tag:blogger.com,1999:blog-106143482023-02-05T22:10:46.281-08:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger1986125tag:blogger.com,1999:blog-10614348.post-47943856761463945532023-02-05T22:06:00.003-08:002023-02-05T22:06:17.064-08:00Questions related to causal diamonds and ZEO
ZEO involves several questions which are not completely understood. Do SSFRs correspond to repeated measurements for a set O of commuting observables? Does BSFR occur when a new set of observables not commuting with the set O are measured? What exactly happens in SSFR?
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<B>1. Questions related to SSFRS</B>
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<B>1.1 SSFRs as a generalization of Zeno effect and weak measurements</B>
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Consider once again the question related to the identification of SSFRs. SSFRs are identified as the TGD counterpart for weak measurements, generalizing the notion of repeated measurements giving rise to the Zeno effect.
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<OL>
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<LI> The most straightforward generalization of the Zeno effect is that in the kinematic degrees of freedom for CDs the sequence of SSFRs corresponds to a sequence of measurements of commuting observables. BSFR would take place always when the set of measured observables changes to a new one, not commuting with the original set.
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<LI> D ,K<sub>z</sub> and J<sub>z</sub> leave the center point of CD, identified as position of CD, invariant. D does not commute with momenta. Should one just accept that momenta and \{D ,K<sub>z</sub>,J<sub>z</sub>\} are two sets of mutually commuting observables and that the change of this set induces BSFR.
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The size of CD and therefore the value of the geometric time would change in the sequence of measurements of D, K<sub>z</sub> and J<sub>z</sub> but not in the sequence of momentum measurements one would have superposition over different sizes of CD and time would be ill-defined as also Uncertainty Principle requires. This would conform with the original view.
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</OL>
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<B>1.2 What really happens in SSFRs?</B>
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I have written a lot of what might happen in SSFRs and BSFRs but I must admit that the situation is still unclear and the proposals depend on what one takes as starting point assumptions, which can be overidealizations.
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On the more general level, the sequence of SSFRs would correspond to dispersion in the moduli space of CDs and if SSFRs correspond to the measurement of same commuting observables identified as generators of SO(2,4) or D\rtimes P or their duals as generalized position in the moduli space, rather simple picture emerges of what can happen.
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BSFR would take place when the new set of observables not commuting with the original set emerges. What are the conditions forcing this? If one assumes that sleep is induced by BSFR, it becomes clear that this does not happen at will but when metabolic energy resources are depleted and the system must rest. The dissipation of the time reversed system looks like self-organization and the system heals during sleep. Also homeostasis would rely on BSFRs in various scales making it possible to stay near quantum criticality.
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But what exactly happens in SSFR? It seems clear that the states at the passive boundary are not changed. But what happens to the passive boundary?
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<OL>
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<LI> Do the contents of sensory experience assigned with the sequence of SSFRs localize
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<B> Option a</B>: to the active boundary of the CD or
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<B> Option b</B>: to the 3-ball at which the half-cones of the CD meet.
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<LI> What happens to the passive boundary itself in SSFR? The scaling occurs for the entire CD but there are two basic options.
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<B> Option 1</B>: The scaling leaves the <I> center point</I> of the CD invariant. Passive boundary is shifted towards past just like active boundary towards future.
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If the sensory experience is assigned to the active boundary (Option a)), option 1) is consistent with what happens when we wake up. The time has been flowing during sleep but we have not been aware of this. The arrow time would be determined solely by the change of the state at the active boundary.
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If the sensory experience is assigned with the 3-ball (option b)) at the center of CD (Option b)), time does not flow in the sequences of SSFRs.
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<B> Option 2</B>: The scaling leaves invariant the tip of CD associated with the passive boundary so that it is not shifted at all but is scaled. This option is consistent with both option a) and b) for the localization of the experience of time flow. However, waking-up from sleep would take at the time when we fell asleep: this does not make sense.
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The model for sleep favours option a)+1) for which CDs would define ever expanding sub-cosmologies changing the arrow of time repeatedly. Any conscious entity would eventually evolve to a cosmology, a kind of God-like conscious entity.
<LI> One can also consider other empirical inputs. There are stars and even galaxies older than the Universe. Their existence is consistent with option a)+1).
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CDs form a scaling hierarchy. CDs in the distant geometric past assignable to stars and galaxies are much smaller than the cosmological CD. The scaling cosmological CD inducing the time flow takes place much faster than the scaling of the much smaller astrophysical CDs. Cosmological time runs much faster and astrophysical CDs remain in the distant geometric past.
<LI> A third test is based on after images, which appear repeatedly. They correspond to sub-CDs of a CD. Could the after images correspond to life cycles of the <I> same</I> sub-CD as I have proposed? This is the case if the sub-CDs are comoving in the scalings of the CD shift. This looks rather natural.
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<B>2. More questions and objections related to ZEO and consciousness</B>
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The best way to make progress is to make questions and objections against the existing view, which is often far from clear. In the following I raise some questions of this kind.
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What could BSFR mean biologically?
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<LI> In have considered the possibility that BSFR could mean as biologically birth in opposite time direction. This however leads to rather complex speculations.
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The most natural assumption is that it means what it says, the emergence of a new CD (see <A HREF= "https://tgdtheory.fi/public_html/articles/Levin.pdf">this</A>) as a perceptive field of a conscious entity. This does not require that biological death would be a birth in the opposite time direction although this cannot be excluded. This means one counter argument less.
<LI> I have considered the idea that in BSFR the size of a CD could decrease dramatically so that the reincarnated CD would be much smaller than before BSFR. This would make possible what one might call childhood. The idea is that the painful memories from the end of the lifecycle could be deleted. This model however requires rather detailed assumptions about how the memories of life cycle are stored at the active boundary of CD. The oldest memories would reside near the tip of CD and newest nearest to the intersection of the half-cones of the CD.
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Is this picture consistent with the view about SFR as a localization in the space of CDs? Since the number of CDs larger than given CD is much larger than those with size smaller than it, one can argue that the size of CD increases in statistical sense without limit in SFRs. If one can assume that death involves localization in the space-like degrees in the space of CDs (E<sup>3</sup> position and size of CD), the reduction of CD size looks rather implausible. If the preceding SSFR involved also this kind of localization then the CD after BSFR would in statistical sense be larger than it was before BSFR.
<LI> Can CDs interact? For instance, can a CD catch the sub-CD defining a mental image of the CD with which it overlaps? This is not the case: it is not possible to catch the spotlight of consciousness.
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CD serves as a correlate for the perceptive field of self. Self is also an active causal agent. This aspect must relate to the zero energy states defined as superpositions of space-time surfaces inside a CD.
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<LI> CD defines a perceptive field, a kind of spotlight of consciousness, which makes it possible to sensorily perceive the space-time surface, which continues outside CD although one can also imagine a situation in which this is not the case. Saying that mental image co-moves means that the spotlight moves.
<LI> Self has also causal powers. SSFRs change the state at the active boundary of CD. This induces changes inside the future light-cone in turn define perturbations of CDs of the geometric future possibly inducing BSFRs.
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Since the superposition of 3-surfaces at the active boundary of CD changes in SSFR, SSFRs have an effect on the geometric future. This is of course the case: our acts of free will affect the world around us but conform with causality.
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Almost deterministic holography for space-time surfaces and zero energy states dramatically reduces the freedom of free will due to state function reductions . The delocalization in WCW taking place in the space of CDS during the analogues of unitary time evolutions preceding SSFR improves the situation.
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One can also imagine a situation in which nothing changes at the boundaries of CD: self is completely passive: this is of course true at the passive boundary and can be true also at the active boundary in special situations. The classical time evolution for preferred extremals is not fully deterministic. Space-time surface is analogous to a 4-D soap film with frames and the case of 2-D soap films suggests that a finite non-determinism is assignable to the frames. This kind of SSFRs would not affect the space-time surface around CD at all. Pure cognition or meditative states might correspond to this kind of SSFRs.
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The notion of ego is central in Eastern philosophies. How could one understand this notion in the ZEO based theory of consciousness?
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<LI> Ego means that mental images want to survive. Self survival instinct is an analogous notion although it refers to the biological body. The quantum state at the passive boundary of the CD defines a good candidate for ego since it is indeed preserved during the sequence of SSFRs during which the set of measured observables is preserved.
<LI> BSFRs means death of self or subself as a sub-CD. Also the external physical perturbations arriving at the passive or active boundary can affect the quantum state at it and can induce BSFR. The self assignable to CD is exposed to perturbations, which might induce BSFR. A simple example of this kind of perturbation would be a blow in the head inducing a loss of consciousness.
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Ego preservation could mean that self does its best to make the periods of time with an opposite arrow of time as short as possible. This is not in conflict with the fact that the durations of sleep and awake states are roughly the same if a given arrow of time means that the time fraction spent in a state with this arrow of time dominates over that in a state with an opposite arrow of time.
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At the magnetic bodies carrying dark matter as phases with large h<sub>eff</sub>, the interactions perturbing the boundaries of CD are expected to be rather weak. One has something analogous to a quantum computer isolated from the external world.
<LI> This suggests a more quantitative definition of the period with a fixed arrow of time. One expects that consciousness with a given arrow of time can have gaps. There is indeed empirical evidence suggesting that our flow of consciousness has gaps. Perhaps the wake-up-sleep ratio of the periods with different arrows of time is what matters. For a given arrow of time, the system would be dominantly in wake-up state or in sleep state.
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At a given level of self-hierarchy there is some average time for a given arrow of time and it is expected to increase at the higher levels. Magnetic bodies carrying dark matter interact only weakly with lower levels of the hierarchy, in particular ordinary matter, would make possible long periods with a given arrow of time, in the first guess proportional to say h<sub>eff</sub>.
<LI> What could biological death as a process at the level of ordinary biomatter mean? Is biological death determined by the situation at the lower hierarchy levels? On the other hand, dark matter at MBs defines a control hierarchy and is gradually thermalized as suggested in see <A HREF= "https://tgdtheory.fi/public_html/articles/SP.pdf">this</A>) so that the ability to perform biocontrol is reduced. Also the ability to gain metabolic energy is reduced and makes it difficult to preserve the arrow of time. Since the average value of h<sub>eff</sub> is reduced, the system becomes more vulnerable to perturbations inducing a BSFR changing the arrow of time.
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</OL>
There are also questions related to metabolism.
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<LI> A metabolic energy feed is needed to preserve the distribution for the values of h<sub>eff</sub>. The energies of quantum states increase with h<sub>eff</sub> and in the absence of a metabolic energy feed, the values of h<sub>eff</sub> at MBs tend to decrease. The system becomes more vulnerable to perturbations and the BSFRs changing the arrow of time occur more often. The system becomes drowsy.
<LI> Sun serves as a fundamental source of metabolic energy but TGD leads to a proposal that also radiation from the core of Earth, which happens to be at the same wavelength range as solar radiation could have served and maybe still serve as a source of metabolic energy.
<LI> I have proposed remote metabolism as a mechanism in which the system contains a subsystem with an opposite arrow which emits energy, say dissipates, in opposite time direction and thus seems to gain metabolic energy if seen from the standard arrow of time.
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This is possible if there is a system able to receive the <I> effective</I> negative energy signals. For instance, a population reversed laser could serve as such a system. The second option is that the environment loses thermal energy so that the second law in its standard form would be violated. For instance, heat could be transferred from a system with a given temperature to a system with higher temperature. The dissipation for the time reversed system looks like self-organization. Sleep periods would in this picture mean gain of metabolic resources and healing.
<LI> Also life with the opposite arrow of time needs metabolic energy. We receive metabolic energy basically from the Sun. Could the Sun serve as a source of metabolic energy also for the time reversed systems? The answer is positive.
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To understand why, one must clarify what the change of the arrow of time means. Time reversed signals have positive energy and only the reversed time direction makes them look like negative energy signals. The sum of energies for the sub systems with opposite arrows of time is conserved apart from effects due to finite sizes of CDs (Uncertainty Principle). Also life with an opposite arrow of time can use solar energy as a metabolic energy source.
<LI> The biological death is assumed to be due to the loss of quantum coherence at the level of MBs inducing a loss of ordinary coherence in short scales implying bodily decay. What could the situation be in the next reincarnation with the same arrow of time? Does the next life with the same arrow of time end at roughly the same time so that the size of the CD would become rather stationary. There would not be much progress.
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Or could the MB be able to preserve the quantum coherence for a longer time in the next reincarnation? Since the quantum coherence of MB naturally explains the coherence of the ordinary biomatter, impossible to understand in the standard physics framework, there is no reason why MB could not achieve this feat in the next incarnation.
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See the article <a HREF= "https://tgdtheory.fi/public_html/articles/CDconformal.pdf">New results about causal diamonds from the TGD view point of view</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/CDconformal.pdf">chapter</A> with the same title.
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For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-17635868145512696012023-01-30T23:39:00.005-08:002023-01-30T23:51:32.528-08:00Fermi bubbles as expanding magnetic bubbles?
Could one apply the proposed view about structure formation based on local Big-Bangs discussed in the article <a HREF= "https://tgdtheory.fi/public_html/articles/magnbubble.pdf">Magnetic Bubbles in TGD Universe</A> to Fermi bubbles (see <A HREF="https://rb.gy/uncffb">this</A>)?
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<B>Basic facts about Fermi bubbles</B>
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Consider first the basic facts.
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<LI> Fermi bubbles are located at the opposite sides of the galactic plane at the center of the galaxy. The radii of the bubbles are 12.5 kly and they expand at a rate of a few Mm/s (of order 10<sup>-2</sup> c).
<LI> Fermi bubbles consist of very hot gas, cosmic rays and magnetic fields. They are characterized by very bright diffuse gamma ray emissions.
<LI> Quite recently, so-called eRosita bubbles were discovered (see <A HREF="https://rb.gy/uncffb">this</A>). They have a size scale, which is twice that for Fermi bubbles. Both Fermi bubbles, eRosita bubbles and microwave haze are believed to be associated with an emission of jets.
<LI> Fermi bubbles could involve new exotic physics. The IceCube array in Antarctica (see <A HREF="https://rb.gy/qslgq4">this</A>) has reported 10 hyper-high-energy neutrinos sourced from the bubbles with highest energies in 20-50 TeV range.
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The most natural identification of Fermi bubbles is as a pair of jets emitted in the explosion associated with the galactic blackhole Sagittarius A<sup>*</sup>. According to the model discussed in the article (see <A HREF="https://rb.gy/uncffb">this</A>), they were born roughly 2.6 million years ago and the process lasted about 10<sup>5</sup> years.
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One particular rough estimate for the release of energy from Sagittarius A<sup>*</sup> is 10<sup>50</sup> Joules, which corresponds to 10<sup>3</sup>M<sub>Sun</sub> (solar mass is M<sub>Sun</sub> ≈ 10<sup>30</sup> kg). The estimate of the article for the energy would correspond to 10<sup>2</sup>M<sub>Sun</sub>.
