an exponentially cutoff power law with photon index Γ =0.7<sub>-0.2</sub><sup>+0.4</sup> and peak energy E<sub>p</sub>=65+/- 5 keV, is harder than those of the bursts usually observed from this and other magnetars.
</p><p>
By the analysis of an expanding dust-scattering ring seen in X-rays with the Neil Gehrels Swift Observatory X-ray
Telescope (XRT) instrument, we derived a distance of 4.4<sub>-1.3</sub><sup>+2.8</sup> kpc for SGR 1935+2154, independent of its possible association with the supernova remnant G57.2+0.8. At this distance, the burst 20-200 keV fluence of (6.1+/- 0.3)× 10<sup>-7</sup> erg cm<sup>-2</sup> corresponds to an isotropic emitted energy of ∼ 1.4× 10</sub><sup>39</sup> erg. This is the first burst with a radio counterpart observed from a soft γ ray repeater and it strongly supports models based on magnetars that have been proposed for extragalactic fast radio bursts.</I>
</p><p>
What could be the interpretation of the finding in the TGD framework? The weirdest feature of the FRB is its gigantic total energy assuming that the radiation is isotropic during the burst. This assumption can be challenged in the TGD framework, where the stellar systems are connected to a monopole flux tube network and radiation flows along flux tubes, which can also branch. This brings strongly in mind the analog of a nervous system in cosmic scales and this analogy is used in what follows.
<OL>
<LI>The duration of pulses is few milliseconds: the duration of nerve pulses is the same. Is this a wink-wink to the Poirots of astrophysics?
<LI>Bursts can arrive regularly for instance with a period of T=16.35 days (see <A HREF="https://cutt.ly/xdNMjQK">this</A>). This brings in the mind of astro-Poirot biorhythm, in particular EEG rhythms. This would not be the only such rhythms: also the period of T<sub>alpha</sub>=160 minutes, for which have proposed an interpretation as a cosmic analog of alpha rhythm is known (see <A HREF= "http://tgdtheory.fi/public_html/articles/cosmoalpha.pdf">this</A>). The ratio T/T<sub>α</sub>=147.15 would give for the analogous brain rhythm the value of 14.7 seconds.
<LI>Let us assume that stellar systems indeed form an analog of neural network connected by flux and assume that the topology of this network is analogous to that defined by axons. In TGD framework neural communications between neurons occur actually by using dark photons with effective Planck constant h<sub>eff</sub>=nh<sub>0</sub> along the flux tubes with the velocity of light so that feedback from brain and even from the magnetic body of brain back to sensory organs as a virtual sensory input becomes possible. The function of nerve pulses is to connect the outgoing branch of the flux tube associated with the axon and those associated with dendrites of the post-synaptic neuron toa longer flux tubes by using neurotransmitters as relays.
<LI>The stellar object as an analog of a neuron would send its dark photon signals along the flux tube assignable to a single axon. Axon would later branch to dendrites arriving to other stellar systems and eventually perhaps to planets as analogs of synaptic contacts. An interesting question is whether also the analogs of nerve pulses and neurotransmitters acting as relays in the synaptic contacts defined by planets could make sense. What could nerve pulses propagating along the flux tube correspond to?
</p><p>
<B> Remark</B>: In the TGD based model of brain there would be also flux tube network analogous to the meridian system of Eastern medicine and responsible for the holistic and spatial aspects of consciousness since more than one flux tube can emanate from a given node making possibly non-linear networks (see <A HREF= "http://tgdtheory.fi/public_html/articles/dmtpineal.pdf">this</A>). Nervous system with tree- like structure would be responsible for the linear and temporal aspects of conscious experience. Tree-like structure would be crucial for the understanding of Alzheimer disease (see <A HREF= "http://tgdtheory.fi/public_html/articles/Alzheimer.pdf"> this</A>). Meridian system would be a predecessor of the neural system.
<LI>The distances of FRBs are of the order of large voids having galaxies at their boundaries and forming lattice-like networks possibly assignable to the tesselations of 3-D hyperbolic space defining cosmic time= constant surfaces. This kind of tesselations could accompany also brain (see <A HREF = "http://tgdtheory.fi/public_html/articles/hyperbolicbrain.pdf"> this</A>). In the fractal Universe of TGD one can wonder whether these voids are analogs of cells or even neurons and form cosmic biological organisms with flux tubes forming a network allowing communications.
</OL>
The basic implication is that the energy of the emitted radiation could be dramatically smaller than that predicted by an isotropic radiation burst. It is interesting to look whether the proposed picture survives quantitative modelling.
<OL>
<LI>The reduction factor r for the total emitted energy would be essentially r= S/A, where S is the area of the "axonal" flux tube and A=4π R<sup>2</sup> is the surface area of the magnetar. One must estimate the value of r.
<LI>Flux quantization for a single sheet of the many-sheeted magnetic flux tube involved would give eBS= hbar<sub>0</sub> h=6h<sub>0</sub> (see <A HREF ="http://tgdtheory.fi/public_html/articles/Millsagain.pdf"> this</A> and <A HREF="http://tgdtheory.fi/public_html/articles/colorvision.pdf">this</A>). The general order of magnitude estimate is eB ∼ hbar<sub>0</sub>/S. If each sheet carries out the same energy, the number of sheets is n=h<sub>eff</sub>/h<sub>0</sub> and the effective area of a flux tube is S= hbar<sub>0</sub>/eB. Does the magnetic field assigned with magnetar correspond to a single sheet or to all sheets? If the field is measured from cyclotron energies assuming h<sub>eff</sub>=h it would correspond to all sheets and the measured magnetic field would be the effective magnetic field B<sub>eff</sub>= nB/6 for h= 6h<sub>0</sub>.
<LI>The branching of the flux tube could correspond to the splitting of the many-sheeted flux tube to tubes with smaller number of sheets and involve reduction of h<sub>eff</sub>. This would give the estimate r= hbar<sub>0</sub>/eBA. Magnetic field of 1 Tesla corresponds to a unit flux quantum with radius - magnetic length . about 2.6× 10<sup>-8</sup> meters. Assuming magnetar radius R=20 km one has r∼ 10<sup>-25</sup>/6.
<LI>The estimate for the total emitted energy assuming isotropic radiation is the energy radiated by the Sun during a century. Sun transforms roughly E<sub>100</sub>=1.3× 10<sup>19</sup> kg of mass to radiation during a century. This gives for the energy emitted in FRB the estimate E= r E<sub>100</sub>∼ 10<sup>-6</sup>/6 kg which is roughly 7.5 Planck masses m<sub>Pl</sub>≈ 2.2× 10<sup>-8</sup> kg. The order of magnitude is Planck mass. The estimate is of course extremely rough.
</p><p>
In any case, the idea that pulses could have mass of order few Planck masses is attractive. Note that a large neuron with radius about 10<sup>-4</sup> meters has a mass of order Planck mass (see <A HREF ="http://tgdtheory.fi/public_html/articles/waterbridge.pdf">this</A>).
<LI>From the total detected energy dE/dS= 6.1× 10<sup>-7</sup> erg m<sup>-2</sup>= 3.8× 10<sup>9</sup> eVm<sup>-2</sup> and total radiated energy E= 7.5 m<sub>Pl</sub> one can estimate the total area S covered by the branched energy flux if it covers the entire area with a shape of disk of radius R. This gives some idea about how wide the branching is. The total energy is E =(dE/dS)× π R<sup>2</sup> giving R= [E/π (dE/dS)]<sup>1/2</sup>∼ .9× 10<sup>9</sup> m. The equitoral radius of the Sun is R<sub>Sun</sub>= .7× 10<sup>9</sup> m. R<sub>Sun</sub>∼ .78 R. This conforms with the idea that the radiation arrives along the axon-like flux tube connecting Sun and the magnetar branching so that it covers the entire Sun.
</OL>
The ratio h<sub>eff</sub>/h should be of the same order of magnitude as the ratio X=E/E<sub>rad</sub>, where E<sub>rad</sub> is the energy of the radio wave photon with frequency 1.4 GHz for h<sub>eff</sub>=h: X∼ h<sub>eff</sub>/h. The ratio Y= X/(h<sub>eff</sub>/h) should satisfy Y∼ 1.
<OL>
<LI>To proceed further, one can use the TGD variant of Nottale's hypothesis. The hypothesis states that one can assign to gravitational flux tubes gravitational Planck constant hbar<sub>gr</sub>. The original hypothesis was ℏ<sub>eff</sub>=ℏ<sub>gr</sub> and the more recent form inspired by the adelic vision states that h<sub>gr</sub> corresponds to a large integer factor of h<sub>eff</sub>. One has ℏ<sub>gr</sub>= GMm/v<sub>0</sub>= r<sub>S</sub>m/2v<sub>0</sub>. Here M is the mass of the large object - now that of magnetar. m is the mass of the smaller quantum coherent object in contact with the gravitational flux tube mediating gravitational interaction as dark graviton exchanges.
</p><p>
v<sub>0</sub> is a velocity parameter. For Sun would have β<sub>0,S</sub>=v<sub>0</sub>/c≈ 2<sup>-11</sup> from the model for the inner planets as Bohr orbits (see <A HREF="http://tgdtheory.fi/pdfpool/astro.pdf">this</A>).
<LI> The Planckian educated guess is m∼ m<sub>Pl</sub> so that one would have hbar<sub>gr</sub>/hbar= r<sub>S</sub>(M)/(2L<sub>Pl</sub>β<sub>0</sub>), where L<sub>Pl</sub> is Planck length and r<sub>S</sub>(M) is the Schwartshild radius of magnetar. This would give Y= X/(ℏ<sub>gr</sub>/ℏ)= .4 if one has r<sub>S</sub>=3 km as for the Sun. r<sub>S</sub> is probably large but smaller than magnetar radius about 20 km. The masses of the magnetars are in the range 1-2 solar masses. For M= 2M<sub>S</sub> one obtains Y=.8.
</p><p>
The rough estimate is not far from Y=1 and suggests that the interacting quantum units at the receiving end have mass of order Planck mass. Interestingly, the mass of a large neuron with radius 10<sup>-4</sup> m is about Planck mass (see <A HREF= "http://tgdtheory.fi/public_html/articles/waterbridge.pdf">this</A>), which supports the view that quantum gravitation in the TGD sense is fundamental for life - even in the cosmic scales.
</OL>
The physical interpretation of the velocity parameter v<sub>0</sub> is one of the key challenges.
<OL>
<LI> The order of magnitude of v<sub>0</sub> is the same as for the rotational velocities in the solar system. I have considered a geometry based interpretation (see <A HREF="http://tgdtheory.fi/public_html/articles/vzero.pdf">this</A> and <A HREF="http://tgdtheory.fi/pdfpool/vzerovariableG.pdf">this</A>).
<LI> The analogy with the neural system encourages the question whether v<sub>0</sub> could have a concrete interpretation as the analog of the nerve pulse conduction velocity assignable to the dark magnetic flux tubes connecting distant systems.
</p><p>
In TGD framework nerve pulses (see <A HREF="http://tgdtheory.fi/pdfpool/pulse.pdf">this</A>) are proposed to be induced by the perturbations of Sine-Gordon soliton sequences for the generalized Josephson junctions assignable to the cell membrane and identifiable as transversal flux tubes assignable to various membrane proteins such as ion channels and pumps. The dark variants of the biologically important ions would give rise to the supra currents.
</p><p>
Could the gravitational flux tubes analogous to axons have this kind of structure and give rise to generalized Josephson junctions with ions serving also in this case as current carriers?
</OL>
To sum up, the proposed interpretation as cosmic neural networks conforms with the basic assumptions of TGD. Most importantly, quantitative predictions are correct. The picture is of course not deduce from axioms: this is pattern recognition with basic principles predicting a lot of new physics.
