tag:blogger.com,1999:blog-106143482024-11-08T20:54:45.084-08:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2267125tag:blogger.com,1999:blog-10614348.post-58624722675242072242024-11-08T03:06:00.000-08:002024-11-08T20:51:24.284-08:00Why doesn't Vega have planets?
The popular article
<A HREF ="https://www.livescience.com/space/astronomy/ridiculously-smooth-james-webb-telescope-spies-unusual-pancake-like-disk-around-nearby-star-vega-and-scientists-cant-explain-it">'Ridiculously smooth': James Webb telescope spies unusual pancake-like disk around nearby star Vega and scientists can't explain it</A> informs that James Webb telescope has found that star Vega probably has no planets.
</p><p>
Vega is a blueish colored star about twice as massive as the Sun and located at distance of about 25 light-years from Earth and is therefore rather near to Sun. By its large mass Vega is predicted to be short lived. Vega is .5 billion years old and considerably younger than Sun. The age of Sun and its planetary system, believed to have condensed simultaneously from a proto disk, is believed to be 4.6 billion years. Due to its fast spin, close proximity to Earth and the fact that its magnetic pole is pointed right at us, Vega appears very bright in the night sky. Vega is the fifth-brightest star visible from Earth to the naked eye in Northern sky (Pohjan Tähti in Finnish).
</p><p>
JWST images reveal that Vega is surrounded by a surprisingly smooth, 100 billion-mile-wide (161 billion kilometers) disk of cosmic dust similar to the similar disk believed to have surrounded Sun for 4.5 billion years ago , confirming that it is not surrounded by any exoplanets. The standard model for the formation of planets and Sun from this kind of disc however predicts that Vega should have planets. This might mean a death blow for the standard narrative of the formation of planets.
</p><p>
The TGD based model for the formation of planets predicts that planets were formed in mini bigbangs, that is explosions in which the parent star lost a surface layer consisting of closed flux monopole flux tubes flowing along the surfacein North-South direction. The surface layer hand roughly the mass of the planet to be formed and condensed later to the planet (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble1.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble2.pdf">this</A>, and <A HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>).
</p><p>
The model is developed in more detail <A HREF ="https://tgdtheory.fi/public_html/articles/Haramein.pdf">here</A> and differs dramatically from the standard model view of the stellar energy production since stellar wind and radiation would be produced at the surface layer consisting of nuclei of a scaled up variant of ordinary hadron physics predicted by padic length scale hypothesis (see <A HREF ="https://tgdtheory.fi/pdfpool/tgdnewphys1.pdf">this</A> and I <A HREF ="https://tgdtheory.fi/pdfpool/tgdnewphys2.pdf">this</A>). I refer to this hadron physics as M<sub>89</sub>= 2<sup>89</sup>-1 hadron physics. M<sub>89</sub> nuclei would have mass scale, which is 512 times that of the nuclei of the ordinary hadron physics, which corresponds to M<sub>107</sub>= 2<sup>107</sup>-1.
</p><p>
Whether the properties of Vega, for instance the fact that according to the standard theory it has lower abundances of elements heavier than <sup>4</sup>He, could explain why these mini bigbangs did not occur for Vega, remains an open question. This would require a more precise understanding of what causes these mini bigbangs. These explosions should have induced the decay of M<sub>89</sub> hadrons to ordinary hadrons so that the entire flux tube layer would have exploded and decayed.
</p><p>
Could some kind of quantum critical phenomenon, stimulated by external perturbation, be in question? The TGD based stellar model predicts that stars have flux tube connections to other stars and also to the galactic blackhole-like object and this could make possible this kind of perturbations. Ordinary solar wind would correspond to similar local explosions. This suggests a similarity with the TGD based models of the sunspot cycle <a HREF= "https://tgdtheory.fi/public_html/articles/Haramein.pdf">this</A> and of geomagnetic reversals and excursions for which I have considered a model based on stochastic resonance (see <a HREF= "https://tgdtheory.fi/public_html/articles/BEreversals.pdf">this</A>).
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/Haramein.pdf">Some Solar Mysteries</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/Haramein.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-62154882628911462692024-11-07T21:13:00.000-08:002024-11-07T21:13:41.315-08:00Early Universe was empty and featureless: really?
I encountered a popular article (see <A HREF="https://blog.sciandnature.com/2024/08/einstein-was-right-after-all-webb.html">this</A>) with the title
"Einstein Was Right After All: Webb Telescope Observes Emptiness in the Extremely Early Universe". The article states that the early universe approached featureless space predicted by the standard cosmology, also predicting that various structures emerged later. To me, the findings of the James Webb telescope suggest something very different. JWT has found highly evolved galaxies and giant blackholes, which should not exist in the very early universe.
</p><p>
On the other hand, in a certain sense the claim conforms with the TGD view predicting that the very early Universe was dominated by string-like objects, 4-surfaces looking like extremely thin strings. I call them cosmic strings. This is of course something very different from the predicton of GRT. Thee matter density due to cosmic behaved like 1/a<sup>2</sup>, where a denotes the cosmic time defined by the Lorentz invariant light-cone proper time. This means that the mass of the comoving volume went to zero like a. In this sense the Universe became empty.
</p><p>
The energy of the cosmic string can be identified as dark energy, somewhat surprisingly also identifiable as galactic dark matter located at the cosmic strings, there would be no halo. The decay of tangles of cosmic strings to ordinary matter as analog of the vacuum energy of inflaton fields would generate the ordinary galactic matter and the energy density of cosmic strings creates the gravitational force explaining the flat velocity spectrum of distant stars.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-41774476073870702842024-11-07T20:42:00.000-08:002024-11-08T20:54:00.630-08:00Blackhole that grew quite too fastMarko Manninen asked for the TGD view concerning the recently found black-hole like object (BH) which seems to gobble the matter from environment much faster than it should (see the popular article <A HREF="https://www.space.com/the-universe/black-holes/fastest-feeding-black-hole-of-the-early-universe-found-but-does-it-break-the-laws-of-physics?">'Fastest-feeding' black hole of the early universe found. But does it break the laws of physics?</A>. This BH counted identified as dwarf blachole, found by the James Webb telescope, should have gotten its mass of more than 7 million solar masses in 12 million years. The rate for its formation would have been 40 times too high.
</p><p>
Objects thought to be black holes often differ in many respects from the black holes of general relativity. In particular, the giant BHs of the very early universe and BHs associated with quasars and the cores of galaxies do so. Star-born BHs could be ordinary blackholes but the giant BHs might be something different. Also the dwarf backhole found by JWT might different. The basic mystery is why the giant BHs can be so large in the very early Universe if they are formed in the expected way. Do the BHs always grow by gobbling up matter from the environment?
</p><p>
TGD leads to a view of BHs different from the GR view in many respects (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>).
<OL>
<LI> In TGD, BHs are not singularities containing their mass at a single point but would correspond to portions of long cosmic strings (extremely thin string-like 3-surfaces), which have formed a tangle and thickened so that they fill the entire volume. BH property would mean that they are maximally dense.
<LI> The thickening of the cosmic string liberates the energy of the cosmic string and BHs would transform in an explosive way into ordinary matter, which is feeded into the environment. The accretion disk would not be associated with the inflowing matter, but would be formed by the outflowing matter as it slows down in the gravitational field and forms a kind of traffic jam. Radiation would escape. The situation would be very similar to the standard picture where the outgoing radiation would be produced by the infalling matter. At the QFT limit of TGD replacing many-sheeted space-time with a region of Minkowski space made slightly curved, the metric in the exterior region would be in a good approximation Schwartschild metric.
<LI> This kind of object would be more like a white hole-like object (WH). Zero-energy ontology indeed predicts Objects resembling ordinary blackholes as the time reversals of WHs. Matter would really fall into them. One can make quite precise predictions about the mass spectrum of these objects (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/Haramein.pdf">this</A>).
</OL>
This vision leads to a model for the formation of galaxies and generation of ordinary matter from the dark energy assignable to the cosmic strings, which would dominate in the very early Universe (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>).
<OL>
<LI> The collisions of the cosmic strings during the primordial string dominated cosmology are unavoidable for topological reasons and would lead to their thickening and heating inducing the formation of WHs and their explosive decay to ordinary matter. This would generate a radiation dominated phase, perhaps when the temperature approaches the Hagedorn temperature as a maximal temperature for string-like objects. These WHs would be the TGD equivalent for the vacuum energy of inflaton fields assumed in inflation theory to decay to ordinary matter.
<LI> The energy of cosmic strings would have Kähler magnetic and volume parts and have interpretation as dark energy. There is now rather convincing evidence for connecting between dark energy and the giant blackholes (see <A HREF="https://www.space.com/dark-energy-black-hole-connection">this</A>).
<LI> An unexpected connection is that galactic dark matter would be dark energy of a cosmic string transversal to the galactic plane and containing galaxies along it: this has been known for decades! There would be no dark matter halo and no exotic dark matter particles. This predicts without further assumptions the flat velocity spectrum of the distant stars rotating galaxies associated with very long cosmic strings and also solves the many problems of the halo models and MOND.
<LI> TGD also predicts dark matter-like macroscopically quantum coherent phases of ordinary matter for which the effective Planck constant h<sub>eff</sub> is large. The generation of these phases at magnetic bodies, for example in biology, solves the problem of missing baryonic matter: that is why baryonic (and also leptonic) matter disappears during the cosmic evolution.
</OL>
Let's return to the question whether TGD can explain why the BHs in question grow so fast. They do not do so by gobbling the matter from the environment but from the long cosmic string. The energy of the thickening string filament is converted into matter and generates a WH. This could happen much faster than the growth of a black hole in the usual way. At this moment it is not possible to estimate the rate of this process but it could also explain how the early Universe can contain these giant blackhole-like objects.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-10282203471825099312024-11-07T19:03:00.000-08:002024-11-07T19:03:40.667-08:00Could geomagnetic reversals and excursions relate to extinctions and collapses of civilizations?
The stimulus for these considerations came from a new perspective to climate change and other phenomena. They could be argued to reflect the ethical and moral decay of our civilization. Could there be a much deeper reason for these phenomena and could they be unavoidable and implied by the basic physics? To put it provocatively: could our ethical and moral standards correlate with our physical environment in some sense?
</p><p>
Climate warming and other phenomena that cause disorder in the biosphere bring to mind the second law of thermodynamics. Could a deeper explanation be based on the second law of thermodynamics of its generalization. We turn too much ordered energy into dis-ordered energy. Could carbon dioxide emissions be a secondary phenomenon?
</p><p>
I did not take these considerations very seriously because it is difficult to see the reduction to the atomic level. The loss of order also manifests itself in a rather abstract form, for example on a social level as violence and inequality. Recently, however, I saw a mention of a study in which I claimed that the increase in entropy produced by human energy consumption starts to be significant at the atomic level. Could the decline of civilization have an explanation in terms of a generalization of the second law forced by TGD?
</p><p>
<B>Some interesting observations</B>
</p><p>
There are several interesting observations which have stimulated the ideas to be discussed in the sequel.
<OL>
<LI>The Earth's magnetic field is changing rapidly near the poles (see <A HREF="https://www.sciencealert.com/is-earths-magnetic-field-on-the-verge-of-flipping-over-an-expert-explains">this</A>). Interestingly, global warming is fastest near the poles. It is expected that the direction of the field can change within a very short period of time. The shortest known polarization change has occurred in a year and global polarization reversals can last hundreds of years. Bjarne Lorentz has proposed on basis of correlations between temperature and the strength of the global magnetic field (see <A HREF="https://www.scirp.org/journal/paperinformation?paperid=93840">this</A>) that the geomagnetic reversal could relate to global warming because it no longer protects the biosphere from cosmic radiation.
</p><p>
This proposal however forces us to give up the standard view about dynamo mechanism as the origin of the Earth's magnetic field. The dynamo mechanism has severe difficulties: in particular, the magnetic field should have disappeared a long time ago. The TGD view of magnetic fields deviates dramatically from the Maxwellian view and leads to an explanation for the stability of the Earth's magnetic field and also predicts a mechanism for the polarization reversals (see <A HREF="https://tgdtheory.fi/public_html/articles/Bmaintenance.pdf">this</A>) . This mechanism has been also applied to the polarization reversals of the solar magnetic field (see <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble2.pdf">this</A>).
</p><p>
In TGD, the magnetic bodies of ordinary physical systems carry macroscopically quantum coherent phases of matter being able to control the associated systems consisting of ordinary matter. TGD inspired quantum biology relies on this notion. Therefore there are good motivations to ask whether the correlation between the weakening of magnetic field and climate warming could exist.
</p><p>
Mainstream scientists do not take the proposal seriously (see <A HREF="https://www.nationalgeographic.com/environment/article/earths-shifting-magnetic-fields-arent-causing-climate-change">this</A>) since there seems to be no standard physics mechanism justifying the claim. Also I am personally skeptical about the proposal that standard physics mechanisms could relate global warming and geomagnetic reversal.
<LI>In the last global reversal of the direction of the magnetic field about 41,000 years ago, the Neanderthals disappeared, although the reversal was short-lived about 250 years. The average period between reversals between long lasting global reversals is 450,000 years. For short lasting global reversals created in excursions, the average period is 10 times shorter, about 45,000 years (see <A HREF="https://www.sci.news/othersciences/geophysics/earths-magnetic-field-directional-changes-08613.html">this</A>). There can also be local excursions and the strength and direction of the magnetic field of Earth indeed fluctuates.
</p><p>
\item Callahan have studied magnetic fields around the world (see <A HREF="https://www.nexusmagazine.com">this</A>) and noticed that the magnetic field and as a consequence the Schumann resonance can be very weak, for instance in the Near East. There are serious social problems in these areas. Why would the strength of the magnetic field correlate with the coherence the social atmoshere? Could the magnetic field strength correlate with the coherence of collective consciousness?
</OL>
<B>Could the entropization of field bodies lead to magnetic reversals and excursions explaining extinctions and declines of civilizations</B>
</p><p>
The above considerations lead to the key idea.
<OL>
<LI>Magnetic bodies control biomatter in TGD. Specifically, the Earth's magnetic body, which would determine the collective consciousness of the Earth's and also affect the consciousness of living organisms since their magnetic bodies interact with the Earth's magnetic body.The magnetic body of the Sun would be also involved.
<LI>Could the fundamental cause of the problems of humanity and the biosphere be the increase of entropy at the level of magnetic bodies. The aging magnetic body would be due to entropization. This mechanism could also explain the aging of biological organisms (see <A HREF="https://tgdtheory.fi/public_html/articles/aging.pdf">this</A>). The entropization would lead to a loss of quantum coherence and the magnetic body would gradually lose control over the processes at the level of the biological body. This would eventually lead to a death struggle of the magnetic body and magnetic body.
</p><p>
More concretely, the monopole flux tube pairs of the Earth's magnetic field would split to short flux tubes. Later they could fuse back to flux tubes with a reversed direction of magnetic field. The process would be the same as in the reversal of the solar magnetic field.
</p><p>
As a result, the quantum coherence scales would shorten and the control of the magnetic body over the bio-matter would be lost. Biomatter would be forced to cope without the help of the magnetic body. During sleep a similar situation takes place and during motor activities and sensory input are absent. The decay of the flux tubes can be local or global and the resulting magnetic flux tubes could be long lasting or only temporary.
<LI> In zero energy ontology (ZEO), the transition period leading to regeneration of the monopole flux tube would correspond to two "big" state function reductions (BSFRs) in macroscopic scale. It can be local or global and also short-term. In BSFR, the magnetic body would lose its consciousness reincarnating with an opposite arrow of time. In the second BSFR it would wake up with the original arrow of time.
<LI>One life cycle of the Earth's magnetic body would end (or a little more gently, the magnetic Mother Gaia would fall asleep and live in another direction of time). Eventually, a new cycle would begin with a new magnetic field. These cycles are analogous to the counterpart of sunspot cycles with a duration of 11+11 years. Could one think of a year cycle with a period about 45,000 years in which the magnetic field with reverted direction is short lived. For us, it might mean the collapse and rebirth of civilization. One can wonder what our fate in the next reversal is?
<LI>There are reasons to ask whether our species is approaching extinction. On the other hand, an enormous progress in science and technology is being made at the same time. This paradox applies more generally, as, for example, biologist Jeremy England has observed (see <A HREF="https://arxiv.org/pdf/1412.1875v1.pd">this</A>). Biological evolution is generally accompanied by an increase in entropy. p-Adic vision about cognition leads to exactly this prediction (see <A HREF="https://tgdtheory.fi/public_html/articles/englandTGD.pdf">this</A>). When the p-adic negentropy associated with quantum entanglement as a measure for the amount of conscious information is large, the standard entropy is also large. The smarter we get, the more we produce entropy.
<LI>Homo sapiens appeared 300,000 years ago. The oldest Neandertal fossils are 430,000 years old. The most recent global and long-lasting direction change, the Brunhes Matuyama reversal, occurred 780,000 years ago.
</p><p>
45,000 years is a reasonable estimate for the average period for the magnetic excursions (see <A HREF="https://www.sci.news/othersciences/geophysics/earths-magnetic-field-directional-changes-08613.html">this</A>). The last magnetic excursion was 41,000 years ago. The reversal lasted only 250 years but Neanderthals disappeared. Also now, a change in direction is taking place: could it lead to the extinction of our species or at least the destruction of civilization within a few hundred years? If these temporary reversals are periodic, our species would have survived 7 reversals. This gives a cause for optimism. But on the other hand, we are doing our best to destroy our civilization.
</OL>
Is it possible to estimate time scales for the duration of the magnetic field orientation from basic physics? The durations of the episodes seem random and the durations of the transitions also vary. p-Adic length scale hypothesis suggests that the periods come in powers of two. Surprisingly, also an esoteric view of the evolution of consciousness predicts so called <A HREF="https://www.bibhudevmisra.com/2024/03/the-yuga-cycle-and-earths-precession.html">Yuga cycle</A> predicting octaves of the basic period and giving nearly the same quantitative predictions.
</p><p>
Period doubling and stochastic resonance, requiring the presence of a periodic perturbation and noise, could explain these characteristics. The first candidate for the periodic perturbation is the period of equinox precession. A better candidate is the orbital period of planet Sedna to which Earth would have monopole flux tube contacts. The noise would be thermal noise due to the aging of the magnetic body of Earth leading to its "death" and reincarnation by magnetic reversal or excursion.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/BEreversals.pdf">Could geomagnetic reversals and excursions relate to extinctions and collapses of civilizations?</A> or the chapter
<a HREF= "https://tgdtheory.fi/pdfpool/magnbubble2.pdf">Magnetic Bubbles in TGD Universe: part II</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-16584652320720996762024-11-04T00:15:00.000-08:002024-11-04T00:15:13.627-08:00Simulation hypothesis and TGD
Heikki Hirvonen asked for my opinion about the simulation hypothesis. I must say that I find difficult to distinguish the <A HREF="https://en.wikipedia.org/wiki/Simulation_hypothesis">simulation hypothesis</A> of Boström from pseudoscience. It says nothing about physics It is not inspired by any problem nor does it solve any problem. And it only creates problems: for instance, who are the simulators and what physics they obey? We would be just computer programs. But how computer programs can be conscious: this is the basic problem of materialism. One can introduce a magic world "emergence" but it only puts the problem under the rug.