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<B>Fermi bubbles as local Big-Bangs?</B>
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Could Fermi bubbles be magnetic bubbles produced by the general mechanism already discussed and perhaps even modellable as local Big Bangs?
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<LI> From the data summarized above, one can deduce that the mass concentrated at the bubbles is below the total energy released from Sagittarius A<sup>*</sup>. It is in the range of 10<sup>2</sup>--10<sup>3</sup> solar masses. This mass need not of course correspond to mass of the Fermi sphere.
<LI> The conservative option is that the expanding bubble has driven mass to the Fermi sphere as in the standard model of the Local Bubble. Recall that Local Bubble has a mass of 10<sup>6</sup> solar masses and is suggested to be caused by 15 supernova explosions emitting typically 10<sup>44</sup> Joules: 10<sup>45</sup> Joules corresponds to mass about 10<sup>-2</sup>M<sub>Sun</sub>. For this option the mass lost by Sagittarius A<sup>*</sup> would be completely negligible with that of the Fermi bubble.
<LI> The TGD inspired option is that the mass of Fermi Bubble is dark gravitational mass (10<sup>2</sup>-10<sup>3</sup>)M<sub>Sun</sub> at the gravitational flux tubes of the dark flux tube tangles emitted by the Sagittarius A<sup>*</sup> as a pair of jets formed by the expanding Fermi spheres. These tangeles would be characterized by gravitational Planck constant.
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The parameters of the local Big-Bang model of Fermi bubbles would be following.
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<LI> The gravitational Planck constant is partially determined by the mass of the galactic blackhole, which is about 4× 10<sup>6</sup>M<sub>Sun</sub>. The value of gravitational Planck constant would be huge and gravitational Compton length r<sub>S</sub>/2β<sub>0</sub>, where r<sub>S</sub>=1.2× 10<sup>7</sup> km is the Schwartschild radius.
<LI> L<sub>loc</sub>= 12.5 kly corresponds to the radius of the bubble and the length of a typical flux tube .
<LI> R<sub>loc</sub>= (3/8π GL<sub>loc</sub>)<sup>-1/4</sup> corresponds to the thickness of the flux tubes and would be of order μm from (L<sub>loc</sub>/L<sub>c</sub>)<sup>1/4</sup> scaling and R<sub>c</sub>≈ 10<sup>-4</sup> m.
<LI> Local Hubble constant corresponds to H<sub>loc</sub>= v/L<sub>loc</sub>∼ 10<sup>3</sup> H<sub>c</sub>, where v=(x/3)× 10<sup>-2</sup>c, x of order 1, is the estimate for the expansion velocity of the bubble. The TGD based model suggests that the identification β<sub>0</sub>=v/c makes sense in the beginning of the expansion. Note that for the Sun-Earth model the value of β<sub>0</sub> is of order .5× 10<sup>-3</sup>.
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<B> Acknowledgements</B>: I want to thank Avril Emil for interesting questions related to the notion of local Big-Bang.
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See the article <a HREF= "https://tgdtheory.fi/public_html/articles/magnbubble.pdf">Magnetic Bubbles in TGD Universe</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/qastro.pdf">Quantum Astrophysics</A>.
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For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-77623226262867396932023-01-29T23:39:00.005-08:002023-01-29T23:39:56.948-08:00How Earth could have formed from gravitationally dark matter at magnetic bubble
The following argument tries to describe the physics of the TGD based model first. I have not evaluated the local Hubble constant before and try to do it. I will concentrate on the TGD inspired model for the formation of Earth. The idea that Earth was formed as the gravitationally dark matter at the magnetic bubble transformed to ordinary matter. This mechanism would explain also the formation of stars at the Local Bubble.
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<B>What happens in rapid local cosmic expansion pulses that replace the uniform expansion in TGD?</B>
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This rapid local expansion is essentially an explosion. A supernova explosion throwing out a shell of matter, and as the interpretation of Local Bubble suggests, also the magnetic bubble, is a good starting point in the modelling.
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<LI> A flux tube containing dark matter (in the sense of TGD) expands rapidly. The thickness of the flux tubes increases rapidly and then settles to a constant value as a new minimum energy situation is found.
<LI> The cross-sectional area S of the flux tube serves as a parameter. The magnetic energy E<sub>m</sub> ∝ 1/S and the volume energy E<sub>V</sub>∝ (its coefficient is analogous to the cosmological constant) associated with the monopole flux are the energies. In equilibrium, the sum E<sub>n</sub>+E<sub>V</sub> is minimized as a function of S (see <a HREF= "https://tgdtheory.fi/public_html/articles/twistactions.pdf">this</A>). The total density for the flux tube determines the effective cosmological constant Λ<sub>loc</sub>, i.e. the effective string tension, which decreases as the flux tube thickens. This means energy release, which causes an explosion.
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<B>The Big Bang analogy as a model</B>
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It is tempting to apply Big-Bang analogy to the explosion phase.
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<LI> The density ρ<sub>d</sub> = 3 Λ/8π G of dark energy would define a map between very long and short length scales identified as L<sub>c</sub>= Λ<sup>-1/2</sup> and R<sub>d</sub>=ρ<sub>d</sub><sup>-1/4</sup>. L<sub>c</sub> could correspond correspond to the horizon radius or age of the local Universe identifiable as the size of associated causal diamond (CD) in zero energy ontology (ZEO) (see <a HREF= "https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>). At the microscopic level, L<sub>c</sub> could correspond to the length of the flux tube and R<sub>c</sub> to its thickness.
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These identifications would relate macroscopic and even astrophysical scales and elementary particle mass scales. I have considered the possible consequences of this map earlier.
<LI> As the energy minimum is reached, the expansion of the flux tube ceases. It can be also thought that H<sub>loc</sub> and Λ<sub>loc</sub> approach cosmological values. Therefore one could model the emerging expanding space sheet as a local Big-Bang with the help of the parameters Λ<sub>loc</sub>, L<sub>loc</sub>, and H<sub>loc</sub>, which have large values at the beginning of the explosion. The explosion would be a scaled down analog for the TGD counterpart of inflation, which would have led to effectively 2-D cosmic strings with 2-D M<sup>4</sup> projection to Einsteinian space-time with 4-D M<sup>4</sup> projection.
<LI> The dark energy density would be ρ<sub>d</sub>=3 Λ<sub>loc</sub>/8π G with Λ<sub>loc</sub>∝ 1/L<sub>loc</sub><sup>2</sup>. L<sub>loc</sub> would be the scale of the space-time sheet determined by the length of the flux extending to a horizon which would correspond to light-like 3-surface, whose possible role as space-time boundaries was understood only quite recently (see <a HREF= "https://tgdtheory.fi/public_html/articles/freezing.pdf">this</A>). L<sub>loc</sub> would quite concretely be the radius of the horizon. The horizon would correspond to the edge of a spacetime sheet.
<LI> For the usual Planck's constant ℏ, one would have the usual cosmological Λ ∝ 1/L<sub>c</sub><sup>2</sup>, where L<sub>c</sub> would be the radius of the horizon and of the order of 10<sup>10</sup> ly. The scale R<sub>c</sub>∝ (8π G/3 Λ)<sup>1/4</sup> would be much smaller than Λ<sub>c</sub> and from the estimate ρ<sub>c</sub> ≈ m<sub>p</sub>/m<sup>3</sup> and proton Compton length 3.48× 10<sup>-15</sup> m would roughly correspond to a wavelength of .75× 10<sup>-4</sup> meters. The peak wavelength of the microwave background is 1 mm. This suggests a biology-cosmology connection.
<LI> If Λ<sub>loc</sub> scales as 1/L<sup>2</sup><sub>loc</sub>, and L<sub>loc</sub> ≈ AU corresponds to the scale of the Earth-Sun system, L<sub>loc</sub> in the Sun-Earth system would be smaller by the factor AU/L<sub>c</sub>≃ 1.6× 10<sup>-15</sup> than at the level of cosmology.
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The scaling of R<sub>c</sub> ≈ 10<sup>-4</sup> m by this factor would give R<sub>loc</sub> ≈ 10<sup>-19</sup> m. This is by factor 1/100 smaller than the Compton scale of intermediate bosons. What could this mean?
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TGD predicts (see <a HREF= "https://tgdtheory.fi/pdfpool/tgdnewphys1.pdf">this</A>) and <a HREF= "https://tgdtheory.fi/public_html/pdfpool/tgdnewphys2.pdf">this</A>) scaled up variants of strong interaction physics assignable at p-adic primes identifiable as Mersenne primes M<sub>n</sub>=2<sup>n</sup>-1 or their Gaussian counterparts M<sub>n,G</sub>= (1+i)<sup>n-1</sup>, M<sub>107</sub> would correspond to ordinary hadron physics and M<sub>89</sub> would correspond LHC energy scale higher by factor 512 than that of ordinary hadron physics. There are several indications for M<sub>89</sub> hadron physics as dark variants of M<sub>89</sub> hadrons with scaled up Compton length. Gaussian Mersennes M<sub>G,79</sub> <I> resp.</I> M<sub>G,73</sub> would correspond to scales, which are by factor 2<sup>14</sup> <I> resp.</I> 2<sup>17</sup> that of ordinary hadron physics. The Compton radius of proton for the M<sub>G,73</sub> hadron physics be of the order of R<sub>loc</sub> ≈ 10<sup>-19</sup> m.
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<B>Matter at the magnetic bubbles is dark</B>
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The fact that monopole flux tubes associated with the magnetic bubble carry dark matter in the TGD sense is not yet taken into account.
<OL>
<LI> TGD predicts a hierarchy of large Planck's constant h<sub>eff</sub> =nh<sub>0</sub> labelling phases of ordinary matter, which behave like dark matter at the flux tubes. In particular, the gravitation Planck's constant ℏ<sub>gr</sub>= GMm/β<sub>0</sub>, β<sub>0</sub><1, which Nottale originally suggested, would make possible quantum gravitational coherence in astrophysical scales in the TGD Universe.
<LI> The gravitationally dark monopole flux tubes would be naturally associated with the magnetic bubble corresponding to the Earth (analogous to the one created in a supernova) and also connect the magnetic bubble with the Sun and mediate gravitational interaction with it. Matter at the magnetic bubble would have been dark before condensing to form Earth for which matter mostly corresponds to the usual value of Planck's constant.
<LI> For gravitationally dark matter, the gravitational Compton wavelength is Λ<sub>gr</sub>= GM/β<sub>0</sub> = r<sub>S</sub>/2β<sub>0</sub> and does not depend on the mass of the particle m at all. This is in accordance with the Equivalence Principle. That particles of all masses have the same Compton wavelength makes gravitational quantum coherence possible and is essential in the TGD inspired quantum biology.
<LI> For the Sun, the Schwartschild radius is 3 km and β<sub>0</sub>= v<sub>0</sub>/c is of order 2<sup>-11</sup> on basis of Nottale's estimates, which came from the model for planetary orbits as Bohr orbits. The Compton wavelength Λ<sub>gr</sub> would be about 6000 km, about the radius of the Earth! Is this a mere accident? The thickness of the dark gravitational flux tube R<sub>loc</sub> would therefore be of the order of the Earth's radius R<sub>E</sub>, and the length L<sub>loc</sub> would be of the order of AU.
</p><p>
The parameters of the local Big-Bang would therefore be R<sub>loc</sub> = R<sub>E</sub> and L<sub>loc</sub>=AU at the beginning of the explosion that led to the creation of the Earth as dark gravitationally dark matter transformed to ordinary. The slowing down of the explosion would be due to the transformation of the gravitationally dark matter to ordinary matter.
</OL>
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<B>What about the value of local Hubble constant?</B>
</p><p>
The previous arguments have not said anything about the value of the local Hubble's constant H<sub>loc</sub> in the beginning of the explosion. Here the formula for ℏ<sub>gr</sub> serves as a guideline.
<OL>
<LI> β<sub>0</sub>=v<sub>0</sub>/c is the velocity parameter appearing in the gravitational Planck constant ℏ<sub>gr</sub>. It could correspond to a typical expansion rate at a distance L<sub>loc</sub> ≈ AU.
</p><p>
In the case of the Sun, β<sub>0</sub>= v<sub>0</sub>/c≃ 2<sup>-11</sup> applies. Could it be the rate of expansion for the Earth-related dark magnetic bubble during the <I> initial stages</I> of the explosion, which would later slow down as dark matter is transformed to ordinary?
<LI> The counterpart of Hubble's formula would give a prediction for the local recession velocity at Earth-Sun distance L<sub>loc</sub>= AU= 4.4× 10<sup>-6</sup> pc as v<sub>loc</sub>=β<sub>0</sub>c= H<sub>loc</sub>× L<sub>loc</sub> i.e. H<sub>loc</sub>= β<sub>0</sub>× c/L<sub>loc</sub>. This gives H<sub>loc</sub> ≃ 3× 10<sup>7</sup> kms<sup>-1</sup> pc<sup>-1</sup>. Cosmic Hubble constant H<sub>c</sub>≃ 72 km s<sup>-1</sup> Mpc<sup>-1</sup> is 11 orders of magnitude smaller.
<LI> The naive L<sub>loc</sub>/L<sub>c</sub> scaling would give a value of H<sub>loc</sub>, which is 15 orders of magnitude smaller. For β<sub>0</sub> =1, i.e. its maximum value which seems to be valid ate the surface of the Earth in quantum biology, the value would be give 14-15 orders smaller, so that the L<sub>loc</sub>/L<sub>c</sub> scaling would seem to make sense in this case.
</OL>
</p><p>
<B>Acknowledgements</B>: I want to thank Avril Emil for interesting questions related to the notion of local Big-Bang.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/magnbubble.pdf">Magnetic Bubbles in TGD Universe</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/qastro.pdf">Quantum 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>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-88161979939441962232023-01-27T23:56:00.004-08:002023-01-28T00:48:47.527-08:00Magnetic Bubbles in TGD Universe
I received a link to a video summarizing the properties of the Local Bubble surrounding the solar system (see <A HREF ="https://rb.gy/m8slm3">this</A>). The Local Bubble represents only one example of magnetic bubbles. The magnetic bubble carries a magnetic field with field lines along its surface. Star formation and interstellar gas seems to concentrate on the bubble.
</p><p>
The article "<I> Star formation near the Sun is driven by expansion of the Local Bubble</I>" by Zucker et al published in Nature (see <A HREF="https://rb.gy/7hdoyo">this</A>) gives basic facts about the Local Bubble surrounding the solar system. The Local Bubble has a radius of about 500 ly. Within 500-light-years of Earth, all stars and star-forming regions sit on the surface of the Local Bubble, but not inside. The total mass is about 10<sup>6</sup> solar masses. The Local bubble is accompanied by magnetized molecular clouds, which reveal the existence of the bubble via the polarization of radio wave radiation.