</p><p>
See the article <A HREF="http://tgdtheory.fi/public_html/articles/FRB.pdf">Fast radio wave bursts: is life a cosmic fractal?</A> or the chapter <A HREF="http://tgdtheory.fi/pdfpool/vzerovariableG.pdf">About the Nottale's formula for h<sub>gr</sub> and the relation between Planck length and CP<sub>2</sub>
length R </A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-40644829790793502832020-08-10T05:18:00.017-07:002020-08-10T05:58:22.957-07:00Nature Physics and physicsDid quite hard work to prepare summary of TGD for a possible publication in Nature Physics. They had not even sent it to referees. Incredible stupidity.
I however sent the artice to Witten, Maldacena, Susskind, and Arkani-Hamed. One might hope that the message managed to bypass their secretaries.
</p><p>
Dear Dr Pitkänen,
</p><p>
Thank you for submitting your manuscript "Summary of Topological Geometrodynamics" which we are regretfully unable to offer to publish.
</p><p>
It is Nature Physics' policy to return a substantial proportion of manuscripts without sending them to referees. Decisions of this kind are made by the editors of Nature Physics according to the demanding editorial criteria of the journal.
</p><p>
In the present case, while your findings may well prove stimulating to others' thinking about such questions, we regret that we are unable to conclude that the work provides the sort of firm advance in general understanding that would warrant publication in Nature Physics.
</p><p>
We are sorry that we cannot respond more positively on this occasion.
</p><p>
Regards,
</p><p>
Nature Physics
</p><p>
I will add the article to my homepage when communications to it work again.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-56641143129119988522020-07-14T21:20:00.011-07:002020-07-15T23:23:34.191-07:00Ballistic resonance as breaking of second law: TGD view point
The popular article "<I> Scientists have discovered a new physical paradox</I>" (see <A HREF="https://cutt.ly/lp6VL4l">this</A>) tells about the work of Vitaly A. Kuzkin et al published in Phys Rev E (see <A HREF="https://cutt.ly/Jp8XHYY">this</A>) as article with title "<I> Ballistic resonance and thermalization in the Fermi-Pasta-Ulam-Tsingou chain at finite temperature</I>" . The article describes very interesting experimental findings, which could provide a direct application of zero energy ontology (ZEO) based theory of self-organization.
</p><p>
<B> The findings and their explanation provided by experimenters</B>
</p><p>
Researchers from the Peter the Great St. Petersburg Polytechnic University (SPbPU) have discovered a new physical effect: the amplitude of mechanical vibrations can grow without external influence in which system converts its thermal energy to mechanical energy. The phenomenon is known as ballistic resonance. The description of the phenomenon involves also an abnormally high heat conductivity - one speaks of ballistic heat conductivity.
</p><p>
The electromagnetic analogy is very high electric conductivity: the work of Bandyopadhyay related to effects of oscillating voltage on currents flowing along microtubules demonstrates ballistic conductivity possibly reflecting underlying super-conductivity (see <A HREF="http://tgdtheory.fi/public_html/articles/mt.pdf">this</A>).
</p><p>
This behavior seems to be in conflict with second law of thermodynamics telling that the vibrations should be attenuated. The researchers propose also a theoretical explanation of this paradox (see <A HREF ="https://cutt.ly/Cp6GFkJ">this</A>) based on a model assuming ballistic heat conduction. One can of course wonder whether the notion of ballistic heat conduction is consistent with second law in its standard form.
</p><p>
Fermi-Past-Ulam-Tsingou problem (see <A HREF="https://en.wikipedia.org/wiki/Fermi–Pasta–Ulam–Tsingou_problem">this</A>) relates to the finding about a theoretical model of a vibrating string with a non-linear dynamics. The expectation was that the situation develops ergodic so that energy is evenly divided between the modes of the string. It however turned out that the behavior was essentially periodic. The model explaining the behavior relies on solitons assignable to Korteveg-de-Vries equation. This phenomenon is different from the ballistic resonance observed in the experiments. In Korteveg de-Vries equation there is no dissipative term and the unexpected phenomenon is that wave pattern preserves it shape. Dissipation without energy feed would attenuate the wave.
</p><p>
<B> ZEO based model for the findings</B>
</p><p>
TGD suggests that a genuine explanation requires a profound change in the thinking about time- in particular the relationship between geometric time and experienced time must be updated. I call the new conceptual framework zero energy ontology ZEO) (see <A HREF="http://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A>). The identification of these two times in standard ontology is in conflict with simple empirical facts, and leads to a paradox related to state function reduction (SFR) taking place in quantum measurement. The non-determinism of SFR is in conflict with the determinism of Schrödinger equation.
<OL>
<LI> According to ZEO in ordinary state function reduction (SFR) the arrow of time subsystem changes: this solves the basic paradox of quantum measurement theory. The experiments of Minev et al (see <A HREF="http://tgdtheory.fi/public_html/articles/Bohrdead.pdf">this</A>) give impressive experimental support for the notion in atomic scales, and sow that SFR looks completely classical deterministic smooth time evolution for the observer with opposite arrow of time. This is just what TGD predicts. Macroscopic quantum jump can occur in all scales but ZEO takes care that the world looks classical! The endless debate about the scale in which quantum world becomes classical would be solely due to complete misunderstanding of the notion of time.
<LI> Non-standard arrow of time forces a generalization of thermodynamics. For time reversed system generalized second law applies in reverse direction of time. Dissipation with reversed arrow of time extracts energy from environment, in particular thermal energy from internal thermal environment. The energy feed necessary for self-organization reduces to dissipation in reversed arrow of time.
</p><p>
This explains why self-organization is possible (see <A HREF="http://tgdtheory.fi/public_html/articles/heffselforg.pdf">this</A>). Standard form of the second flow would imply that also energy flows between systems go to zero: this would mean thermodynamical equilibrium everywhere - heat death. This has led to desperate theoretical proposals such as life as gigantic thermodynamical fluctuation. The recent empirical understanding suggests that this giant fluctuation would have occurred in the scale of the entire Universe and continue forever!
<LI> Macroscopic quantum coherence is however a necessary prerequisite for macroscopic effects. TGD predicts hierarchy of phases of ordinary matter residing at magnetic body (MB) of the system with value of effective Planck constant h<sub>eff</sub>= nh<sub>0</sub> (h=6h<sub>0</sub>) of h<sub>eff</sub>behaving like dark matter and controlling ordinary matter (see <A HREF="http://tgdtheory.fi/public_html/articles/heffselforg.pdf">this</A>).. The larger the value of h<sub>eff</sub>, the longer the scale of quantum coherence scale at MB. MB acts as master for ordinary matter in the role of slave and induces coherent behaviour. This gives rise to self-organization.
</OL>
This picture could explain the observations of self induced resonance using thermal energy. A subsystem or its MB in time reversed mode would extract the thermal energy. There are many other applications. The phenomenon of stochastic resonance in which system extracts energy from external noise could have explanation along these lines. Stochastic resonance plays an important role in sensory perception by making possible amplification of weak signal in large background. There is evidence for it even in astrophysical scales. In biology metabolic energy could be extracted from metabolites and maybe also from thermal energy by time reversed dissipation by some subsystems related to metabolism.
</p><p>
TGD picture does not exclude the possibility of delicate models mimicking this behavior in the framework of thermodynamics. The basic challenge in this kind of effective model is to describe the presence time reversed dissipation inducing self-organization and the presence of dark matter at magnetic body phenomenologically. Energy feed as parameter gives rise to states far from thermodynamical equilibria.
</p><p>
For instance, the thermodynamics of ion distributions inside and outside cell is far far from thermodynamical equilibrium and and non-equilibrium thermodynamics has been developed for the modelling of this kind of systems utilizing the notions of ionic pumps and channels. The phenomenological description introduces chemical potentials as parameters to describe the non-equilibrium situation in the framework ordinary thermodynamics. Chemical potentials would model the neglected presence of h<sub>eff</sub>>h phases of dark matter at magnetic body of the system.
</p><p>
See the article <A HREF="http://tgdtheory.fi/public_html/articles/zeoballistic.pdf">Ballistic resonance and zero energy ontology</A> or the chapter <A HREF="http://tgdtheory.fi/pdfpool/UandM.pdf">Zero Energy Ontology and Matrices</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-4501284899883202752020-07-14T00:28:00.003-07:002020-07-16T19:19:43.007-07:00Is there a chronon of time?
This posting was inspired by a <A HREF=" https://www.livescience.com/what-are-smallest-ticks-of-time.html">popular article</A> telling about the proposal that Planck length is not the fundamental length as
often believed but the fundamental chronon is much longer.
</p><p>
The idea about fundamental unit of time - usually assumed to be given by Planck time about 10<sup>-44</sup> seconds - is rather naive if taken to mean discretization of time. The article proposes a variant of this idea and identifies the fundamental chronon as a fundamental periodicity of dynamics and deduces for it a value about 10<sup>-33</sup> seconds from observed bounds to the variation of dynamical periods. This value is by 11 orders of magnitude longer than Planck time. Personally I am a little bit skeptic about reliability of these bounds since very short times are involved.
</p><p>
Planck time is deduced from a mere dimensional analysis argument by feeding in speed of light c, Planck constant h, and Newton's constant G so that it is rather ad hoc noton. Therefore it has been surprising to me at least how seriously people have taken it. Moreover, Planck length appears in theories - in superstring theory in particular - typically as an ad hoc formal parameter with no direct geometric interpretation. In general relativity this leads to non-renormalizability and it is not possible to quantize gravitation in this framework. In superstring theories it led to landscape catastrophe: even a smallest change in the physics at Planck length scales changes completely the physics at long length scales: butterfly effect in the theory space.
</p><p>
For these reasons the question whether there exists some fundamental length-/time unit or several of them is a key problem of recent day physics. Could there be some fundamental length scale or possibly several of them with a clear geometric interpretation? In TGD Universe this is indeed the case.
<OL>
<LI> Planck length is derived quantity and CP<sub>2</sub> length scale defines the fundamental length, which from p-adic mass calculation for electron mass roughly 10<sup>4</sup> times longer than Planck length. Space-time is continuuous but CP<sub>2</sub> length serves as a fundamental unit of length, kind of length stick.
<LI> p-Adic length scale hypothesis (PLH) predicts actually infinite hierarchy of length/time units as p-adic length scale hypothesis stating that these units are proportional to sqrt(p), p preferred p-adic prime. p-Adic length scale hypothesis in this general form emerges both from M<sup>8</sup>-H duality and p-adic mass calculations.
<LI> A stronger form of PLH states that certain primes near powers of 2 are physically favored so that in the most general case one obtains a hierarchy of length and time units coming as half octaves. This form of hypothesis not well-understood although it conforms with period doubling in chaotic systems. Also powers of other small primes are possible and there is some evidence for the powers of 3. This would relate the preferred length scales of physics in long scales to CP<sub>2</sub> scale.
<LI> TGD predicts second length scale hierarchy corresponding to the hierarchy of effective values h<sub>e</sub>ff=nh<sub>0</sub> of Planck constant (h=6h<sub>0</sub>) labelling phases of ordinary matter behaving like dark matter. n corresponds number theoretically to the dimension for extension of rationals. This makes possible a hierarchy of quantum coherence length coming as n/6-multiples of the ordinary Compton length. Quantum coherence in long length scales is the most important implication and the coherence of living matter would be due to quantum coherence at magnetic body - distinguishing between TGD and Maxwellian and QFT view about classical fields. There is considerable evidence for the existence of h<sub>eff</sub> hierarchy from various anomalies, in particular from those in living matter.
<LI> Also now the challenge is testing of this hypothesis in macroscopic length scales: we cannot directly access short scales. The idea is simple: measure ratios of p-adic mass scales. They do not depend on CP<sub>2</sub> scale nor on the value of n. The ratios of dark quantum scales - say dark Compton lengths - are typically given by the ratio n<sub>1</sub>/n<sub>2</sub> of integers involved.
</p><p>
This allows precise tests by measuring mass and length scale ratios rather than masses and length scales. For instance, the possibility of scaled variants of hadron physics and electroweak physics allow to test the hypothesis. There are indeed indications for scaled up variants of mesons with mass scale differing by a factor 512 from that for ordinary hadrons. The Compton lengths would be same as for ordinary hadrons for n/6=512: the dark Compton scale for p-adically scaled up meson be same as ordinary Compton length making possible resonant coupling. If the valence electron of atom is dark, its Bohr radius is scaled up by (n/6)<sup>2</sup>: these states might be misinterpreted as Rydberg states.