</p><p>
Some systems can of course create simulations of the external world and even themselves. Neuroscience talks about self model, which is a very real thing. Modern society is busily simulating the physical world and its activities. But this has nothing to do with Boström's hypothesis about a mysterious outsider as a simulator and ourselves as computer programs, who never can know who this mysterious simulator is (God of AI age).
</p><p>
It is however interesting to look whether the simulation hypothesis might have some analogies in TGD.
<OL>
<LI> TGD predicts a hierarchy of field bodies as space-time surfaces which are counterparts of the Maxwellian and more general gauge fields. Field bodies are predicted to be conscious entities carrying phases of ordinary matter with a large value of effective Planck constants making the quantum coherent systems in large scales. They give rise to a hierarchy of conscious entities.
</p><p>
For instance, EEG would communicate information from biological body to field body control signals from field body to biological body. In quantum biology field bodies serve as bosses or more like role models for the ordinary biomatter. If I am forced to talk about simulation, I would say that the biological body is a simulation of the magnetic body.
<LI> In TGD cognition has p-adic corelates as p-adic space-time surfaces. Cognitive representations correspond to their intersections with real space-time surfaces and consist of a discrete set of points in an extension of rationals. They could be called simulations since cognition is a conscious representation of the sensory (real) world. All physical systems would have at least rudimentary cognitive consciousness and would be performing these "simulations".
</OL>
For the TGD view about Universe as a conscious quantum Platonia see <A HREF="https://tgdtheory.fi/public_html/articles/compuTGD.pdf">this</A>. For the TGD view
of how computers could become conscious see <A HREF="https://tgdtheory.fi/public_html/articles/tgdcomp.pdf">this</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-71531796069599792582024-11-03T23:53:00.000-08:002024-11-03T23:53:45.834-08:00Tegmark's Platonia and TGD Platonia
Max Tegmark has published a book titled "Our Mathematical Universe" (see <A HREF="https://en.wikipedia.org/wiki/Our_Mathematical_Universe">this</A> about the idea that only mathematical objects exist objectively and mathematical object exists if this is possible in a mathematically consistent way.
</p><p>
Also TGD leads to this view. The basic problem shared with materialism is that the existence of mere mathematical objects does subjective existence. In TGD quantum jumps for the spinor fields in Platonia identified as the "world of classical worlds" consisting of space-time surfaces in $H=M<sup>4</sup>×CP<sub>2</sub>$ obeying holography = holomorphy principle brings in consciousness and zero energy ontology solves the basic problem of quantum measurement theory and allows the experience of free will.
</p><p>
One of the participants of the discussion gave a short summary of the ontology of Tegmark. Tegmark proposes a multiverse with four levels, each more complex and abstract than the last:
<OL>
<LI> Level I (Observable Universe): This is the most familiar level. In this view, the observable universe is just one of many pockets in an enormous (potentially infinite) space, all governed by the same physical laws.
<LI> Level II (Bubble Universes): Here, each universe (or "bubble") might have different physical constants and properties. It s like having different rules for physics in each universe one could have a different speed of light, while another might not have gravity at all.
<LI> Level III (Many-Worlds Interpretation): This level involves quantum mechanics. Every time a quantum event occurs, the universe "branches" into different outcomes, creating countless parallel universes. Think of it like a choose-your-own-adventure book that explores all possible story paths.
<LI> Level IV (Ultimate Mathematical Universe): This is where MUH comes in. Level IV is a collection of every possible mathematical structure, even those that don t resemble anything we would call a universe. According to MUH, each mathematical structure is a complete, self-contained universe. If a structure is logically consistent, it exists.
</OL>
What about quantum Platonia according to TGD?
<OL>
<LI> In TGD only the level I Universe expanded from real universe to adelic one to describe correlates of cognition is needed. The physical Universe is fixed by the condition that the structures involved exist mathematically. In the TGD framework the mathematical existence of the twistor lift of TGD fixes H=M<sup>4</sup>×CP<sub>2</sub> completely. Also number theoretical arguments fix H. Also standard model symmetries and interaction fix H. Space-time dimension is fixed to D=4 by the existence of pair creation made possible by exotic smooth structures as standard smooth structure with point-like defects identifiable as vertices for fermion pair creation. The mathematical existence of the Kähler geometry of the "world of classical worlds" (WCW) (space-time surfaces satisfying holography) fixes it. This was already observed by Freed for the loop space. Infinite-D existence is highly unique.
<LI> Level II Universe would be multiverse and is not needed in TGD since H=M<sup>4</sup>×CP<sub>2</sub> is fixed by mathematical existence and no spontaneous compactification leading to multiverse takes place. Inflation is replaced in TGD with the transformation of galactic dark matter as dark energy of cosmic strings to ordinary matter and there are no inflation fields forcing the multiverse (see <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>).
<LI> Level III Universe is not needed. The new quantum ontology, zero energy ontology (ZEO), leads to the solution of the quantum measurement problem and no interpretations are needed. It also leads to a theory of consciousness and a new view about the relation of geometric and subjective time. The implications are non-trivial in all scales, even in cosmology. One could of course call the hierarchy of field bodies as an analog of the multiverse.
<LI> Level IV Universe corresponds to WCW and WCW spinor fields M<sup>8</sup>-H duality relating number theoretic and geometric visions of TGD, holography= holomorphy vision, and Langlands duality in 4-D case implying that space-time surfaces are representations for complex numbers. Space-time surfaces can be multiplied and summed: this arithmetic is induced by the function field arithmetics for generalized analytic functions of H coordinates (3 complex and one hypercomplex coordinate).
</p><p>
Space-time surfaces correspond to roots for pairs of this kind of functions and form hierarchies beginning with hierarchies of polynomials with coefficients in extensions of rationals but containing also analytic functions of this kind and even general analytic functions. The quantum counterparts of mathematical concepts like abstraction, concept, set, Hilbert space, Boolean algebra follow using the arithmetics of space-time surfaces.
<LI> Consciousness emerges from quantum jumps between quantum states as spinor fields of WCW representing quantum concepts. WCW spinors correspond to Fock states for the fermions of H and their Fock state basic forms a representation of Boolean algebra. One can say that logic emerges via the spinor structure of WCW which is a square root of geometry. Number theoretic vision implies the increase of algebraic complexity and hence evolution.
</p><p>
ZEO allows the quantum Platonia to learn about itself by generating memory in SFRs and also makes memory recall possible: the failure of exact classical determinism for the space-time surfaces as analogs of Bohr orbits makes this possible. The seats of non-determinism represent memory sites (see <a HREF= "https://tgdtheory.fi/public_html/articles/memorytgd.pdf">this</A>). Quantum Platonia evolves as a conscious entity as the WCW spinor fields defining conscious entities disperse to more and more algebraically complex regions of it.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/compuTGD.pdf">Space-time surfaces as numbers, Turing and Gödel, and mathematical consciousness</A> and the chapter <a HREF= "https://tgdtheory.fi/public_html/articles/compuTGD.pdf">About Langlands correspondence in the TGD framework</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-2963571162609699722024-11-03T23:11:00.000-08:002024-11-03T23:11:53.772-08:00The mirror Universe hypothesis of Turok and Boyle from the TGD point of view
The popular article <A HREF="https://www.space.com/the-universe/cosmic-inflation-did-the-early-cosmos-balloon-in-size-a-mirror-universe-going-backwards-in-time-may-be-a-simpler-explanation">'Cosmic inflation:' did the early cosmos balloon in size? A mirror universe going backwards in time may be a simpler explanation</A> by Neil Turok, tells about the proposal of Neil Turok and Latham Boyle stating that the early Universe effectively contained the CP, or equivalently T mirror image, of the ordinary Universe and claims that this hypothesis solves some problems of the cosmology.
</p><p>
The article contains some mutually conflicting statements related to the interpretation of time reversal: I don't know whom to blame.
</p><p>
<B> What is meant with time reversal?</B>
</p><p>
Time reversal has two different meanings, which are often confused. It can refer to time reflection or change of the arrow of time. This confusion appears also in the article.
<OL>
<LI> The article states that T refers to a time reflection symmetry. The article also
states that time flows backwards in the mirror universe. These two statements are not consistent. Either the authors or the popularizers have confused T and time reversal in thermodynamic sense.
<LI> The arrow of time is fixed in standard QFT and therefore in thermodynamics. In quantization this means a selection of vacuum. What we call annihilation operators, annihilate the vacuum. For the other option, their hermitian conjugates would annihilate the vacuum with the opposite arrow of time.
<LI> In the zero energy ontology (ZEO) of TGD, these arrows of time are associated with quantum states, which remain unaffected at the passive boundary of CD in the sequence of "small" state function reductions. This time reversal has nothing to do with T or CP. "Big" SFRs (BSFRs) change the roles of active and passive boundaries and change the arrow of time. These two arrows of time are in a central role in the TGD inspired cosmology and also in biology.
<LI> Could the ordinary matter in phases with opposite arrows of time behave like a mirror universe? The arrow of time changes in BSFRs and means a death or falling asleep of a conscious entity. By a simple statistical argument half of the matter is ordinary and time reversed "sleep" states (half of the universe "sleeps"). Note that there is a scale hierarchy of conscious entities.
</p><p>
The phases of matter with opposite arrows of time cannot see each other by classical signals. The detection process requires what is essentially pair creation of fundamental fermions. One could therefore say that in TGD the mirror universe exists in a well-defined sense.
<LI> In fact, the change of arrow of time in BSFRs is possible in arbitrarily long scales due to the hierarchy of Planck constant making quantum coherence possible even in astrophysical scales. This implies that the evolution of astrophysical objects is a sequence of states with opposite arrows of time. Living forth and back in geometric time implies that their evolutionary age is much longer than the geometric age and this explains stars and galaxies older than the universe.
</OL>
<B> 2. Problems related to the mirror universe hypothesis</B>
</p><p>
<OL>
<LI> Suppose the mirror image in the theory of Turok et al is indeed T mirror image. One must explain why it is invisible for us. The proposal is that the mirror universe might be a mere mathematical trick. This makes me feel uneasy.
<LI> In the proposed model the mirror image would consist mostly of antimatter and the unobservability of the mirror universe would apparently solve the problem due to matter antimatter asymmetry. This does not however solve the problem why there the amount of matter/antimatter in the universe/its mirror is so small. One must explain why CP breaking leads to this asymmetry.
</p><p>
The TGD explanation of matter antimatter asymmetry suggests that antimatter is confined within cosmic strings and matter outside them and that the decay of the cosmic strings to ordinary matter as a counterpart of the inflation process violates CP symmetry and leads to the asymmetric situation.
</OL>
<B>3. Can the hypothesis solve the problem of dark matter?</B>
</p><p>
The proposed hypothesis states that dark matter consists of right handed neutrinos and that they interact with ordinary matter only gravitationally.
<OL>
<LI> The problem is that the standard model does not predict right-handed neutrinos so that the mirror universe would contain only the antiparticles of left handed neutrinos which would interact and would not be therefore be dark. Standard model should be modified.
<LI> In TGD, right-handed neutrinos are indeed predicted and their covariantly constant modes would behave like dark matter. Covariantly constant right handed neutrinos are the only massless spinor modes of M<sup>4</sup>×CP<sub>2</sub> spinors but might mix with higher massive color partial waves. They could also represent an analog of supersymmetry. In TGD ν<sub>R</sub>:s would appear as building bricks of fermions and bosons. Can ν<sub>R</sub>:s exist as free particles? Number theoretic vision and Galois confinement suggests that this is not possible. Therefore ν<sub>R</sub>:s would not solve the problem of galactic dark matter.
</p><p>
In TGD the dark (magnetic and volume) energy of cosmic strings explains galactic dark matter but one cannot of course exclude the presence of right handed neutrinos and other fermions inside cosmic strings. Whether quantum-classical correspondence is true in the sense that the classical energy of cosmic strings actually corresponds to the energy of fermions inside them, remains an open question.
</OL>
<B> 4. Does the mirror universe solve the entropy problem</B>
</p><p>
It is also claimed that the mirror universe solves the problem related to entropy. On basis of the popular article I could not understand the argument.
<OL>
<LI> Second law suggests that the very early Universe should have a very low entropy. This is in a sharp conflict with radiation dominated cosmology.
<LI> In TGD this is not so simple, since both arrows of time are possible and both thermodynamics are possible and time reversed dynamics increases entropy in the opposite direction of geometric time so that it apparently decreases in the standard arrow of time. This effect is actually used to reduce the entropy of phase conjugate laser beams.
</p><p>
In TGD however the very early Universe would consist of cosmic strings which would make collisions (here the dimension of space-time is crucial) causing their thickening and transformation to ordinary matter. This would lead to radiation dominated cosmology.
</p><p>
But what is the entropy of the cosmic string dominated phase? The cosmic string dominated phase could have a very low entropy if the geometric excitations are absent (note that cosmic strings are actually 3-D and only effectively 1-D). The number of excited states (deformations) of the string increases rapidly with temperature. This implies Hagedorn temperature as a maximal temperature for cosmic strings.
</p><p>
Was the very early Universe in Hagedorn temperature or was it heated from a very low temperature to Hagedorn temperature and made a transition to a radiation dominated phase by the thickening to monopole flux tubes and subsequent decay to ordinary matter? If I must make a guess I would say that the temperature was very low.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">Latest progress in TGD</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter with the same title </A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-29742854497583961142024-11-03T01:48:00.000-07:002024-11-03T01:48:58.792-07:00Could quantum field theories be universal
The findings of Nima Arkani Hamed and his collaborators (see <A HREF="https://www.quantamagazine.org/physicists-reveal-a-quantum-geometry-that-exists-outside-of-space-and-time-20240925/">this</A>), in particular Carolina Figueiredo, suggest a universality for the scattering amplitudes predicted quantum field theories. Is it possible to understand this universality mathematically and what could its physical meaning be?
</p><p>
The background for these considerations comes from TGD, where holography = holomorphy principle and M<sup>8</sup>-H duality relating geometric and number theoretic visions fixing the theory to a high degree.
<OL>
<LI> Space-time surfaces are holomorphic surfaces in H=M<sup>4</sup>× CP<sub>2</sub> and therefore minimal surfaces satisfying nonlinear analogs of massless field equations and representing generalizations of light-like geodesics. Therefore generalized conformal invariance seems to be central and also the Hamilton-Jacobi structures (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) realizing this conformal invariance in M<sup>4</sup> in terms of a pair formed by complex and hypercomplex coordinate, which has light-like coordinate curves.
<LI> Quantum criticality means that minima as attractors and maxima as repulsors are replaced with saddle points having both stable and unstable directions. A particle at a saddle point tends to fall in unstable directions and end up to a second saddle point, which is attractive with respect to the degrees of freedom considered. Zero energy ontology (ZEO) predicts that the arrow of time is changed in "big" state function reductions (BSFRs). BSFRs make it possible to stay near the saddle point. This is proposed to be a key element of homeostasis. Particles can end up to a second saddle point by this kind of quantum transition.
<LI> Quantum criticality has conformal invariance as a correlate. This implies long range correlations and vanishing of dimensional parameters for degrees of freedom considered. This is the case in QFTs, which describe massless fields.
</p><p>
Could one think that the S-matrix of a massless QFT actually serves as a model for transition between two quantum critical states located near saddle points in future and past infinity? The particle states at these temporal infinities would correspond to incoming and outgoing states and the S-matrix would be indeed non-trivial. Note that masslessness means that mass squared as the analog of harmonic oscillator coupling vanishes so that one has quantum criticality.
</OL>
What can one say of the massless theories as models for the quantum transitions between two quantum critical states?
<OL>
<LI> Are these theories free theories in the sense that both dimensional and dimensionless coupling parameters associated with the critical degrees of freedom vanish at quantum criticality. If the TGD inspired proposal is correct, it might be possible to have a non-trivial and universal S-matrix connecting two saddle points even if the theories are free.
<LI> A weaker condition would be that dimensionless coupling parameters approach fixed points at quantum criticality. This option looks more realistic but can it be realized in the QFT framework?
</OL>
QFTs can be solved by an iteration of type DX<sub>n+1</sub>= f(X<sub>n</sub>) and it is interesting to see what this allows to say about these two options.
<OL>
<LI> In the classical gauge theory situation, X<sub>n+1</sub> would correspond to an n+1:th iterate for a massless boson or spinor field whereas D would correspond to the free d'Alembertian for bosons and free Dirac operator for fermions. f(X<sub>n</sub>) would define the source term. For bosons it would be proportional to a fermionic or bosonic gauge current multiplied by coupling constant. For a spinor field it would correspond to the coupling of the spinor field to gauge potential or scalar field multiplied by a dimensional coupling constant.
<LI> Convergence requires that f(X<sub>n</sub>) approaches zero. This is not possible if the coupling parameters remain nonvanishing or the currents become non-vanishing in physical states. This could occur for gauge currents and gauge boson couplings of fermions in low enough resolution and would correspond to confinement.
<LI> In the quantum situation, bosonic and fermionic fields are operators. Radiative corrections bring in local divergences and their elimination leads to renormalization theory. Each step in the iteration requires the renormalization of the coupling parameters and this also requires empirical input. f(X<sub>n</sub>) approaches zero if the renormalized coupling parameters approach zero. This could be interpreted in terms of the length scale dependence of the coupling parameters.
<LI> Many things could go wrong in the iteration. Already, the iteration of polynomials of a complex variable need not converge to a fixed point but can approach a limit cycle and even chaos. In more general situations, the system can approach a strange attractor. In the case of QFT, the situation is much more complex and this kind of catastrophe could take place. One might hope that the renormalization of coupling parameters and possible approach to zero could save the situation.
</OL>
It is interesting to compare the situation to TGD? First some general observations are in order.
<OL>
<LI> Coupling constants are absorbed in the definition of induced gauge potentials and there is no sense in decomposing the classical field equations to free and interaction terms. At the QFT limit the situation of course changes.
<LI> There are no primary boson fields since bosons are identified as bound states of fermions and antifermions and fermion fields are induced from the free second quantized spinor fields of H to the space-time surfaces. Therefore the iterative procedure is not needed in TGD.
<LI> CP<sub>2</sub> size defines the only dimensional parameter and has geometric meaning unlike the dimensional couplings of QFTs and string tension of superstring models. Planck length scale and various p-adic length scales would be proportional to CP<sub>2</sub> size. These parameters can be made dimensionless using CP<sub>2</sub> size as a geometric length unit.