</p><p>
It is believed that the Local Bubble has been formed in a burst of star formation in the center of the bubble. These stars would have died as supernovae and the matter from supernova explosions would have pushed gas and compressed it to form the Local Bubble. According to the Nature article (see <A HREF="https://rb.gy/7hdoyo">this</A>), the research team calculated that at least 15 supernovae have gone off over millions of years and pushed gas outward, creating a bubble where seven star-forming regions dot the surface.
</p><p>
These bubbles bring in mind the large voids (see <A HREF="https://tinyurl.com/jyqcjhl">this</A>), whose boundaries carry galaxies. They are discussed from the TGD point of view <A HREF ="https://tgdtheory.fi/public_html/articles/tgdcosmo.pdf">here</A>. One ends up with the question, whether galaxies are formed at the surfaces of large voids and stars at the surfaces of the magnetic bubbles. Could also the formation of planets be understood in this way? TGD predicts that cosmic expansion takes place as rapid "jerks", and this view has application to the mystery of Cambrian Explosion (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/preCE.pdf">this</A>). Could these local Big-Bangs give rise to a universal mechanism for the formation of structures? If so, then Earth and Moon must have the same composition. The finding that this is indeed the case (see <A HREF="https://rb.gy/4sq5ho">this</A>), came as a total surprise.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/magnbubble.pdf">Magnetic Bubbles in TGD Universe</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/qastro.pdf">Quantum 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>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-87790863649319474392023-01-26T06:08:00.008-08:002023-02-05T22:10:03.882-08:00New results about causal diamonds from the TGD view point of viewI found two interesting results related to the notion of causal diamond (CD) playing a central role in quantum TGD. One interpretation is as a quantization volume and the second interpretation is as a geometric representation of the perceptive field of conscious entity. CDs can be said to define the backbone of the "world of classical worlds" (WCW) central for quantum TGD.
</p><p>
For these reasons it is interesting to ask the precise mathematical definition of the moduli space of CDs. TGD suggests a definition as the semidirect product D⋊ P/SO(3) of scaling group and Poincare group divided by SO(3) subgroup leaving the CD invariant: this gives 8-D space. The definition that inspired this article is based on conformal group and gives also 8-D space SO(2,4)/SO(1,3)\times SO(1,1). The metric signature is (4,4) for both spaces and they could be identical. These definitions are compared and one can consider the conditions under which both identification can give rise to representations of the Poincare group as expected with the scaling group reduced to a discrete subgroup.
</p><p>
Second result relates to the finding that special conformal transformations in the time direction defined by CD leave CD invariant. The corresponding hyperbolic flows correspond to a motion with constant acceleration to which the so-called Unruh effect is associated. One can consider an SL(2,R) algebra assignable to a conformal quantum mechanics and assign a hyperbolic time evolution operator to this flow. The conformal 2-point functions associated with this operator correspond to thermal partition functions with thermal mass defined by the temperature which is essentially the inverse of the CD scale.
</p><p>
Holography does not allow us to consider these flows for the space-time surfaces insid CD but the action of the hyperbolic evolution operator on quantum states at the boundaries of CD is well-defined. This raises interesting questions related to TGD inspired consciousness, where subsequent scalings of CD in state function reductions (SFRs) give rise to the correlation of subjective time and geometric time defined as the distance between the tips of CD. The SFRs associated with the hyperbolic time evolution operator would not affect CD and would correspond to "timeless" state of consciousness.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/CDconformal.pdf">New results about causal diamonds from the TGD view point of view</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/CDconformal.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>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-12031229926024993192023-01-18T01:46:00.003-08:002023-01-18T22:50:04.870-08:00About the selection of the action defining the Kähler function of the "world of classical worlds" (WCW)
<B>About the selection of the action defining the Kähler function of the "world of classical worlds" (WCW)</B>
</p><p>
The proposal is that space-time surfaces correspond to preferred extremals of some action principle, being analogous to Bohr orbits, so that they are almost deterministic. The action for the preferred extremal would define the Kähler function of WCW (see <A HREF="https://tgdtheory.fi/pdfpool/kahler.pdf">this </A> and <A HREF="https://tgdtheory.fi/pdfpool/wcwnew.pdf">this </A>).
</p><p>
How unique is the choice of the action defining WCW Kähler metric?
The problem is that twistor lift strongly suggests the identification of the preferred extremals as 4-D surfaces having 4-D generalization of complex structure and that a large number of general coordinate invariant actions constructible in terms of the induced geometry have the same preferred extremals.
</p><p>
<B>1. Could twistor lift fix the choice of the action uniquely?</B>
</p><p>
The twistor lift of TGD (see <A HREF="https://tgdtheory.fi/pdfpool/twistquestions.pdf"> this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/TGD2021.pdf">this </A>, <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>) generalizes the notion of induction to the level of twistor fields and leads to a proposal that the action is obtained by dimensional reduction of the action having as its preferred extremals the counterpart of twistor space of the space-time surface identified as 6-D surface in the product T(M<sup>4</sup>)× T(CP<sub>2</sub>) twistor spaces of T(M<sup>4</sup>) and T(CP<sub>2</sub>) of M<sup>4</sup> and CP<sub>2</sub>. Only M<sup>4</sup> and CP<sub>2</sub> allow a twistor space with Kähler structure (see <A HREF="https://tinyurl.com/pb8zpqo">this</A>) so that TGD would be unique. Dimensional reduction is forced by the condition that the 6-surface has S<sup>2</sup>-bundle structure characterizing twistor spaces and the base space would be the space-time surface.
<OL>
<LI> Dimensional reduction of 6-D Kähler action implies that at the space-time level the fundamental action can be identified as the sum of Kähler action and volume term (cosmological constant). Other choices of the action do not look natural in this picture although they would have the same preferred extremals.
<LI> Preferred extremals are proposed to correspond to minimal surfaces with singularities such that they are also extremals of 4-D Kähler action outside the singularities. The physical analogue are soap films spanned by frames and one can localize the violation of the strict determinism and of strict holography to the frames.
<LI> The preferred extremal property is realized as the holomorphicity characterizing string world sheets, which generalizes to the 4-D situation. This in turn implies that the preferred extremals are the same for any general coordinate invariant action defined on the induced gauge fields and induced metric apart from possible extremals with vanishing CP<sub>2</sub> Kähler action.
</p><p>
For instance, 4-D Kähler action and Weyl action as the sum of the tensor squares of the components of the Weyl tensor of CP<sub>2</sub> representing quaternionic imaginary units constructed from the Weyl tensor of CP<sub>2</sub> as an analog of gauge field would have the same preferred extremals and only the definition of Kähler function and therefore Kähler metric of WCW would change. One can even consider the possibility that the volume term in the 4-D action could be assigned to the tensor square of the induced metric representing a quaternionic or octonionic real unit.
</OL>
Action principle does not seem to be unique. On the other hand, the WCW Kähler form and metric should be unique since its existence requires maximal isometries.
</p><p>
Unique action is not the only way to achieve this. One cannot exclude the possibility that the Kähler gauge potential of WCW in the complex coordinates of WCW differs only by a complex gradient of a holomorphic function for different actions so that they would give the same Kähler form for WCW. This gradient is induced by a symplectic transformation of WCW inducing a U(1) gauge transformation. The Kähler metric is the same if the symplectic transformation is an isometry.
</p><p>
Symplectic transformations of WCW could give rise to inequivalent representations of the theory in terms of action at space-time level. Maybe the length scale dependent coupling parameters of an effective action could be interpreted in terms of a choice of WCW Kähler function, which maximally simplifies the computations at a given scale.
<OL>
<LI> The 6-D analogues of electroweak action and color action reducing to Kähler action in 4-D case exist. The 6-D analog of Weyl action based on the tensor representation of quaternionic imaginary units does not however exist. One could however consider the possibility that only the base space of twistor space T(M<sup>4</sup>) and T(CP<sub>2</sub>) have quaternionic structure.
<LI> Kähler action has a huge vacuum degeneracy, which clearly distinguishes it from other actions. The presence of the volume term removes this degeneracy. However, for minimal surfaces having CP<sub>2</sub> projections, which are Lagrangian manifolds and therefore have a vanishing induced Kähler form, would be preferred extremals according to the proposed definition. For these 4-surfaces, the existence of the generalized complex structure is dubious.
</p><p>
For the electroweak action, the terms corresponding to charged weak bosons eliminate these extremals and one could argue that electroweak action or its sum with the analogue of color action, also proportional Kähler action, defines the more plausible choice. Interestingly, also the neutral part of electroweak action is proportional to Kähler action.
</OL>
Twistor lift strongly suggests that also M<sup>4</sup> has the analog of Kähler structure. M<sup>8</sup> must be complexified by adding a commuting imaginary unit i. In the E<sup>8</sup> subspace, the Kähler structure of E<sup>4</sup> is defined in the standard sense and it is proposed that this generalizes to M<sup>4</sup> allowing also generalization of the quaternionic structure. M<sup>4</sup> Kähler structure violates Lorentz invariance but could be realized at the level of moduli space of these structures.
</p><p>
The minimal possibility is that the M<sup>4</sup> Kähler form vanishes: one can have a different representation of the Kähler gauge potential for it obtained as generalization of symplectic transformations acting non-trivially in M<sup>4</sup>. The recent picture about the second quantization of spinors of M<sup>4</sup>× CP<sub>2</sub> assumes however non-trivial Kähler structure in M<sup>4</sup>.
</p><p>
<B>2. Two paradoxes</B>
</p><p>
TGD view leads to two apparent paradoxes.
<OL>
<LI> If the preferred extremals satisfy 4-D generalization of holomorphicity, a very large set of actions gives rise to the same preferred extremals unless there are some additional conditions restricting the number of preferred extremals for a given action.
<LI> WCW metric has an infinite number of zero modes, which appear as parameters of the metric but do not contribute to the line element. The induced Kähler form depends on these degrees of freedom. The existence of the Kähler metric requires maximal isometries, which suggests that the Kähler metric is uniquely fixed apart from a conformal scaling factor \Omega depending on zero modes. This cannot be true: galaxy and elementary particle cannot correspond to the same Kähler metric.
</OL>
Number theoretical vision and the hierarchy of inclusions of HFFs associated with supersymplectic algebra actings as isometries of WcW provide equivalent realizations of the measurement resolution. This solves these paradoxes and predicts that WCW decomposes into sectors for which Kähler metrics of WCW differ in a natural way.
</p><p>
<B>2.1 The hierarchy subalgebras of supersymplectic algebra implies the decomposition of WCW into sectors with different actions</B>
</p><p>
Supersymplectic algebra of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> is assumed to act as isometries of WCW (see <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>). There are also other important algebras but these will not be discussed now.
<OL>
<LI> The symplectic algebra A of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> has the structure of a conformal algebra in the sense that the radial conformal weights with non-negative real part, which is half integer, label the elements of the algebra have an interpretation as conformal weights.
</p><p>
The super symplectic algebra A has an infinite hierarchy of sub-algebras (see <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>) such that the conformal weights of sub-algebras A<sub>n(SS)</sub> are integer multiples of the conformal weights of the entire algebra. The superconformal gauge conditions are weakened. Only the subalgebra A<sub>n(SS)</sub> and the commutator [A<sub>n(SS)</sub>,A] annihilate the physical states. Also the corresponding classical Noether charges vanish for allowed space-time surfaces.
</p><p>
This weakening makes sense also for ordinary superconformal algebras and associated Kac-Moody algebras. This hierarchy can be interpreted as a hierarchy symmetry breakings, meaning that sub-algebra A<sub>n(SS)</sub> acts as genuine dynamical symmetries rather than mere gauge symmetries. It is natural to assume that the super-symplectic algebra A does not affect the coupling parameters of the action.
<LI> The generators of A correspond to the dynamical quantum degrees of freedom and leave the induced Kähler form invariant. They affect the induced space-time metric but this effect is gravitational and very small for Einsteinian space-time surfaces with 4-D M<sup>4</sup> projection.
</p><p>
The number of dynamical degrees of freedom increases with n(SS). Therefore WCW decomposes into sectors labelled by n(SS) with different numbers of dynamical degrees of freedom so that their Kähler metrics cannot be equivalent and cannot be related by a symplectic isometry. They can correspond to different actions.
</OL>
<B>2.2 Number theoretic vision implies the decomposition of WCW into sectors with different actions</B>
</p><p>
The number theoretical vision leads to the same conclusion as the hierarchy of HFFs. The number theoretic vision of TGD based on M<sup>8</sup>-H duality (see <A HREF = "https://tgdtheory.fi/public_html/articles/fusionTGD.pdf"> this</A>) predicts a hierarchy with levels labelled by the degrees n(P) of rational polynomials P and corresponding extensions of rationals characterized by Galois groups and by ramified primes defining p-adic length scales.
</p><p>
These sequences allow us to imagine several discrete coupling constant evolutions realized at the level H in terms of action whose coupling parameters depend on the number theoretic parameters.
</p><p>
<B> 2.2.1 Coupling constant evolution with respect to n(P)</B>
</p><p>
The first coupling constant evolution would be with respect to n(P).
<OL>
<LI> The coupling constants characterizing action could depend on the degree n(P) of the polynomial defining the space-time region by M<sup>8</sup>-H duality. The complexity of the space-time surface would increase with n(P) and new degrees of freedom would emerge as the number of the rational coefficients of P.
<LI> This coupling constant evolution could naturally correspond to that assignable to the inclusion hierarchy of hyperfinite factors of type II<sub>1</sub> (HFFs). I have indeed proposed (see <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>) that the degree n(P) equals to the number n(braid) of braids assignable to HFF for which super symplectic algebra subalgebra A<sub>n(SS)</sub> with radial conformal weights coming as n(SS)-multiples of those of entire algebra A. One would have n(P)= n(braid)=n(SS). The number of dynamical degrees of freedom increases with n which just as it increases with n(P) and n(SS).
<LI> The actions related to different values of n(P)=n(braid)=n(SS) cannot define the same Kähler metric since the number of allowed space-time surfaces depends on n(SS).
</p><p>
WCW could decompose to sub-WCWs corresponding to different actions, a kind of theory space. These theories would not be equivalent. A possible interpretation would be as a hierarchy of effective field theories.
<LI> Hierarchies of composite polynomials define sequences of polynomials with increasing values of n(P) such that the order of a polynomial at a given level is divided by those at the lower levels. The proposal is that the inclusion sequences of extensions are realized at quantum level as inclusion hierarchies of hyperfinite factors of type II<sub>1</sub>.