</OL>
Concerning disretization of space-time TGD allows different view.
<OL>
<LI> Physics as number theory vision predicts that hierarchy of extensions of rationals defines evolutionary hierarchy. A generalization of real numbers to adeles labelled by extensions of rationals is assumed. For given extension of rationals adeles form a book like structure having as pages real numbers and extensions of p-adic number fields induced by extension of rationals. The pages are glued together along the back of the book consisting of points in given extension of rationals common to reals and extensions of all p-adic number fields. This hierarchy corresponds to evolutionary hierarchy and the dimension n of extension has identification as effective Planck constant h<sub>eff</sub>.
<LI> Space-time itself becomes a book-like structure. Real space-time surfaces are replaced with adelic surfaces, which containing real sheet and p-adic sheets glued together along the back of a book consisting of points with imbedding space coordinates in given extension of rationals. The points of space-time surface with coordinates in given extension of rationals form a discrete cognitive representaton, which is unique and improves with the dimension of extension so that at the limit of algebraic numbers it is dense set of space-time surface.
<LI> I call this discretization identifiable as intersection of sensory world (reals) and cognitive worlds as cognitive representation. The discretizaton reflects the limitations of cognition which must always discretize. In M<sup>8</sup> picture space-time surface are "roots" of octonionic polynomials and the polynomial defines the extension of rationals via its roots. At M<sup>8</sup> level there are also essentially unique imbedding space coordinates making discretization unique.
</OL>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com1tag:blogger.com,1999:blog-10614348.post-32964822837436106572020-07-09T20:42:00.005-07:002020-07-16T02:05:24.531-07:00What next in TGD?
Last night I was thinking about possible future project in TGD. The construction of scattering amplitudes has been the dream impossible that has driven me for decades. Maybe the understanding of fermionic M<sup>8</sup>-H duality provides the needed additional conceptual tools.
<OL>
<LI> M<sup>8</sup> picture looks simple. Space-time surfaces in M<sup>8</sup> can be constructed from real polynomials with real (rational) coefficients, actually knowledge of their roots is enough. Discrete data - roots of the polynomial!- determines space-time surface as associative or co-associative region! Besides this one must pose additional condition selecting 2-D string world sheets and 3-D light-like surfaces as orbits of partonic 2-surfaces. These would define strong form of holography (SH) allowing to map space-time surfaces in M<sup>8</sup> to M<sup>4</sup>×CP<sub>2</sub>.
<LI> Could SH generalize to the level of scattering amplitudes expressible in terms of n-point functions of CFT?! Could the n points correspond to the roots of the polynomial defining space-time region!
</p><p>
Algebraic continuation to quaternion valued scattering amplitudes analogous to that giving space-time sheets from the data coded SH should be the key idea. Their moduli squared are real - this led to the emergence of Minkowski metric for complexified octonions/quaternions) would give the real scattering rates: this is enough! This would mean a number theoretic generalization of quantum theory.
<LI> One can start from complex numbers and string world sheets/partonic 2-surfaces. Conformal field theories (CFTs) in 2-D play fundamental role in the construction of scattering string theories and in modelling 2-D statistical systems. In TGD 2-D surfaces (2-D at least metrically) code for information about space-time surface by strong holography (SH) .
</p><p>
Are CFTs at partonic 2-surfaces and string world sheets the basic building bricks? Could 2-D conformal invariance dictate the data needed to construct the scattering amplitudes for given space-time region defined by causal diamond (CD) taking the role of sphere S<sup>2</sup> in CFTs. Could the generalization for metrically 2-D light-like 3-surfaces be needed at the level of "world of classical worlds" (WCW) when states are superpositions of space-time surfaces, preferred extremals?
</OL>
The challenge is to develop a concrete number theoretic hierarchy for scattering amplitudes: R→C→Q→O - actually their complexifications.
<OL>
<LI> In the case of fermions one can start from 1-D data at light-like boundaries LB of string world sheets at light-like orbits of partonic 2-surfaces. Fermionic propagators assignable to LB would be coded by 2-D Minkowskian QFT in manner analogous to that in twistor Grassmann approach. n-point vertices would be expressible in terms of Euclidian n-point functions for partonic 2-surfaces: the latter element would be new as compared to QFTs since point-like vertex is replaced with partonic 2-surface.
<LI> The fusion (product?) of these Minkowskian and Euclidian CFT entities corresponding to different realization of complex numbers as sub-field of quaternions would give rise to 4-D quaternionic valued scattering amplitudes for given space-time sheet. Most importantly: there moduli squared are real! A generalization of quantum theory (CFT) from complex numbers to quaternions (quaternionic "CFT").
<LI> What about several space-time sheets? Could one allow fusion of different quaternionic scattering amplitudes corresponding to different quaternionic sub-spaces of complexified octonions to get octonion-valued non-associative scattering amplitudes. Again scattering rates would be real. A further generalization of quantum theory?
</OL>
There is also the challenge to relate M<sup>8</sup>- and H-pictures at the level of WCW. The formulation of physics in terms of WCW geometry leads to the hypothesis that WCW Kähler geometry is determined by Kähler function identified as the 4-D action resulting by dimensional reduction of 6-D surfaces in the product of twistor spaces of M<sup>4</sup> and CP<sub>2</sub> to twistor bundles having S<sup>2</sup> as fiber and space-time surface X<sup>4</sup>⊂ H as base. The 6-D Kähler action reduces to the sum of 4-D Kähler action and volume term having interpretation in terms of cosmological constant.
</p><p>
The question is whether the Kähler function - an essentially geometric notion - can have a counterpart at the level of M<sup>8</sup>.
<OL>
<LI>SH suggests that the Kähler function identified in the proposed manner can be expressed by using 2-D data or at least metrically 2-D data (light-like partonic orbits and light-like boundaries of CD). Note that each WCW would correspond to a particular CD.
<LI> Since 2-D conformal symmetry is involved, one expects also modular invariance meaning that WCW Kähler function is modular invariant, so that they have the same value for X<sup>4</sup>⊂ H for which partonic 2-surfaces have induced metric in the same conformal equivalence class.
<LI>Also the analogs of Kac-Moody type symmetries would be realized as symmetries of Kähler function. The algebra of super-symplectic symmetries of the light-cone boundary can be regarded as an analog of Kac-Moody algebra. Light-cone boundary has topology S<sup>2</sup>× R<sub>+</sub>, where R<sub>+</sub> corresponds to radial light-like ray parameterized by radial light-like coordinate r. Super symplectic transformations of S<sup>2</sup>× CP<sub>2</sub> depend on the light-like radial coordinate r, which is analogous to the complex coordinate z for he Kac-Moody algebras.
</p><p>
The infinitesimal super-symplectic transformations form algebra SSA with generators proportional to powers r<sup>n</sup> . The Kac-Moody invariance for physical states generalizes to a hierarchy of similar invariances. There is infinite fractal hierarchy of sub-algebras SSA<sub>n</sub>⊂ SSA with conformal weights coming as n-multiples of those for SSA. For physical states SSA<sub>n</sub> and [SSA<sub>n</sub>,SSA] would act as gauge symmetries. They would leave invariant also Kähler function in the sector WCW<sub>n</sub> defined by n. This would define a hierarchy of sub- WCWs of the WCW assignable to given CD.
</p><p>
The sector WCW<sub>n</sub> could correspond to extensions of rationals with dimension n, and one would have inclusion hierarchies consisting of sequences of n<sub>i</sub> with n<sub>i</sub> dividing n<sub>i+1</sub>. These inclusion hierarchies would naturally correspond to those for hyper-finite factors of type II<sub>1</sub>.
</p><p>
See the article <A HREF="http://tgdtheory.fi/public_html/articles/M8Hfermion.pdf">Fermionic variant of M<sup>8</sup>-H duality</A> or the chapter <A HREF="http://tgdtheory.fi/pdfpool/UandM.pdf">ZEO and matrices</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-1759853448129770122020-07-07T05:19:00.004-07:002020-07-08T23:34:06.571-07:00M8-H duality for fermions M<sup>8</sup>-H duality in bosonic sector is rather well understood but the situation is different in the fermionic sector. The basic guideline is that also fermionic dynamics should be algebraic and number theoretical.
<OL>
<LI>Spinors should be octonionic. I have already earlier considered their possible physical interpretation.
<LI> Dirac equation as linear partial differential equation should be replaced with a linear algebraic equation for octonionic spinors which are complexified octonions. The momentum space variant of the ordinary Dirac equation is an algebrac equation and the proposal is obvious: PΨ=0, where P is the octonionic continuation of the polynomial defining the space-time surface and multiplication is in octonionic sense. The masslessness condition restricts the solutions to light-like 3-surfaces m<sub>kl</sub>P<sup>k</sup>P<sup>l</sup>=0 in Minkowskian sector analogous to mass shells in momentum space - just as in the case of ordinary massless Dirac equation. P(o) rather than octonionic coordinate o would define momentum. These mass shells should be mapped to light-like partonic orbits in H.
<LI>This picture leads to the earlier phenomenological picture about induced spinors in H. Twistor Grassmann approach suggests the localization of the induced spinor fields at light-like partonic orbits in H. If the induced spinor field allows a continuation from 3-D partonic orbits to the interior of X<sup>4</sup>, it would serve as a counterpart of virtual particle in accordance with quantum field theoretical picture.
</p><p>
<B> Addition</B>: A really pleasant surprise that came this morning-9.7.2020 - sounds melodramatic but I do not want to forget it - it could have come more than decade ago but did not. The octonionic inner product for complexified octonionic 8-momenta with conjugation with respect to commuting imaginary unit i gives 8-D Minkowski norm squared. Same about quaternonic norm for complexified quaternionic momenta. Minkowski space with signature of (1,-,-1,-1) for metric follows from number theory alone! This conforms with the very idea of M<sup>8</sup>-H duality that geometry and number theory are dual in physics. Already this single finding makes M<sup>8</sup>-duality a "must".
</p><p>
See the article <a HREF= "http://tgdtheory.fi/public_html/articles/M8Hfermion.pdf">Fermionic variant of M<sup>8</sup>-H duality</A> or the chapter <A HREF="http://tgdtheory.fi/pdfpool/ratpoints3.pdf">Does M<sup>8</sup> duality reduce classical TGD to octonionic algebraic geometry?: Part III</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-27839178622487689062020-06-29T23:07:00.000-07:002020-06-29T23:07:16.996-07:00John Baez about Noether's theorem in algebraic approach
John Baez gives very nice summary (see <A HREF="https://johncarlosbaez.wordpress.com/2020/06/29/noethers-theorem-2/">this</A> of the triple of states, observables, and generators of symmetries from purely algebraic point of view. Jordan Banach algebra with commutative product A*B= (AB+BA)/2 would play the role of observables. The operators correspond to symmetry generators commuting with observables and the unitary evolutions generated by them in this algebra are trivial. One could say that this defines analogy of Noether's theorem usually deduced for the symmetries of action principle.
</p><p>
To me the weakness of the algebraic approach is that it says very little about the dynamics- it woul be just unitary evolution generation by some generator of symmetry. Second problem is mentioned at the end of the posting is how classical relates to quantal. And there is nothing about quantum measurement problem so that basically an attempt to reproduce wave mechanics using operators is in question.
</p><p>
My own view - zero energy ontology (ZEO) - goes much beyond quantum mechanics of simple systems.
<OL>
<LI> The basic problem of quantum measurement theory is the starting point. The notion of quantum state is modified. In wave mechanics and quantum field theories it is based on <I> initial value problem</I> in configuration space (space of positions for particle). Initial state is wave function - a superposition of possible initial values in configuration space. Time evolution is formulated in terms of unitary evolution defined by exponential of Hamiltonian and reduces to Schroedinger equation.
</p><p>
What happens in quantum measurements is not consistent with this time evolution. This is the problem.