</OL>
The counterpart of the coupling constant evolution emerges at the QFT limit of TGD.
<OL>
<LI> Coupling constant evolution is determined by number theory and is discrete. Different fixed points as quantum critical points correspond to extensions of rationals and p-adic length scales associated with ramified primes in the approximation when polynomials with coefficients in an extension of rationals determine space-time surfaces as their roots.
<LI> The values of the dimensionless coupling parameters appearing in the action determining geometrically the space-time surface (K\"ahler coupling strength and cosmological constant) are fixed by the conditions that the exponential of the action, which depends n coupling parameters, equals to its number theoretic counterparts determined by number theoretic considerations alone as a product of discriminants associated with the partonic 2-surfaces (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/compuTGD.pdf">this</A>). These couplings determine the other gauge couplings since all induced gauge fields are expressible in terms of H coordinates and their gradients.
<LI> Any general coordinate invariant action constructible in terms of the induced geometry satisfies the general holomorphic ansats giving minimal surfaces as solutions. The form of the classical action can affect the partonic surfaces only via boundary conditions, which in turn affects the values of the discriminants. Could the partonic 2-surfaces adapt in such a way that the discriminant does not depend on the form of the classical action? The modified Dirac action containing couplings to the induced gauge potentials and metric would determine the fermioni scattering amplitudes.
<LI> In TGD the induction of metric, spinor connection and second quantized spinor fields of H solves the problems of QFT approach due to the condition that coupling parameters should approach zero at the limit of an infinite number of iterations. Minimal surfaces geometrizes gauge dynamics. Space-time surfaces satisfying holography = holomorphy condition correspond to quantum critical situations and the iteration leading from one critical point to another one is replaced with quantum transition.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">TGD as it is towards end of 2024: part I</A> or a <a HREF= "https://tgdtheory.fi/pdfpool/TGD2024I.pdf">chapter</A> with the same title.
</p><p>
For a summary ofhttps://draft.blogger.com/u/0/blog/posts/10614348 earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-55672037197183437332024-11-01T00:30:00.000-07:002024-11-01T01:31:02.391-07:00Challenging some details of the recent view of TGD
The development of the mathematical TGD has been a sequence of simplifications and generalizations. Holography = holomorphy vision removes path integral from quantum physics and together with the number theoretic vision might make the bosonic action unnecessary. This means that this vision allows us to solve field equations explicitly and the solution does not depend on the bosonic action.
</p><p>
TGD allows to get rid of primary bosonic fields and fermions are free free fermions at the level of the imbedding space and their localization to space-time surfaces makes them interaction. Pair creation is made possible by the presence of exotic smooth structures possible only in 4-D space-time.
</p><p>
This however leads to a problem with the sign of energy. This problem disappears when one realizes that fundamental fermions can have tachyonic momenta and that only the physical l states as their bound states, which are Galois singlets, have non-negative mass squared and positive energy.
</p><p>
<B>Could the classical bosonic action completely disappear from TGD?</B>
</p><p>
Number theoretic vision of TGD and holography = holomorphy principle (see <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">this</A>) forces to challenge the necessity of the classical bosonic action.
<OL>
<LI> Any general coordinate action defining the K\"ahler function K and constructible in terms of the induced geometry gives the same minimal space-time surfaces as extremals and only the boundaries and partonic orbits depend on the action since the boundary conditions stating conservation laws depend on the action. Spinor lift suggests K\"ahler action for the 6-D twistor surfaces as a unique action principle. But is it necessary?
<LI> The conjecture exp(K) ∝ D<sup>n</sup>, n an integer, or its generalization to exp(K) ∝ (DD<sup>*</sup>)<sup>n</sup>, where D is a product of discriminants for the polynomials assignable to partonic 2-surfaces define a discrete set of points as their roots, would allow to express vacuum functional completely in terms of number theory. Coupling parameters would be present but evolve in such a way that the condition would hold true.
<LI> The discriminant D is defined also when the roots assignable to the partonic 2-surfaces are real or even complex numbers. This would conform with the strong form of holography. One could get completely rid of the bosonic action principle. The holomorphy = holography principle would automatically give the non-linear counterpart of massless fields satisfied by the space-time surfaces as minimal surfaces. Could the classical action completely disappear from the theory?
</OL>
<B>Could the fermionic interaction vertices be independent of the bosonic action principle?</B>
</p><p>
Could the interaction vertices for fermions be independent of the bosonic action principle?
<OL>
<LI> The long-held idea is (see <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>), the vertices appearing in the scattering amplitudes are determined by the modified Dirac equation (see <A HREF="https://tgdtheory.fi/public_html/articles/modDir.pdf">this</A>) determined by the bosonic action associated with the partonic orbits as couplings to the induced gauge potentials. Twistor lift suggests that this action contains volume term and K\"ahler action.
</p><p>
But is the modified Dirac action necessary or even physically plausible? The problem is that for a general bosonic action the modified gamma matrices, defined in terms of canonical momentum currents, do not commute to the induced metric unlike the modified Dirac action determined by the mere volume term of the bosonic action. This led to the proposal that this option, consistent also with the fact that, irrespective of the bosonic action, space-time surfaces are minimal surfaces outside singularities at which generalized holomorphy fails, is more plausible.
<LI> Fermion pair creation (and emission of bosons as Galois singlet bound states of fermions and antifermions is possible only for 4-D space-time surfaces. The existence of exotic smooth structures in dimension D=4 (see <A HREF="https://tgdtheory.fi/public_html/articles/symplorbsm.pdf">this</A>) makes possible pair creation vertices (see <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>). A given exotic smooth structure corresponds to the unique standard ordinary smooth structure with defects and vertices would correspond to defects at which the fermion line turns backwards in time. The defects would be associated with partonic 2-surfaces at which the generalized holomorphy of the function pair (f<sub>1</sub>,f<sub>2</sub>) with respect to generalized complex coordinates of H (one of them is hypercomplex coordinate) fails, perhaps only at the defect.
<LI> There is an objection against this proposal. The creation of fermion pairs with opposite sign of single fermionic energy suggests that a given light-like boundary of CD can contain fermions with both signs of energy. This does not conform with the assumption that the sign of the <I> single</I> particle energy is fixed and opposite for the opposite boundaries of CD. Should one only require that the total energy has a fixed sign at a given boundary of the CD?
</p><p>
Could one only require that the sign of the energy is fixed only for physical states formed as many-fermions states and identified as Galois singlets and that the physical states can also contain negative energy tachyonic fermions or antifermions. Could this make sense mathematically?
</OL>
<B>Extension of the fermionic state space to include tachyonic fundamental fermions as analogs of virtual fermions</B>
</p><p>
I recently received from Paul Kirsch a link to an interesting article about the possibility to describing tachyons in a mathematically consistent way (see <A HREF="https://arxiv.org/abs/2308.00450">this</A>). The basic problem is that for tachyons the number of positive energy particles is not well-defined since Lorentz transformation can change positive energy tachyons to negative energy tachyons and vice versa. The proposed solution of the problem is the doubling of the Hilbert space which includes both incoming and outgoing states. To me this looks like a mathematically sensible idea and might make sense also physically.
</p><p>
Surprisingly, this proposal has a rather concrete connection with zero energy ontology (ZEO).
<OL>
<LI> In the simplest formulation of ZEO (see <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/zeocriticality.pdf">this</A>), the fermionic vacua at the passive <I> resp.</I> active boundaries of CD correspond to the fermionic vacua annihilated by annihilation operators <I> resp.</I> creation operators as their hermitian conjugates. In the standard QFT only the second vacuum is accepted and this allows only a single arrow of geometric time.
<LI> ZEO allows both arrows and a given zero energy state is a state pair for which the fermionic state at the passive boundary of CD remains fixed during the sequence of small state function reductions (SSFRs) and corresponding time evolution which lead to the increase of CD in a statistical sense. The state at the active boundary changes and this corresponds to the subjective time evolution of a conscious entity, self. SSFRs are the TGD counterparts of repeated measurements for observables which commute with the observables whose eigenstates the states at the passive boundary are.
<LI> The doubled state space is highly analogous to the space of fermionic states in ZEO involving positive and negative energy physical particles at the opposite boundaries of CD. If one also allows single fermion tachyonic states then one could have fermions with wrong sign of energy at a given boundary of CD. If bosons correspond to fermion-antifermion pairs such that either fermion or antifermion is tachyonic, one obtains boson emission and physical bosons can have correct sign of mass squared. In the vertex identified as a defect of the standard spinor structure, either fermion or antifermion would be tachyonic. Since several vertices involving the change of the sign of the fermion or antifermion momentum are possible, outgoing physical fermions and antifermions with a correct sign or energy can be produced. Recall that both the physical leptons and quarks involve fermion-antifermion pairs in the recent picture based on closed monopole flux tubes associated with a pair of Minkowskian space-time sheets.
<LI> Tachyonic single fundamental fermion states (quarks or leptons) are natural in the number theoretic vision of TGD (see <A HREF="https://tgdtheory.fi/public_html/articles/twisttgd1.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/twisttgd2.pdf">this</A>). The components of the fermionic momenta for a given extension of rationals are algebraic integers and mass squared for them can be tachyonic. These states are analogs of virtual fermions of the standard QFT which also can have tachyonic momenta. Physical states are assumed to be Galois singlets so that the total momentum for a bound state of fermions and antifermions has integer valued components and mass squared is integer. The condition that mass squared energy have a fixed sign for the physical states at a given boundary of the CD is natural and has been made.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">TGD as it is towards end of 2024: part II</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/TGD2024II.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-84063076415227364722024-10-30T01:04:00.000-07:002024-10-30T22:47:39.587-07:00Tegmark and TGDMax Tegmark has proposed that all that exists at the fundamental level is mathematics. Tegmark could be called a Platonist. What exists at the fundamental level would be Platonia, the world of mathematical objects. In some way, Tegmark wants to add consciousness to Platonia (see <A HREF="https://arxiv.org/pdf/1401.1219">this</A>) and of course faces the same problem as the materialists.
</p><p>
There is no hint of what qualia, the contents of consciousness, could be attached to mathematical objects. What would happen when 2<sup>1/2</sup> gets depressed or falls in love with 3<sup>1/2</sup>. What happens when 5<sup>1/2</sup> suffers jealousy towards roots of higher order polynomials because they are more complex algebraic numbers. What emotions could the roots of a polynomial feel and what sensory qualia could they experience? What about more complex structures like sets and Hilbert spaces?
</p><p>
Something is needed and it is a geometric representation of numbers and a quantum jump and its representation: it brings in awareness and free will.
<OL>
<LI> A representation of numbers as physical quantum objects is needed. Frenkel wondered in his marvellous AfterMath podcast (see <A HREF="
https://youtu.be/7eejAeqYFCg?si=z5y84GMEq3a1hYo3">this</A>) how the numbers are physically represented. Frenkel emphasized that numbers cannot not presented in spacetime. TGD offers a solution to the puzzle: numbers are represented as spacetime surfaces in H= M<sup>4</sup>×CP<sub>2</sub>. Holography=holomorphy vision (see <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">this</A>) makes this representation possible. The details of the emerging view are discussed in the article describing the TGD view of Langlands correspondence (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>) and in the article describing the two ways to interpret space-time surfaces as numbers (see <A HREF="https://tgdtheory.fi/public_html/articles/compuTGD.pdf">this</A>).
<OL>
<LI> The spacetime surface can correspond to numbers in a functional algebra with product (f<sub>1</sub>,f<sub>2</sub>)*(g<sub>1</sub>,g<sub>2</sub>)= (f<sub>1</sub>f<sub>2</sub>,g<sub>1</sub>g<sub>2</sub>) or, more restrictively, as elements of a function field with product (f<sub>1</sub>,g)*(g<sub>1</sub>,g)= (f<sub>1</sub>f<sub>2</sub>,g) with g fixed so that one obtains a family of function fields.
<LI> Space-time surfaces also correspond to complex numbers: M<sup>8</sup>-H duality (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>). The discriminant determined by the product of the differences roots of the function for 2-D parton surfaces determines the discriminant, which is a complex number in the general case and defined also for general analytic function. In school days we encountered the discriminant while solving roots of a second order polynomial.
</OL>
Space-time surfaces form an entire evolutionary hierarchy (or rather hierarchies) depending on how algebraically complex they are. Also p-adic number fields and their extensions as correlates of cognition emerge naturally through the hierarchy of algebraic extensions of rationals.
</OL>
Now we have the numbers represented as space-time surfaces and one can ask how abstractions so central for mathematical thinking emerge. For instance, how could sets and Hilbert spaces and operators in Hilbert spaces could?
<OL>
<LI> Since we are in the quantum world, we start to build wave functions in WCW, the Platonia. More specifically we construct WCW spinor field, Ψ in space and therefore also in the space the complex numbers represented as spacetime surfaces. We get quantum Platonia. The WCW spinors correspond to many-fermion Fock states in quantum field theory for a given 4-surafce and Ψ assigns to the space-time surfaced such a spinor. The spinor fields of WCW are induced from the second quantized free spinor fields of H and the 4-dimensionality of space-time surfaces and associated exotic smooth structures make possible fermion-pair creation but only in 4-D space-time.
<LI> WCW spinor field Ψ can be restricted, for example, to the set of positive and odd numbers, i.e. corresponding spacetime surfaces. The subset of WCW in which Ψ is non-vanishing, defines a subset of numbers and the concept in the classical sense as the set of its instances. For example, one obtains the concept of an odd number as a set of space-time surfaces representing odd integers. Ψ can be also restricted to the roots of polynomials of a certain degree (corresponding space-time surfaces): this gives the notion of the root of a polynomial of a given degree. Quantum concept is not a mere set but an infinite number of different WCW spinor fields that give different perspectives on the concept.
<LI> There is also a second way to define the notion of set: Boolean algebraic definition is possible using function algebra consisting of pairs (f<sub>1</sub>,f<sub>2</sub>) of a some function field obtained by keeping f<sub>2</sub>==g fixed. The product in the function field induces the product of surfaces and this product is just the union of space-time surfaces. A given set of ordinary complex numbers represented in terms of discriminants defined by the roots of analytic functions defined at partonic 2-surfaces corresponds to the product of the spacetime surfaces corresponding to the numbers in the sense of functional algebra.
</p><p>
What is of fundamental importance is that these space-time surfaces in general have a discrete set of intersection points so that there is an interaction in fermionic degrees of freedom and one obtains n-point scattering amplitudes. Fermionic Fock states restricted to the intersection indeed define naturally a Boolean algebra.
</OL>
See for instance the article <a HREF= "https://tgdtheory.fi/public_html/articles/compuTGD.pdf">Space-time surfaces as numbers, Turing and Gödel, and mathematical consciousness</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/compuTGD.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-59219004133030959292024-10-27T00:12:00.000-07:002024-10-27T00:14:24.608-07:00Space-time surfaces as numbers, Turing and Gödel, and mathematical consciousness
The stimulus for this work came the links to Bruno Marchal's posts by Jayaram Bista (see
<A HREF="https://www.facebook.com/2jaya1bista/posts/pfbid0EPvHfmaDqjHjWi9gRHxqMnssSQggAP5ieGXfRkU5JEZiHcE887vvqqjfy2upuJCzl?comment_id=413142121479178">this</A>). The original comments compared the world views behind two Platonisms, the Platonism based on integers or rationals and realized by the Turing machine as a Universal Computer and the quantum Platonism of TGD (see <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">this</A>). Marchal also talks about Digital Mechanism and claims that it is not necessary to assume a fixed physical universe "out there". Marschal also speaks of mathematical theology and claims that quantum theory and even consciousness reduce to Digital Mechanism.
</p><p>
Later these comments expanded to a vision about the geometric correlates of arithmetic and even more general mathematical consciousness based on the vision about space-time surfaces as generalized numbers and providing also a representation of the ordinary complex numbers.
</p><p>
This also led to a more detailed view about the TGD realization (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>) of Langlands correspondence (LC) in which geometric and function field versions naturally correspond to each other and the LC itself boils down to the condition that cobordisms for the function pairs (f<sub>1</sub>,f<sub>2</sub>) defining the space-time surfaces as their roots are realized as flows in the infinite-D symmetry group permuting space-time regions as roots of a function pair (f<sub>1</sub>,f<sub>2</sub>) acting in the "world of classical worlds" (WCW) consisting of space of space-time surfaces satisfying holography = holomorphy principle.
</p><p>
That space-time surfaces form an algebra with respect to multiplication and that this algebra decomposes to a union of number fields (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>) means a dramatic revision of what computation means. The standard view of computation as a construction of arithmetic functions is replaced with a physical picture in which space-times as 4-surfaces have interpretation as almost deterministic computations. Space-time surfaces allow arithmetic operations and also the counterparts of functional composition and iteration are well-defined. This would suggest a dramatic generalization of the computational paradigm and it is interesting to ponder what this might mean.
</p><p>
This also leads to a vision about the fundamental geometric correlates of arithmetic and even more general mathematical consciousness based on the vision about space-time surfaces as generalized numbers and providing also a representation of the ordinary complex numbers. The notion of concept, such as a set as a collection of its instances, can be realized at the level of WCW in terms of the locus of the WCW spinor field when space-time surfaces correspond to numbers in generalized sense or to ordinary complex numbers. Second realization analogous to Boolean algebra is in terms of the product of space-time surfaces as elements of the generalized number field. Also the notion of linear space can be realized in this way by realizing the ordering of the elements of the set geometrically. Also the notion of function can be realized.
</p><p>
Of course, my personal view of computation and metamathematics is rather limited: I am just a humble physicist thinking simple thoughts but my sincere hope is that mathematicians would realize how deep the implications of the new physics based number concept has.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/compuTGD.pdf">Space-time surfaces as numbers, Turing and Gödel, and mathematical consciousness</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/compuTGD.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-40584246468040900482024-10-22T22:04:00.000-07:002024-10-22T22:04:20.162-07:00Quantum Platonia and space-time surfaces as numbersYesterday evening we had a very interesting Zoom discussion with Marko and Ville related to Large Language Models (LLMs) and computationalism in general. We also discussed Platonism, propagated by Max Tegmark. The idea that only mathematical objects exist and that they can exist as long as they do not lead to internal logical contradictions is extremely fascinating and economical.
</p><p>
The basic problem of Tegmark's theory is that conscious experiences are absent from Platonia. Mathematical objects are most naturally zombies. It is really hard to imagine, for example, how the square root two could have intentions and free will.
</p><p>
In the zero energy ontology (ZEO) of TGD, the habitants of the Quantum Platonia would be quantum states defined as superpositions of space-time surfaces of H= M<sup>4</sup>×CP<sub>2</sub>, satisfying holography = holomorphy principle, which guarantees that one gets rid of path integral full of divergences. The choice of H is unique by the mathematical existence of TGD and so called M<sup>8</sup>-H duality leading in turn to a 4-D variant of Langlands correspondence is essential and brings the entire number theory part of TGD. Geometric and number theoretic views are dual.