</p><p>
A given inclusion hierarchy corresponds to a sequence n(SS)<sub>i</sub> such that n(SS)<sub>i</sub> divides n(SS)<sub>i+1</sub>. Therefore the degree of the composite polynomials increases very rapidly. The values of n(SS)<sub>i</sub> can be chosen to be primes and these primes correspond to the degrees of so called prime polynomials (see <A HREF="https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>) so that the decompositions correspond to prime factorizations of integers. The "densest" sequence of this kind would come in powers of 2 as n(SS)<sub>i</sub>= 2<sup>i</sup>. The corresponding p-adic length scales (assignable to maximal ramified primes for given n(SS)<sub>i</sub>) are expected to increase roughly exponentially, say as 2<sup>r2<sup>i</sup></sup>. r=1/2 would give a subset of scales 2<sup>r/2</sub> allowed by the p-adic length scale hypothesis. These transitions would be very rare.
</p><p>
A theory corresponding to a given composite polynomial would contain as sub-theories the theories corresponding to lower polynomial composites. The evolution with respect to n(SS) would correspond to a sequence of phase transitions in which the action genuinely changes. For instance, color confinement could be seen as an example of this phase transition.
<LI> A subset of p-adic primes allowed by the p-adic length scale hypothesis p≈ 2<sup>k</sup> defining the proposed p-adic length scale hierarchy could relate to n<sub>S</sub> changing phase transition. TGD suggests a hierarchy of hadron physics corresponding to a scale hierarchy defined by Mersenne primes and their Gaussian counterparts (see <A HREF="https://tgdtheory.fi/pdfpool/tgdnewphys1.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/tgdnewphys2.pdf">this</A>). Each of them would be characterized by a confinement phase transition in which n<sub>S</sub> and therefore also the action changes.
</OL>
<B> 2.2.2 Coupling constant evolutions with respect to ramified primes for a given value of n(P)</B>
</p><p>
For a given value of n(P), one could have coupling constant sub-evolutions with respect to the set of ramified primes of P and dimensions n=h<sub>eff</sub>/h<sub>0</sub> of algebraic extensions. The action would only change by U(1) gauge transformation induced by a symplectic isometry of WCW. Coupling parameters could change but the actions would be equivalent.
</p><p>
The choice of the action in an optimal manner in a given scale could be seen as a choice of the most appropriate effective field theory in which radiative corrections would be taken into account. One can interpret the possibility to use a single choice of coupling parameters in terms of quantum criticality.
</p><p>
The range of the p-adic length scales labelled by ramified primes and effective Planck constants h<sub>eff</sub>/h<sub>0</sub> is finite for a given value of n(SS).
</p><p>
The first coupling constant evolution of this kind corresponds to ramified primes defining p-adic length scales for given n(SS).
<OL>
<LI> Ramified primes are factors of the discriminant D(P) of P, which is expressible as a product of non-vanishing root differents and reduces to a polynomial of the n coefficients of P. Ramified primes define p-adic length scales assignable to the particles in the amplitudes scattering amplitudes defined by zero energy states.
</p><p>
P would represent the space-time surface defining an interaction region in N--particle scattering. The N ramified primes dividing D(P) would characterize the p-adic length scales assignable to these particles. If D(P) reduces to a single ramified prime, one has elementary particle <A HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>), and the forward scattering amplitude corresponds to the propagator.
</p><p>
This would give rise to a multi-scale p-adic length scale evolution of the amplitudes analogous to the ordinary continuous coupling constant evolution of n-point scattering amplitudes with respect to momentum scales of the particles. This kind of evolutions extend also to evolutions with respect to n(SS).
<LI> physical constraints require that n(P) and the maximum size of the ramified prime of P correlate (see <A HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>).
</p><p>
A given rational polynomial of degree n(P) can be always transformed to a polynomial with integer coefficients. If the integer coefficients are smaller than n(P), there is an upper bound for the ramified primes. This assumption also implies that finite fields become fundamental number fields in number theoretical vision (see <A HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>).
<LI> p-Adic length scale hypothesis (see <A HREF= "https://tgdtheory.fi/public_html/articles/padmass2022.pdf">this</A>) in its basic form states that there exist preferred primes p≈ 2<sup>k</sup> near some powers of 2. A more general hypothesis states that also primes near some powers of 3 possibly also other small primes are preferred physically. The challenge is to understand the origin of these preferred scales.
</p><p>
For polynomials P with a given degree n(P) for which discriminant D(P) is prime, there exists a maximal ramified prime. Numerical calculations suggest that the upper bound depends exponentially on n(P).
</p><p>
Could these maximal ramified primes satisfy the p-adic length scale hypothesis or its generalization? The maximal prime defines a fixed point of coupling constant evolution in accordance with the earlier proposal. For instance, could one think that one has p≈ 2<sup>k</sup>, k= n(SS)? Each p-adic prime would correspond to a p-adic coupling constant sub-evolution representable in terms of symplectic isometries.
</OL>
Also the dimension n of the algebraic extension associated with P, which is identified in terms of effective Planck constant h<sub>eff</sub>/h<sub>0</sub>=n labelling different phases of the ordinary matter behaving like dark matter, could give rise to coupling constant evolution for given n(SS). The range of allowed values of n is finite. Note however that several polynomials of a given degree can correspond to the same dimension of extension.
</p><p>
<B>2.3 Number theoretic discretization of WCW and maxima of WCW Kähler function</B>
</p><p>
Number theoretic approach involves a unique discretization of space-time surface and also of WCW. The question is how the points of the discretized WCW correspond to the preferred extremals.
<OL>
<LI> The exponents of Kähler function for the maxima of Kähler function, which correspond to the universal preferred extremals, appear in the scattering amplitudes. The number theoretical approach involves a unique discretization of space-time surfaces defining the WCW coordinates of the space-time surface regarded as a point of WCW.
</p><p>
In (see <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this </A>) it is assumed that these WCW points appearing in the number theoretical discretization correspond to the maxima of the Kähler function. The maxima would depend on the action and would differ for ghd maxima associated with different actions unless they are not related by symplectic WCW isometry.
<LI> The symplectic transformations of WCW acting as isometries are assumed to be induced by the symplectic transformations of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> (see <A HREF="https://tgdtheory.fi/pdfpool/kahler.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/compl1.pdf">this</A>). As isometries they would naturally permute the maxima with each other.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/cp2etc.pdf">Reduction of standard model structure to CP<sub>2</sub> geometry and other key ideas of TGD</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/fusionTGD.pdf">Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole</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>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-61418944939355770182023-01-16T04:10:00.005-08:002023-01-16T20:52:49.361-08:00Reduction of standard model structure to CP_2 geometry and other key ideas of TGDOriginally this article was an appendix meant to be a purely technical summary of basic facts about CP<sub>2</sub> but in its recent form it tries to briefly summarize those basic visions about TGD which I dare to regarded stabilized. I have added links to illustrations making it easier to build mental images about what is involved and represented briefly the key arguments. This chapter is hoped to help the reader to get fast grasp about the concepts of TGD.
</p><p>
The basic properties of embedding space and related spaces are discussed and the relationship of CP<sub>2</sub> to the standard model is summarized. The basic vision is simple: the geometry of the embedding space H=M<sup>4</sup>× CP<sub>2</sub> geometrizes standard model symmetries and quantum numbers. The assumption that space-time surfaces are basic objects, brings in dynamics as dynamics of 3-D surfaces based on the induced geometry. Second quantization of free spinor fields of H induces quantization at the level of H, which means a dramatic simplification.
</p><p>
The notions of induction of metric and spinor connection, and of spinor structure are discussed. Many-sheeted space-time and related notions such as topological field quantization and the relationship many-sheeted space-time to that of GRT space-time are discussed as well as the recent view about induced spinor fields and the emergence of fermionic strings. Also the relationship to string models is discussed briefly.
</p><p>
Various topics related to p-adic numbers are summarized with a brief definition of p-adic manifold and the idea about generalization of the number concept by gluing real and p-adic number fields to a larger book like structure analogous to adele (see <A HREF="https://tgdtheory.fi/public_html/articles/adelephysics.pdf">this</A>). In the recent view of quantum TGD (see <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>), both notions reduce to physics as number theory vision, which relies on M<sup>8</sup>-H duality (see <A HREF="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A> ) and is complementary to the physics as geometry vision.
</p><p>
Zero energy ontology (ZEO) (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A>) has become a central part of quantum TGD and leads to a TGD inspired theory of consciousness as a generalization of quantum measurement theory having quantum biology as an application. Also these aspects of TGD are briefly discussed.
</p><p>
The preparation of this article led to one very interesting question. The twistor lift 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>) leads to the proposal that the preferred extremals of the 4-D dimensionally reduced 6-D Kähler action reduces to the sum of 4-D Kähler action and volume term. These extremals are analogues of soap films spanned by frames: minimal surfaces with singularities. Outside the frames, these minimal 4-surfaces are simultaneous extremals of Kähler action. This is guaranteed if the holomorphicity of string world sheets generalizes to the 4-D case. The interpretation is in terms of quantum criticality.
</p><p>
These surfaces are actually extremals for a very large class of actions. Does it make sense to ask which 4-D action is the correct one? The 4-D action defines a Kähler function of a Kähler metric of "world of classical worlds". Do different actions define different Kähler metrics or are the metrics actually identical when some constraints on the couplings are posed. If the WCW metrics defined by different actions are equivalent, the Kähler functions differ by an addition of a gradient of a complex function to the Kähler gauge potential defined by Kähler function.
</p><p>
The number theoretic vision of TGD based on M<sup>8</sup> predicts a discrete coupling constant evolution with levels labelled by degrees of rational polynomials and corresponding extensions of rationals characterized by Galois groups and by ramified primes defining p-adic length scales (see <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>). Hierarchies of composite polynomials define inclusion sequences of extensions. These sequences would correspond to discrete coupling constant evolutions.
</p><p>
What could be the counterparts of these evolutions at the level of H=M<sup>4</sup>× CP<sub>2</sub> and WCW? Could they be characterized by the values of coupling parameters defining the action defining the Kähler function of WCW but giving rise to the same Kähler metric of WCW? Could the coupling constant evolution correspond to a sequence of U(1) gauge transformations of WCW and identifiable as symplectic transformations of WCW?
</p><p>
WCW could decompose to sub-WCWs corresponding to different actions and coupling constant evolutions, a kind of theory space. These theories would not be equivalent. Rather, a theory corresponding to a given composite would contain as subtheories the theories corresponding to lower polynomial composites. A possible interpretation would be as hierarchies of effective field theories. The choice of the action in an optimal manner in a given scale could be seen as a choice of the most appropriate effective field theory.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/cp2etc.pdf">Reduction of standard model structure to CP_2 geometry and other key ideas of TGD</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>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-22028360238800671192023-01-13T00:23:00.003-08:002023-01-13T00:23:50.676-08:00TGD view of Michael Levin's work
In this article I discuss the finding of Michael Levin's group related to morphogenesis and also the general ideas inspired by this work. The findings demonstrate that the hypothesis that genotype fixes the phenotype apart from adaptations is wrong. Already epigenesis challenges genetic determinism and the view emerging from the experiments is that the patterns of membrane potentials of cells of early embryo determine patterns of electric fields in multicellular length scales and that code for the outcome of the morphogenesis. One can say that these patterns code for the goal directed behavior and have the basic properties of memory. The manipulations of these patterns in the early embryonic stage can modify the outcome of the morphogenesis so that one can speak of a novel organism. Also the manipulations of say gut cells can produce organs such as ectopic eye.
</p><p>
One can regard multicellular systems as predecessors of neural systems. Ion channels and pumps are present in both systems. In nervous systems synaptic contacts replace the gap junctions. Nerve pulse patterns are replaced by waves associated with gap-junction connected multicellular systems.
</p><p>
Levin introduces notions like cognition, intelligence and self not usually used in the description of morphogenesis and represents a vision about medical applications of the new view
</p><p>
The TGD view of morphogenesis is compared with Levin's vision. The basic picture relies on the notions of magnetic and electric bodies, to the phases of ordinary matter with effective Planck constant h<sub>eff</sub>=nh<sub>0</sub> behaving like dark matter and making possible macroscopic quantum coherence, and to zero energy ontology (ZEO) providing a quantum measurement theory free of the basic paradox. ZEO is implied by almost deterministic holography forced by general coordinate invariance. Holography implies that structure is almost equivalent to function.
</p><p>
This framework explains the basic finding that the goal of the morphogenesis is determined by the patterns of electric fields during the early embryo period. TGD also suggests the universality of the genetic code and several variants of the genetic code- Mo´orphogenetic code might reduce to a variant of genetic code realized by cell membranes and larger structures instead of ordinary DNA. TGD predicts the analog of nerve pulse with the increment of membrane potential in mV range. These patterns would play a key role also in neural systems.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/Levin.pdf">TGD view of Michael Levin's work</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/Levin.pdf"></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>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-20366224446075957412023-01-04T23:47:00.005-08:002023-01-05T01:14:09.223-08:00Expanding Earth Hypothesis and Pre-Cambrian EarthSome questions led to a development of a more detailed TGD version of the Expanding Earth hypothesis explaining Cambrian Explosion (CE). A more detailed view of the pre-Cambrian biology, geology, and thermal evolution emerges and one can relate it to the standard view. This involves topics like faint Sun paradox, the mechanism of Great Oxygenation Event, understanding the TGD counterparts of supercontinents Rodinia and Pannotia preceding CE, snowball Earth, and CE that led to a sudden emergence of highly advanced multicellulars.
</p><p>
Also a more detailed view of what happened in the Cambrian explosion induced by the increase of the radius of Earth by factor 2 emerges (in the TGD Universe, a smooth continuous cosmological expansion is replaced with a sequence of short lasting and fast expansions). One ends up with a detailed model for the phase transition leading to the increase of the Earth radius.
</p><p>
This phase transition requires a considerable energy feed provided by the phase transition thickening monopole flux tubes of the magnetic body of Earth and liberating energy. The analogy with the recent Mars pre-Cambrian Earth had a solid core analogous to the inner core. In the phase transition to a liquid outer core with much larger volume. Part of the newly formed outer core could in turn have transformed to form a part of the mantle increasing its thickness.
</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 chapter <a HREF= "https://tgdtheory.fi/pdfpool/precns.pdf">Quantum gravitation and quantum biology in TGD Universe</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>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-47131213630010083232022-12-28T14:34:00.003-08:002022-12-28T14:34:28.763-08:00What topics are allowed for a decent finnish stargazer?
I wrote yesterday a comment to the blog article by Syksy Räsänen, which appeared at the page of Ursa, an organization of finnish stargazers. The blog article of Räsänen is in finnish (see <A HREF="https://www.ursa.fi/blogi/kosmokseen-kirjoitettua/tuulien-kaantymista/">this</A>). The comment was on the question whether standard model could be much more than people have though hitherto.
Here is my comment which was originally in finnish:
</p><p>
<I> "I made this question for 43 years ago. I asked whether standard model symmetries are much more profound that we have imagined. I also answered the question. The geometry of complex projective space CP<sub>2</sub> codes for the gauge symmetries, quantum numbers, and classical gauge fields if space-times are 4-D surfaces in 8-D embedding space M<sup>4</sup>× CP<sub>2</sub> at the fundamental level .