<OL>
<LI> In TGD one replaces initial value problem with a <I>boundary value problem</I> with boundary corresponding to values at times t1 and t2 (this is a simplification).
<LI>One defines states as superpositions of deterministic <I> classical time evolutions</I> - preferred extremals - analogous to Bohr orbits having the property that boundary value problem is equivalent to initial value problem. Once on knows configuration at t1, one knows it at t2.
<LI>Quantum states are superpositions of these preferred extremals from t1 to t2 and quantum jump replaces this kind of superposition with a new one. I call this approach zero energy ontology (ZEO).
<LI> The basic problem of quantum measurement theory disappears since there are two causalities: that of quantum jump and classical causality, and there is no need to break the deterministic time evolution analogous to that given by Schroedinger equation in quantum jump. There are two times: experienced time as sequence of quantum jumps and geometric time. One ends up with a theory of consciousness without moment of consciousness identifiable as state function reduction. Also a ZEO theory of self-organization emerges. This is of course only the basic idea. For instance, one must understand how correlation between experienced time and geometric time emerges.
<LI> One the many implications of ZEO is new view about quantum tunnelling: it must have classical time evolution as quantum correlate. This leads to a new view about tunnelling in nuclear reactions relying essentially on the change of the arrow of time in ordinary state function reduction. Just today I received link telling about strange phenomenon occurring in what is believe to be ordinary electron tunnelling. The electron getting through the barrier radiates energy which increases with the height of the barrier. I discusse the ZEO based explanation in a related posting <A HREF="https://matpitka.blogspot.com/2020/06/new-support-for-tgd-view-about-quantum.html">New support for TGD view about quantum tunnelling</A> .
</OL>
</p><p>
How to realize this picture and how unique is it? Here one must leave the realm of wave mechanics.
<OL>
<LI> Loosely speaking, in TGD framework point-like particle is replaced with 3-D surface in M<sup>4</sup>× CP<sub>2</sub> and its orbit as preferred extremal of action principle, whatever it might be, defines space-time region. A generalization of string model is in question. Also a generalization of general relativity solving its problem due to the loss of Poincare symmetries is in question.
<LI> This leads to a generalization of Einstein's geometrization program: replace configuration space with the "world of classical worlds" (WCW) and give it Kaehler geometry to realize geometrization of quantum theory. Points of WCW are 3-surfaces or equivalently 4-surfaces: this reduces holography and reduces it to general coordinate invariance.
</p><p>
WCW spinor fields would represent physical states as "wave functions". Configuration space gamma matrices would be superpositions of fermionic oscillator operators so tha also fermions are geometrized. The mere existence of WCW Kaehler geometry requires maximal isometries and this fixes TGD highly uniquely. Freed realize the uniqueness for loop spaces.
</OL>
How to realize the crucial preferred extremal property making initial value problem equivalent with boundary value problem?
<OL>
<LI> Here the maximal isometry group of WCW enter the game. The symmetry algebra is replaced with an analog of infinite-D symplectic algebra acting as isometries of WCW induced from symplectic transformations at delta M<sup>4</sup><sub>+</sub>xCP<sub>2</sub> labelled by integer valued conformal weights assignable to the radial light-like coordinate of light-cone bounary δM<sup>4</sup><sub>+</sub> defining second boundary of causal diamond cd identified as the intersection of future and past directed light-cones.
<LI> The crucial point is that this algebra - call it A - has fractal hierarchy of sub-algebras A<sub>n</sub> with conformal weights coming as multiples of n=1,2,... which very probably corresponds to a hierarchy of hyper-finite factors of type II<sub>1</sub> forming inclusion hierarchies labelled by sequences ...n<sub>1</sub> divides n<sub>2</sub> divides....
<LI> Infinite-D sub-algebra A<sub>n</sub> appears would have vanishing classical Noether charges in the class of preferred extremals associated with A<sub>n</sub>. Also [A<sub>n</sub>,A] would have the same property.This is like posing the condition that analogous sub-algebra of say Kac-Moody algebra annilates physical states. The space-time surfaces in question would be minimal surfaces satisfying the additional condition that they extremize also what I call Kaehler action, and being analogous to Maxwell action.
</OL>
</p><p>
See the article <A HREF="http://tgdtheory.fi/public_html/articles/zeoquestions.pdf">Some comments related to Zero Energy Ontology (ZEO)</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com6tag:blogger.com,1999:blog-10614348.post-10862239728163517412020-06-29T22:57:00.002-07:002020-06-29T23:35:10.670-07:00New support for TGD view about quantum tunnellingThere is a popular article in Phys.org describing a <A HREF="https://phys.org/news/2020-06-physicists-surprisingly-strong-high-nanogaps.html">highly interesting finding</A> made by condensed matter physicist Doug Natelson and his colleagues at Rice and the University of Colorado Boulder. Light emission associated with the tunnelling of electrons through a nano-scaled potential barrier between Gold electrodes has been observed. The intensity of emission is larger by factor 10,000 than predicted and this suggests new physics.
</p><p>
By definition tunnelling means that electrons get through the potential barrier without getting energy - classical picture would require this. Now it however seems that electron receives energy and the higher the barrier the larger energy is needed. Should one challenge the notion of tunnelling? Could it have a classical counterpart?
</p><p>
In TGD framework all quantum phenomena should have classical counterparts, also tunnelling. Therefore the tunnelling electron would actually get energy to get over the potential barrier classically.
<OL>
<LI> In zero energy ontology (ZEO) solving the basic problem of quantum measurement theory quantum states are superpositions of deterministic classical time evolutions, preferred extremals. Classical physics is exact part of quantum theory. The key prediction is that in ordinary, "big", state function reductions (BSFRs) the arrow of time is changed. In small SFRs (SSFRs) - analogs of weak measurements - this does not happen. ZEO leads to a theory of self-organization in which energy feed to self-organizing system corresponds to dissipation for time reversed state associated with dissipating system.
<LI> Tunnelling could mean in TGD framework that electrons make a BSFR reversing the arrow of time. In time reversed state they dissipate in reverse time direction: in standard time direction of observer they receive energy in standard time direction allowing them to get over the potential barrier. In the second BSFR establishing the original arrow of time they would liberate the energy and the higher the barrier, the larger the liberated energy and the brighter the light emission. The tunnelling in this sense would be already self-organization phenomenon involving BSFR. This dynamical tunnelling does not exclude the analog of wave-mechanical tunnelling as a non-dynamical process. The dynamical tunnelling could actually lead to asymptotic states in which particle is at both sides of the forbidden region or even in forbidden region but with extraction of classical energy from environment so high that this is not forbidden anymore.
</OL>
For ZEO see the article <A HREF="http://tgdtheory.fi/public_html/articles/zeoquestions.pdf">Some comments related to Zero Energy Ontology (ZEO)</A>. For TGD view about tunnelling in nuclear reactions see <A HREF="http://tgdtheory.fi/public_html/articles/darkcore.pdf">Solar Metallicity Problem from TGD Perspective</A>
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-30877643324349741002020-06-27T02:52:00.010-07:002020-06-29T02:36:11.161-07:00New ideas about the transition to ferromagnetic phase
I received a link to a highly interesting <A HREF =" https://www.quantamagazine.org/a-childs-puzzle-has-helped-unlock-the-secrets-of-magnetism-20190124">article</A> about ferromagnetism</A>. According to the article, Yi Li, a physicist working at John Hopkins University and his two graduate students, Eric Bobrow and Keaton Stubis, seem to have made a considerable progress in understanding how the system of electron spins in lattice ends up to a ferromagnetic sate. This ferromagnetism is known as itinerant ferromagnetism and involves vacancies, sites without electron, which can be moved freely without affecting the energy of the state.
</p><p>
<B> 1. The ideas related to the work of Li et al</B>
</p><p>
The problem considered by Li et al how the ferromagnetic state could emerge from an arbitrary state with some numbers of spin up and spin down states at lattice sites connected by edges.
<OL>
<LI> Permutation of electrons with same spin leave the ferromagnetic state invariant and does not cost energy while permutations in arbitrary configuration can do so.
<LI> Li et al considered a simple 4× 4 lattice with single vacancy and noticed a connection with so called 15-puzzle involving 15 tiles and single vacancy with neighboring tiles of vacancy able to move to its position. The observation is following. If one has spin lattice containing single vacancy, one can number the sites by a number running from 1 to N (now 15) in arbitrary manner. If so called connectedness condition holds true one can realize any permutation of these numbers. This means that 15-puzzle has always a solution. In particular, one can arrange the situation that the numbers form an ordered sequence from 1 to N so that numbers n and n+1 are nearest neighbors.
</p><p>
The result found by Li et al first for 2-D 4× 4 lattice with single vacancy generalizes to lattices, which are non-separable in the sense the removal of a lattice site does not separate any pair of spins - they are still connected by an edge-loop.
<LI> The curve solving the 15-puzzle goes through all points of the 4× 4 lattice and is generally known as Hamiltonian curve. It becomes Hamiltonian cycle if the numbers 1 and N are nearest neighbors.
<LI> The basic problem of this approach is that the theorem is true only for single vacancy and does not allow generalization to a larger number of vacancies. It is however known that ferromagnetism is possible up to fraction 1/3 for vacancies. The challenge is to generalize the result of Li et al.
</OL>
</p><p>
<B> 2. Some reasons to get interested</B>
</p><p>
In TGD framework there are good reasons of getting interested on these results.
<OL>
<LI> The result of Li et al states that ferromagnetic phase transition might be understood in terms of shifting of lattice vacancy if the lattice with single defect allows deformaton of any configuration of spin labelled by numbers n running from 1 to N to a closed curve connecting nearest neighbors along which n increases. Could there be a connection with Hamiltonian curves making sense for lattice like structures (actually all graphs)? Could Hamiltonian curve have some deeper physical meaning or is it only an auxialiary notion useful for representing the possibility to realize all points of the lattice with vacancy by shifting it suitably?
</p><p>
Hamiltonian curve connects neighboring points of a lattice and goes through all points without self-intersections. Icosahedral geometry appears in biology and one can ask whether this kind of cycles could be actually realized physically - say as flux tubes at icosahedron and tetrahedron, which play key role in TGD inspired biology. Flux tube are actually fundamental objects in TGD Universe in all scales. For instance, final states of stars could correspond to flux tube spaghettis consisting of single volume filling flux tube (see <A HREF ="http://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>).
<LI> If the Hamiltonian cycle is something physical it could correspond to flux tube. The notion of magnetic flux tube central in TGD might allow application to ferromagnetism. TGD predicts two kinds of flux tubes: Maxwellian ones and monopole flux tubes with magnetic fields requiring no currents to generate them: they are not not allowed by Maxwell's theory.
</p><p>
The preservation of the Earth's magnetic field predicted to decay rather rapidly as currents generating it dissipate supports the view that it contains monopole flux part which from biological input would correspond to endogenous magnetic field B<sub>end</sub>, which is a fraction 2/5 about the nominal value of B<sub>E</sub>=.5 Gauss. The presence of magnetic fields in cosmological scales is also a mystery finding a solution in terms of monopole flux tubes.
<LI> Monopole flux tubes must be closed. Closed non-intersecting flux tubes connecting nearest neighbors in lattice would correspond to Hamiltonian cycles. In TGD inspired biology Hamiltonian cycles associated with icosahedron and tetrahedron provide a realization of the vertebrate genetic code (see <A HREF="http://tgdtheory.fi/public<sub>h</sub>tml/articles/harmonytheory.pdf">this</A>) but it is still somewhat of mystery why the points of icosahedron and tetrahedron, which are lattices (tesselations) at sphere, would be connected by a curve. Quantum classical correspondence suggests that magnetization corresponds to flux tubes connecting magnetic dipoles as formal analogs of monopole-antimonopole pairs. Could magnetic flux tubes provide a concrete realizaon for these Hamiltonan cycles?
<LI> Closed monopole flux tubes seem to be unrealistic for the description of ferromagnetism, which suggests the presence of N parallel flux tubes carrying magnetization M and defining a braid connecting opposite ends of ferromagnet. The monopole fluxes could arrive as single flux along parallel space-time sheet carrying field H defined by single thick flux tube. Test particle would experience B= M+H.