</p><p>
The quantum jumps between zero energy states makes the Quantum Platonia conscious. In quantum jump, the final state contains classical information from previous states and quantum jumps. Therefore the Universe learns and is able to remember since the classical physics for the space-time surfaces implementing holography is not completely deterministic and makes possible memory recall (see <A HREF= "https://tgdtheory.fi/public_html/articles/memoryc.pdf">this</A>). The number-theoretic vision forces the increase of the algebraic complexity of space-time surfaces during the sequence of quantum jumps, which means evolution.
</p><p>
The most beautiful thing is that the space-time surfaces, represented as roots for pairs of polynomials with rational coefficients, correspond to integers (also more general analytic functions of generalized complex coordinates of H are possible). The integer corresponds to the products of discriminants D of polynomials associated with the regions (partonic 2-surfaces) of the space-time surface. The classical universe as a space-time surface is a number! The basic arithmetics could not emerge at a more fundamental level.
</p><p>
On the geometric side, the vacuum functional is identified as the exponent of the Kähler function (geometry) having a space-time surface as its argument . One the number theory side it corresponds to a power of D by M<sup>8</sup>-H duality (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>). Therefore the natural number theoretic and geometric invariants of the space-time surface correspond to each other: this is in agreement with the Langlands correspondence.
</p><p>
The discriminant D splits into the product of ramified primes, which have a direct physical interpretation that I arrived at about 30 years ago from p-adic mass calculations. The spacetime surface decomposes into particles corresponding to these primes.
</p><p>
Some mathematician, maybe it was Kronecker, said that God created the integers and the rest is man-made. In the TGD Universe, God also created algebraic integers, in fact an infinite hierarchy of these because he wanted evolution, and also these can be realized as space-time surfaces. There is no reason why God could not have also created transcendentals. Or maybe they have not yet emerged in the number theoretic evolution. The re-creation of the Universe continues forever. And one must not forget p-adic number fields and adeles since cognition is needed.
</p><p>
For the TGD as its is now see for instance the articles <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">this</A>.
</p><p>
For the most recent results related to the number theoretic aspects of TGD see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/compuTGD.pdf">this</A> .
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com1tag:blogger.com,1999:blog-10614348.post-90588783620507715822024-10-22T04:42:00.000-07:002024-10-22T22:52:12.280-07:00Space-time surfaces as numbers and conscious arithmetics at the fundamental level
The idea that the Universe could be performing arithmetics with space-time surfaces as classical worlds is fascinating. What could the physical meaning of the product and sum be and could they correspond to real physical interactions to which one can assign scattering amplitudes?
</p><p>
<B>Sum and product for the space-time surfaces</B>
</p><p>
In the case of the sum, the basic restriction is the condition that the space-time surfaces appearing as summands allow a common Hamilton-Jacobi structure (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) in M<sup>4</sup> degrees of freedom in turn inducing it for the space-time surfaces. The summed space-time surfaces must have a common hypercomplex coordinate with light-like coordinate curves and a common complex coordinate. For the product this is not required.
<OL>
<LI> One can form analogs of integers as products of polynomials inducing products of space-time surfaces as their roots. The product is defined as the root of (f<sub>1</sub>,g)*(f<sub>2</sub>,g)=(f<sub>1</sub>f<sub>2</sub>,g)). The space-time surface defined by the product is the union of the space-time surfaces defined by the factors but an important point is that they have a discrete set of intersection points. In this case there are no restrictions on Hamilton-Jacobi structures.
</p><p>
One can argue that the product represents a mere free two-particle state in topological and geometric sense. On the other hand, fermionic n-point functions defining scattering amplitudes are defined in terms of these intersection points and could give a quantum physical realization giving information of the quantum superpositions of space-time surfaces as quantum theorems. This would raise dimensions D=4 and D=8 in a completely unique role.
<LI> Could the sum of space-time surfaces (f<sub>1</sub>,g)=(0,0) and (f<sub>2</sub>,g)=(0,0) defined as a root of (f<sub>1</sub>,g)+(f<sub>2</sub>,g)=(f<sub>1</sub>+f<sub>2</sub>,g)) define a topologically and geometrically non-trivial interaction? If the functions f<sub>1</sub> and f<sub>2</sub> have interiors of causal diamonds CD<sub>1</sub> and CD<sub>2</sub> with different tips as supports (does the complex analyticity allow this?) and CD<sub>1</sub> and CD<sub>2</sub> are located within a larger CD then both f<sub>1</sub> and f<sub>2</sub> are nonvanishing only in the intersection CD<sub>1</sub>∩CD<sub>2</sub>.
</p><p>
Generalized complex analyticity requires a Hamilton-Jacobi structure (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) inside CD. It must have a common hypercomplex coordinate and complex M<sup>4</sup> coordinate inside CD and therefore inside CD<sub>1</sub>∩ CD<sub>2</sub> and also inside CD<sub>1</sub> and CD<sub>2</sub>? Suppose that this condition can be satisfied.
</p><p>
Outside CD<sub>1</sub>∩ CD<sub>2</sub> either f<sub>1</sub> and f<sub>2</sub> is identically vanishing and one has f<sub>1</sub>=0 and f<sub>2</sub>=0 as disjoint roots representing incoming particles in topological sense. In the intersection CD<sub>1</sub>∩ CD<sub>2</sub> f<sub>1</sub>+f<sub>2</sub>=0 represents a root having interpretation as interaction. f<sub>i</sub> "interfere" in this region and this interference is consistent with relativistic causality.
</p><p>
One could also assign to the sum a tensor product in fermionic degrees of freedom and define n-point functions and restrict their arguments to the self-intersection points of the intersection region CD<sub>1</sub>∩ CD<sub>2</sub>. One could also say that the sum represents z=x+y in such a way that both summands and sum are realized geometrically.
</OL>
At this moment it is unclear whether both product and sum or only product or some could be assigned with topological particle interactions. From the number theoretic point of perspective one would expect that both are involved.
</p><p>
<B>Could the Hilbert space of pairs (f<sub>1</sub>,f<sub>2</sub>) have an inner product defined by the intersection of corresponding space-time surfaces?</B>
</p><p>
The pairs (f<sub>1</sub>,f<sub>2</sub>) can be formally regarded as elements of a complex Hilbert space. There is however a huge gauge invariance: the multiplication of f<sub>i</sub> by analytic functions, which are non-vanishing inside the CD, does not affect the space-time surface. The localization of the scalar multiplication means a huge reduction in the number of degrees of freedom. Note that the multiplication with a scalar does not change the spacetime surface but this does not destroy the field property. Since f<sub>1</sub>= constant=c does not correspond to any space-time surface (this would require c=0) the multiplication with a constant does not correspond to a multiplication with a space-time surface.
</p><p>
The local complex scalings are local variants of complex scalings of Hilbert space vectors which do not affect the state: one cannot however replace Hilbert space by a projective space and the same applies now. Could space-time surfaces define a classical representation for the analogs of local wave functions forming a local counterpart of a Hilbert space?
</p><p>
How could one realize the Hilbert space inner product?
<OL>
<LI> Could one consider a sensible inner product for the pairs (f<sub>1</sub>,g) having CD as a dynamic locus (SSFRs) (see <A HREF="https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>). The only realistic option consistent with the local scaling property seems to be that the locus of the integral defining the inner product must be the intersection of the space-time surfaces defined by (f<sub>i</sub>,g<sub>i</sub>).
By their dimension, the space-time surfaces have in the generic case a discrete set of intersection points so that the inner product is non-trivial. What suggests itself is that the inner product is determined by the intersection form of the space-time surfaces, most naturally its trace. The norm would in turn correspond to self-intersection form. Does this give rise to a positive definite inner product?
<LI> The situation would be the same as in the fermionic degrees of freedom where also intersection points would appear as arguments of n-point functions. That 4-D surfaces are in question conforms with the idea of generalized complex and symplectic structures reducing the number of degrees of freedom from 8 to 4.
</OL>
<B>Could ordinary arithmetic operations be realized consciously in terms of arithmetic operations for the space-time surfaces?</B>
</p><p>
Could arithmetic operations be realized at the fundamental level. We have learned in the basic school algorithms for the basic arithmetics as stable associations and the basic arithmetics does not involve conscious thought except in the beginning when we learn the rules by concrete examples. This is very similar to what large language models do.
</p><p>
However, idiot savants (see the books "The man who mistook his wife for this hat" and "Musicophilia" by Oliver Sacks) can decompose numbers into prime factors without any idea about the concept of prime numbers and certainly do not do this consciously by an algorithm or by logical deduction. Could this process occur spontaneously at a fundamental level and for some reason idiot savants could be able to do this consciously, perhaps because they are not able to do this using usual cognitive tools. I have considered the TGD inspired model for this (see <A HREF="https://tgdtheory.fi/pdfpool/numbervision.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/intsysc.pdf">this</A>). The basic idea of various models is the same. The decomposition of a number to its factors is a spontaneous quantum process observed by the idiot savant.
<OL>
<LI> The first first thing to notice that division is the time reversal of multiplication: one has co-algebra structure. ZEO (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/zeocriticality.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A>) allows both operations and co-operations and the decomposition of an integer to factors would correspond to a product with a reversed arrow of time. Could pairs of BSFR involving temporary time reversal be involved and be easier for idiot savants than for people with ordinary cognitive abilities? Could the arrow of time in ordinary cognition be highly stable and make these feats impossible? Could the time reversal for the formation of the product of space-time surfaces as generalized numbers make ordinary conscious arithmetics possible?
<LI> M<sup>8</sup>-H duality and geometric Langlands correspondence (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>) suggest that the exponent of the Kähler function ex(K) for the region of the space-time surface represented by the polynomial with integer coefficients is some power D<sup>m</sup> of the discriminant D of a polynomial, which has integer coefficients. D decomposes to a product of powers of ramified primes p<sub>i</sub>, which are p-adically special. For a product (P<sub>1</sub>,g)*(P<sub>2</sub>,g)= (P<sub>1</sub>P<sub>2</sub>,g) of space-time surfaces, the exponent of Kähler function is product of those for factors and thus product of powers of D<sub>m</sub> for f<sub>1</sub> and f<sub>2</sub>. A polynomial must be involved and I have considered the possibility that a particular discriminant D could correspond to a partonic 2-surface determining polynomial assignable to the singularity of the space-time surfaces as a minimal surface (see <A HREF ="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>).
<LI> One can say that for polynomials (P<sub>1</sub>,P<sub>2</sub>) with integer coefficients, the space-time surface represents an ordinary integer identifiable as D with exp(K) ∝ D<sup>m</sup>. For a topological single particle state, P is irreducible but can be unstable against a splitting to 2 surfaces unless the D is prime. If exp(K) is conserved in the decay process, the splitting can produce a pair of space-time surfaces such that one has D=D<sub>1</sub>D<sub>2</sub>. This would represent physically the factorization of an integer to two factors, co-multiplication as the reversal of the multiplication operation. ZEO allows both.
</p><p>
The preservation of the exponeänt of the Kähler function in the splitting reflects quantum criticality meaning that the initial and final states are superpositions of space-time surfaces with the same value of exp(K). The thermodynamic analog is a microcanonical ensemble is a closed system in a thermodynamic equilibrium involving only states of the same energy.
<LI> This consideration generalizes trivially to the case of the sum. The product for the discriminants corresponds to the sum for their logarithms. If the system is able to physically represent the logarithm of the discriminant and also experience this representation consciously, then the product of space-time surfaces corresponds to the product of discriminants and to sum of their logarithms.
</p><p>
The natural base for the logarithm is defined by some ramified prime p appearing in the discriminant. The measurement corresponding to the measurement of the exponent k of p<sup>k</sup> would be scaling pd/dp corresponding to the scaling generator of conformal algebra extended to a 4-D algebra in the TGD framework.
</p><p>
If discriminant involves only a single ramified prime, the p-adic logarithm is uniquely defined. Just as in the case of co-product, the space-time surface representing integer k=k<sub>1</sub>+k<sub>2</sub> represented by an irreducible polynomial (f,g) splits to two space-time surfaces (f<sub>1</sub>,g) and (f<sub>2</sub>,g) representing representing integers k<sub>1</sub> and k<sub>2</sub>.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/compuTGD.pdf">Space-time surfaces as numbers <I> viz.</I> Turing and Gödel</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/Frenkel.pdf">About Langlands correspondence in the TGD framework</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-41068261398692301302024-10-19T04:18:00.000-07:002024-10-19T04:18:04.428-07:00Zero energy ontology, holography = holomorphy vision and TGD view of qualia
Zero energy ontology (ZEO) and holography = holomorphy vision providing an exact solution of classical field equations allow to solve some earlier problems of TGD inspired theory of consciousness and to sharpen earlier
interpretations. Holography = holomorphy vision generalizes 2-D conformal invariance to 4-D situation and provides a universal solution of field equations in terms of minimal surfaces defined as roots for pairs of generalized analytic functions of the generalized complex coordinates of H=M<sup>4</sup>× CP<sub>2</sub> (one of the coordinates is hypercomplex coordinate with light-like coordinate curves) (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) and <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>).
</p><p>
Consider first the implications of ZEO (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A>).
<OL>
<LI> ZEO predicts that in "big" state function reductions (BSFRs) as counterparts of ordinary SFRs the arrow of time changes. "Small" SFRs (SSFRs) are the counterpart for repeated measurements of the same observables, which in standard QM leave the system unaffected (Zeno effect). In SSFRs, the state of the system however changes but the arrow of time is preserved. This has profound implications for the understanding of basic facts about consciousness.
<LI> The sequence of SSFR corresponds to a sequence of delocalizations in the finite-dimensional space of causal diamonds CD =cd× CP<sub>2</sub> (see <A HREF="https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>) and consists of delocalizations (dispersion) followed by localizations as analogs of position measurements in the moduli parameterizing the CD. This sequence gives rise to subjective existence, self.
<LI> BSFR has interpretation is accompanied by reincarnation with an opposite arrow of geometric time. BSFR means the death of self as a sequence of "small" SFRs (SSFRs) and corresponds to falling asleep or even death. Death is therefore a completely universal phenomenon. The next BSFR means birth with the original arrow of time: it can be wake-up in the next morning or reincarnation taking place considerably later, life time is the first guess for the time scale. This follows from the fact that causal diamond CD =cd× CP<sub>2</sub> increases in size during the sequence of SSFRs.
<LI> What forces the ZEO is holography which is slightly non-deterministic due to the classical non-determinism of an already 2-D minimal surface realized as a soap film for which the frame spanning it does not fix it uniquely. This means that the 4-D space-time surface located inside CD and identifiable as the analog of Bohr orbit determined by holography must be taken as a basic object instead of a 3-surface. In SSFRs, the state at the passive light-like boundary of CD is unaffected just as in Zeno effect but the state at the active boundary changes. Due to the dispersion in the space of CDs the size of CD increases in statistical sense and the geometric time identifiable as the distance between the tips of CD increases and correlates with the subjective time identifiable as sequence of SSFRs.
<LI> In standard quantum theory, the association of conscious experience with SFRs does not allow us to understand conscious memories since the final state of state function reduction does not contain any information about the earlier states and state function reductions. Zero energy ontology leads to a concrete view of how conscious memories can be realized in the TGD Universe (see <A HREF="https://tgdtheory.fi/public_html/articles/memorytgd.pdf">this</A>). The superposition of space-time surfaces between fixed initial state and changing final state of SSFR contains the classical information about previous states and state function reductions and makes memory possible. The slight non-determinism of the classical time evolution implies loci of non-determinism as analogs of soap film frames and memory recall corresponds to a quantum measurement at these memory seats.
<LI> SSFRs correspond to repeated measurements of the same observable and the eigenvalues of the measured observables characterize the conscious experience, "qualia", partially. Also new commuting observables related to the non-determinism can appear and the set of observables can be also reduced in size. The superposition of the space-time surfaces as analogs of non-deterministic Bohr orbits however changes in the sequence of SSFRs and the associated classical information changes and can give rise to conscious experiences perhaps involving also the qualia remaining constant as long as self exists.
</p><p>
The eigenvalues associated with the repeatedly measured observables do not change during the sequence of SSFRs and one can ask if they can give rise to a conscious experience, which should be assignable to change. Could these constant qualia be experienced by a higher level self experiencing self as sub-self defining a mental image? This higher level self would indeed experience the birth and death of subself and therefore its qualia.
</p><p>
The observables at the passive boundary of CD correspond qualia of higher level self and the additional observables associated with SSFRs correspond to those of self. They would be associated with self measurements.
<LI> Note that self dies when the measured observables do not commute with those which are diagonalized at the passive boundary. It is quite possible that these kinds of temporary deaths take place all the time. This would allow learning by trial and error making possible conscious intelligence and problem solving since the algebraic complexity is bound to increase: this is formulated in terms of Negentropy Maximization Principle (see <A HREF="https://tgdtheory.fi/public_html/articles/NMPcrit.pdf">this</A>).
</OL>
ZEO and holography = holomorphy vision allow us to understand some earlier problems of TGD inspired theory of consciousness and also to sharpen the existing views.
</p><p>
<B>Two models for how sensory qualia emerge</B>
</p><p>
Concerning sensory qualia (see <A HREF="https://tgdtheory.fi/pdfpool/qualia.pdf">this</A>) I have considered two basic views.
<OL>
<LI> The first view is that the sensory perception corresponds to quantum measurements of some observables. Qualia are labelled by the measured quantum numbers.
<LI> The second, physically motivated, view has been that qualia correspond to increments of quantum numbers in SFR (see <A HREF="https://tgdtheory.fi/pdfpool/qualia.pdf">this</A>). This view can be criticized since the quantum numbers need not be well-defined for the initial state of the SFR. One can however modify this view: perhaps the redistribution of quantum numbers leaving the total quantum numbers unaffected, is what gives rise to the sensory qualia.
</p><p>
The proposed physical realization is based on the sensory capacitor model of qualia. Sensory receptors would be analogous to capacitors and sensory perception would correspond to dielectric breakdown. Sensory qualia would correspond to the increments of quantum numbers assignable to either cell membrane in the generalized di-electric breakdown. The total charges of the sensory capacitor would vanish but they would be redistributed so that both membranes would have a vanishing charge. Membranes could be also replaced with cell exterior and interior or with cell membrane and its magnetic body. Essential would be emergence or disappearance of the charge separation.
</p><p>
This picture conforms with the recent view about the role of electric and gravitational quantum coherence assignable to charged and massive systems. In particular, electric Planck constant would be very large for charged systems like cell, neuron, and DNA and in the dielectric breakdown and its time reversal its value would change dramatically.