</p><p>
TGD generalized string model 7 years before its breakthgouh 1984. 2-D world sheet of string became 4-D space-time surface. Iy was possible to avoid the horrors of spontaneous compactivitation and brane world: as we know they eventually led to the collapse of superstring empire.
</p><p>
TGD also provided a solution to the energy problem of general relativity, which in turn closely relates to the failure of the quantization of general relativity. The lost Poincare incariance of general relativity is lifted to Poincare invariance at the level of H=M<sup>4</sup>× CP<sub>2</sub>. This gives back the basic conservation laws.
Colleagues still refuse to take TGD seriously. Could the time be ripe for using common sense. The funding agencies get nervous when no heurekas have been heard from the workshops of theoreticians for half century." </I>
</p><p>
I could have added also the following lines of text demonstrating that CP<sub>2</sub> is unique also for mathematical reasons.
<OL>
<LI> CP<sub>2</sub> follows by M<sup>8</sup>-M<sup>4</sup>× CP<sub>2</sub> duality from the number theoretic vision dual to geometric vision of physcs (geometrization of entire quantum theory). In number theoretical vision, complexified M<sup>8</sup> corresponds to complexified octonions. Associativity is the number theoretical counterpart of variational principle. Color SU(3) corresponds to SU(3) subgroup of octonionic automorphisms.
<LI> M<sup>4</sup> and CP<sub>2</sub> are the only 4-D manifolds that allow twistor space with Kaehler structure so that TGD is unique. Twistorialization of TGD means geometrization of also twistor fields as 6-D surfaces in the product of twistor spaces T(M<sup>4</sup>) and T(CP<sub>2</sub>) and relies on 6-D Kähler action having as preferred extremals 6-D surfaces having interpretation as the twistor space of space-time surface (S<sup>2</sup> bundle structure induced from T(M<sup>4</sup>)×T(CP<sub>2</sub>)).
</OL>
It was not surprising that Syksy Räsänen did not publish comment but expressed strong words of caution suggesting that I my critical comment was hate speech. Anyone can decide whether this is the case. It was also encouraged the decent participants should make only questions about starry sky, space, and star hobby. I admit that my comment did not satisfy the latter criterion.
</p><p>
Reader can wonder what might be the real reason for the censorship? Last 40 years after the publication of my thesis 1982 (maded possible by very positive referee statement by Wheeler), I have been on blacklist in Finland (no financial support, no research jobs). At this moment I can however relax: I was right.
</p><p>
The censorship has now badly failed and references to TGD appear on daily basis from several reaseach fields. The reason is that in the TGD framework quantum measurement theory extends to a theory of consciousness and cognition having quantum biology as an application. Most of finnish colleagues are however strangely silent and censorship continues.
</p><p>
TGD can be found <A HREF= "https://tgdtheory.fi/"> at my homepage</A> and most of the material have been published in the journals founded by Huping Hu.
</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-68634394226676942592022-12-19T21:27:00.011-08:002022-12-23T23:14:20.551-08:00Goedel's theorem and TGDThe following is a response to Lawrence Crowell in the discussion group "The Road to unifying Relativistic and Quantum Theories".
The topic of discussion related to Gödel's theorem and its possible connection with consciousness proposed by Penrose.
</p><p>
My own view is that quantum jump as state function reduction (SFR) cannot reduce to a deterministic calculation and can be seen as a moment of re-creation or discovery of a new truth not following from an existing axiomatic system summarizing the truths already discovered. My emphasis in the sequel is on how the number theoretic vision of the TGD proposed to provide a mathematical description of (also mathematical) cognition could allow us to interpret the unprovable Gödel sentence and its negation.
</p><p>
I decided to look more precisely at the Gödel number for polynomials with integer coefficients (no common factor coefficients) to which all rational polynomials can be scaled without changing the roots. Most of the classical physical content, if not all of it, can be coded by the coefficients [a<sub>0</sub>,...,a<sub>N</sub>] of the polynomial.
</p><p>
The Gödel numbering assigning to P an Gödel number G would be
</p><p>
G=p<sub>1</sub><sup>a<sub>0</sub></sup>p<sub>2</sub><sup>a<sub>1</sub></sup>...p<sub>N+1</sub><sup>a<sub>N</sub></sup>,
</p><p>
where p<sub>i</sub> is i:th prime and is an injection.
</p><p>
The discriminant D is the determinant of an (2N-1)×(2N-1) matrix defined by P and its derivative dP/dx ([a<sub>1</sub>,2a<sub>2</sub>,...,Na<sub>N</sub>]) and is an integer decomposing to a product of ramified primes of P.
</p><p>
The first guess for Gödel's undecidable statement would that there exist polynomial P for which one has G=D. The number D coding a sentence, whatever it is, would be its own Gödel number. Why this guess? At least this statement is short;-). Can this statement be undecidable?
<OL>
<LI> The equation involves both D as a polynomial of a<sub>i</sub> and G involving transcendental functions p<sub>i</sub><sup>a<sub>i</sub></sup> (essentially exponential functions) so that one goes outside the realm of rationals and algebraic numbers.
<LI> D=G is analog of Diophantine equation for a<sub>1</sub>,....,a<sub>N</sub> and both powers and exponential p<sub>i</sub><sup>a<sub>i</sub></sup> appear. If the coefficients a<sub>i</sub> are allowed to be a complex numbers, one can ask whether the complex solutions of G=D could form an N-1-D manifold. One can however assume this since p<sub>i</sub><sup>a<sub>i</sub></sup> leads outside the realm of algebraic numbers and one does not have a polynomial equation.
<LI> The existence of an integer solution to D=G would mean that the primes p<sub>i</sub> for which a<sub>i</sub> are non-vanishing, correspond to ramified primes of P with multiplicity a<sub>i</sub> so that the polynomials would be very special if solutions exist.
<LI> It might be possible to solve the equation for any finite field G<sub>p</sub>, that is in modulo p approximation. Here one can use Fermat's little theorem p<sub>i</sub><sup>p</sup>= p<sub>i</sub> mod p. If integer solutions exist, they exist for every G<sub>p</sub>.
</OL>
What about the physical interpretation?
<OL>
<LI> The polynomials P define space-time surfaces and one possible interpretation is that the ramified primes of P define external particles for a space-time region representing particle scattering. The polynomials P which reduce to single ramified prime would represent forward scattering of a single "elementary" particle.
<LI> In zero energy ontology, ordinary quantum states are replaced by superpositions of almost deterministic time evolutions so that also "elementary" particle would correspond to a scattering event. What exists would be events and TGD would predict not only scattering events but densities of particles as single particle scattering events inside a given causal diamond causal diamond representing quantization volume.
<LI> What kind of scattering events would these analogues of Godel sentences correspond? Representations of new mathematical axioms as scattering events, not provable from existing axioms?
</OL>
Exactly what we cannot prove to be true or not true for these special polynomials? What does the sentence labelled by G= D state?
<OL>
<LI> Integer D would express the sentence. D codes for the ramified primes. Their number is finite and we know them once we know P. Does the unprovable Gödel sentence say that there exists a polynomial P of some degree N, whose ramified primes are the primes p_k associated with a<sub>i</sub>? Or dös it say that there exists polynomial satisfying G=D in the set of polynomials of fixed degree N.
<LI> Is it that we cannot prove the existence of integer solution a<sub>i</sub> to P=G using a finite computation. Is this due to the appearance of the functions p<sub>i</sub><sup>a<sub>i</sub></sup> or allowance of arbitrarily large coefficients a<sub>i</sub>? The p-adic solutions associated with finite field solutions have an infinite number of coefficients and can be p-adic transcendentals rather than rationals having periodic pinary expansions.
<LI> Polynomials of degree N satisfying D=G are very special. The ramified primes are contained in a set of N+1 first primes p<sub>i</sub> so that D is rather small unless the coefficients a<sub>i</sub> are large. D is a determinant of 2N-1×2N-1 matrix so that its maximum value increases rapidly with N even when one poses the constraint a<sub>i</sub>< N. Rough estimates and explicit numerical calculations demonstrate that determinants involving very large primes are possible, in particular those involving single ramified prime identified as analogues of elementary particles, D can reduce to single large prime: D=P.
</p><p>
What about the polynomials P in the vicinity of points of the space of polynomials of degree N satisfying D=0: they correspond to N+1 ramified primes, which are minimal (note that the number of roots is N). D is a product of the root differences and 2 or more roots coincide for D=0. D is a smooth function of real arguments restricted to the integer coefficients. The value of D in the neighborhood of D=0 can be however rather large. Note that the proposed Gödel numbering fails for D=0, and therefore makes sense only for polynomials without multiple roots.
<LI> For D(P)=0 one has a problem with the equation G=D. G(P) is well-defined also now. The condition D(P)=0=G(P) does not however make sense. The first guess is that for 2 identical roots, P is replaced with dP/dx in the definition of D: D(P)-->D(dP/dx). D is nonvanishing and the ramified primes p<sub>i</sub> do exist for dP/dx. Therefore the condition D(dP/dx)=G(P) makes sense. For n identical roots one must use have D(d<sup>n-1</sup>P/dx<sup>n-1</sup>)=G(P).
<LI> Interestingly, in TGD the hypothesis that the coefficients of polynomials of degree N are smaller than N, is physically very natural (see <A HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>) and would make the number of polynomials to be considered finite so that in this case one can check the existence of a G=D sentence in a finite time. It seems rather plausible that for given N, no G=D sentence, which satisfies the conditions a<sub>i</sub>< N, does exist.
</p><p>
One can of course criticize the hypothesis a<sub>i</sub>< N implying a strong correlation between the degree N of P and the maximal size of ramified primes of P identified as p-adic primes characterizing elementary particles. One can argue that in absence of this correlation predictivity is lost. This hypothesis also makes also finite fields basic building bricks of number theoretic vision of TGD (see <A HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>).
<LI> Could this give rise to a realization of undecidability at the level of conscious experience and cognition relying on number theoretic notions. How?
</p><p>
Quantum states are superpositions of space-time surfaces determined by polynomials P and if the holography of consciousness is true, conscious experience reflects the number theoretic properties of these polynomials if associated to a localization to a given polynomial P in a "small" state function reduction (SSFR). This would be position measurement in the "world of classical worlds" (WCW)? The proof of the statement D=G would mean that a cognizing system becomes conscious of the D=G space-time surface by a localization to it.
</p><p>
Suppose that for a given finite N and condition a<sub>i</sub>< N, G=D sentences do not exist. Hence one can say that G=D sentences go outside the axiomatic system realized in terms of the polynomials considered. Even the space of all allowed polynomials identified as a union of spaces with varying value for degree N would not allow this. G=D sentences would be undecidable by the condition a<sub>i</sub>< N.
</p><p>
One can of course criticize the hypothesis a<sub>i</sub>< N implying a strong correlation between the degree N of P and the maximal size of ramified primes of P identified as p-adic primes characterizing elementary particles. One can argue that in absence of this correlation predictivity is lost. This hypothesis also makes also finite fields basic building bricks of number theoretic vision of TGD (see <A HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">this</A>).
</OL>
See the articles <A HREF="https://tgdtheory.fi/public_html/articles/GoedelTGD.pdf">Gödel's Undecidability Theorem and TGD</A> and <A HREF="https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">Finite Fields and TGD</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-80115671214180406772022-12-16T01:35:00.005-08:002022-12-16T19:28:50.831-08:00How do AdS/CFT- and TGD based holographic dualities relate?The article "Traversable wormhole dynamics on a quantum processor"
by Jafferis et al published in Nature received a lot of media attention. My original reaction was due to frustration caused by the media hype. What was done was a quantum computer simulation of the so-called SYK (Sachdev-Ye-Kitaev) model proposing AdS/CFT duality for a particular condensed matter system.
</p><p>
The attempts to understand what is involved soon led to a realization that since TGD predicts the analog of AdS/CFT holographic duality, the quantum computational aspects of the experiment should be understandable also using the holographic duality of TGD. This raises the question whether can one translate the notions of AdS holography to TGD holography. In particular, what could be the TGD counterparts for the notions of wormhole and negative energy shock waves needed to stabilize the wormhole. This article deals with these kinds of questions and leads to a rather detailed view of TGD based holography.
</p><p>
See the article
<a HREF= "https://tgdtheory.fi/public_html/articles/AdSTGD.pdf">How do AdS/CFT- and TGD based holographic dualities relate?</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/AdSTGD.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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-28947484818094802622022-12-15T00:11:00.013-08:002022-12-16T01:36:47.568-08:00Comparison of AdS/CFT duality with the TGD based holographic duality
This posting is a continuation to an earlier posting <I> Are wormholes really created in quantum computer?</I> (see <A HREF="https://matpitka.blogspot.com/2022/12/are-wormholes-really-created-in-quantum.html">this</A>).
</p><p>
In the experiment considered, the so-called SYK model (Sachev-Ye-Kitaev) was simulated using a quantum computer. The model is constructed to realize AdS<sub>2</sub>/CFT correspondence and the quantum computer simulates the 1-D quantum system dual to wormhole in 2-D AdS<sub>2</sub>.
</p><p>
The problem is that the AdS<sub>2</sub> is completely fictitious so that the physics at this side cannot be tested. However, TGD also predicts holographic duality between 3-D surfaces as boundaries of space-time surfaces and identifiable as outer boundaries of physical objects and the interior of the space-time takes the role of AdS. In particular, the system considered in the experiment should allow TGD based dual description.
</p><p>
The thesis <I> Holographic quantum matter : toy models and physical platforms</I> (see <A HREF ="https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/24/items/1.0400095">this</A>) of Etienne Lantagne-Hurtubise gives a nice description of the SYK model and the following comments are based on the introduction of the thesis.
</p><p>
TGD should give a classical description of quantum dynamics coded by 3-D data holographically in terms of classical physics in the interior of space-time surface. Therefore the challenge is to also describe the reported findings.
</p><p>
<B> How do AdS/CFT holography and TGD holography relate to each other?</B>
</p><p>
There are obvious questions to be answered. How closely AdS/CFT and TGD holography could relate and how do they differ? Could there exist some kind of AdS/CFT-TGD dictionary?
<OL>
<LI> AdS/CFT correspondence predicts 4→ 5 holography for AdS<sub>5</sub> interpreted as an emergent 5-D space-time. M<sup>4</sup> would carry gauge fields and theory would be conformally invariant. The gravitational holography is 3→ 4. Skeptics could argue that there is total mess: for instance, what happens to the general relativistic description of gauge fields using 4-D space time? Should one have 3→ 4 gravitational holography followed by 4→ 5 for gauge fields?
<LI> TGD predicts 3→4 holography. Instead of AdS one has space-time but is realized as a 4-D surface. Light-like 3-surfaces with extended conformal symmetries due to their metric 2-dimensionality defined boundaries of 4-D space-time surfaces and contain holographic data defining the space-time surface and also the data defining the fermionic part of quantum state.