</OL>
</p><p>
The following considerations are not much more than first impressions and probably require updating.
</p><p>
<B>3. TGD based view</B>
</p><p>
Flux tubes are the new element of condensed matter physics predicted by TGD. Could they provide insights into ferromagnetism?
</p><p>
<B> 3.1 Starting from text book picture about ferromagnetism</B>
</p><p>
To develop TG view about ferromagnetism it is best to start from the text book picture.
<OL>
<LI> In the standard model of ferromagnetism one assumes the presence of field B identified as sum B= M+H of magnetization and field H equal to B outside the magnet. M is due to magnetic dipoles besides magnetic field B and the interaction of spins with H is important. B is usually regarded as the fundamental field M and and H appear as auxiliary notions and their relation to B requires a model for the system: typically H, B, and B are assumed to be linearly related.
<LI>The field M could be naturally assigned with a flux tube connecting the spins - perhaps at nearest neighbor lattice points. What about H? In standard model H and B are parallel for the ferromagnetic configuration. If B is assigned with the flux tube connecting the magnetic moments and B is parallel to H, this would suggest a flux tube consisting of long straight portions parallel to each other.
</p><p>
In the many-sheeted space-time of TGD M and B can reside at different space-time sheets, which are parallel so that they are on top of each other in M<sup>4</sup>×CP<sub>2</sub>. The decomposition to sum would have representation as a set theoretic union.
</p><p>
The test particle would experience the sum of the magnetic fields associated with the two sheets. Could M and H as the return flux associated with M and superpositing with the external contribution to H correspond to these two space-time sheets so that particle would experience their sum B=M+H? If so, ferromagnetism could be seen as a direct signature of many-sheeted space-time.
</OL>
</p><p>
<B> 3.2 Could also monopole flux tubes be important?</B>
</p><p>
There is still one important aspect related to the TGD view about magnetic field which might play important role. TGD predicts two kind of flux tubes. The first kind of flux tubes could be called Maxwellian and the corresponding magnetic fields require current to generate them. There are also flux tubes having closed cross section and carrying monopole fluxes. No currents are required to generate corresponding magnetic fields. Could also these flux tubes having no current as sources be present? This would mean new physics.
<OL>
<LI>The first thing to notice is that the interpretation of magnetization M is as a magnetic field generated by magnetic moments. The usual interpretation is that spins are analogous to magnetic moments created by currents consisting of rotating charge. Now there is no such rotating charge. Second interpretation is as magnetic moments identifiable as infinitesimal monopole pairs.
<LI> Could one think that the flux tubes containing sequence magnetic moments correspond to monopole flux and that closing this loop could give rise to monopole magnetic field? Ordinary Maxwellian part could be also present and have current as source. How M and H would relate to these. Could M correspond to the monopole part and H the Maxwellian part?
</p><p>
Are spins necessary for the existence of a monopole flux tube? Could quantum classical correspondence require this? Could dark charged matter assigned with the monopole flux tubes correspond to the magnetic moments of say dark valence electrons with non-standard value of h<sub></sub> so that M would be represented by monopole flux tubes classically? If the return flux represented by H is absent, flux tube must give rise to a Hamiltonian cycle. If H is present, it would be enough to have flux tubes representing N braid strands fusing to single monopole flux carrying the return flux.
</p><p>
Formation of a flux loop defining Hamiltonian cycle would be a new kind of phenomenon analogous to spontaneous magnetization requiring no external field H. Spontaneous magnetization would be however something different. A trivial braid consisting of N parallel strands representing M and parallel to it locally with return flux arriving along single large flux tube carrying H would be formed in ferromagnetic transition and also in spontaneous magnetization.
</OL>
</p><p>
<B> 3.3 Bringing in thermodynamics</B>
</p><p>
One can try to make this more concrete by bringing in thermodynamics.
<OL>
<LI> Assume that there exists single flux tube - connecting all the lattice points (magnetic moments) or possibly N flux tubes parallel to local magnetization M and giving rise to a braid like structure representing the topology of flux lines of M connecting opposite boundaries of magnet.
<LI> In the general case, the points of the lattice could be connected by a flux tubes connecting points, which need not be nearest neighbors. The first guess is that the magnetic interaction energy of spins at the ends of the flux tube portion connecting them decreases with the distance between spins. There sould be also magnetic energy associated with the field H at the space-time sheet carrying the return flux. Thermodynamics would bring in entropy and free energy F=E-TS would be mimimized. Entropy maximization would favor long random flux tubes and energy minimization short flux tubes.
</p><p>
One expects that flux tube has free energy F increasing with flux tube length. If one does not allow self-intersections - as suggested by repulsive Coulomb interaction and Fermi statistics - the flux tube could be either Hamiltonian cycle or consist of analogs of braid strands: in the case of ferromagnetism the strands would be parallel to each other. The interacton energy would be same for all Hamiltonian cycles if determined by nearest neighbour interactions.
<LI> In the general case with lattice replaced by graph one expects that a large number of Hamiltonian cycles not related by rotation to each other exists so that one would have large number of states with same minimum energy. Could this somehow correspond to spin glass state allowing large number of degenerate states? The flux tube need not be closed. In ferromagnetic configuration this would be the case.
<LI> How would the assignment of spin direction to the lattice points affect the situation? Could the numbers N<sub>+</sub> and N<sub>-</sub> of spin up and spin down electrons determine the flux tube configuration by (Gibbs) energy minimization?
</OL>
</p><p>
<B> 3.4 Could 2-braid describe the transition to ferromagnetism?</B>
</p><p>
In the work of Li et al discussed in the article, the permutations of lattice points are induced by moving the vacancy around. This picture inspired the considerations above but is too limited. In fact the work of Li et al only directed attention to Hamiltonian cycles and braids formed by the non-closed analogs.
<OL>
<LI> TGD picture brings in mind braid-knot connection. One can replace braid assiciated with M with a knot by connecting the magnetic moments at the opposite ends of the braid by trands of a trivial braid at parallel space-time sheet. This trivial braid would carry the return flux having interpretation in terms of field H.
</p><p>
The flux tubes of trivial braid could also fuse to single thicker flux tube carrying the total return flux associated with M. This would conform with the idea that H provides a description of the system in longer length scale being analogous to a smoothed out total magnetic field acting as self-consistent background.
</p><p>
This stimulates a critical question. Could one assume that only H assignable to big flux tube has constant direction and magnitude and that M is represented as flux tubes connecting dipoles can in principle correspond to any permutation of atoms. For this option the spontaneous magnetization would correspond to a superposition of different configurations with same weights and would be invariant under permutations as in the argument of Li et al involving no flux tubes. This option does not look attractive.
<LI> What braid picture allows to say about the transition to ferromagnetism? Could the transition be realized by deforming the flux tubes associated with M and forming a non-trivial braid be induced by permutation of the lattice points taking the non-trivial braid to trivial one? This would be like opening the braid. The lattice points in the initial and final state would correspond to the ends of a dynamical evolution. The permutation would be realized as a time-like braiding with braid strands in time direction.
</p><p>
Mathematically braid group corresponds to the covering group of permutation group and quantum group representations correspond to the representations of braid groups. The description of the transition could provide a new application of quantum groups.
</OL>
The description as time-like braiding is not however complete since there isan additional structure involved: the flux tubes connecting the magnetic dipoles in lattice and defining a braid or even more complex configuration having flux tube connections between non-neighboring poins.
<OL>
<LI> If there is no return flux assignable to H, M corresponds to a closed flux tube carrying monopole flux the dynamical time-like dynamcial braiding would lead to a Hamiltonian cycle in this case and the number of final state configurations would be finite, there is degeneracy. Could spin glass phase correspond to this situation?
<LI> In ferromagnetism final state would contain N parallel strands carrying the monopole flux assignable to M and the return flux H would arrive along parallel thick flux tube. In general configuration these strands can be braided. The transition to ferromagnetism would represent time-like braiding of an ordinary 3-D braiding of flux tube strands connecting the opposite boundaries of ferromagnetic. In the initial state braid would be non-trivial and the flux tubes of braid would not have minimal length and minimum energy. In the the final ferromagnetic state braid would be trivial with parallel flux tubes.
</p><p>
Mathematically this process would correspond to what is called 2-braiding: I have proposed that 2-braidings are important in TGD inspired biology as a topological description of dynamical processes. An interesting interpretation is as a topological analog for problem solving. I have also proposed that in biosystems topological quantum computation programs are represented as this kind 2-braidings for flux tubes (see <A HREF="http://tgdtheory.fi/pdfpool/dnatqc.pdf">this</A> and <A HREF="http://tgdtheory.fi/pdfpool/dnatqccodes.pdf">this</A>.)
</p><p>
Ferromagnetism would correspond to an opening of a non-trivial braid. If the return flux arrives along flux tubes this is possible smoothly only if the knot defined in this manner is trivial. To achieve opening, the 2-braiding must involve reconnections, which correspond to cutting the knot strand and reconnecting the pieces in new manner: this is how Alexander opened his knot. Fermi statistics and repulsive Coulomb interaction do not fabour this mechanism. If the return flux arrives along single flux tube, the opening could correspond to a smooth deformation without reconnections transferring the braidedness to the parallel space-time sheet, where it is "neutralized" by fusing the flux tubes to single flux tube.
</OL>
See the article <a HREF= "http://tgdtheory.fi/public_html/articles/ferromagn.pdf">TGD based view about ferromagnetism</A> or the chapter <a HREF= "http://tgdtheory.fi/pdfpool/qcritdark1.pdf">Quantum criticality and dark matter: part I</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-65286346187012552692020-06-25T20:05:00.001-07:002020-06-25T20:05:15.000-07:00Planning to move to Mars?: have you asked the opinion of your magnetic body?
There has been a lot of talk about the colonization of Mars. I was asked about possible problems involved. In the following I consider the question only from TGD point of view about life.
</p><p>
The new element of TGD based quantum biology is the notion of magnetic body carrying dark matter as phases of ordinary matter labelled by the effective value h<sub>eff</sub> =nh<sub>0</sub> of Planck constant (h= 6h<sub>0</sub> is a good guess). MB is the boss controlling ordinary matter by using dark photons transforming to ordinary photon and vice versa. Actually one has hierarchy of values of h<sub>eff</sub> and master slave hierarchy.
</p><p>
Cyclotron frequencies and generalize Josephson frequencies are in a central roles in the communications between MB and biological body relying on frequency and energy resonance if the values of h<sub>eff</sub> are identical or only energy resonance if they are not same.
</p><p>
Frequencies are thus fundamental for the control level of life and the question is whether MB can adapt and change its frequency spectrum. Also Schumann frequency is known to be important for life and in Mars its scae 2 times that in Earth. These problems might make already the travel to Mars dangerous to say nothing about living there.
</p><p>
<B>1. Cyclotron frequencies and Schumann frequencies</B>
</p><p>
On basis of findings done already at seventies about unexpected effects of ELF em fields on vertebrate brain, EEG resonances seem correspond to cyclotron frequencies in endogeneous magnetic field of B<sub>end</sub>=.2 Gauss which is 2/5 of the nominal value B<sub>E</sub>=.5 Gauss of Earth's magnetic field. A possible interpretation is that B<sub>end</sub> corresponds to field strength for the monopole flux part of B<sub>E</sub>. It is stable against dissipation since no current is needed to create it unlike ordinary Maxwellian magnetic field. This explains why B<sub>E</sub> has not decayed away long time ago by the decay of the current creating it.
</p><p>
Cyclotron frequencies are in a key role in TGD based quantum biology. The value spectrum of h<sub>eff</sub> determining bio-photon energies is in central role: dark photon energies are given by E=h<sub>eff</sub>×f.