If this is the case the dynamic character of effective Planck constant involving phase transition of ordinary to dark matter and vice versa would be essential for understanding qualia.
<LI> As the above argument demonstrated, the qualia can be decomposed to internal and external qualia. The internal qualia correspond to self-measurements of sub-self occurring in SSFRs whereas the external qualia correspond to the qualia measured by self having sub-self as a mental image. They are not affected during the life-time of the mental image. Whether the self can experience the internal qualia of subself is far from clear. The sensory capacitor model would suggest that this is the case. Also the model for conscious memories suggests the same. The internal qualia would correlate with the classical dynamics for the space-time surfaces appearing in the superposition defining the zero energy state and make possible, not only conscious memory and memory recall based on the failure of precise classical determinism, but also sensory qualia as subselves experienced as sensory mental images.
</OL>
<B>Geometric and flag manifold qualia and the model for the honeybee dance</B>
</p><p>
One can decompose qualia to the qualia corresponding to the measurement of discrete observables like spin and to what might be called geometric qualia corresponding to a measurement of continuous observables like position and momentum. Finite measurement resolution however makes these observables discrete and is realized in the TGD framework in terms of unique number theoretic discretization of the space-time surface.
</p><p>
Especially interesting qualia assignable to twistor spaces of M<sup>4</sup> and CP<sub>2</sub>.
<OL>
<LI> Since these twistor spaces are flag manifolds, I have talked about flag-manifold qualia. Their measurement corresponds to a position measurement in the space of quantization axes for certain quantum numbers. For angular momentum this space would be S<sup>2</sup>= SO(3)/SO(2) and the localization S<sup>2</sup> would correspond to a selection of the quantization axis of spin. For CP<sub>2</sub>=SU(3)U(2) the space of the quantization axis for color charges corresponds to 6-D SU(3)(U(1)× U(1), which is identifiable as a twistor space of CP<sub>2</sub>.
<LI> The twistor space of M<sup>4</sup> can be identified locally as M<sup>4</sup>× S<sup>2</sup>, where S<sup>2</sup> is the space of light-like rays from a point of M<sup>4</sup>. This space however has a non-trivial bundle structure since for two points of M<sup>4</sup> connected by a light-like ray, the fibers intersect.
</OL>
What is the corresponding flag manifold for M<sup>4</sup>?
<OL>
<LI> The counterpart of the twistor sphere would be SO(1,3)/ISO(2), where ISO(2) is the isotropy group of massless momentum identifiable as a semidirect product of rotations and translations of 2-D plane. SO(1,3)/ISO(2) corresponds to the 3-D light-cone boundary (other boundary of CD) rather than S<sup>2</sup> since it has one additional light-like degree of freedom. Is the twistor space as a flag manifold of the Poincare group locally M<sup>4</sup>× SO(1,3)/ISO(2). This is topologically 7-D but metrically 6-D. Since light rays are parametrized by S<sup>2</sup> one can also consider the possibility of replacing M<sup>4</sup>× SO(1,3)/ISO(2) with S<sup>2</sup> in which case the twistor space would be 6-D and represented a non-trivial bundle structure.
<LI> Could one restrict M<sup>4</sup> to E<sup>3</sup> or to hyperbolic 3-sphere H<sup>3</sup> for which light-cone proper time is constant? In these cases the bundle structure would trivialize. What about the restriction of M<sup>4</sup> to the light-like boundaries of CD? The restriction to a single boundary gives non-trivial bundle structure but seems otherwise trivial. What about the union of the future and past boundaries of CD? The bundle structure would be non-trivial at both boundaries and there would also be light-like rays connecting future and past light-like boundaries.
</p><p>
The unions ∪<sub>i</sub> H<sup>3</sup><sub>i</sub>(a<sub>i</sub>) of hyperbolic 3-spaces corresponding different values a=a<sub>i</sub> of the light-cone propert time a emerge naturally in M<sup>8</sup>-H duality and could contain the loci of the singularities of space-time surfaces as analogs of frames of soap filmas. Also these would give rise to a non-trivial bundle structure.
</p><p>
These identifications differ from the usual identification of the M<sup>4</sup> twistor space as CP<sub>3</sub>: note that this identification of the M<sup>4</sup> twistor space is problematic since it involves compactification of M<sup>4</sup> not consistent with the Minkowski metric. Holography = holomorphy vision in its recent form involves a general solution ansatz in terms of roots of two analytic functions f<sub>1</sub> and f<sub>2</sub> and f<sub>2</sub>=0 (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>), which identifies the twistor spheres of the twistor spaces of M<sup>4</sup> and CP<sub>2</sub> represented as metrically 6-D complex surfaces of H. M<sup>4</sup> twistor sphere corresponds to the light-cone boundary in this identification. This identification map also defines cosmological constant as a scale dependent dynamical parameter.
</OL>
A basic application for the twistor space of CP<sub>2</sub> has been in the TGD based model (see <A HREF="https://tgdtheory.fi/pdfpool/qualia.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/Shipmanagain.pdf">this</A>) for the findings of topologist Barbara Shipman (see <A HREF="https://math.cornell.edu/~oliver/Shipman.gif">this</A>) who made the surprising finding that the twistor space of CP<sub>2</sub>, naturally assignable to quarks and color interactions, emerges in the model for the dance of honeybee. This kind of proposal is nonsensical in the standard physics framework but the predicted hierarchy of Planck constants and p-adic length scales make possible scaled variants of both color and electroweak interactions and there is a lot of empirical hints for the existence of this hierarchy, in particular for the existence as a scaled up variants of hadron physics leading to a rather radical proposal for the physics of the Sun (see <A HREF="https://tgdtheory.fi/public_html/articles/Haramein.pdf">this</A>).
</p><p>
Shipman found that the honeybee dance represents position in SU(3)/U(1)× U(1) coding for the direction and distance of the food source in 2-D plance! Why should this be the case? The explanation could be that the space-time surfaces as intersections of 6-D counterparts of the twistor spaces ISO(2)× ∪<sub>i</sub> H<sup>3</sup>(a=a<sub>i</sub>) <I> resp.</I> SU(3)/U(1)× U(1) identified as a root of analytic function f<sub>1</sub> <I> resp.</I> f<sub>2</sub> (see <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A>) have space-time surface as 4-D intersection so that honeybee dance would map the point of the flag manifold SU(3)/U(1)× U(1) to a point of M<sup>4</sup>× S<sup>2</sup> or ∪<sub>i</sub> H<sup>3</sup>(a=a<sub>i</sub>)× ISO(2) (locally). The restriction to a 2-D subset of points could be due to the measurement of the distance of the food source represented by the point of H<sup>3</sup><sub>i</sub> (or M<sup>4</sup>).
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/qualia2022.pdf">Some objections against TGD inspired view of qualia</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/qualia.pdf">General Theory of Qualia</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-13421862555383561092024-10-18T00:05:00.000-07:002024-10-18T01:38:17.107-07:00IIT and TGD
Gary Ehlenberg sent a link to an article about Integrated Information Theory of consciousness (IIT) (see <A HREF="https://royalsocietypublishing.org/doi/10.1098/rstb.2014.0167">this</A>). The article gives a nice summary of IIT. Gary wondered whether quantum theory is completely left out. The suspicion of Gary was correct: there is no mention of quantum theory.
</p><p>
It is good to attach here the abstract of the article "Consciousness: here, there and everywhere?" of Tononi and Koch published in the Philosophical Transactions of the Royal Society B in to give a general perspective.
</p><p>
<I> The science of consciousness has made great strides by focusing on the behavioural and neuronal correlates of experience. However, while such correlates are important for progress to occur, they are not enough if we are to understand even basic facts, for example, why the cerebral cortex gives rise to consciousness but the cerebellum does not, though it has even more neurons and appears to be just as complicated. Moreover, correlates are of little help in many instances where we would like to know if consciousness is present: patients with a few remaining islands of functioning cortex, preterm infants, non-mammalian species and machines that are rapidly outperforming people at driving, recognizing faces and objects, and answering difficult questions.
</p><p>
To address these issues, we need not only more data but also a theory of consciousness one that says what experience is and what type of physical systems can have it. Integrated information theory (IIT) does so by starting from experience itself via five phenomenological axioms: intrinsic existence, composition, information, integration and exclusion. From these it derives five postulates about the properties required of physical mechanisms to support consciousness.
</p><p>
The theory provides a principled account of both the quantity and the quality of an individual experience (a quale), and a calculus to evaluate whether or not a particular physical system is conscious and of what. Moreover, IIT can explain a range of clinical and laboratory findings, makes a number of testable predictions and extrapolates to a number of problematic conditions.
</p><p>
The theory holds that consciousness is a fundamental property possessed by physical systems having specific causal properties. It predicts that consciousness is graded, is common among biological organisms and can occur in some very simple systems. Conversely, it predicts that feed-forward networks, even complex ones, are not conscious, nor are aggregates such as groups of individuals or heaps of sand. Also, in sharp contrast to widespread functionalist beliefs, IIT implies that digital computers, even if their behaviour were to be functionally equivalent to ours, and even if they were to run faithful simulations of the human brain, would experience next to nothing.</I>
</p><p>
The article lists the 5 basic postulates of IIT leading to a numerical measure for the level of consciousness of a system. I wrote about IIT years ago and compared it with the TGD inspired theory of consciousness (see <A HREF="https://tgdtheory.fi/pdfpool/tononikoch.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/panel2016.pdf">this</A>). It is interesting to take a fresh look at IIT since the mathematical and physical understanding of TGD has evolved dramatically during these 8 years.
<OL>
<LI> The basic criticism is already raised by the idea that conscious experience means property of a system, consciousness. This reflects the materialistic view that conscious experience is a property of the system just as the mass and leads to the well-known philosophical problems. Materialism leads to problems with free will for instance.
<LI> The key problem is what subjective existence means and here materialism, idealism and dualism fail. Here quantum theory comes to the rescue and allows us to assign subjective existence as experience to state function reduction (SFR), or rather the interval between two SFRs. The SFRs would be those which in standard wave mechanics correspond to repeated measurements of the same observables and in that context would have no effect on the system. In the zero energy ontology of TGD the state of system changes and "small" SSFRs give rise to the experienced flow of subjective time correlating with that of geometric time .
<LI> Also the assumption that the consciousness just exists or does not, is too simplistic. Already Freud realized Id-ego-super-ego triality and physics based picture strongly suggests that conscious entities form hierarchies just as physical systems do. There would exist very naturally a hierarchy of selves. They would have subselves, perhaps as mental images, etc.. and being subselves of higher levels selves. This would however be a dramatic deviation from the western world view. Although IIT assumes panpsychism, the lack of this realization reflects the brain centered view of neuroscience very analogous to the Earth centered world view before the emergence of astrophysics.
<LI> I saw no mention related to the problem of time: what is the relation between geometric time of physicists and the flow of subjective time which is the essential element of conscious experience.
<LI> About what death and sleep mean, IIT does not say anything at the philosophical level. Loss of consciousness can be explained as a reduction of the level of integration (more or less connectedness of the system) measured by the number Φ.
<LI> Metabolic energy feed is essential for life and consciousness and I saw no mention of this.
</OL>
There are 5 postulates which are proposed to give rise to a criteria for when the system is conscious.
</p><p>
<B> 1. Intrinsic existence</B>
</p><p>
Cause-effect power is taken as a key criterion. Cause effect power is understood classically since quantum theory is not involved. Cause effect power has several corresponds in TGD.
<OL>
<LI> In TGD the classical correlate of cause-effect power at the space-time level is holography stating that 3-D data (3-surface dictates the space-time surface as analog of Bohr orbit. There is however a slight failure of determinism and this forces us to take these 4-D Bohr orbits as basic objects. They are classical correlates for almost deterministic behavioral patterns and SSFRs between different superpositions of Bohr orbits give rise to subjective time evolution.
<LI> In TGD "small" SFRs (SSFRs) are t quantum correlates of cause-effect power. "Big" SFRs (BSFRs) give rise to the death (sleep state) of the system and reincarnation with an opposite arrow of geometric time. Second BSFR means wake-up.
</p><p>
BSFRs are essential for understanding biological processes like homeostasis. A pair of BSFRs means sleep period during which the entropy of the system is reduced and the system wakes up as a less entropic system. This is essential in the battle of the living systems against second law.
<LI> Causal diamond (CD= cd×CP<sub>2</sub>) is the correlate of the cause-effect power at the level of the H=M<sup>4</sup>×CP<sub>2</sub>. cd has geometry of causal diamond and the two light-like boundaries are in asymmetric relation. At the passive boundary the states do nt changes in SSFRs. It can be said to be the causal agent. At the active boundary they change. Also the size of CD increases in statistical sense and geometric time corresponds to the increasing temporal distance between the tips of CD. In BSFR the roles of active and passive boundaries of CD change.
</p><p>
I must admit that I did not understand the illustrations of cause-effect structure involving Boolean algebra. Boolean functions are one way to see causality. In physics, classical deterministic time evolution defines a more general cause-effect structure.
</OL>
<B>2. Composition</B>
</p><p>
Systems are structured. In standard physics, where space-time is infinite and without topological structure, there is no fundamental definition for what this means and only phenomenological models are possible. In TGD, many-sheeted 3-space decomposes to a union of 3-surfaces which can fuse and decay and these processes occur also in scales essential for life and consciousness and also we perceive the many-sheeted space-time and these processes directly but our education make it impossible to realize this.
</p><p>
<B>3. Information</B>
</p><p>
Cause-effect repertoire is taken as a basic concept behind the notion of information.
<OL>
<LI> In TGD, a cause-effect repertoire corresponds to different 4-D Bohr orbits associated with the same 3-surfaces holographic data. These are the space-time correlates for the behaviours.
<LI> As the algebraic complexity of the space-time surface increases, the size of the repertoire increases. The dimension of extension of rationals assignable to the space-time regions measures this complexity and is assumed to define effective Planck constant which in turn gives a measure for the scale of quantum coherence serving as a measure for the evolutionary level of the system. This means deviation from the standard quantum theory with single Planck constant. Field bodies as carriers of dark phases of ordinary particles means a second deviation made possible by the new view of classical fields.
<LI> Number theoretic view of TGD is something completely new and allows to define the notion of conscious information. p-Adization and adelization in turn gives correlates of cognition and one can assign to the system an entanglement negentropy as the sum of its p-adic variants. Entanglement negentropy is positive and increases with the complexity of the system. It is larger than real entanglement entropy and its increase implies the increase of the latter: cognition produces unavoidably ordinary entropy.
<LI> The number theoretic entanglement negentropy could be seen as a counterpart of an integrated information and measures the cognitive level of the system and the level of cognitive consciousness.
</p><p>
Number theoretic evolution as an unavoidable increase of complexity in the sequence of state function reductions forces the increase of this entanglement entropy so that the potentially conscious information of the system necessarily increases.
<LI> The ZEO based view of quantum jump (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A>, <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>) allows to understand how systems are able to have memories about their states before SSFRs: in standard quantum theory this is not possible. Therefore Universe making SSFRs and BSFRs learns more and more about itself and is able to remember what it has learned (see <A HREF="https://tgdtheory.fi/public_html/articles/memorytgd.pdf">this</A>).
</p><p>
In IIT, the qualia space is identified as cause-effect space. In the TGD framework SSFR leads to a final state containing information about the previous quantum state since it is identified as a superposition of classical space-time surfaces leading from the fixed initial state at the passive boundary of the CD to the active boundary of CD. The original proposal that qualia are simply labelled by the quantum numbers measured in SSFR is not quite correct. The qualia also involve classical information about the SSFR via the superposition of space-time surfaces between initial (fixed) and final classical states: this would be the counterpart for the cause-effect.
</OL>
<B>4. Integration</B>
</p><p>
The counterpart of integration in the TGD framework is entanglement.
<OL>
<LI> Entanglement entropy to which one can assign adelic negentropy measures the degree of entanglement and integration. In SFR the entanglement is reduced: the system decomposes to two parts. This is the basic aspect of conscious experience. About this says IIT nothing.
<LI> Monopole flux tubes connecting parts of the system to a single coherent whole provide a classical correlate for the entanglement and in SFRs
the flux tube connections between the two parts of the system could split. More precisely, pairs of flux tubes connecting the subsystems reconnect to U-shaped flux tubes associated with the systems: the connection is split, SFR has occurred.
<LI> In biology reconnection is fundamental, for instance for bio-catalysis and for the recognition of molecules by the immune system.
Death of the system means splitting of these flux tubes. These flux tubes carry dark matter as large h<sub>eff</sub> phases. There must be a metabolic energy feed to prevent the values of h<sub>eff</sub> from decreasing. This leads to reduction of the cognitive level and geometrically to the shortening of the U-shaped flux tubes so that the system loses the control of its environment and receives information from a smaller volume.
</OL>
<B> 5. Exclusion </B>
</p><p>
Exclusion postulate states that cause effect structure must be definite. The notion is described in terms of a phenomenological set theoretic picture. I did not understand the Boolean illustrations of the cause effect structure. The notion of maximal irreducibility can be understood in TGD as maximal connectedness or at least connectedness of the 3-surface by connecting flux tubes (or in the weakest sense, the 4-surfaces as analog of Bohr orbit).
</p><p>
What precisely defined cause-effect structure could mean in ZEO? The state at the passive boundary of CD remains fixed during the sequences of SSFRs determining the life-cycle (wake-up period of self) so that one can can say that classically the almost deterministic evolution of the space-time surface is implied by the 3-surface at the passive boundary, it acts as a causal agent. The small failure of determinism means that there are also intermediate "agents" slightly affecting the time evolution. They also make possible memory and force ZEO solving the basic problem of the quantum measurement theory and allowing also free will.
</p><p>
<B>What is missing from IIT?</B>
</p><p>
The postulates of IIT are inspired by computationalism and materialistic neuroscience and have no connection to (quantum) physics or biology. The hierarchy of selves is a central notion missing completely in IIT and this hierarchy is essential for a real understanding of conscious entities. The levels of the hierarchy interact. For instance, the field body (magnetic body) carrying dark matter as large h<sub>eff</sub> phases of dark matter serves as a boss of the biological body carrying ordinary matter. Cognitive hierarchies as hierarchies of extensions of rationals giving rise to directed entanglement hierarchies are also something not possible in the standard physics.
</p><p>
These hierarchies are also essential for understanding evolution. In particular, classical gravitational and electromagnetic fields give rise to field bodies with very long quantum coherence lengths, even of astrophysical size and these scales are predicted to be fundamental for understanding life and consciousness in ordinary living matter.
</p><p>
The somewhat surprising prediction of IIT is that ordinary computers need not be conscious. In TGD this is possible only if the quantum coherence time is longer than the clock period but the contents of consciousness need not correlate with the program. The change of the arrow of time in BSFRs makes possible the analogs of feedback loops at various layers of the self hierarchy and learning by trial and error and would be the basic aspect of living systems.