</p><p>
4-D general coordinate invariance implies almost exact holography and classical deterministic dynamics becomes an exact part of quantum TGD: one has what one might call Bohr orbitology. This picture has a number theoretic counterpart at the level of M<sup>8</sup>: associativity assigns 4-D surface of M<sup>8</sup><sub>c</sub> to the roots of rational polynomials represented as 3-D mass shells in M<sup>4</sup><sub>c</sub> ⊂ M<sup>8</sup><sub>c</sub>.
</OL>
</p><p>
<B> Do the time loops of AdS has time-like loops have a TGD counterpart?</B>
</p><p>
AdS time loops have indeed TGD countepart. The reason is that 4-D space-times are completely exceptional.
<OL>
<LI> 4-D, and only 4-D, space-times allow exotic smooth structures (see <A HREF="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A>)! A continuum of exotic smooth structures are possible. Exotic smooth structure can be always regarded as ordinary smooth structure apart from a discrete set of points.
</p><p>
Exotics break cosmic censorship so that global hyperbolicity fails and the initial-value problem becomes ill-defined because of time-like loops. Time-like loops are a heavy counter argument against AdS/CFT duality. They are however encountered also for the TGD variant of the holographic duality.
</p><p>
Could it be that time-like loops are not a nuisance but something fundamental forcing the space-time dimension to be D=4.
<LI> In the TGD framework holography predicts the smooth structure of the space-time surface so that the non-uniqueness is not a problem.
</p><p>
The discrete set of points spoiling the standard smooth structure is an analogue for a set of point-like defects. Outsides this set the standard smooth structure fails. The proposal (see <A HREF="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A>) is that this set of points is assignable to particle reaction vertices in TGD and have a topological interpretation. Two partonic 2-surfaces with opposite homology charges (monopole fluxes) touch at defect point and fuse together to a single particle 2-surface.
<LI> This makes possible time loops which are essential for understanding pair creation in TGD. It is essential that the interiors of the orbits of wormhole contacts have an Euclidian signature: this is obviously a completely new element when compared to AdS/CFT. The boundaries between these Euclidian regions and Minkowskian regions of the space-time surface are light-like and correspond to the orbits of wormhole throats at opposite Minkowskian sheets (see <A HREF="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A>).
The creation of a fermion pair would correspond to a change of the time direction of the fermion at the defect point of the exotic smooth structure.
<LI> Could exotic smooth structures make possible quantum computations as evolution forth-and-back in space-time in the TGD framework? Could the time loops serve as microscopic classical correlates for this and could the defects give a topological realization for what happens. Note that wormhole throats can in principle have large sizes and scale like h<sub>eff</sub> and can be very large for gravitational Planck constant h<sub>gr</sub>.
<LI> Could wormholes correspond in the TGD framework to magnetic flux tubes? Or could they correspond to light-like orbits of wormhole throats/partonic 2-surfaces appearing analogous to lines of topological counterparts of Feynman diagrams? Orbits of wormhole contacts identified as orbits of pairs of wormholes give rise to light-like orbits of wormhole throats, which are always paired. Fermionic quantum numbers are associated with the light-like lines of the wormhole throat. They represent building bricks of elementary particle orbits. Could these structures be seen as analogues of wormholes?
</OL>
</p><p>
<B> What is the TGD counterpart of time reversal of the SYK model?</B>
</p><p>
Time reversal is central in the SYK model.
<OL>
<LI> Time reversed of time evolution as unitary time evolution with Hamiltonian having opposite sign is central in the model. This notion is somewhat questionable since usually one requires that the energy eigenvalues are positive. In TGD, this time evolution could correspond to a sequence of SSFRs in the reversed time direction following BSFR.
<LI> Shock wave in the wormhole appears as a negative energy signal. This could correspond to time reversed classical signals having effectively negative energy and propagating along the flux tube or the counterpart of the wormhole in TGD. Time reversal would be induced by BSFR.
<LI> One could also interpret reversed time evolution as a generation of Hawking radiation. Negative energy particles falling to the blackhole would correspond to the time reversed signal propagating from right to left after BSFR has occurred in the experiment considered.
</OL>
</p><p>
<B> TGD counterparts of scrambling time evolution and descrambling as its time reversal</B>
</p><p>
Scrambling means generation of quantum chaos. Descrambling does the opposite and is in conflict with the second law unless the arrow of time changes. For a unitary time evolution descrambling can be considered if the negative of Hamiltonian makes sense.
</p><p>
Scrambling corresponds to a random unitary time evolution inducing mixing as dispersion of entanglement in the entire system. Actually a sequence of scramblings characterized by scrambling times described by random Hamiltonians is assumed to take place. Scrambling time is assumed to depend on blackhole entropy S= A/4Gℏ= 4π GM<sup>2</sup>/ℏ roughly as
</p><p>
T<sub>s</sub>= r<sub>s</sub> ×O(S<sup>1/2</sup> log(S)) ,
</p><p>
where r<sub>s</sub> = 2GM is Schwarzschild time. Blackholes are assumed to be very fast scramblers.
<OL>
<LI> A sequence of "small" state function reductions (SSFRs) as the TGD counterparts of "weak" measurements of quantum optics, generalizes Zeno effect to a subjective time evolution of self. The sequence of SSFRs as analog of a sequence of unitary time evolutions
</p><p>
Scrambling could correspond to a sequence of SSFRs as an analogue for a sequence of random unitary evolutions in TGD. Since one has a sequence of SSFRs, scrambling might correspond to the emergence of thermodynamics chaos.
</p><p>
An alternative interpretation of chaos is an increase of complexity. Mandelbrot fractal is complex but not chaotic in the thermodynamic sense. Could scrambling correspond to an effective increase of the extension of rationals during the sequence of SSFRs? More and more roots of polynomials defining light-cone propertime a=constant hyperboloids become visible at the increasing space-time surface inside the CD. This option does not look plausible.
<LI> De-scrambling time evolution is in conflict with intuition. In TGD, de-scrambling could correspond to scrambling with an opposite arrow of time emerging in "big" SFR (BSFR) and therefore dissipation with a reverse arrow of time looking like self-organization for an observer with an opposite arrow of time. This process is fundamental in biology and would correspond to processes like healing. BSFR corresponds to a "death" or falling asleep in TGD inspired theory of consciousness and self lives forth and back in geometric time.
<LI> It is interesting to look for the TGD counterpart of scrambling time T<sub>s</sub>. For hbar →, where ℏ<sub>gr</sub> = GM<sup>2</sup>/β<sub>0</sub> is the gravitational Planck constant and β<sub>0</sub>≤1 is a velocity parameter, one obtains
</p><p>
T<sub>s</sub>= r<sub>s</sub> ×4π β<sub>0</sub>log(β<sub>0</sub>) .
</p><p>
Scrambling time would be negative for β<sub>0</sub>< 1: could the interpretation be that scrambling takes place with opposite arrow of time? Blackhole entropy is equal to β<sub>0</sub> and smaller than 1 and practically zero. One must of course take this expression for the scrambling time with a big grain of salt and as found in the previous posting, TGD allows us to consider a more general picture in which the correspondence with blackholes is not so concrete.
</OL>
See the earlier posting <A HREF="https://matpitka.blogspot.com/2022/12/are-wormholes-really-created-in-quantum.html">Are wormholes really created in quantum computer?</A>
and the article
<a HREF= "https://tgdtheory.fi/public_html/articles/AdSTGD.pdf">How do AdS/CFT- and TGD based holographic dualities relate?</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-68997740929367055572022-12-13T20:04:00.003-08:002022-12-13T20:08:23.414-08:00Ignition of nuclear fuel achieved in hot fusion: what does this mean?
The claimed breakthrough in hot fusion (see <A HREF="https://phys.org/news/2022-12-scientists-fusion-energy-breakthrough.html">this</A>) is the latest hype in our hype-filled world. Ignition, which initiates energy production, must be achieved but this is only a small step in the ladder leading to a real fusion.
</p><p>
One of the problems of which I learned only some time ago is the following: the energy feed does not appear to raise the temperature as expected but goes somewhere. The underlying physics is poorly understood. The TGD inspired solution could be in terms of Hagedorn temperature predicted for flux tube like objects, analogs of strings, predicted by TGD. New degrees open and the temperature does not increase and reactions do not start to produce energy. This problem should be solved (see <A HREF="https://matpitka.blogspot.com/2022/07/tgd-solution-of-12-year-old-puzzle.html">this</A>) .
</p><p>
The hypish news tells that ignition has been achieved. This is certainly a big achievement. There is an energy feed by hundreds of lasers on an energy pellet and this system indeed ignites and starts to produce more energy than the input energy from lasers. However, the entire system however needs energy input, which is exponentially higher than the energy required by lasers so that there is a long way to go for nuclear fusion.
</p><p>
This one little step in progress, which one can hope to lead to real hot fusion. But is it so?
</p><p>
In the TGD Universe, "cold fusion" using dark nuclei (in the TGD sense) would be an alternative solution to the problem. The huge energy feed needed in heating the system to the required temperature would be overcome. As a matter of fact, cold fusion could actually heat the system to the temperature required by hot fusion. Also stellar nuclei as fusion reactors could have emerged in this way. But this is not the time for new theoretical physics so it will take decades before cold fusion can be taken seriously.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/proposal.pdf">Could TGD provide new solutions to the energy problem?</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-56919872415017360742022-12-12T20:54:00.003-08:002022-12-12T23:25:48.695-08:00The findings of the James Webb telescope from the TGD point of viewThe findings of the James Webb telescope have revolutionized the views about galaxy formation in the early Universe. I have commented these findings briefly in "Some anomalies of astrophysics and cosmology" (see <A HREF="https://tgdtheory.fi/public_html/articles/acano.pdf">this</A>) but have not found time for further comments.
</p><p>
Scientific American has an article with title "JWST's First Glimpses of Early Galaxies Could Break Cosmology"
(see <A HREF = "https://www.scientificamerican.com/article/jwsts-first-glimpses-of-early-galaxies-could-break-cosmology/">this</A>), which provide a nice summary of the first findings of the telescope. This gave an opportunity to sharpen the somewhat fuzzy view of how the findings of James Webb telescope relate to TGD.
</p><p>
What was found first, was a galaxy dubbed as "GLASS-z13". It was found by Rohan Naidu and led to an article published within a few days. The discovery of the GLASS-z13 was followed by a discovery by numerous even more distant galaxies. The very existence and the properties of these galaxies came as a total surprise.
<OL>
<LI> From the redshift of about z=13, the GLASS-z13 was dated back 300 million years after the big bang that is thought to have occured 13.8 billion years ago. According to the standard view of galaxy formation (so called Lambda CDM model involving dark matter as exotic particles), galaxies with such a large distance are not expected to even exist. According to the standard model, the formation of galaxies should have begun at the cosmic age of about 400 million years. The galaxy found by Naidu would have emerged more than 70 millions years too early.
<LI> The images of the galaxies from so early era were expected to be extremely dim. The galaxies discovered were however anomalously bright.
<LI> The large size of the galaxies came as a total surprise. The age of the galaxies increases with its age and the conclusion was that the galaxies had to be much more mature than the standard model for the formation of galaxies allows. This leads to a paradox since the first galaxies should be very young.
</OL>
During the years, I have developed a TGD based model of galaxy formation. The model is supported by the ability to explain the increasing number of anomalies of the standard model (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/acano.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/galanomalies.pdf">this</A>).
</p><p>
Monopole flux tubes are the basic element of the TGD view of galaxy formation. They are present in all length scales in the TGD Universe and distinguish TGD from both Maxwell's electrodynamics and general relativity.
<OL>
<LI> Flux tubes can carry monopole flux, in which case they are highly stable. The cross section is not a disk but a closed 2-surface so that no current is needed to create the magnetic flux. The flux tubes with vanishing flux are not stable against splitting.
<LI> Flux tubes relate to the model for the emergence of galaxies (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>) and explain galactic jets propagating along flux tubes (see <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>). Dark energy and possible matter assignable to the cosmic strings predicts correctly the flat velocity spectrum of stars around galaxies.
<LI> In the MOND model it is assumed that the gravitational force transforms for certain critical acceleration from 1/r<sup>2</sup> to 1/r force. In TGD this would mean that the 1/ρ force caused by the cosmic string would begin to dominate over the 1/ρ<sup>2</sup> force (ρ denotes transversal distance from string). The predictions of MOND TGD are different since in TGD the motion takes place in the plane orthogonal to the cosmic string.
<LI> The flux tubes can appear as torus-like circular loops. Also flux tube pairs carrying opposite fluxes, resembling a DNA double strand, are possible and might be favoured by stability. Flux tubes are possible in all scales and connect astrophysical structures to a fractal quantum network. The flux tubes could connect to each other nodes, which are deformations of membrane-like entities having 3-D M^4 projections and 2-D E<sup>3</sup> projections (time= constant) (also an example of "non-Einsteinian" space-time surface).
<LI> Pairs of monopole flux tubes with opposite direction of fluxes can connect two objects: this could serve as a prerequisite of entanglement. The splitting of a flux tube pair to a pair of U-shaped flux tubes by a reconnection in a state function reduction destroying the entanglement. Reconnection would play an essential role in bio-catalysis.
<LI> Flux tube pairs can form helical structures and stability probably requires helical structure. Cosmic analog of DNA could be in question: fractality and gravitational quantum coherence in arbitrarily long scales are a basic prediction of TGD so that monopole flux tubes should appear in all scales. Also flux tubes inside flux tubes inside and hierarchical coilings as for DNA are possible.
</OL>
Could one understand the paradoxical findings in the TGD view of galaxy formation?
<OL>
<LI> According to the standard model, these galaxies were formed quite too early. The standard mechanism of formation is a gravitational condensation of stars and interstellar to form galaxies. Dark matter halo plays a key role in the process. The model is however plagued by several contradictions. As a matter of fact, empirical facts suggest that there is no dark halo. The MOND model explains many of the anomalies but is in conflict with the Equivalence Principle and in conflict with standard Newtonian gravitation. The TGD based model replaces dark matter halo with long cosmic strings carrying dark energy and possibly also dark matter. One does not lose either Equivalence Principle or Newtonian gravitation.
</p><p>
The TGD based view of galaxy formation is diametrically opposite to the standard view, being analogous to the generation of ordinary matter via the decay of the inflation field in the inflationary cosmology. Ordinary matter would have been created by the decay of the energy of cosmic strings to ordinary matter as they formed tangles. This led to a thickening of cosmic strings to monopole flux tubes and to a reduction of string tension so that energy was liberated as ordinary matter. In particular, galactic dark matter and the flat velocity spectrum of distant stars find an elegant explanation.
</p><p>
In this view galaxies started to emerge already during the TGD analogue of the inflationary period.