</p><p>
The cyclotron energy spectrum in Earth would be in bio-photon range (visible and UV) and same for all charged particles - there is no dependence on mass of charged particle since one has hbar<sub>eff</sub>= hbar<sub>gr</sub>= GMm/v<sub>0</sub> at gravitational flux tubes. hbar<sub>gr</sub>= GMm/v<sub>0</sub> is gravitational Planck constant fundamental introduced first by Nottale. v<sub>0</sub> is velocity parameter with value about v<sub>0</sub>/c= 2<sup>-11</sup> in the case of Sun. It might relate to the parameters of the system but could be also almost universal parameter (it is near electron proton mass ratio).
</p><p>
The cyclotron energy spectrum in Earth would be in bio-photon range and same for all charged partcles - there is no dependence on mass since one has hbar<sub>eff</sub>= hbar<sub>gr</sub>= GMm/v<sub>0</sub> at what I call gravitational flux tubes. This would make possible the control of molecular transitions by transforming dark photons to visible and UV photons first. MB could control molecular transitions and act as "boss". Quite generally, the layers of MB with different values of h<sub>eff</sub> would form a master slave hierarchy with ordinary biomatter at bottom.
</p><p>
Schumann resonances correspond to resonance frequencies for the radiation fields of Earth. In the approximation that the conductivity of the medium is infinite, the wavelengths depend on the radius R<sub>E</sub> of Earth only. Lowest wavelength corresponds in good approximation to lambda= 2πR<sub>E</sub>. Lowest Schumann frequency has nominal value 7.8 Hz. These frequencies are in EEG range.
</p><p>
<B> Remark:</B> I remember having read in some source that 10 Hz frequency corresponding to alpha band in brain is needed in space and is produced artificially. I could not find the original source.
</p><p>
<B>2. Coupling between Schumann frequencies and cyclotron frequencies</B>
<OL>
<LI> Schumann frequencies are is in the range of EEG frequencies, which strongly suggests resonant coupling with the cyclotron transitions corresponding to frequencies near to Schumann frequencies.
<LI> For instance, the cyclotron frequency 7.5 Hz for K<sup>+</sup> ions is near to the nominal value 7.8 Hz of the lowest Schumann frequency. K<sup>+</sup> currents through K<sup>+</sup> channels cell membrane are known to be important for what happens in anesthesia and when organism falls asleep and thus for consciousness.
</p><p>
What happens when organism falls asleep is of course not quite clear. The membrane voltage increases and nerve pulse generation becomes improbable. Metabolism continues and this means consciousness in TG framework but not sensory and motor consciousness. Could the apparent loss of consciousness mean fusion of self with higher level self representing the collecting consciousness of magnetic Mother Gaia? Could it be that during sleep we could form a larger collective consciousness representing "human condition" (see <A HREF="http://tgdtheory.fi/public<sub>html</sub>/articles/anesthesianewest.pdf">this</A>) .
<LI> Irradiaton by frequency around 7 Hz is also necessary in the experiments of HIV Nobelist Montagnier involve remote DNA replication (see <A HREF="http://tgdtheory.fi/pdfpool/remotereplication.pdf">this</A>) and <A HREF="http://tgdtheory.fi/public<sub>html</sub>/articles/darkdnanew.pdf">this</A>) .
<LI> Irradiation by Schumann frequency around 60 Hz appears leads to healing of cancer cell population in lab (see <A HREF="http://tgdtheory.fi/public<sub>html</sub>/articles/nanotesla.pdf">this</A>) .
<LI> Also higher Schumann resonances could represent resonant coupling between Mother Gaia and brains of vertebrates allowing realization of levels of collective consciousness. Coherent collective gene expression in various scales (organ, organism, group, population,...) is one of the possible testable implication.
</OL>
<B> 3. Possible problems related to different values of magnetic fields in Earth and Mars</B>
</p><p>
The first problem relates to the magnetic field of Mars. Martian magnetic field has been believed to be weak but the recent findings suggests that it might be present and order of magnitude as in Earth (see <A HREF="http://tgdtheory.fi/public<sub>html</sub>/articles/Mars.pdf">this</A>) .
<OL>
<LI> TGD based view about life requires B<sub>end</sub> which could be monopole part of B<sub>E</sub>. Flux tubes can carry monopole flux or not - the latter option is realized in the case of ordinary Maxwellian magnetic field. Monopole flux would be biologically important and it would be in Earth 2/5 of total flux. It could be of course different in Mars. Different value of B<sub>end</sub> in Mars could lead to severe difficulties since cyclotron frequencies are in a key role in TGD based quantum biology.
<LI> Also the value spectrum of hbar<sub>gr</sub>= GMm/v<sub>0</sub> determining biophoton energies is in central role: one has for energies E=h<sub>eff</sub>×f. In Mars the mass parameter M and velocity parameter v<sub>0</sub> in h<sub>gr</sub> could be different and this could have fatal consequences for bio-control by the magnetic body of earthly biosystems.
<OL>
<LI> In the case of Earth M seems to correspond to the mass of "inner inner core" of Earth. If M is same for Mars (planets would be like atoms having varying number of identical "shells"), then it would be enough to have same value B/v<sub>0</sub> to keep the spectrum same. The value of B is under control by varying the flux tube thickness and this control mechanism would be used in terrestial biology.
<LI> The optimistic guess is that v<sub>0</sub> has universal spectrum and the value is same in Mars and Earth. A not necessarily good guess is that the velocity v<sub>0</sub> scales like the rotation frequency of planet. Here we would have good luck! The Martian day has essentially the same length as day in Earth. The value of v<sub>0</sub> would be same! In this case hbar<sub>gr</sub> could be the same! Sounds too optimistic!
<LI> One can imagine also second option. The strength of monopole flux magnetic field B<sub>end</sub> =.2 Gauss at flux tubes is free parameter and magnetic bodies could vary its value by varying thickness of flux tubes: this would be a basic biological control mechanism for instance in water and allow water to develop antennas sensitive to the cyclotron frequencies of invader molecules and detect them: this would be water memory and basis of the immune system.
</OL>
</p><p>
<B> 4. Problems related to different Schumann frequencies</B>
</p><p>
Schumann frequency scale in Mars is roughly twice that in Earth since radius is about 2 times smaller: around 15.6 Hz instead of 7.8 Hz for lowest Schumann frequency. Schumann frequency is known to be important for us although this is not well-understood. This might cause severe problems.
</p><p>
The scaling of Schumann frequencies by 2 might cause bad complications but we do not really understand their effect even in Earth.
</p><p>
We of course do not have thorough knowledge about B in Mars. There are auroras but earlier it was believed that magnetic field in large scales is very small.The latest findings suggest in TGD framework that there is monopole flux tube part of order B<sub>end</sub> (see <A HREF ="http://tgdtheory.fi/public<sub>html</sub>/articles/Mars.pdf">this</A>).
</p><p>
One can consider a possible solution to Schumann frequency doubling problem. Scale also the cyclotron frequencies by factor 2!
<OL>
<LI> At Earth the lowest Schumann frequency 7.8 Hz corresponds to cyclotron frequency 7.5 Hz of K<sup>+</sup> ion quite well and this might make possible resonant coupling between Mother Gaia and magnetic bodies of living system. If the B<sub>end</sub>=.2 Gauss is scaled by factor 2 in Mars to about .4 Gauss, cyclotron frequency scale doubles and one would have 15 Hz cyclotron frequency for K<sup>+</sup> not far from Schumann.
<LI> Could human MB scale up the cyclotron frequencies by factor 2? Note that TGD based model for Cambrian explosion (see <A HREF="http://tgdtheory.fi/public<sub>html</sub>/articles/expearth.pdf">this</A>) predicts that Schumann frequency doubled in geologically short time scale (extremely long from human perspective). The lifeforms that would have bursted from underground oceans to the surface survived this transition. One could test what happens if artificially produced counterpart of Schumann frequency is doubled in artificial conditions using Faraday cage.
</OL>
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-73494441263132703242020-06-24T20:25:00.001-07:002020-06-24T20:25:40.327-07:00Schumann resonances and consciousnessThe role of Schumann resonances for consciousness is highly interesting in TGD framework, where the notion of magnetic body (MB) carrying dark matter as h<sub>e</sub>ff=n*h<sub>0</sub> phases is in key role. MB would control biological body by dark photons - probably at cyclotron frequencies - and receive information as dark generalized Josephson radiation from cell membrane with the modulation of membrane potential inducing frequency modulation coding for the sensory data (see <A HREF="http://tgdtheory.fi/pdfpool/pulse.pdf">this </A>) .
</p><p>
On basis of findings done already at seventies about unexpected effects of ELF em fields on vertebrate brain, EEG resonances seem correspond to cyclotron frequencies in endogeneous magnetic field of B<sub>e</sub>nd=.2 Gauss which is 2/5 of the nominal value B<sub>E</sub>=.5 Gauss of Earth's magnetic field. A possible interpretation is that B<sub>e</sub>nd corresponds to field strength for the monopole flux part of B<sub>E</sub>. It is stable against dissipation since no current is needed to create it unlike ordinary Maxwellian magnetic field. This explains why B<sub>E</sub> has not decayed away long time ago by the decay of the current creating it.
</p><p>
Cyclotron frequencies are in a key role in TGD based quantum biology. The value spectrum of h<sub>e</sub>ff determining bio-photon energies is in central role: dark photon energies are given by E=h<sub>e</sub>ff*f. The cyclotron energy spectrum in Earth would be in bio-photon range (visible and UV) and same for all charged particles - no dependence on mass since one has hbar<sub>e</sub>ff= hbar<sub>g</sub>r= GMm/v<sub>0</sub> at what I call gravitational flux tubes. This would make possible for MB to control molecular transitions and act as "boss". Quite generally, the layers of MB with different values of h<sub>e</sub>ff would form a master slave hierarchy with ordinary biomatter at bottom.
<OL>
<LI> Schumann frequencies are is in the range of EEG frequencies, which strongly suggests resonant coupling with the cyclotron transitions corresponding to frequencies near to Schumann frequencies.
<LI> For instance, the cyclotron frequency 7.5 Hz for K<sup>+</sup> ions is near to the nominal value 7.8 Hz of the lowest Schumann frequency. K<sup>+</sup> currents through K<sup>+</sup> channels cell membrane are known to be important for what happens in anesthesia and when organism falls asleep and thus for consciousness.
</p><p>
What happens when organism falls asleep is of course not quite clear. The membrane voltage increases and nerve pulse generation becomes improbable. Metabolism continues and this means consciousness in TG framework but not sensory and motor consciousness. Could the apparent loss of consciousness mean fusion of self with higher level self representing the collecting consciousness of magnetic Mother Gaia? Could it be that during sleep we could form a larger collective consciousness representing "human condition" (see <A HREF="http://tgdtheory.fi/.public_html/articles/anesthesianewest.pdf">this</A>) .
<LI> Irradiaton by frequency around 7 Hz is also necessary in the experiments of HIV Nobelist Montagnier involve remote DNA replication. See (see <A HREF="http://tgdtheory.fi/pdfpool/remotereplication.pdf">this </A> and <A HREF="http://tgdtheory.fi/.public_html/articles/darkdnanew.pdf">this</A>) .
<LI> Irradiation by Schumann frequency around 60 Hz appears leads to healing of cancer cell population in lab (see <A HREF="http://tgdtheory.fi/.public_html/articles/nanotesla.pdf">this</A>) .
<LI> Also higher Schumann resonances could represent resonant coupling between Mother Gaia and brains of vertebrates allowing realization of levels of collective consciousness. Coherent collective gene expression in various scales (organ, organism, group, population,...) is one of the possible testable implications.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-32671856819789897302020-06-22T20:01:00.001-07:002020-06-22T20:01:59.137-07:00Has Pluto experienced a period of fast expansion?
The <A HREF="https://www.space.com/pluto-hot-formation-subsurface-ocean.html">surprise of this morning</A> was that Pluto seems to have experienced a rapid expansion and might have had underground oceans.
</p><p>
Actually not a surprise if one lives in TGD Universe. TGD predicts that all astrophysical objects, including planets, might have experienced this kind of periods. In general relativity these periods would correspond smooth cosmological expansion of this objects: the absence this smooth expansion is indeed an enigma - astrophysical objects co-move with expanion in large scale but do not expand themselves. Earth would have experienced this expansion during Cambrian explosion.