</p><p>
Whether ordinary computers could be conscious is an interesting question and in TGD one ends up with a quantitative criterion for this in terms of the clock frequency (see <A HREF="https://tgdtheory.fi/public_html/articles/tgdcomp.pdf">this</A>). For the Earth's gravitational body, the lower bound for the clock frequency is 67 Hz. For the solar gravitational body, the clock frequency should be above 50 Hz which is the average EEG frequency and satisfied for the ordinary computers. Does this mean that the users of computers can entangle with them? It has been claimed that when a chicken entangles with a robot whose motion is based on a random number generator, the robot seems to take the role of Mother.
</p><p>
See <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">TGD as it is towards end of 2024: part I</A>
and <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">TGD as it is towards end of 2024: part II</A>. See also the article <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf"> About Langlands correspondence in the TGD framework</A> describing the connection between number theoretic and geometric visions of physics.
</p><p>
See also the chapter <A HREF="https://tgdtheory.fi/public_html/articles/panel2016.pdf">Questions about IIT</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com2tag:blogger.com,1999:blog-10614348.post-17196061158867966412024-10-17T02:12:00.000-07:002024-10-19T23:32:58.042-07:00A TGD based resolution of the tension between neutrino mass scale deduced from neutrino mixing and from gravitational lensing
I learned about very interesting findings related to neutrinos (see <A HREF="https://www.sciencenews.org/article/neutrino-mass-phenomenon-cosmology">this</A>). The 3 neutrino families are known to mix and from various experiments, also from those performed in the laboratory, one can deduce estimates for the analog of the CKM matrix describing the mixing. This also allows us to estimate the sum of the neutrino masses.
</p><p>
One can also deduce information about neutrino masses from cosmology. The information comes from gravitational lensing. The gravitational lensing increases with so called clumpiness which measures how the inhomogeneities of mass density are. If one assumes standard cosmology with cold dark matter, one expects that the larger the average neutrino mass scale is, the larger the effects of the neutrino mass density on the clumpiness of the universe is.
</p><p>
According to the popular article, DESI maps out cosmic structures to determine the expansion rate through an effect known as baryon acoustic oscillations, sound waves that imprinted circular patterns on the very early universe. By tracing those patterns at different points in the universe s history, scientists can track its growth, kind of cosmic tree rings are in question.
</p><p>
Combining the measurements of clumpiness from the cosmic microwave background and the expansion rate from DESI two things that neutrinos affect makes it possible for scientists to deduce estimates for the sum of neutrino masses. The upper limit turned out to be unexpectedly small, about .07 eV. This is very near to the lower bound for the sum, about .06 eV deduced from the neutrino mixing. There are even experiments suggesting an upper limit of .05 eV in conflict with neutrino mixing data.
</p><p>
The outcome suggests that something goes wrong with the standard cosmology. Could it be that neutrinos do not affect the clumpiness so much as believed? Could neutrinos be lighter in the early cosmology? Or is the view of how clumpiness is determined, entirely wrong? Could the mechanism behind the gravitational lensing be something different from what it is believed to be?
</p><p>
This brings to mind what is called the clumpiness paradox about which I have written a blog posting (see <A HREF="https://matpitka.blogspot.com/2023/06/clumpiness-paradox-of-cold-dark-matter.html">this</A>). Clumpiness paradox means that the clumpiness depends on the scale in which it is estimated. Clumpiness is smaller in long length scales. One proposal is that in long length scales clumpiness is determined to a high degree by the mass density of ultralight axions. The clumps have been now observed also in shorter scales. The strange conclusion is that cold dark matter is colder in short scales. One would expect just the opposite to be true.
</p><p>
The scale dependence of clumpiness suggests a fractal distribution of matter and dark matter. Indeed, in the TGD framework, cosmic strings thickened to monopole flux tubes forming scale hierarchy would be responsible for the gravitational lensing and the thickness of the monopole flux tubes would characterize the lensing. The explanation for the large size of the clumps in long scales would be the large size of the Compton length proportional to effective Planck constant h<sub>eff</sub>=nh<sub>0</sub>. In the case of gravitational Planck constant h<sub>eff</sub>= h<sub>gr</sub>= GMm/β<sub>0</sub>, β<sub>0</sub> a velocity parameter, assignable to the monopole flux tubes connecting pairs formed by a large mass M and small mass m, the gravitational Compton length is equal to Λ<sub>gr</sub>= GM/β<sub>0</sub>= r<sub>s</sub>/2β<sub>0</sub>, r<sub>s</sub> Schwartshild radius of M increasing with the size scale of structure (note that there is no dependence on m). The larger the scale of the studied astrophysical object, the larger Λ<sub>gr</sub> as minimal gravitational quantum coherence length is, and the smaller the clumpiness in this scale.
</p><p>
This would predict the effect of neutrinos and also other particles on lumping and gravitational lensing is negligible. Cosmic strings would explain the lumping. The model would also explain why the upper bound for the sum of neutrino masses is inconsistent with the findings from neutrino mixing.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the Recent TGD Based View Concerning Cosmology and Astrophysics</A>
or the <A HREF="https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-47587253298016218592024-10-12T21:46:00.000-07:002024-10-20T01:24:41.053-07:00Why the dark energy density is inversely proportional to the surface area of the volume studied?
Sabine Hossenfelder commented in her posting "Surprise Comeback: Dark Energy Could Be Holographic After All" (see <A HREF="https://www.youtube.com/watch?v=NHrL4fkyWKI">this</A>) the idea that the mysterious dark energy might not be real but an outcome of holography and assignable to the 3-D surface which in holography contains the information determining the dynamic in the interior of the space-time. The comments were inspired the the article "Evolution of perturbations in the model of Tsallis holographic dark energy" (see <A HREF="https://arxiv.org/abs/2406.10383">this</A>) by Astashenok and Tepliakov..
</p><p>
The starting point observation is that the dark energy density is in a good approximation found to be proportional to 1/S, where S is the surface area of a large sphere surrounding the region studied. By the way, Sabine makes a little mistake here: she talks about dark energy rather than dark energy density. The reader can check this from the article of by Astashenok and Tepliakov. The model of Tsallis has been given up long ago but the authors represent an argument that since dark energy is not ordinary cosmic fluid, ordinary perturbation theoretic analysis does not apply.
</p><p>
TGD suggests however a much simpler explanation of the finding. In TGD, dark energy is identifiable as a galactic dark matter and consists of magnetic and volume energy assignable to very long monopole flux tubes with a huge string tension. No galactic dark matter halo nor exotic dark matter particles are needed. The galactic velocity spectrum is correctly predicted from the string tension which is also predicted.
</p><p>
To see whether TGD can explain the finding that dark energy density is proportional to 1/S, one must estimate the average density of dark energy in a large cylindrical volume around a long cosmic string. The dark energy is proportional to the length L of the string. The volume is roughly V=SL, where S, is the surface area of the cross section of the cylinder. Therefore one has that dark energy density satisfied E/V= E/SL= 1/S. Just as has been found.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/anomcoll.pdf">Some strange astrophysical and cosmological findings from the TGD point of view</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> .
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-75674189819238512602024-10-07T20:57:00.000-07:002024-10-07T20:57:09.290-07:00Is it possible to have objective laws of physics?
Daniel Oriti (see <A HREF="https://www.newscientist.com/article/mg26435120-900-the-physicist-who-argues-that-there-are-no-objective-laws-of-physics/">this</A>) concludes that there are no objective laws of physics. 40 years ago, the views were very different but the dramatic failure of the superstring approach together with the multiverse catastrophe changed the optimistic opinions. It is of course psychologically much easier to conclude that there are no objective laws than to admit that my generation failed to find them.
</p><p>
The answer to the question depends on what one means with objective reality. If space-time is taken as objective reality, there is no such thing as objective reality, something existing independent of observer.
In the TGD framework, one can speak only of space-time surfaces in H=M<sup>4</sup>×CP<sub>2</sub> as analogs of Bohr orbits for particles as 3-surfaces, and obeying almost deterministic holography forcing the Bohr orbits to be basic dynamical objects. Zero energy ontology (ZEO) is the new ontology solving the basic paradox of quantum measurement theory. Quantum states are quantum superpositions of these "Bohr orbits".
</p><p>
There are global objective laws: they reduce the mathematical existence of TGD. H isn fixed by existence of the twistor lift and number theory-geometry duality (M<sup>8</sup>-H duality) and holography= holomorphy principle giving holomorphic 4-surfaces, as minimal surfaces, and as extremals of any general coordinate invariant action constructible in terms of the induced geometry. Action makes itself visible only at singularities. Induction fixes the dynamics for fermions: second quantized free spinor fields in H.
Fermion pair creation is possible thanks to the 4-D spacetime allowing exotic smooth structures as defects of standard one. The point-like defects define vertices and are also identifiable as (self-) intersections of space-time surfaces. Dimensions D=4 and D=8 for space-time and H are crucial for non-trivial physics.
</p><p>
Space-time surfaces are expressible as roots for pairs(f<sub>1</sub>,f<sub>2</sub>) of analytic functions of 4 generalized complex coordinates of H (one is hypercomplex coordinate with light-like coordinate curves). They form an algebra induced by the arithmetic operators for f<sub>i</sub>. This algebra decomposes to a union of number fields with f<sub>2</sub> fixed. Space-times are thus generalized numbers: this realizes geometric Langlands correspondence (see <A HREF="https://tgdtheory.fi/public<sub>h</sub>tml/articles/Frenkel.pdf">this</A> and <A HREF="https://tgdtheory.fi/public<sub>h</sub>tml/articles/compuTGD.pdf">this</A>) .
</p><p>
The space of space-time surfaces defining a number system, the world of classical worlds (WCW) and it exists objectively. Subjective existence means sequence of quantum jumps between states defined by WCW spinor fields, this means hopping around in WCW. ZEO allows a realization of conscious memory so that the system learns all the subjective time about physics (see <A HREF="https://tgdtheory.fi/public_html/articles/memorytgd.pdf">this</A>).
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-53062590885863139352024-10-03T23:37:00.000-07:002024-10-22T22:20:17.762-07:00Negative group delay and Zero Energy Ontology
Paul Kirsch sent an interesting link to a finding to an article "Experimental evidence that a photon can spend a negative amount of time in an atom cloud" (see <A HREF="https://arxiv.org/abs/2409.03680">this</A>).
</p><p>
The finding is very interesting from from the point of view of zero energy ontology (ZEO) defining the ontology of classical and quantum TGD (see <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/zeonewest.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/zeocriticality.pdf">this</A>). Could the negative group delay be understood in terms of a time period with a reversed arrow of time spent by the photon around an atom?
<OL>
<LI> Absorption and re-emission by atom would correspond to two types of "big" state function reductions (BSFRs) taking place. In the first BSFR photon would "die" by absorption by an atom. Photon would however reincarnate with an opposite arrow of time. The same would happen in the second BSFRs and photon would reincrane with the original arrow of time.
</p><p>
According to the recent view of ZEO, after the second BSFR the photon would emerge geometrically later than it was absorbed in the first BSFR. The photon wave packet would come out as less entropic, that is younger. This effect would be like waking up as a less entropic, in this sense a younger person after a well slept night.
<LI> Does the group delay measure this effect? If the aging of the wave packet means widening then this might be the case. Free photon wave packet keeps its shape since it does not disperse. The widening must be of thermodynamic origin and would be due to SSFRs replacing the wave packet gradually with a wider one.
<LI> In TGD, the shape preserving wave packet has as a classical geometric correlates a "massless extremal" (ME) representing a pulse propagating in a precise direction. The shape of pulse does not change but "small" state function reductions (SSFRs) would replace ME with a new one representing in general a wider pulse. This would be dissipation: ME would age. The pair of BSFRs induced by atomic absorption would lead to a reincarnation as a younger ME.
This would be the counterpart for the group delay.
</OL>
The finding creates a tongue in cheek consideration related to my personal life. I suffer from bad sleep and wake-up continually. BSFR means falling asleep or in an extreme case death at some level of the personal self hierarchy. Temporary reversals of the arrow of time in pairs of BSFRs would provide a universal trial and error mechanism in conscious information processing and quantum biology. For instance, homeostasis as a way to stay near quantum criticality would be based on continual change of the arrow of time. If the temporary deaths indeed provide a way to fight against the second law, they might slow down aging. The personal curse would be actually a blessing?
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcondmatshort.pdf">TGD and Condensed Matter</A> or a <a HREF= "https://tgdtheory.fi/pdfpool/TGDcondmatshort.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-85027724260587009602024-10-03T22:58:00.000-07:002024-10-04T23:47:25.419-07:00Surfaceology and TGD
The inspiration coming from the work of Nima Arkani-Hamed and colleagues concerning the twistor Grassmannian approach provided a strong boost for the development of TGD. I started from the problems of the twistor approach and ended up with a geometrization of the twistor space in terms of sub-manifold geometry with twistor space represented as a 6-surface. Also the twistor space of CP<sub>2</sub> played a key role.
</p><p>
This led to rather dramatic results. Most importantly, the twistor lift of TGD is possible only for H=M<sup>4</sup>× CP<sub>2</sub> since only M<sup>4</sup> and CP<sub>2</sub> allow twistor space with Kähler structure: TGD is unique. The most recent result is that one can formulate the twistor-lift in terms of 6-surfaces of H (rather than 6-surfaces in the product of the twistor spaces of M<sup>4</sup> and CP<sub>2</sub>). These twistor surfaces represent twistor spaces of M<sup>4</sup> and CP<sub>2</sub> or rather their generalizations, their intersection would define the space-time surface. Therefore one can formulate the twistor lift without the the 12-D product of twistor spaces of M<sup>4</sup> and CP<sub>2</sub>.
</p><p>
During last years I have not followed the work of Nima and others since our ways went in very different directions: Nima was ready to give up space-time altogether and I wanted to replace it with 4-surfaces. I was also very worried about giving up space-time since twistor is basically a notion related to a flat 4-D Minkowski space.
</p><p>
However, in Quanta Magazine there there was recently a popular article telling about the recent work of Nima Arkani Hamed and his collaborators (see <A HREF="https://www.quantamagazine.org/physicists-reveal-a-quantum-geometry-that-exists-outside-of-space-and-time-20240925/">this</A>). The title of the article was "Physicists Reveal a Quantum Geometry That Exists Outside of Space and Time". The article discusses the notions of amplituhedron and associahedron which together with the twistor Grassmann approach led to considerable insights about theories with N=4 supersymmetry. These theories are however rather limited and do not describe physical reality. In the fall of 2022, a Princeton University graduate student named Carolina Figueiredo realized that three types of particles lead to very similar scattering amplitudes. Some kind of universality seems to be involved. This leads to developments which allow to generalize the approach based on N=4 SUSY.
</p><p>
This approach, called surfaceology, still starts from the QFT picture, which has profound problems. On the other hand, it suggests that the calculational algorithms of QFT lead universally to the same result and are analogous to iteration of a dynamics defined in a theory space leading to the same result irrespective of the theory from which one starts from: this is understandable since the renormalization of coupling constants means motion in theory space.
</p><p>
How does the surfaceology relate to TGD?
<OL>
<LI> What one wants are the amplitudes, not all possible ways to end up them. The basic obstacle here is the belief in path integral approach. In TGD, general coordinate invariance forces holography forcing to give up path integral as something completely unnecessary.
<LI> Surfaceology and brings strongly in mind TGD. I have talked for almost 47 years about space-time as surfaces without any attention from colleagues (unless one regards the crackpot label and the loss of all support as such). Now I can congratulate myself: the battle that has lasted 47 years has ended in a victory. TGD is a more or less mature theory.
</p><p>
It did not take many years to realize that space-times must be 4-surfaces in H=M<sup>4</sup>×CP<sub>2</sub>, which is forced by both the standard model symmetries including Poincare invariance and by the mathematical existence of the theory. Point-like particles are replaced with 3-surfaces or rather the 4-D analogs of their Bohr orbits which are almost deterministic. These 4-surfaces contain 3-D light-like partonic orbits containing fermion lines. Space-time surfaces can in turn be seen as analogs of Feynman graphs with lines thickened to orbits of particles as 3-surfaces as analogs of Bohr orbits.
<LI> In holography=holomorphy vision space-time surfaces are minimal surfaces realized as roots of function pairs (f<sub>1</sub>,f<sub>2</sub>) of 4 generalized complex coordinates of H (the hypercomplex coordinate has light-like coordinate curves). The roots of f<sub>1</sub> and f<sub>2</sub> are 6-D surfaces analogous to twistor spaces of M<sup>4</sup> and CP<sub>2</sub> and their intersection gives the space-time surface. The condition f<sub>2</sub>=0 defines a map between the twistor spheres of M<sup>4</sup> and CP<sub>2</sub>. Outside the 3-D light-like partonic orbits appearing as singularities and carrying fermionic lines, these surfaces are extremals of any general coordinate invariant action constructible in terms of the induced geometry. In accordance with quantum criticality, the dynamics is therefore universal.
</p><p>
Holography=holomorphy vision generalizes ordinary holomorphy, which is the prerequisite of twistorialization. Now light-like 4-D momenta are replaced with 8-momenta
which means that the generalized twistorialization applies also to particles massive in 4-D sense.
</OL>
This indeed strongly resembles what the popular article talks about surfaceology: the lines of Feynman diagrams are thickened to surfaces and lines are drawn to the surfaces which are however not space-time surfaces. Note that also Nima Arkani-Hamed admits that it would be important to have the notion of space-time.
</p><p>
The TGD view is crystallized in Geometric Langlands correspondence is realized naturally in TGD and implying correspondence between geometric and number theoretic views of TGD.
<OL>
<LI> Space-time surfaces form an algebra decomposing to number fields so that one can multiply, divide, sum and subtract them. The classical solution of the field equations can be written as a root for a pair of analytic functions of 4 generalized complex coordinates of H. By holography= holomorphy vision, space-time surfaces are holomorphic minimal surfaces with singularities to which the holographic data defining scattering amplitudes can be assigned.
<LI> What is marvelous is that the minimal surfaces emerge irrespective of the classical action as long as it is general coordinate invariant and constructed in terms of induced geometry: action makes itself visible only at the partonic orbits and vacuum functional. This corresponds to the mysterious looking finding of Figueiredo.
</p><p>
There is however a unique action and it corresponds to Kähler action for 6-D generalization of twistor space as surface in the product of twistor spaces of M<sup>4</sup> and CP<sub>2</sub>. These twistor spaces of M<sup>4</sup> and CP<sub>2</sub> must allow Kahler structure and this is only possible for them. TGD is completely unique. Also number theoretic vision as dual of geometric vision implies uniqueness. A further source of uniqueness is that non-trivial fermionic scattering amplitudes exist only for 4-D space-time surfaces and 8-D embedding space.