<LI> The high apparent luminosity of these galaxies is the second mystery. Are the galaxies indeed so luminous as they seem to be? Or could it be that the standard view of how light emitted by galaxies is distributed is somehow wrong?
</p><p>
In the TGD framework, the space-time of general relativity is replaced with a fractal network of nodes defined by various structures including galaxies, stars, planets,... Monopole magnetic flux tubes connect the nodes and the light propages as beams of dark photons (in the TGD sense) along these flux tubes. A light beam travelling along a flux tube is not attenuated at all if the cross section of the flux tube stays constant. Therefore the intensity of the light beam is not reduced with distance. In GRT it would be reduced since there would be no splitting to beams. This would explain why the apparent luminosities of the galaxies are anomalously high.
<LI> The unexpectedly large size of the galaxies implies a long age if one believes in the standard view of galactic evolution. This paradox finds a solution in zero energy ontology (ZEO), which defines the ontology of quantum TGD. ZEO solves the basic paradox of quantum measurement theory and is forced by the holography implied in the TGD framework by 4-D general coordinate invariance.
</p><p>
In ZEO, the arrow of time changes in ordinary quantum jumps ("big" state function reductions, BSFRs). The repeated change of the arrow of time in the sequence of BSFRs implies that the system can be said to live forth and back in geometric time. Aging does not correspond to "center of mass motion" in time direction but this forth and back motion. In the TGD inspired biology, BSFR is analogous to death or falling asleep.
</p><p>
In "small" SFRs (SSFRs) the arrow of time is not changed and they are counterparts of weak measurements introduced by quantum opticians. They generalize the quantum measurements associated with the Zeno effect, in which a system is frozen and its state does not change. Now the sequence of SSFRs would define a conscious entity, self.
</p><p>
In TGD, gravitational quantum coherence is possible in all scales and galaxies would be astrophysical quantum systems performing BSFRs. Even astrophysical objects such as galaxies would live forth and back in time. This would give rise to galaxies and stars older than the Universe if one tries to explain their age using the standard view of the relationship between experienced time and geometric time.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/acano.pdf">Some anomalies of astrophysics and cosmology</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/galjets.pdf">TGD View of the Engine Powering Jets from Active Galactic Nuclei</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com3tag:blogger.com,1999:blog-10614348.post-5838527297997043252022-12-11T01:59:00.018-08:002022-12-16T01:37:19.486-08:00Are wormholes really created in quantum computer?The most recent really heavy hype is by "Quantum gravity in Lab" movement and involves publicity stunt related to the article "Traversable wormhole dynamics on a quantum processor"
(see <A HREF ="https://www.nature.com/articles/s41586-022-05424-3">this</A>)
by Jafferis et al published in Nature.
</p><p>
Already the title of the article has a very high hype content. The tweet of the journal Quanta (a popular journal usually satisfying very high standards) published the following tweet:
</p><p>
<I> Physicists have built a wormhole and successfully sent information from one end to the other</I>. The stormy reception of the article and of the tweet forced Quanta to change the tweet to <I> Experimental physicists built the mathematical analog of a wormhole inside a quantum computer by simulating a system of entangled particles</I>.
</p><p>
The Quanta article contains for instance the statement
<I> The team developed quantum software that could reproduce wormhole inspired teleportation on both quantum computers</I>. This was later corrected to
<I> Experimental physicists built the mathematical analog of a wormhole inside a quantum computer by simulating a system of entangled particles</I>.
This statement is still far from an honest statement telling only what was actually done: <I> Physicists have simulated a model of wormhole in a system argued but not proven to obey AdS/CFT duality by using a quantum computer. This simulation had been done already earlier using an ordinary computer</I>.
</p><p>
Peter Woit commented in Not Even Wrong this hyper-superhype rather critically in two postings (see <A HREF = "https://www.math.columbia.edu/~woit/wordpress/?p=13229">this</A> and <A HREF="https://www.math.columbia.edu/~woit/wordpress/?p=13229">this</A>).
</p><p>
Also Scott Aaronson, who is one of quantum computation gurus, expressed his very critical views shared by most quantum computation professionals (see <A HREF="https://scottaaronson.blog/?p=6871">this</A> and <A HREF="https://www.math.columbia.edu/~woit/wordpress/?p=13229">this</A>).
Here is the core part of Scott Aarronson's commentary.
</p><p>
<I> Tonight, David Nirenberg, Director of the IAS and a medieval historian, gave an after-dinner speech to our workshop, centered around how auspicious it was that the workshop was being held a mere week after the momentous announcement that a wormhole had been created on a microchip (!!) in a feat that experts were calling the first-ever laboratory investigation of quantum gravity, and a new frontier for experimental physics itself. Nirenberg speculated that, a century from today, people might look back on the wormhole achievement as today we look back on Eddington s 1919 eclipse observations providing the evidence for general relativity.
</p><p>
I confess: this was the first time I felt visceral anger, rather than mere bemusement, over this wormhole affair. Before, I had implicitly assumed: no one was actually hoodwinked by this. No one really, literally believed that this little 9-qubit simulation opened up a wormhole, or helped prove the holographic nature of the real universe, or anything like that. I was wrong.
</I>
</p><p>
There is also a very nice popular article "The truth about wormholes and quantum computers" representing a harsh criticism (see <A HREF="https://bigthink.com/starts-with-a-bang/wormholes-quantum-computers/">this</A>).
</p><p>
The combination of all kinds of fashionable pop science related to quantum computation, quantum gravitation, wormholes, EPR= EP, AdS/CFT, etc.... yields this kind of pseudo-science. It has been extremely frustrating to witness the stagnation of theoretical physics to pop science during these more than four decades.
</p><p>
Critics however agree that when one drops all this irrelevant hype away, the work of quantum computer pioneers satisfies the highest standards. It is regrettable that excellent experimentation and engineering is not enough for funding but must be iced with a sugar layer of bad theoretical physics.
</p><p>
Although this kind of hyperhypes do not deserve the attention they receive, I decided to look what I could learn and how could I relate this picture to TGD where holography forced by 4-D general coordinate invariance is also central and defines quantum classical correspondence. Classical physics is an exact part of quantum theory and is realized as Bohr orbitology equivalent to holography. Could I perhaps analyze the experiment in the TGD framework or suggest something analogous and maybe learn something new from TGD?
</p><p>
<B> A. Traversable wormhole dynamics on a quantum processor</B>
</p><p>
In the following I summarize my understanding of the various notions involved with the experiment. These include AdS/CFT duality, traversable wormholes, and negative energy shock waves mentioned in the abstract.
</p><p>
<B> A.1 Abstract of "Traversable wormhole dynamics on a quantum processor"</B>
</p><p>
Here is the abstract of the article
"Traversable wormhole dynamics on a quantum processor" Daniel Jafferis et al.
(see <A HREF="https://www.nature.com/articles/s41586-022-05424-3">this</A>).
</p><p>
<I> The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary.
</p><p>
The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev Ye Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography.
</p><p>
We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model.
</p><p>
A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits.
</p><p>
Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics.
</p><p>
Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.
</I>
</p><p>
There is a long list of questions to be answered.
<OL>
<LI> What does the term AdS<sub>2</sub> holography mean? How does it relate to ordinary, "real" quantum gravitation?
<LI> What does "traversable wormhole" mean?
<LI> What does the negative energy shockwave, argued to open the wormhole for quantum teleportation, mean in general relativity? What interaction between quantum computers, modelled as blackholes, does the negative energy shock wave correspond at the level of the quantum computer system?
</OL>
<B> A.2 What does AdS/CFT duality mean?</B>
</p><p>
My non-specialist's view of AdS/CFT is the following.
<OL>
<LI> AdS/CFT is not part of string theory.
<LI> It is not a proposal to describe gravitation but gauge interactions in terms of effective gravitation assigned to effective AdS<sub>n</sub>x S<sup>10-n</sup>. AdS<sub>5</sub> would have 4-D Minkowski space as boundary and standard model would be dua to a theory of effective gravitation in AdS<sub>5</sub>.
<LI> The fact that has been forgotten is that the list of physics successes of AdS/CFT duality is very short, actually non-existing. Even if AdS/CFT is regarded as mathematically well-defined, this does not save it from the ultimate fate of wrong theories.
<LI> The basic statement is a field theory with conformal symmetries at the boundary of AdS (say 4-D Minkowski space) is dual to a theory of gravitation in the interior of Ads.
<LI> In the beginning AdS/CFT with n=5 so that the boundary is 4-D Minkowski space, was tried to apply QCD, to nuclear physics and many other cases. The idea was to deduce predictions from the physics of the AdS side. The attempts failed.
</OL>
Why did AdS/CFT fail?
<OL>
<LI> The probable reason is that the basic mathematical framework, although probably correct using physics standards, does not correspond to the physical situation.
</p><p>
For instance, AdS is a pathological space-time geometry having time-like loops violating cosmic censorship and spoiling the initial value problem. In fact, the SYK model simulated in the experiments, postulates an interaction between blackholes which prevents the occurrence of these time-like loops and this interaction would make possible quantum teleportation!
<LI> The real reasons for the failure are at a much deeper level. Quantum field theory (QFT) itself is to be blamed. QFT relies on the notion of a point-like particle and fails (of course divergence problems and the non-existence of path integral have tried to tell this to us for more than half a century).
<LI> The idea that 4-D conformally symmetric field theory is something fundamental rather than mere approximate QFT limit is probably wrong. Also the Einsteinian view of gravitation has a fundamental problem: one loses basic conservation laws of special relativity. Both sides of the duality are sick.
</OL>
<B>A.3 What are traversable wormholes in GRT</B>
</p><p>
One can learn of traversable wormholes from the thesis of Alex Simpson
(see <A HREF="https://arxiv.org/pdf/2104.14055.pdf">this</A>). The thesis describes a family of solutions of Einstein' equations characterized by one parameter a. The solutions have time translations and rotations as symmetries and in contrast to naive expectations the radial coordinate varies from -∞ to +∞ rather than from 0 to ∞.
</p><p>
The general solution of the family is given by
</p><p>
ds<sup>2</sup>= (1-2GM/X)dt<sup>2</sup>- dr<sup>2</sup>/(1-2GM/X)+ (r<sup>2</sup> +a<sup>2</sup>)(dθ<sup>2</sup>) +sin<sup>2</sup>(θ)dθ<sup>2</sup>)
</p><p>
X=(1-2GM/(r<sup>2</sup> +a<sup>2</sup>)<sup>1/2</sup>)
</p><p>
The coordinates r and t vary in the range (-∞,+∞). r<sub>S</sub>= 2GM is Schwartschild radius.
</p><p>
Some comments are in order.
<OL>
<LI> a=0 gives Schwarzschild solution and in this case r=0 corresponds to a single point as the singularity of spherical coordinates. For <sup>2</sup>>0 r=0 corresponds to a sphere with radius a. In the TGD framework this would be obtained if there is a magnetic monopole flux through the monopole throat.
<LI> The study of radial geodesics provides information about the object. One has for the radial velocity dr/st= +/- (1-X). For a>r<sub>s</sub> this is always nonvanishing. Therefore the radiation from r< 0 blackhole can propagate to r> 0 blackhole.
</p><p>
For Schwartschild solution with a=0, dr/dt it vanishes at Schwartschild radius so that light cannot classically escape from blackhole interior.
</p><p>
For a< r<sub>s</sub>, dr/dt vanishes for two radii r<sub>+/-</sub>= +/- (r<sub>S</sub><sup>2</sup> -a<sup>2</sup>)<sup>1/2</sup> so that these acts as horizons and the two blacholes are isolated.
</OL>
It is known that the traversable wormholes are not stable without a condition requiring a negative vacuum energy density. I must admit that in the case of AdS/CFT duality I do not really know what wormholes mean. One should deform the AdS metric just like one deforms the Minkowski metric to obtain the analogues of blackhole and wormhole.
</p><p>
<B> A.4. What negative energy shock waves are and why they are needed?</B>
</p><p>
The basic problem against the idea of quantum gravitational view of teleportation is that wormholes are unstable against splitting. Neither space ships nor information can travel from blackhole to another one. Wormholes are not traversable: geodesics cannot connect the blackholes but stop at the horizon.
</p><p>
The introduction of the article
"Traversable wormholes via a double trace deformation" by Gao et al (see <A HREF="https://arxiv.org/pdf/1608.05687.pdf">this</A>) describes how traversable wormholes might be generated.
</p><p>
The conditions making wormholes traversable would look like follows.
<OL>
<LI> Negative energy shock waves are needed to open the wormhole throat so that classical signals can propagate between the blackholes and make quantum teleportation possible. One says that the wormhole becomes traversable. What do these negative energy shock waves mean in GRT context?
<LI> Quantum gravitational deformation of metric such would make the average energy density negative. The first problem is that QFTs do not allow this. Second problem is that after the sad fate of superstring theory, no generally accepted theory of quantum gravitation exists. The third problem, not usually noticed, is that the notions of energy and other Poincare charges are lost in GRT.
<LI> One can however forget these little nuisances and assume that negative energy densities are possible. Negative energy condition means technically that there exists an infinitely long null geodesic going through the blackhole-like entity such that the integral of the trace of energy momentum tensor is negative along the geodesic. This means that negative energy signals can propagate through the entire geodesic and make possible classical communications necessary for teleportation.
</p><p>
The averaged null energy condition (ANEC), presumably stating the vanishing or even non-negativity of the trace, is said to fail if this is the case. It is also mentioned that physically the failure of the condition implies that light-rays focused at the other end of the wormhole, defocus at the other end. I didn't quite understand how this follows from the condition.
<LI> The existence of this kind of defocusing of geodesics is excluded by several conditions. As already noticed, the averaged null energy condition (ANEC) denies their existence. Neither does the generalized second law, stating that the area of blackhole horizon increases, allow them. It would seem that the hopes for traversable wormholes are rather meager.
<LI> Here comes however AdS<sub>2</sub> to rescue. Before continuing, note that AdS<sub>2</sub> duality is not for gravitation but for the gravitational dual of a conformally invariant QFT, such as gauge theories. Therefore we can allow things which we would condemn as nonsense in real quantum gravitation.
</p><p>
The problem is that AdS has 1 time-like dimension but has closed time-like directions. AdS is imbedded in 3-D space with line element ds<sup>2</sup>= dt<sub>1</sub><sup>2</sup> + dt<sub>1</sub><sup>2</sup> -dz<sup>2</sup> containing 2 time-like directions and a 2-sphere with time-like metric containing circular time loops.
</p><p>
These time-like loops imply at the level of AdS a violation of cosmic censorship and global hyperbolicity. As a consequence, the standard initial value problem with 3-D initial data is ill-defined since the signals from the surface of initial data return back. This also implies that the blackhole horizon extending through the wormhole intersects itself. The radial direction for AdS between the blackholes is time-like and effectively a compact circle. One has a causal anomaly. This is bad.