</p><p>
The underground oceans would make possible evolution of life without problems from cosmic rays and meteorites and radioactivity (for instance) could provide the metabolic energy.
</p><p>
This would solve Fermi's paradox: most planets could be carriers of intraplanetary invisible-to-outsider life waiting the next fast expansion and burst to the surface of the planet.
</p><p>
See http://tgdtheory.fi/public_html/articles/expearth.pdf .
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-76929509974680918772020-06-21T21:10:00.000-07:002020-06-21T21:10:08.661-07:00New evidence for two values of Hubble constant
Sabine Hossenfelder tells about a further evidence for the Hubble constant discrepancy and refers to this
<A HREF="https://public.nrao.edu/news/challenge-model-of-universe/">popular article </A> discussing new kind of local measurements independent of other measurements also giving 10 per cent higher value than the value deduce from CMB measurements in much longer scales.
</p><p>
In the many-sheeted cosmology of TGD the cosmic parameters are length scale dependent. The natural guess is that the two measurements could correspond to sHubble constant in different p-adic length scales. The naive dimensional guess based inspired by the p-adic length scale hypothesis would suggest that Hubble constant could come as half octaves. The ratio of the two values is however around .1 much nearer to unity than 2<sup>-1/2</sup>≈.71.
</p><p>
Some time there was a popular article about a possible explanation of Hubble constant discrepancy (see <A HREF="http://tinyurl.com/yd783ow6">this</A>). The article told about a proposal of Lucas Lombriser discussed in the article <I>Consistency of the local Hubble constant with the cosmic microwave background</I> (see <A HREF="http://tinyurl.com/ycd4aenh">this</A>) for an explanation of this discrepancy. The proposal is that the local region around our galaxy having size of order few hundred Mly - this is the scale of the large voids forming a honeycomb like structure containing galaxies at their boundaries - has average density of the matter 1/2 of that elsewhere.
</p><p>
This would fit nicely with the TGD picture. I do not bother to repeat the argument given in the earlier <A HREF="https://matpitka.blogspot.com/2020/04/a-solution-of-hubble-constant.html"> blog posting</A>. The point is that in TGD the string tension of magnetic flux tubes comes by p-adic length scale hypothesis in powers of 2. The density of matter is generated by the decay of matter and energy of cosmic string like objects to ordinary matter as they thicken to flux tubes. If the string tension of local void is by a factor 1/2 smaller than for a typical void, the density of ordinary matter would be smaller by this factor. One could say that local void would be a forerunner in cosmic evolution. This is of cousre highly interesting from the persperctive of biological evolution, in particular Fermi paradox).
</p><p>
To sum up, this model would rely on the prediction that there are two kinds of flux tubes and that the cosmic evolution proceeds by phase transitions increasing p-adic length scale by half octave reducing the energy density by factor 1/2 at flux tubes. The local void would be one step further in cosmic evolution as compared to a typical void.
</p><p>
See the article <a HREF= "http://tgdtheory.fi/public_html/articles/twohubblenew.pdf">The problem of two Hubble constants</A> or the chapter <a HREF= "http://tgdtheory.fi/pdfpool/cosmomore.pdf">More about TGD and Cosmology</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-58030665400763185192020-06-18T07:10:00.001-07:002020-06-18T07:10:35.437-07:00How are the space-time surfaces assignable to the opposite boundaries of CD glued together?<B>How do the solutions assignable to the opposite boundaries of CD relate to each other?</B>
</p><p>
Causal diamond identified basically as intersection of future and past directed light-cones is basic notion in zero energy ontology. It has 4-D variant cd<sub>4</sub>, 8-D Minkowski variant cd<sub>8</sub>, and H=M<sup>4</sup>× CP<sub>2</sub>-variant CD= cd<sub>4</sub>× CP<sub>2</sub>.
</p><p>
Space-time surfaces in M<sup<8</sup> picture are defined as roots for "real" or "imaginary" part of complexified octonion valued polynomial obtained by algebraically continuing first real valued polynomial with rational coefficients to complex valued polynomial by replacing real argument with complex argument $z$ commuting with octonions and then perfoming continuation to complexified octonion valued polynomial. One can continue at first step to a polynomial of z or of z** and complex conjugation has interpretation as particle- antiparticle conjugation.
</p><p>
To construct the solutions to the polynomial equations one must consider the equations near both boundaries of CD and glue them together smoothly. I have not consider this problem earlier. In principle, the polynomials associated with them could be different in the general formulation discussed in but they could be also same (see <A HREF="http://tgdtheory.fi/public_html/articles/chaostgd.pdf">this</A> and <A HREF="http://tgdtheory.fi/public_html/articles/SSFRGalois.pdf">this</A>). How are the solutions associated with opposite boundaries of CD glued together in a continuous manner?
<OL>
<LI> The polynomials assignable to the opposite boundaries of CD are allowed to be polynomials of o <I> resp.</I> (o-T): here T is the distance between the tips of CD.
<LI >CD brings in mind the realization of conformal invariance at sphere: the two hemispheres correspond to powers of z and 1/z: the condition z*= 1/z at unit circle is essential and there is no real conjugation. How the sphere is replaced with 8-D CD which is also complexified. The absence of conjugation looks natural also now: could CD contain a 3-surface analogous to the unit circle of sphere at which the analog of z*= 1/z holds true? If so, one has P(o,z)=P(1/o,z) and the solutions representing roots fo P(o,z) and P(1/o,z) can be glued together.
</p><p>
Note that 1/o can be expressed as o*/oo* when the Minkowskian norm squared oo* is non-vanishing and one has polynomial equation also now. This condition is true outside the boundary of 8-D light-cone, in particular near the upper boundary of CD.
</p><p>
The counter part for the length squared of octonion in Minkowskian signature is light-one proper time coordinate a<sup>2</sup>=t<sup>2</sup>-r<sup>2</sup> for M<sup>8</sup><sub>+</sub>. Replacing o which scaled dimensionless variable o<sub>1</sub>= o/(T/2) the gluing take place along a=T/2 hyperboloid.
</OL>
One has algebraic holomorphy with respect to o but also anti-holomorphy with respect to o is possible. What could these two options correspond to? Could the space-time surfaces assignable to self and its time-reversal relate by octonionic conjugation o→o* relating two Fock vacuums annihilated by fermionic annihilation <I> resp.</I> creation operators?
</p><p>
See the article <A HREF="http://tgdtheory.fi/public_html/articles/paddarkscales.pdf">About M<sup>8</sup>-H-duality, p-adic length scale hypothesis and dark matter hierarchy</A> or the chapter <A HREF="http://tgdtheory.fi/pdfpool/UandM.pdf">Zero energy ontology and matrices</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com2tag:blogger.com,1999:blog-10614348.post-35692495772004436862020-06-18T04:57:00.006-07:002020-06-18T22:16:13.224-07:00Indications for an axionlike state in mass range 1-7 keV from XENON
There was a popular article about <A HREF = "https://tinyurl.com/yaqoo2y9">bump </A> claimed by XENON group and suggesting the existence of an axion-like state with mass in the range 1-7 keV. Also <A HREF ="https://resonaances.blogspot.com/2020/06/hail-xenon-excess.html">Jester </A> discusses the evidence for the claimed bump.
</p><p>
Originally XENON searched evidence for WIMPs - weak interacting very massive particles. They would have made themselves visible via scattering from ZENON nuclei. Nothing was found.
</p><p>
Second candidate for dark matter particles are very light axions, which could be produced copiously in Sun. They would not have any detectable effect on heavy XENON atom but they could scatter from electrons and ionize XENON atom. The <A HREF="https://resonaances.blogspot.com/2020/06/hail-xenon-excess.html?">figure</A> in the posting of Jester summarizes the energy spectrum of the observed ionization events. The figure shows approximately constant backgroud below 30 keV down to 1 keV below which it drops abruptly suggesting threshold. There are also indications for a peak around 1-2 keV. There is 3.5 sigma excess of events in the range 1-7 keV.
</p><p>
The mass of the dark particle candidate is in the range 1-7 keV. TGD allows to imagine several options but for all of them one would have analog of pion as dark matter candidate.
<OL>
<LI> TGD Universe is fractal and this predicts p-adically scaled variants of hadron physics and electroweak physics. Mass squared scales would come as powers of 2. Mersenne primes and Gaussian Mersennes define especially promising candidates.
<OL>
<LI> M<sub>89</sub> hadron physics (see <A HREF="http://tgdtheory.fi/pdfpool/tgdnewphys.pdf">this</A>) would be scaled up variant of ordinary hadron physics (M<sub>107</sub>) and would make itself visible at LHC. The masses of M<sub>89</sub> hadrons would be scaled up by factor 512 from those of ordinary hadrons. There is evidence for bumps with predicted masses and the original proposal as Higgs did not work and they were forgotten. The mesons of this physics would be dark with h<sub>eff</sub>/h<sub>0</sub>=n≈ 512 so that the Compton lengths would be those of ordinary mesons and they would appear at quantum criticality for what was expected to be de-confiment phase transition.
<LI> There are indications for the particles of these physics having mass scaled by a power of 2 from that for say ordinary meson. Could the particle be a scaled down pion of some kind. There are actually several candidates for scaled variants of pion. There is evidence for so called X boson with mass around 16-17 MeV proposed to be spin 1 bosonof a fifth force (see <A HREF="http://arxiv.org/abs/1604.07411">this</A>). In TGD framework the identification as pion-like state is more natural and provides new insights on the relation between weak and strong interactions (see <A HREF="http://tgdtheory.fi/public_html/articles/Xboson.pdf">this</A>). There is also quite recent evidence for pionlike exotic particle with mass not far from that of pion showing itself in the decays of long-lived kaon: there is actually evidence for scaled variants of pion also from earlier experiments. These pieces of evidence are discussed from TGD point of view in (see <A HREF ="http://tgdtheory.fi/public_html/articles/pionlikestate.pdf"> this</A>) (see <A HREF="https://tinyurl.com/y9clyf5y">this</A>).
<LI>In biologically important length scales there are as many as 4 Gaussian Mersenne M<sub>G,n</sub>=(1+i)<sup>n</sup>-1 with n=151, 157, 163, 167 defining p-adic length scales in the range 10 nm (cell membrane thickness) and 2.5 μm (cell nucleus size) and might involve scaled variants of hadron and electroweak physics.
</OL>
p-Adic length scale hypothesis also allows the possibility of p-adically scaled variants of leptons and quarks with mass scaled down or up by a power of 2 and there are some indications for this kind of states. For instance, the claimed axion-like state could be a scaled down pion as bound state of scaled down quarks.
<LI> Heavy ion collisions near Coulomb wall gave already around seventies indicatons for a pion-like state of mass 1 MeV decaying to electron positron pair. TGD inspred interpretation (see <A HREF="http://tgdtheory.fi/pdfpool/leptc.pdf">this</A>) was in terms of electropion identified as bound state of color octet electrons. TGD view about color indeed allows colored excitation of leptons since color is not spin-like but angular momentum like quantum number assignable to CP<sub>2</sub> color partial waves. Later evidence for muon and tau analogs of this state has emerged. The decay widths of weak bosons do not allow
color octet ptons in MeV scale and this forced the interpretation that they are dark in some sense and appear ony at quantum criticality - now at collision energies around Coulomb wall.
</p><p>
Leptopion could also be color bound state of quark and antiquark. As noticed, there is evidence for several bound states of this kind.
<LI> The TGD based model for "cold fusion" (see <A HREF="http://tgdtheory.fi/pdfpool/coldfusionagain.pdf">this</A>, <A HREF ="http://tgdtheory.fi/pdfpool/krivit.pdf"> this</A>), and <A HREF ="http://tgdtheory.fi/pdfpool/proposal.pdf"> this</A>) led to a new view about nuclear physics (see <A HREF="http://tgdtheory.fi/pdfpool/darkcore.pdf">this</A>) in which dark nuclei appear also as intermediate states of ordinary nuclear reactions. Dark nuclei as nuclear string with distance of about electron Compton length would be crucial for "cold fusion" and would have dark nuclear binding energies in few keV range.