<LI> Scattering amplitudes reduce at fermionic level to n-point functions of free field theory expressible using fermionic propagators for free leptonic and quark-like spinor fields in H with arguments restrict to the discrete set of self-intersections of the space-time surfaces and in more general case to intersections of several space-time surfaces. This works only for 4-D space-time surfaces and 8-dimensional H. Also pair creation is possible and is made possible by the existence of exotic smooth structures, which are ordinary smooth structures with defects identifiable as the intersection points. Therefore there is a direct correspondence with 4-D homology and intersection form (see <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A>). One can say that TGD in its recent form provides an exact construction recipe for the scattering amplitudes.
<LI> There is no special need to construct scattering amplitudes in terms of twistors although this is possible since the classical realization of twistorialization is enough and only spin 1/2 fermions are present as fundamental particles. Since all particles are bound states of fundamental fermions propagating along fermion lines associated with the partonic orbits, all amplitudes involve only propagators for free fermions of H. The analog of twistor diagrams correspond to diagrams, whose vertices correspond to the intersections and self-intersections for space-time surfaces.
</OL>
For the the recent view of TGD see <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">this</A> and <A HREF="<https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">this</A>. For the Geometric Langlands duality in the TGD framework see <A HREF =">https://tgdtheory.fi/public_html/articles/Frenkel.pdf">this</A> .
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-41196919254302215222024-10-03T03:18:00.000-07:002024-10-07T21:11:23.963-07:00How a rubbing with a microfiber manages to shatter the "bullet proof" windshield of Musk Cybertruck? I learned from Heikki Hirvonen an about Musk Cybertruck windshield that was told to be "bullet proof" but turned out to be quite not so (see <A HREF="https://www.youtube.com/watch?v=LMWwImDX3ks">this</A>). Even worse, it has been found that interaction with microfiber and the material of Musk Windshield creates some specific style of resonance that would then shatter that material. This brings to mind opera sopranos shattering wine glasses. One might think that the system considered must be critical so that very small periodic perturbations can induce very large changes if they are of the right kind and have a correct frequency.
</p><p>
<B> 1. Why should one worry about sopranos shattering wine glasses?</B>
</p><p>
One might wonder what the point is in building complex new physics scenarios for how sopranos manage to break wine glasses. This has been understood a long time ago.</p><p> But is this really the case? We are used to thinking that physics somehow mysteriously transforms from quantum to classical on some scale. Quantum coherence, which is not possible above atomic scales, would be replaced by classical coherence on long scales. If this is assumed, glass-breaking sopranos cease to look mysterious. This thinking has actually no justifications but only restates what is a fact. When you give this thinking up, the imagined self-evidences collapse. Phenomena that were undeniably a bit strange become impossible.
</p><p>
In TGD, a new view of spacetime comes to rescue. The spacetime surface defines the coherence region in both classical and quantum sense. Field bodies make long-scale quantum coherence and, as its correlate, classical coherence, possible. The entire scale of the space-time surface corresponds to the scale of classical coherence and quantum coherence (i.e. related to the magnetic body). Long-scale quantum coherence accompanies classical coherence.
</p><p>
Classical long-scale coherence has a quantum counterpart and would be related to classical long-range gravitational and electromagnetic fields. Gravitational and em Planck's constant, whose values can be enormous compared to h, quantify the hypothesis. This windshield effect is just one example of many.
</p><p>
<B> 2. Background observations and assumptions</B>
</p><p>
It is good to start with some background observations.
<OL>
<LI> The super strength of the glass could mean that it does not break under the deformations studied. Throwing piece rock and rubbing with microfiber do not belong to the class of allowed deformations. So what could be the deformations that do not break the glass?
</p><p>
Could it be that only deformations have been tested where pressure is applied to the windshield, i.e. an impulse current in the direction of the impulse, but not deformations involving shear, i.e. the direction of the impulse current is perpendicular to the transferred impulse. The second difference is that there is a direct contact with the microfiber.
</p><p>
Rubbing creates a shear. The microfiber is pressed against the surface and pushed horizontally at the same time: both pressure in the normal direction and shear in the direction of the surface are created. For example, in hydrodynamics, the very poorly understood generation of vortices at the interface (turbulence is due to shear). The creation of vortices is forced by the conservation of angular momentum. In TGD based quantum hydrodynamics, this process is essentially a quantum critical process on macroscales (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDhydro.pdf">this</A>).
</p><p>
Could it be that the strength of the glass, as defined in the way I guessed, was exactly the reason for the breakage. Would the glass be too rigid in this sense and unable to flex and break?
</p><p>
Or could the glass be fragile in terms of certain types of deformations that have not been taken into account? Pressure wouldn't create them, but shear could do so. The characteristics of the microfiber could also be important.
</OL>
<B>3. What kind of model could be imagined for the phenomenon?</B>
</p><p>
The TGD based model for the phenomenon relies on gravitational quantum coherence predicted to be possible in astrophysical scales and also possible quantum criticality. The gravitational magnetic bodies of both the Sun and Earth are assumed to play a key role. The reason is that macroscopic quantum coherence requires very large values of the effective Planck constant. It is assumed that the gravitational Compton frequency of the Sun defines a gravitational quantum coherence scale and sets a lower bound for the frequencies assignable to the acoustic oscillations inducing the instability of the windshield .
</p><p>
One can also consider other mechanisms of macroscopic quantum coherence. Cyclotron frequencies for the endogenous magnetic field of Earth are in EEG range and would correspond to energies above thermal energy and play a key role in the TGD inspired quantum biology and might be involved with the microfibers. This would require transformation of dark cyclotron radiation to sound waves and require a ferro electret property typical for organic materials. Quantum criticality making possible a generation of large $h_{eff}$ phases is involved and warping deformations possible for planar or nearly planar systems are considered as a possible realization of the quantum criticality.
<OL>
<LI> Could the strength of the glass be defined so that when a weight is placed on the glass plate, it does not develop dent: this would mean that no curvature is generated. For example, a planar sheet of metal is a good example. It does not break easily.
</p><p>
However, a flat metal or glass plate (flatness is important!) is very sensitive against development of warping, which only bends but does not curve the flat surface so that it remains flat (curvature tensor vanishes). The fluttering of a metal plate is a good example of this. Another kind example is a sheet of paper unstable against fluttering. Such time-dependent warpings would decompose to 1-dimensional plane waves propagating along the surface of the metal of glass. They would be very much like transversal sound waves.
</p><p>
What is important is that warping is a critical phenomenon due the large number of flat warped surfaces (the warping profile can correspond to any differentiable function). In TGD criticality involves the development of large h<sub>eff</sub> phases and long-range quantum correlations, which gives strong clues concerning the understanding of the situation.
<LI> Already Euler thought about what happens when a weight is placed on a bar bent upwards (Euler buckling) (see <A HREF="https://en.wikipedia.org/wiki/Euler's_critical_load">this</A>). At a critical weight, a collapse occurs. This is one of the basic applications of catastrophe theory. The critical amplitude of the warping wave would be analogous to the critical weight for which the glass would break.
<LI> One might think that the action principle contains an energy density term that is proportional to the square of the 2-D curvature (see <A HREF="scalar (https://en.wikipedia.org/wiki/Scalar_curvature">this</A>) for the induced metric and vanishing for warped configurations. There would be an enormous vacuum degeneracy. Stability against deformations generating curvature requires that the coefficient of this term is very large. A lot of energy would be needed to produce a dent. But bending without curving brings in the Troyan horse.
</p><p>
Action would of course also contain a term proportional to the surface area, which would correspond to the normal tension that tends to oppose the increase of the surface area. For warping, the energy would be only needed to increase the surface area. Could warping waves, possibly created by the rubbing with microfiber, lead to the breakage? Shear should provide the needed momentum and energy resonance should strengthen the warping wave.
</OL>
<B> 4. What happens when the window shield breaks?</B>
<OL>
<LI> A catastrophe theorist might state that the system is characterized by, for example, a cusp catastrophe. When the critical shear is reached, the system undergoes a sudden transition: the system breaks down.
<LI> If one starts from the quantum level, the reduction of quantum coherence comes first to mind. In collapse the quantum coherence length would decrease dramatically from the size of the whole system to the size of the fragments. If the quantum coherence with the magnetic body of the glass surface takes care of the coherence of the glass, then it would have to decrease. In the h<sub>eff</sub> distribution, the average value of h<sub>eff</sub> would decrease.
</p><p>
This is however only the outcome, not the primary cause. Long-scale quantum coherence and quantum criticality together with energy feed occurring at resonance frequency and increasing the value of h<sub>eff</sub> would be the reasons leading to the limit at which the system collapses.
<LI> Why would rubbing with microfiber induce a critical shear leading to the breaking and loss of quantum coherence? Warping waves are a good candidate. The windglass would start to shake in the vertical direction. When the amplitude of the warping wave would exceed the critical limit, the result would be collapse and breaking into pieces. Rubbing with microfiber would feed into the system the necessary energy needed to generate h<sub>eff</sub> phases and this would occur at quantum criticality associated with the warping waves.
</OL>
<B> 5. Identifying the resonance frequency</B>
</p><p>
This should include a frequency resonance that would correspond to the wavelength of the wave identifiable as a natural length scale for microfiber and/or glass. One would expect the flutter frequency to be on the Hertz scale and the acoustic resonance frequency of the windshield is a good guess. The sequel will certainly arouse academic head shaking, but it is based on the fact that in the TGD world, the planets and the sun form a quantum-coherent system, the effect of which can be seen on Earth at all levels, especially in biology. Second justification was given already in the beginning: our belief that we understand the classical world is based on an illusion about a mysterious transition from quantum to classical.
<OL>
<LI> Microfiber has a wavelength λ ≈ 1 micrometer as a natural scale. The IR energy scale 1 eV of infrared photons would correspond to that and it can be assumed to be the basic scale. Could photons with this energy transform into bundles of dark photons with much longer wavelength; they, in turn, would eventually end up via intermediate steps into bundles of ordinary phonons or even into a Bose-Einstein condensate or a coherent state as a quantum analog of classical state.
<LI> Let's start with the Earth's gravitation (see <A HREF="https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/precns.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/tgdcomp.pdf">this</A>). The gravitational Compton length Λ<sub>gr</sub> related to the Earth's gravitation Planck's constant is .5 cm (half of the Schwartschild radius), independently of particle mass, and the associated frequency is f<sub>gr</sub>= 67 GHz. The frequency is quite too big. Furthermore, the Earth's gravitation is now not decisive because the warping is not in the vertical direction but closer to the tangential direction. In any case Earth's gravitation is not enough.
<LI> One must follow the example of Icarus and hope for better luck. The Sun's gravitational constant gives a frequency of f<sub>gr</sub>=50 Hz, which is the average EEG frequency and important resonance frequency of the EEG central in communications between the brain and its magnetic body (see <A HREF="https://tgdtheory.fi/pdfpool/eegII.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/np2023.pdf">this</A>). This is a reasonable frequency. The corresponding gravitational wavelength Λ= c/f<sub>gr</sub> is half the radius of the Earth.
</p><p>
Needless to emphasize that this makes no sense unless one accepts the astrophysical quantum coherence assigned with gravitation and that the oscillation takes place on the magnetic body of the glass plate on the scale of the Earth's radius.
<LI> A strong objection is that f<sub>gr</sub> does not depend at all on the geometry of the glassy system, in particular on the size scale of the windshield. A reasonable expectation is that the model should apply also to shattering of wine glasses.
</p><p>
A more general assumption is that the allowed frequencies are above the threshold defined by f<sub>gr</sub>= 50 Hz defining the gravitational quantum period. At frequencies above f<sub>gr</sub> gravitational quantum coherence would make itself visible. However, the frequencies coming as harmonics of f<sub>gr</sub> could be especially interesting. This assumption is analogous to that appearing in the proposal for how gravitational quantum coherence could become important in classical computers (see <A HREF="https://tgdtheory.fi/public_html/articles/tgdcomp.pdf">this</A>). In any case, the assumption f≥f<sub>gr</sub> is rather strong and gives lower bounds for the quantal resonance frequencies.
</OL>
Could the resonance (basically acoustic warping wave) correspond to a frequency above f<sub>gr</sub> or be identifiable as the frequency of dark photons generated at the magnetic body of the Sun?
<OL>
<LI> The phonons of the acoustic wave would couple to the dark photons, produced by shear, at the magnetic body. This is where microfiber would take the role of a Trojan horse. Note that in liquid flow for which shear occurs near boundaries, the conservation of angular momentum forces the production of vortices which in TGD based hydrodynamics would be associated with dark monopole flux tubes. Also now, Z<sup>0</sup> magnetic vortices could be created.]
<LI> The frequencies above f<sub>gr</sub> would be the same, but the energy of a dark photon would correspond to the energy of many "warping phonons": a Bose-Einstein condensate/coherent state analogy of phonons would be created. Assuming proton-Earth pair, one has ℏ<sub>gr</sub>(Earth,proton) proportional to m<sub>p</sub>M<sub>E</sub>. This gives 1 eV energy scale, which corresponds to 1 micrometer wavelength for ordinary photons.
</p><p>
The critical reader has probably noticed that the magnetic bodies of both the Sun and the Earth are included, characterized by ℏ<sub>gr</sub>(Sun,proton) and ℏ<sub>gr</sub>(earth,proton) respectively. The gravitational Compton length Λ<sub>gr</sub>(Sun,proton) of Sun is R<sub>E</sub>/2, which is the size scale for the Earth's magnetic body. Also ℏ<sub>gr</sub>(Earth,proton) is required. Could one think that dark photons for which h<sub>eff</sub>= h<sub>gr</sub>(Sun,proton) are created first, and that these break up into bunches of dark photons with h<sub>eff</sub>= h<sub>gr</sub>(Earth,proton). The frequency would remain the same. These in turn break up into bunches of "warping phonons" with the same frequency.
<LI> If the propagation speed of the warping wave is roughly estimated to be the sound velocity in glass, that is v=4540m/s, then the wavelength would be Λ = v/f= 90.6 m if one assumes that the value of f is smallest possible that is f=f<sub>gr</sub>= 50 Hz. The wavelength is quite too long as compared to the dimensions of the windshield. v should be 2 orders of magnitude smaller, coincidentally(?) the same order as the conduction velocity of the nerve impulse. Note also that a micrometer is the scale of a cell nucleus. However, f<sub>gr</sub>=50 Hz defines only a lower bound for the quantum resonance frequency. A resonance frequency dictated by the geometry is in question and roughly scales like the inverse size of the system.
</p><p>
In the case of wine glass, one expects a frequency scale, which is by two orders of magnitude larger, in the kHz scale. The E note at the hearing threshold corresponds to 20.6 Hz and, according to net source, for a wine glass some octave of E is a reasonable estimate for the resonance frequency. The resonance frequency is k:th octave of this frequency and assuming that λ is of order .1 m, one obtains an estimate that 7:th octave is a reasonable guess. This is of order kHz. In the case of a windshield, one would expect λ to be 5 to 10 times longer so that the frequency could be around 3 or 4 octaves.
</OL>
<B> 6. Summary</B>
</p><p>
Microfiber rubbing would induce warping waves, whose amplitude would increase in resonance and lead to shattering.
<OL>
<LI> First, dark photons (piezoelectricity) would be generated at the solar magnetic body and then decay to bunches of dark photons at the magnetic body of Earth with energy of order eV, corresponding to the scale of the basic structure of the microfiber. Their frequency would be abe f<sub>gr</sub>=50 Hz corresponding to the gravitational Compton wavelength of the Sun, which is of the order of the Earth's radius/2. The dependence of the resonance frequency on the geometry requires that f<sub>gr</sub> defines only a lower bound for f and its interpretation of f<sub>gr</sub> is as a quantum coherence period.
<LI> h<sub>eff</sub>= h<sub>gr</sub>(Earth,proton) photons would in turn decay to a "warping phonon" beam with frequency above f<sub>gr</sub>=50 Hz. Phonons would form a coherent state or BE condensate. This could lead to an acoustic laser effect and amplification, and the result would be resonance and catastrophe, analogous to Euler buckling, when the warping amplitude becomes too large. Here, quantum criticality, which is naturally associated with warping waves, would be essential, it would make the Trojan horse effect possible.
</OL>
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/shatterglass.pdf">How a rubbing with a microfiber manages to shatter the "bullet proof" windshield of Musk Cybertruck?</A> or the chapter <A HREF= "https://tgdtheory.fi/pdfpool/TGDcondmatshort.pdf">TGD and Condensed Matter</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-10444875406410510902024-10-02T03:35:00.000-07:002024-10-06T19:25:23.116-07:00Space-time surfaces as numbers: what could this mean from the point of view of metamathematics?
These comments were inspired by the links to Bruno Marchal's posts by Jayaram Bista (see
<A HREF="https://www.facebook.com/2jaya1bista/posts/pfbid0EPvHfmaDqjHjWi9gRHxqMnssSQggAP5ieGXfRkU5JEZiHcE887vvqqjfy2upuJCzl?comment_id=413142121479178">this</A>). The comments compare the world views behind two Platonisms, the Platonism based on integers or rationals and realized by the Turing machine as a Universal Computer and the quantum Platonism of TGD. Marchal also talks about Digital Mechanism and claims that it is not necessary to assume a fixed physical universe "out there". Marschal also speaks of mathematical theology and claims that quantum theory and even consciousness reduce to Digital Mechanism.
</p><p>
In the TGD Universe, the space-time surfaces form an algebra with respect to multiplication and that this algebra decomposes to a union of number fields means a dramatic revision of what computation means. The standard view of computation as a construction of arithmetic functions is replaced with a physical picture in which space-times as 4-surfaces have interpretation as almost deterministic computations. Space-time surfaces allow arithmetic operations and also the counterparts of functional composition and iteration are well-defined.
</p><p>
<B>Replacement of the static universe with a Universe continuously recreating itself</B>
</p><p>
It seems to me that the problems of computationalism emerge from a single ontological assumption: the "system", be it Universe in some sense or God, is fixed. In quantum TGD this is not the case. The Quantum Universe, which could be seen as a counterpart for God, is continually recreating itself and this means the unavoidable increase of algebraic complexity since the dimensions associated with extensions of rationals defining space-time regions unavoidably increase. This in turn implies evolution.
</p><p>
In zero energy ontology (ZEO) "small" state function reductions (SSFRs), whose sequence generalizes Zeno effect, which has no effect on physical state. SSFRs have and their sequence gives rise to conscious entities, selves. This makes possible memory: the outcome of SSFR has classical information about the initial state and also about the transition. Therefore the Universe remembers and learns consciously: one can talk about Akashic records.