</p><p>
Remarkably, they would have scaled down dark nuclear binding energies in few keV range. This because the binding energy scale of ordinary nuclear physics about 7 MeV would be scaled down by the ratio 2<sup>-10</sup>≈ 10<sup>-3</sup> of the p-adic length scales of proton and electron labelled by k=107 and k=127 to a value about 7 keV, which represents the upper end of the range 1-7 keV. There is also evidence that X ray emission with energies of this order of magnitude from Sun affects nuclear decay rates at Earth.
</p><p>
The pion-like particles could be indeed dark in TGD sense (ordinary particle but with h<sub>eff</sub>=n× h<sub>0</sub>>h). Could the axion candidate be scaled down variant of electro-pion with mass 1 MeV with k=127: if the mass of electro-pion scales down like the nuclear binding energy, the scaling k=107 → 127 would take the mass of electro-pion to 1 keV. Also scaled down pion formed by quarks could be in question.
</OL>
To sum up, the recent axion-like state would add only one item to the increasing list of pion-like states allowed by p-adic fractality of TGD Universe. One might hope that despite their high specialization colleagues could eventually wake-up to see the big picture behind the anomalies.
</p><p>
See the article <a HREF= "http://tgdtheory.fi/public_html/articles/pionlikestate.pdf">Exotic pion like states as "infra-red" Regge Trajectories and a new view about nuclear physics</A> or the chapter <a HREF= "http://tgdtheory.fi/pdfpool/tgdnewphys1.pdf">New Physics Predicted by TGD: Part I</A>.
</p><p>
For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com1tag:blogger.com,1999:blog-10614348.post-70150184376592219872020-06-15T04:01:00.008-07:002020-06-17T22:03:36.783-07:00Skyrmions in TGD
I received a <A HREF="https://tinyurl.com/ycathr3u">link</A> to an article telling about <A HREF="https://tinyurl.com/yddwhr2o">research</A> carried out for condensed matter skyrmions, which are very general condensed matter quasiparticles. They were found to replicate like DNA and cells. I realized that I have not clarified myself the possibility of skyrmions on TGD world and decided to clarify my thoughts.
</p><p>
<B>What skyrmions are?</B>
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Consider first what skyrmions are.
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<LI>Skyrmions are topological entities. One has some order parameter having values in some compact space S. This parameter is defined in say 3-ball such that the parameter is constant at the boundary meaning that one has effectively 3-sphere. If the 3rd homotopy group of S characterizing topology equivalence classes of maps from 3-sphere to S is non-trivial, you get soliton-llike entities, stable field configurations not deformable to trivial ones (constant value).
Skyrmions can be assigned to space S which is coset space SU(2)<sub>L</sub>× SU(2)<sub>R</sub>/SU(2)<sub>V</sub>, essentially S<sup>3</sup> and are labelled by conserved integer-valued topological quantum number.
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One can imagine variants of this. For instance, one can replace 3-ball with disk. SO(3)=S<sup>3</sup> with 2-sphere S<sup>2</sup>. The example considered in the article corresponds to discretized situation in which one has magnetic dipoles/spins at points of say discretized disk such that spins have same direction about boundary circle. The distribution of directions of spin can give rise to skyrmion-like entity. Second option is distribution of molecules which do not have symmetry axis so that as rigid bodies the space of their orientations is discretized version of SO(3). The field would be the orientation of a molecule of lattice and one has also now discrete analogs of skyrmions.
<LI>More generally, skyrmions emerge naturally in old-fashioned hadron physics, where SU(2)<sub>L</sub>× SU(2)<sub>R</sub>/SU(2)<sub>V</sub> involves left-handed, right-handed and vectorial (diagonal) subgroups of SO(4)=SU(2)<sub>L</sub>× SU(2)<sub>R</sub>. The realization would be in terms of 4-component field (π,σ), where π is charged pion with 3 components - axial vector - and σ which is scalar. The additional constraint π•π +σ<sup>2</sup>= constant defines 3-sphere so that one has field with values in S<sup>3</sup>. There are models assigning this kind of skyrmion with nucleon, atomic nuclei, and also in the bag model of hadrons bag can be thought of as a hole inside skyrmion. These models seem to have something to do with reality so that a natural question is whether skyrmions might appear in TGD.
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<B>Skyrmion number as winding number</B>
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In TGD framework one can regard space-time as 4-surface in either octonionic M<sup>8</sup><sub>c</sub> - "c" refers here to complexification by an imaginary unit i commuting with octonions- or in M<sup>4</sup>× CP<sub>2</sub>. For the solution surfaces M<sup>8</sup> has natural decomposition M<sup>8</sup>=M<sup>2</sup>× E<sup>6</sup> and E<sup>6</sup> has SO(6) as isometry group containing subgroup SU(3) having automorphisms of octonions as subgroup leaving M<sup>2</sup> invariant. SO(6)=SU(4) contains SU(3) as subgroup, which has interpretation as isometries of CP<sub>2</sub> and counterpart of color gauge group. This supports M<sup>8</sup>-H duality, whose most recent form is discussed <A HREF="http://tgdtheory.fi/public_html/articles/paddarkcodes.pdf">here</A>.
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The map S<sup>3</sup>→ S<sup>3</sup> defining skyrmion could be taken as a phenomenological consequence of M<sup>8</sup>-H duality implying the old-fashioned description of hadrons involving broken SO(4) symmetry (PCAC) and unbroken symmetry for diagonal group SO(3)<sub>V</sub> (CCV). The analog of (π,σ) field could correspond to a B-E condensate of pions (π,σ).
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The obvious question is whether the map S<sup>3</sup>→ S<sup>3</sup> defining skyrmion could have a deeper interpretation in TGD framework. I failed to find any elegant formulation. One could however generalize and ask whether skyrmion like entities characterize by winding number are predicted by basic TGD.
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<LI>In the models of nucleon and nuclei the interpretation of conserved topological skyrmion number is as baryon number. This number should correspond to the homotopy class of the map in question, essentially winding number. For polynomials of complex number degree corresponds to winding number. Could the degree n=h<sub>eff</sub>/h<sub>0</sub> of polynomial P having interpretation as effective Planck constant and measure of complexity - kind of number theoretic IQ - be identifiable as skyrmion number? Could it be interpreted as baryon number too?
<LI> For leptons regarded as local 3 anti-quark composites in TGD based view about SUSY \citesusyTGD the same interpretation would make sense. It seems however that the winding number must have both signs. Degree is n is however non-negative.
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Here complexification of M<sup>8</sup> to M<sup>8</sup><sub>c</sub> is essential. One an allow both holomorphic and anti-holomorphic continuations of real polynomials P (with rational coefficients) using complexification defined by commutative imaginary unit i in M<sup>8</sup><sub>c</sub> so that one has polynomials P(z) <I> resp.</I> P(z*) in turn algebraically continued to complexified octonionic polynomials P(z,o) <I> resp.</I> P(z*,o).
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Particles <I> resp.</I> antiparticles would correspond to the roots of octonionic polynomial P(z,o) resp. P(z*,o) meaning space-time geometrization of the particle-antiparticle dichotomy and would be conjugates of each other. This could give a nice physical interpretation to the somewhat mysterious complex roots of P.
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<B>More detailed formulation</B>
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To make this formulation more detailed on must ask how 4-D space-time surfaces correspond to 8-D "roots" for the "imaginary" ("real") part of complexified octonionic polynomial as surfaces in M<sup>8</sup><sub>c</sub>.
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<LI>Equations state the simultaneous vanishing of the 4 components of complexified quaternion valued polynomial having degree n and with coefficients depending on the components of O<sub>c</sub>, which are regarded as complex numbers x+iy, where i commutes with octonionic units. The coefficients of polynomials depend on complex coordinates associated with non-vanishing "real" ("imaginary") part of the O<sub>c</sub> valued polynomial.
<LI>To get perspective, one can compare the situation with that in catastrophe theory in which one considers roots for the gradient of potential function of behavior variables x<sup>i</sup>. Potential function is polynomial having control variables as parameters. Now behavior variable correspond "imaginary" ("real") part and control variables to "real" ("imaginary") of octonionic polynomial.
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For a polynomial with real coefficients the solution divides to regions in which some roots are real and some roots are complex. In the case of cusp catastrophe one has cusp region with 3-D region of the parameter defined by behavior variable x and 2 control parameters with 3 real roots, the region in which one has one real root. The boundaries for the projection of 3-sheeted cusp to the plane defined by control variables correspond to degeneration of two complex roots to one real root.
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In the recent case it is not clear whether one cannot require the M<sup>8</sup><sub>c</sub> coordinates for space-time surface to be real but to be in M<sup>8</sup>=M<sup>1</sup>+iE<sup>7</sup> .
<LI>Allowing complex roots gives 8-D space-time surfaces. How to obtain real 4-D space-time surfaces?
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<LI> One could project space-time surfaces to real M<sup>8</sup>=M<sup>1</sup>+iE<sup>7</sup> to obtain 4-D real space-time surfaces. In time direction the real part of root is accepted and is same for the root and its conjugate. For E<sup>7</sup> this would mean that imaginary part is picked up.
<LI>If one allows only real roots, the complex conjugation proposed to relate fermions and anti-fermions would be lost.
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<LI>One can select for 4 complex M<sup>8</sup><sub>c</sub> coordinates X<sup>k</sup> of the surface and the remaining 4 coordinates Y<sup>k</sup> can be formally solved as roots of n:th degree polynomial with dynamical coefficients depending on X<sup>k</sup> and the remaining Y<sup>k</sup>.
This is expected to give rise to preferred extremals with varying dimension of M<sup>4</sup> and CP<sub>2</sub> projections.
<LI> It seems that all roots must be complex.
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<LI>The holomorphy of the polynomials with respect to the complex M<sup>8</sup><sub>c</sub> coordinates implies that the coefficients are complex in the generic point M<sup>8</sup><sub>c</sub>. If so, all 4 roots are in general complex but do not appear as conjugate pairs. The naive guess is that the maximal number of solutions would be n<sup>4</sup> for a given choice of M<sup>8</sup> coordinates solved as roots.
An open question is whether one can select subset of roots and what happens at t=r<sub>n</sub> surfaces: could different solutions be glued together at them.
<LI> Just for completeness one can consider also the case that the dynamical coefficients are real - this is true in the E<sup>8</sup> sector and whether it has physical meaning is not clear. In this case the roots come as real roots and pairs formed by complex root and its conjugate. The solution surface can be divided into regions depending on the character of 4 roots. The n roots consist of complex root pairs and real roots. The members or complex root pairs are mapped to same point in E<sup>8</sup>.
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<B> Could skyrmions in TGD sense replicate?</B>
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What about the observation that condensed matter skyrmions replicate? Could this have analog at fundamental level?
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<LI>The assignment of conserved topological quantum number to the skyrmion is not consistent with replication unless the skyrmion numbers of outgoing states sum up to that of the initial state. If the system is open one can circumvent this objection. The replication would be like replication of DNA in which nucleotides of new DNA strands are brought to the system to form new strands.
<LI>It would be fascinating if all skyrmions would correspond to space-time surfaces at fundamental M<sup>8</sup> level. If so, skyrmion property also in magnetic sense would be induced by from a deeper geometric skyrmion property of the MB of the system. The openness of the system would be essential to guarantee conservation of baryon number. Here the fact that leptons and baryons have opposite baryon numbers helps in TGD framework. Note also ordinary DNA replication could correspond to replication of MB and thus of skyrmion sequences.
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See the article <A HREF="http://tgdtheory.fi/public_html/articles/paddarkscales.pdf">About M<sup>8</sup>-H-duality, p-adic length scale hypothesis and dark matter hierarchy</A> or the chapter <A HREF="http://tgdtheory.fi/pdfpool/UandM.pdf">Zero energy ontology and matrices</A>.
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For a summary of earlier postings see <a HREF= "http://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
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<A HREF="http://www.tgdtheory.fi/tgdmaterial.html">Articles and other material related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0