</p><p>
This dynamical view of the Universe recreating itself and becoming more intelligent by learning about what it was before the previous SSFR is very different from the view of the Universe as a Turing machine or Universal Computer. These notions are static notions (Universe "out there") and computation is based on integers. In the TGD view one obtains an entire hierarchy of computationalisms based on the hierarchy of extensions of rationals. Even transcendental extension can be considered. TGD Universe as a counterpart of the Turing machine is also conscious and has free will.
</p><p>
<B> A generalization of number</B>
</p><p>
Also the notion of number generalizes from integers N to space-time surfaces. Space-time surfaces can be multiplied and summed and form an algebra. This algebra decomposes to a union of number fields with product,division, sum and subtraction. One can identify space-time surfaces forming analogs for hierarchies of algebraic integers, algebraic rationals, etc... So that the mathematics performed by Quantum Platonia is considerably more complex than counting by 5+5 fingers!
</p><p>
These structures are defined by the corresponding structures for function algebras and fields defined in terms of analytic functions of 8 generalized complex coordinates of H=M<sup>4</sup>×CP<sub>2</sub>. One of the coordinates is a hypercomplex coordinate with light-like coordinate curves.
<OL>
<LI> In TGD space-time surfaces are numbers. Their dynamics is almost deterministic (at singularities the determinism fails and this forces us to take space-time surfaces instead of 3-surfaces as basic objects). The space-time surface as an almost deterministic time evolution is analogous to a proof of a theorem. The assumptions correspond to the initial state 3-surface and the outcome of the theorem to the final 3-surface. Second interpretation is as analogs of deterministic computer programs. Space-time surface as a proof of a theorem is analogous to its own Gödel number as a generalized number.
<LI> Cognition always requires a discretization and the space of space-time surfaces ("world of classical worlds", WCW) allows a hierarchy of discretizations. The Taylor coefficients of the two analytic functions defining space-time belong to some extension of rationals forming a hierarchy. Therefore a given space-time surface corresponds to a discrete set of integers/rationals in an extension so that also WCW is discretized. For polynomials and rational functions this set is discrete. This gives a hierarchy. At the level of the space-time surface an analogous discretization in terms of an extension of rationals takes place.
<LI> Gödel number for a given theorem as almost deterministic time evolution of 3-surface would be parametrized by the Taylor coefficients in a given extension of rationals. Polynomials are simplest analytic functions and irreducible polynomials define polynomial primes having no decomposition to polynomials of a lower degree. They might be seen as counterparts of axioms.
<LI> One can form analogs of integers as products of polynomials inducing products of space-time surfaces. The space-time surfaces are unions for the space-time surfaces defined by the factors but an important point is that they have a discrete set of intersection points. Fermionic n-point functions defining scattering amplitudes are defined in terms of these intersection points and give a quantum physical realization giving information of the quantum superpositions of space-time surfaces as quantum theorems.
</OL>
<B> Could space-time surfaces replaced as integers replace ordinary integers in computationalism?</B>
</p><p>
It is interesting to play with the idea that space-time surfaces as numbers, in particular integers, could define counterparts of integers in ordinary computationalism and metamathematics.
</p><p>
What might be the counterpart for the possibility to represent theorems as integers deduced using logic and for the Gödel numbering for theorems by integers?
<OL>
<LI> In TGD space-time surfaces are numbers. Their dynamics is almost deterministic (at singularities the determinism fails and this forces us to take space-time surfaces instead of 3-surfaces as basic objects). The space-time surface as an almost deterministic time evolution is analogous to a proof of a theorem. The assumptions correspond to the initial state 3-surface and the outcome of the theorem to the final 3-surface. Second interpretation is as analogs of deterministic computer programs. Space-time surface as a proof of a theorem is analogous to its own Gödel number as a generalized number.
<LI> Cognition always requires a discretization and the space of space-time surfaces ("world of classical worlds", WCW) allows a hierarchy of discretizations. The Taylor coefficients of the two analytic functions defining space-time belong to some extension of rationals forming a hierarchy. Therefore a given space-time surface corresponds to a discrete set of integers/rationals in an extension so that also WCW is discretized. For polynomials and rational functions this set is discrete. This gives a hierarchy. At the level of the space-time surface an analogous discretization in terms of an extension of rationals takes place.
<LI> Gödel number for a given theorem as almost deterministic time evolution of 3-surface would be parametrized by the Taylor coefficients in a given extension of rationals. Polynomials are simplest analytic functions and irreducible polynomials define polynomial primes having no decomposition to polynomials of a lower degree. They might be seen as counterparts of axioms.
<LI> One can form analogs of integers as products of polynomials inducing products of space-time surfaces. The space-time surfaces are unions for the space-time surfaces defined by the factors but an important point is that they have a discrete set of intersection points. Fermionic n-point functions defining scattering amplitudes are defined in terms of these intersection points and give a quantum physical realization giving information of the quantum superpositions of space-time surfaces as quantum theorems.
</OL>
<B>Adeles and Gödel numbering</B>
</p><p>
Adeles in TGD sense inspire another interesting development generalizing the Gödelian view of metamathematics.
<OL>
<LI> p-Adic number fields are labelled by primes and finite fields induced by their extensions. One can organize the p-adic number fields to adele and the same applies to their extensions so that one has an infinite hierarchy of algebraic extensions of the rational adele. TGD brings something new to this picture.
<LI> Two p-adic number fields for which elements are power series in powers of p<sub>1</sub> resp. p<sub>2</sub> with coefficients smaller than p<sub>1</sub> resp. p<sub>2</sub>, have common elements for which expansions are in powers of integers n(k<sub>1</sub>,k<sub>2</sub>)= p<sub>1</sub><sup>k<sub>1</sub></sup>×p<sub>2</sub><sup>k<sub>1</sub></sup>, k<sub>1</sub>>0, k<sub>2</sub>>0. This generalizes to the intersection of p<sub>1</sub>,p<sub>2</sub>,..., p<sub>n</sub>. One can decompose adeles for a union of p-adic number fields which are glued together along these kinds of subsets. This decomposition is general in the description of interactions between p-adic sectors of adeles. Interactions are localized to these intersections.
<LI> Mathematical cognition would be based on p-adic numbers. Could one think that ordinary integers should be replaced with the adelic integers for which the p<sub>i</sub>:th factor would consist of p-adic integers of type p<sub>i</sub>.
</p><p>
These integers are not well-ordered so that the one cannot well-order theorems/programs/etc... as in Gödel numbering.
</p><p>
The number of p-adic integers is much larger than natural numbers since the pinery expansion can contain an infinite number of terms and one can map p-adic integers to real numbers by what I call canonical identification. Besides this one has fusion of various p-adic number fields.
</OL>
An interesting question is how this changes the Gödelian views about metamathematics. It is interesting to play with the idea that space-time surfaces as numbers, in particular generalized integers, could define counterparts of integers in ordinary computationalism and metamathematics.
</p><p>
<B>Numbering of theorems by space-time surfaces?</B>
</p><p>
What might be the counterpart for the possibility to represent theorems as integers deduced using logic and for the Gödel numbering for theorems by integers?
<OL>
<LI> In TGD space-time surfaces are numbers. Their dynamics is almost deterministic (at singularities the determinism fails and this forces us to take 4-D space-time surfaces instead of 3-surfaces as basic objects). The space-time surface as an almost deterministic time evolution is analogous to a proof of a theorem. The assumptions correspond to the initial state 3-surface and the outcome of the theorem to the final 3-surface. Second interpretation is as an analog of a deterministic computer program. The third interpretation as a biological function. Space-time surface as a proof of a theorem is analogous to its own Gödel number, but now as a generalized number. One can define the notions of prime , integer , rational and transcendental for the space-time surfaces.
</p><p>
The counterparts of primes, determined by pairs of irreducible polynomials, could be seen as axioms. The product operation for space-time surfaces generates unions of space-time surfaces with a discrete set of intersection points, which appear as arguments of fermionic n-point functions allowing to define fermionic scattering amplitudes. Also other arithmetic operations are possible.
</p><p>
Also functional composition, essential in computationalism, is possible. One can take any analytic h(z) function of a complex coordinate z and form a functional composite h(f<sub>1</sub>(...)) or h(f<sub>2</sub>(...)). One can also iterate this process. This would make it possible to realize recursion, essential in computationalism. This iteration leads also to fractals.
<LI> Cognition always requires a discretization and the space of space-time surfaces ("world of classical worlds", WCW) allows a hierarchy of discretizations. The Taylor coefficients of the two analytic functions f<sub>1</sub>,f<sub>2</sub> defining space-time belong to some extension E of rationals forming a hierarchy. Therefore a given space-time surface corresponds to a discrete set of integers/rationals in an extension of rationals so that also WCW is discretized for given E. For polynomials and rational functions this set is discrete. This gives a hierarchy. At the level of the space-time surface an analogous discretization in terms of E takes place.
<LI> Gödel number for a given theorem as almost deterministic time evolution of 3-surface would be parametrized by the Taylor coefficients in a given extension of rationals. Polynomials are simplest analytic functions and irreducible polynomials define polynomial primes having no decomposition to polynomials of a lower degree. Polynomial primes might be seen as counterparts of axioms. General analytic functions are analogous to transcendentals.
<LI> One can form analogs of integers as products of polynomials inducing products of space-time surfaces as their roots. The space-time surfaces are unions for the space-time surfaces defined by the factors but an important point is that they have a discrete set of intersection points. Fermionic n-point functions defining scattering amplitudes are defined in terms of these intersection points and give a quantum physical realization giving information of the quantum superpositions of space-time surfaces as quantum theorems.
</OL>
See the articles <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">TGD as it is towards end of 2024: part I</A>, <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">TGD as it is towards end of 2024: part II</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/Frenkel.pdf">About Langlands correspondence in the TGD framework</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-88551765098141788602024-09-26T04:48:00.000-07:002024-09-30T03:44:02.245-07:00More precise views about some aspects of the icosa tetrahedral realization of the genetic code
The article <A HREF="https://tgdtheory.fi/public_html/articles/icosatetra.pdf">Progress in the understanding of the icosa tetrahedral realization of the genetic code</A> provides an answer to the question how many icosahedrons, octahedrons and tetrahedrons meet at the vertex of ITT: the answer comes by studying the vertex figure of ITT: these numbers are 12, 30, and 20. The study of the vertex figure of ITT suggests that the ITT can be constructed as a "blow-up" of the icosahedral tessellation (IT) by replacing icosahedral vertices with tetrahedra and dodecahedral vertices by pentagons and adding between icosahedral tetrahedra and dodecahedra octahedra as analogs of edges. Icosahedral and dodecahedral bioharmonies correspond to 12-note <I>resp.</I> assignable to Western <I>resp.</I> Eastern music. One can ask whether octahedral 4-codons should also be allowed.
</p><p>
The picture provided by RID is consistent with the earlier notion of "super-icosahedron". The model of the genetic code generalizes: besides the icosahedral Hamilton cycles (HCs) and codons for the three icosahedral codes and the tetrahedral HC and corresponding codons, also a unique dodecahedral HC and associated 5-codons plus pentahedral HC and codons are in principle possible. The fundamental region deduced from RID corresponds to a sequence of 10 or 12 DNA codons as proposed already earlier on the basis "super-icosahedron model" (see <A HREF="https://tgdtheory.fi/public_html/articles/tessellationH3">this</A>).
</p><p>
The model allows us to understand the symmetry breaking of genetic codons. In particular, tetrahedral codons correspond to 3 stop codons and the codon coding for trp. A given codon corresponds either to I/T or D/pentahedron. The fundamental region represents a sequence of 10 or 12 DNAs so that all codons of the Hamiltonian cycle are used and the HC corresponds to a section of DNA. Fundamental region represents both DNA strands.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/icosatetra.pdf">Progress in the understanding of the icosa tetrahedral realization of the genetic code</A> or the chapter <a A HREF="https://tgdtheory.fi/pdfpool/tessellationH3.pdf">About honeycombs of hyperbolic 3-space and their relation to the genetic code</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-49167875890542603962024-09-24T05:35:00.000-07:002024-09-24T05:35:25.364-07:00Some strange astrophysical and cosmological findings from the TGD point of view
Anomalies in both astrophysics and cosmology have been rapidly accumulating during the last years. The most recent astrophysical anomalies that I have encountered relate closely also to the TGD view of biology and consciousness.
<OL>
<LI> There is evidence that Earth had a ring before the Cambrian Explosion (see <A HREF="https://doi.org/10.1016/j.epsl.2024.118991">this</A>). The proposed explanation based on the TGD variant of the Expanding Earth hypothesis (see <A HREF="https://tgdtheory.fi/public_html/articles/preCE.pdf">this</A>). The ring would have existed already before the Cambrian Explosion along the equator but the rapid expansion of the Earth (radius was doubled) implied that Earth catched the ring resulting in a large number of meteor craters along the equator and a temporary cooling of the climate caused by the shadow of the ring.
<LI> The scent of space (see <A HREF="https://www.science.org.au/curious/space-time/smells-space#:~:text">this</A>) is a strange phenomenon reported by astronauts. It is now known that olfaction involves at the fundamental level infrared light. The scent could relate to so called PAHs (see <A HREF="https://www.brunonic.org/Nicolaus/fromthestarstot.htm">this</A> and <A HREF="https://www.amazon.com/Astronomical-biochemical-origins-search-universe/dp/8877940921">this</A>), which are aromatic molecules with several rings. PAH are known to produce the so called unidentified infrared bands (UIBs) for a radiation arriving from the interstellar space, even from regions containing no stars or involving no star formation. The mechanism could be non-chemical and involve the generalization of Pollack effect transferring ordinary protons to dark protons at the magnetic body and their dropping back back and in this way producing the infrared photons.
<LI> The surprisingly strong evidence that the position of Mars (see <A HREF="https://www.facebook.com/groups/473920566008054/user/23423644/">this</A>) correlates strongly with the stock market crashes is in conflict with the basic beliefs of physicalist. During the crashes the distance of Mars tends to be at the other side of the Sun than Earth. The TGD based explanation would rely on the loss of the predicted quantum coherence in astrophysical scales due the splitting of the monopole flux tubes connecting Earth and Mars (this mechanism might be at work although Mars has no large scale magnetic field). This would lead to a partial loss of quantum control at the level of collective consciousness and lead to panic reactions.
</OL>
There are also numerous cosmological anomalies.
<OL>
<LI> The surplus of deuterium nuclei in the cosmic ray spectrum (see <A HREF="https://www.sci.news/physics/deuteron-flux-13175.html#google_vignette">this</A>) is difficult to understand in the standard physics framework. There is also evidence for pairs of deuterium-anti-deuterium nuclei and even helium-antihelium nuclei (see <A HREF="https://www.youtube.com/watch?v=LVU-hwZgnuA">this</A>).
</p><p>
The TGD inspired model of stars discussed in (see <A HREF="https://tgdtheory.fi/public_html/articles/Haramein.pdf">this</A>) deviates dramatically from the standard model and proposes that M<sub>89</sub> hadron physics with mass scale 512 times that for the ordinary hadron physics might be involved. There is some evidence for M<sub>89</sub> mesons from LHC. The decay of the monopole flux tubes carrying dark M<sub>89</sub> nuclei as analogs of ordinary nuclei along the solar surface would produce solar energy and solar wind. The flux of M<sub>89</sub> nuclei arriving along monopole flux tubes from the Milky Way giant blackhole would provide the energy and serve also as a metabolic energy source of dark nuclei in the solar interior forming a state analogous to a cell.
</p><p>
The decay of M<sub>89</sub> mesons could produce nucleon-antinucleon pairs but the production of deuterium-anti-deuterium pairs and even Helium-anti-Helium pairs is not so plausible. An alternative explanation is the decay of monopole flux tubes containing sequences of ordinary or M<sub>89</sub> anti-nuclei.
<LI> There is evidence that galaxies rotating in different directions relative to the Milky Way have different redshifts and that the difference increases with distance: the explanation in terms of tired light (see <A HREF="https://doi.org/10.3390/particles7030041">this</A>) does not seem plausible. This suggests that they have slightly different Hubble constants. TGD suggests explanation in terms of the variation of slightly different values of effective Planck constant h<sub>eff</sub> near to h in both cases: also the fluctuations of CMB temperature and accelerated expansion could be understood in this way (see <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>).
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/anomcoll.pdf">Some strange astrophysical and cosmological findings from the TGD point of view</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-51689727812156235582024-09-20T21:31:00.000-07:002024-09-23T20:02:25.215-07:00Did Earth have a ring before the Cambrian Explosion and did the rapidly expanding Earth catch the ring?
I encountered a link to a very interesting popular article "Did Earth have a ring like Saturnus?" (see <A HREF="https://futurism.com/the-byte/earth-ring-like-saturn">this</A>) telling about the article "Evidence suggesting that earth had a ring in the Ordovician" of Tomkins et al published in Earth and Planetary Science Letters (see <A HREF="https://doi.org/10.1016/j.epsl.2024.118991">this</A>).
</p><p>
The proposal is that the ring would have formed as a large asteroid was caught by the Earth. The tidal forces of Earth would have destroyed the asteroid so that it became a ring along the equator of the Earth. The ring created a shadow. If it formed along the equator, it could have initiated global cooling about 465 years ago: the so-called Hirnantian Icehouse followed 20 million years later. There are as many as 21 meteor strikes along the equator and this is very implausible if the meteors would have arrived from random directions.
</p><p>
This is a highly interesting finding from the point of view of the Expanding Earth hypothesis inspired by TGD. About 524 million years ago the so-called Cambrian Explosion occurred. Highly evolved multicellular life forms suddenly emerged. A possible explanation of this mystery could be a fast expansion of the Earth: radius would have increased by about factor 2: these fast expansions could be the TGD counterpart of smooth cosmic expansion. This would have led to the bursting of underground oceans containing the multicellular life to the surface of the Earth. It is not difficult to invent objections against the idea but the new physics predicted by TGD allows to circumvent them and the model explains a large number of anomalies to the evolution of Earth. For the TGD view of the Expanding Earth Hypothesis see for instance <A HREF="https://tgdtheory.fi/public_html/articles/preCE.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/preCEagain.pdf">this</A> .
</p><p>
The ring would have formed about 60 million years later and existed for a time measured 10 million years as a natural unit. Could one think that Earth had already before this time a ring and the Expanding Earth caught the ring? This could explain why the ring was along the equator, something not obvious if the ring was formed by the asteroid rotating around the Earth. This would have produced the 21 meteor strikes along the equator, a phenomenon which is extremely implausible if the meteors did not originate from the same source. The expansion of the Earth would have gradually increased the width of the shadow and the collision with the ring would have generated dust in the atmosphere and caused an additional shadowing effect causing the cooling of the climate.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/preCE.pdf">Expanding Earth Hypothesis and Pre-Cambrian Earth</A> or the <a HREF= "https://tgdtheory.fi/public_html/articles/preCEch.pdf">chapter</A> with the same title.
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0