<LI> One must save the causality. The postulated interaction between the boundaries of the wormhole comes to rescue at this time and solve the problem that we have created. This interaction would save causality and would also imply failure of ANEC, and therefore make the wormhole traversable. Negative energy is interpreted in terms of effective Casimir effect.
</p><p>
Of course, it would be much easier to not postulate at all the AdS duality and be satisfied with the fact that we have been able to simulate certain quantum model using quantum computers.
</OL>
It must be added that the cosmic censorship hypothesis is in conflict with the existence of exotic smooth structures even in flat R<sup>4</sup> since they imply the existence of closed time-like geodesics. Dimension D=4 is indeed completely exceptional in this sense and this should be important as an important message by theoreticians. I have discussed the possible existence and interpretation of smooth exotics in the TGD framework
where holography also fixes the smooth structure (see <A HREF="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A>).
</p><p>
<B> B. The TGD view</B>
</p><p>
In the following I describe a possible TGD based interpretation of the experiment.
</p><p>
<B> B.1 The TGD counterpart of AdS/CFT duality</B>
</p><p>
TGD is a proposal, which solves the energy problem of general relativity and generalizes string models by replacing strings with 3-D surfaces. In the TGD framework, 4-D general coordinate invariance leads to a holography and analog of AdS/duality having interpretation as quantum classical correspondence.
<OL>
<LI> In the TGD framework, light-like 3-surfaces appear as fundamental objects and are metrically effectively 2-D. These 3-D objects are related by holography (forced by general coordinate invariance in TGD) to 4-D objects defining space-time as a 4-D surface in M<sup>4</sup>×CP<sub>2</sub>.
</p><p>
These 3-D surfaces possess a conformal symmetry which is much larger than the usual 2-D conformal conformal symmetry, which is already infinite-D.
<LI> In AdS/CFT, the dimensions related by holography are wrong: in AdS<sub>5</sub> one has 4→5 and AdS<sub>5</sub> is non-physical unless one wants to believe in the emergence of space-time, a second fashionable but remarkably unsuccessful idea.
<LI> In TGD holography corresponds 3→4, which is the case also in the duality proposed between blackhole horizon and interior. In this duality everything has precise physical meaning and both sides of the duality can be tested unlike in AdS/CFT duality for which AdS is a completely fictitious notion.
</OL>
The basic aspects of the TGD counterpart of horizon-interior duality are as follows.
<OL>
<LI> The TGD variant of duality is forced by the 4-D general coordinate invariance and is not a separate principle.
<LI> In quantum theory this duality corresponds to Bohr orbitology: space-time surface is analogous to Bohr orbit of 3-surface generalizing the notion of particle.
<LI> Classical theory as Bohr orbitology becomes an exact part of quantum theory.
<LI> This duality leads to what I call zero energy ontology in which these 4-D Bohr orbits replace time=constant snapshots as basic objects. This leads to a solution of the basic paradox of quantum measurement theory and has profound implications in quantum biology and theory of consciousness.
</OL>
<B>B.2 Magnetic flux tubes as TGD counterparts of traversable wormholes</B>
</p><p>
Could these traversable wormholes have TGD analogues and could they provide a dual or a classical correlate for the quantum description as the quantum classical correspondence suggests. One must remember that the TGD view of quantum differs considerably from the standard view.
<OL>
<LI> New view of space-time predicts topological field quantization and the notion of field body. The notion of magnetic body (MB) consisting of flux tubes and flux sheets is in a central role in TGD.
<LI> The number theoretic vision of TGD predicts hierarchy of dark matter as phases of ordinary matter labelled by values of effective Planck constant: dark matter would reside at the field body, in particular at MB. These phases of ordinary matter might be highly relevant for quantum computation, which is in the standard framework formulated using standard quantum mechanics.
<LI> TGD predicts zero energy ontology (ZEO) one predict is that the TGD counterpart of ordinary state function reduction (SFR) reverses the arrow of time. Could this give rise to quantal versions of time loops.
</OL>
In TGD monopole flux tubes are natural candidates for traversable wormholes.
<OL>
<LI> Wormholes of GRT are not stable. Monopole flux tubes are stabilized by the very fact that monopole flux is conserved so that the flux tube cannot be split.
<OL>
<LI> If one has a pair of flux tubes with opposite fluxes connecting two systems, reconnection can split the flux tubes to U-shaped flux loops. This is a basic mechanism in the TGD inspired quantum biology.
<LI> Could the reconnection of flux tube loops to a flux tube pair generate an analogue ofa traversable wormhole with classical signals propagating along the flux tube pair and making possible quantum teleportation?
<LI> Could thus involve "big" SFR changing the arrow of time and giving rise to effective negative energy signals propagating backwards in time?
</OL>
</p><p>
Could this correspondence be made more quantitative and detailed.
<OL>
<LI> Could one assign to wormhole throats and entire wormhole scales which are analogous to r<sub>S</sub> and the parameter a and could the condition a>r<sub>S</sub> have an analog in TGD framework.
</p><p>
<LI> The first trial starts from wormhole contacts as they are identified in TGD.
<OL>
<LI> The expectation is that at least for elementary particles the wormhole throat radius is of order CP<sub>2</sub> radius and therefore extremely small. Mass would be of order m=10<sup>-4</sup> m<sub>Pl</sub> and could correspond to a mesoscopic mass: a water blob of size 10<sup>-4</sup> meters has mass of order Planck mass. Could this give some idea how to proceed?
<LI> The Earth's gravitational field has a key role in TGD inspired quantum biology since gravitational quantum coherence is possible in even astrophysical scales. Gravitational Compton length Λ<sub>gr</sub>= h<sub>gr</sub>/m GM</v<sub>0</sub> defines a fundamental quantum gravitational size scale. One has scale of about .45 cm for Earth mass M<sub>E</sub> and v<sub>0</sub>=c.
</OL>
<LI> The condition a> r<sub>s</sub> for the traversability need not generalize as such in the TGD framework. Therefore it is better to start from the physical picture rather than trying to mimic wormhole physics.
</P><p>
This kind condition should tell when the reconnection for U-shaped flux tubes is possible. This suggests that the parameter a characterizes the length of the U-shaped flux tubes connecting the two quantum systems. This length scale should be more than half the distance between the two systems as analogues of blackholes so that the half-distance d/2 would be the counterpart of r<sub>S</sub> and the typical length of the U-shaped flux tube would be the counterpart of a. The length of the flux tube depends on the value of h<sub>eff</sub> and on the p-adic length scale assignable to the flux tube.
<LI> For an ordinary wormhole, the formula a> r<sub>s</sub> guaranteeing traversability can be satisfied if the mass parameter m decreases below a but remains unaffected. This would correspond to a generation of negative vacuum energy reducing m below a/2G. Does this have any generalization to the TGD framework?
<LI> Now the distance d between the systems could decrease or the length of U-shaped flux tubes could increase so that reconnection becomes possible.
</p><p>
The postulated interaction between the two systems should give rise to the analog of negative energy shock wave. In the TGD framework, the reconnection of flux tubes could be the interaction generating a communication line. The GRT analogue for the negative energy shock wave could be Hawking radiation. The system at right would receive positive energy and the system at left would receive negative energy, or equivalently, send positive energy.
</p><p>
The positive energy received by the system at right would serve as a metabolic energy feed and would change the distribution of values of h<sub>eff</sub> in it. The values of h<sub>eff</sub> would tend to increase. Therefore also entanglement negentropy content of the system would increase meaning that entanglement is created. At the left side the opposite would occur. One can say that information is transformed between the two systems.
<LI> Could "big" SFR (BSFR, that is the ordinary SFR) in the scale of the entire system be involved. This would imply a change of the arrow of time and one could say that the system at right sends negative energy signals to the system at left and gets positive energy as a recoil acting as metabolic energy. This mechanism is a basic metabolic mechanism in the TGD inspired quantum biology. The energy for dark analogs of Hawking photons would be large although frequencies could be small. For h<sub>gr</sub> = GM<sub>E</sub>m/v<sub>0</sub>, the energies would be in visible range for frequencies of order 10 Hz.
</p><p>
The simplest interpretation is that the first BSFR creates reconnection and maximal entanglement between the systems and and the second BSFR corresponds to de-reconnection and the quantum measurement destroying the entanglement. The classical communication during the entanglement period induces the transfer of internal entanglement. One could see this phenomenon also as quantum tunneling for information.
</OL>
Is this very rough picture consistent with the more detailed description of the simulation (see <A HREF="https://inqnet.caltech.edu/wormhole2022/">this</A>)?
<OL>
<LI> Prepare an entangled state between two copies of H: one is the left side of the wormhole, and the other is the right side of the wormhole. This entangled state is dual to a wormhole at time t=0. The devised through learning small SYK-like system has 7 Majorana fermions on the left and 7 Majorana fermions on the right; encoding all 14 fermions in superconducting qubits requires 7 qubits.
<I>Comment</I>: the initial state is quantum entangled. If the existence of flux tube pair(s) serves as a correlate for entanglement, BSFR changing the arrow of time must take place.
<LI> Evolve the wormhole backwards in time according to H. This moves the horizons of the left and right mouths of the wormhole.
<I>Comment</I>: The time evolution backwards in time could correspond to a sequence of SSFR ("small" SFRs as counterparts for "weak" measurements preserving the arrow of time). What could the motion of the wormhole mouths correspond to? Suppose that the half-distance d between the two systems corresponds to the parameter r<sub>S</sub> and the length L of flux U-shaped flux tubes corresponds to the parameter a. If this is the case, the motion would correspond to the decrease of the length of the U-shaped flux tubes so that the condition L> d/2 as an analogy for the condition a>r<sub>S</sub> ceases to be true and the U-shaped flux tubes become too short to reconnect anymore.
<LI> Prepare two maximally entangled qubits: call the first one the reference qubit and the other the probe qubit. We later attempt to send the probe qubit through the wormhole, and we will be able to check if it made it through by comparing against the reference qubit. These two additional qubits bring the total circuit size to 9 qubits.
<I>Comment</I>: this step could correspond to a BSFR changing the arrow of time to normal.
<LI> Swap the probe qubit with one of the qubits in the left quantum system of the wormhole. This inserts the entanglement probe qubit into the wormhole. Evolve the wormhole forwards in time according to H. As this happens, the information of the probe qubit gets chaotically scrambled throughout the entire quantum system.
<I>Comment</I>: This step could correspond to a time evolution by SSFRs with the standard arrow of time.
<LI> Apply an entangling interaction between the two sides of the wormhole. In the gravitational dual, this corresponds to sending an energy shockwave through spacetime. We can apply an interaction that gives this shockwave negative energy to prop open the wormhole and make it traversable, or we can choose a positive energy shockwave to close the wormhole and prevent information from getting across.
<I>Comment</I>: This step could correspond to a reconnection of U-shaped flux tubes to a flux tube pair connecting the two systems and entangling them, perhaps maximally.
<LI> Evolve the wormhole forwards in time according to H. As this happens, information of the probe qubit undergoes further chaotic dynamics. The dynamics refocus the information onto the right side of the wormhole.
<I>Comment</I>: this step could be a BSFR followed by a sequence of SSFRs with standard arrow of time. The entanglement would become visible for the observer with a standard arrow of time.
<LI> Measure the amount of entanglement between the rightmost qubit of the right system and the reference qubit. More entanglement means more information was transferred from the left system to the right system. In our experiment, we observed more entanglement when a negative energy shockwave was used compared to a positive energy shockwave, which is consistent with the interpretation that some quantum information was transferred via the traversable wormhole mechanism.
</OL>
</p><p>
There are still some questions to be considered.
<OL>
<LI> In the TGD framework, the expectation is that the radial coordinate r for the family of blackhole-like objects corresponds to the radial coordinate of E<sup>3</sup> ⊂M<sup>4</sup> and is therefore non-negative.
</p><p>
One can however ask whether one could have parallel space-time sheets connected by a wormhole contact with an Euclidean signature of the induced metric and whether the negative values of r could be natural for the radial coordinate at the other space-time sheet. Both sheets would be covered by a single coordinate.
<LI> One must also ask whether the connected space-time sheets could correspond to opposite arrows of time, which changes in "big" state function reductions (BSFRs). If so, wormhole contacts would mediate interaction between quantum states with opposite arrows of time. The wormhole throat with Euclidean signature does not have a definite arrow of time and could mediate this interaction. In this picture elementary particles, at least bosons, would be pairs of particles with opposite arrows of time. Can this make sense?
</OL>
</p><p>
See the article
<a HREF= "https://tgdtheory.fi/public_html/articles/AdSTGD.pdf">How do AdS/CFT- and TGD based holographic dualities relate?</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-87340376373998818062022-12-06T22:28:00.003-08:002022-12-08T19:12:22.468-08:00The ultrametric topology of discretized "world of classical worlds"
For more than a month, I have been preparing an article related to the role of finite fields in TGD. I however feel that "Finite Fields and TGD" is now in rather "final" shape and I expect that no new ideas will emerge anymore.
</p><p>
One of the unexpected outcomes is that I now understand the discretization of the "world of classical worlds" (WCW) using polynomials P(x) with integer coefficients as representations of 4-surfaces.
<OL>
<LI> The polynomials P(x) satisfy strong additional conditions implying that finite fields can be regarded as basic building bricks in the mathematical structure of TGD besides all other basic number fields.
<LI> Polynomial P(x) defines a set of mass shells via its roots containing a set of 3-surfaces and defining holographic data fixing space-time surface almost uniquely by M<sup>8</sup>-H correspondence. The holography is forced by general coordinate invariance and there is no need to postulate it as a separate principle.
<LI> The discretization of WCW by polynomials, assumed to correspond to extrema or even maxima for the exponent of K\"ahler function of WCW, replaces WCW with a discrete set. Polynomials P(x) can have fixed degree k, or degree smaller than some maximum degree k<sub>max</sub>, or satisfy some more general condition.
<LI> These restrictions reflect the basic feature of the spin glass energy landscape, namely that annealing as repeated heating and cooling allows to build localized thermodynamic equilibria localized inside some valley since thermal excitations are not able to kick the system out of the valley (failure of ergodicity).</p><p>
Elementary particles with D=P would result during cosmic evolution as repeated annealing when the degeneracy d(D) of polynomials with fixed value of D=P is fixed.
</OL>
WCW has the fractal structure of a spin glass energy landscape containing valleys inside valleys inside... valleys. This discretized WCW is expected to have ultrametric topology and to decompose to sectors with p-adic topologies. The challenge is to understand what this means.
<OL>
<LI> Spin glass energy landscape is realized number-theoretically in terms of the polynomials P(x) with integer coefficients and contains always a finite number of space-time surfaces, a hierarchy of analogues of Riemann zeta emerge defined as
</p><p>
ζ= ∑ d(D) D<sup>-k</sup> .
</p><p>
These zeta functions have interpretation as partition functions and provide probabilistic description of the number-theoretically discretized WCW. The analogy with Riemann zeta suggests that k=1 corresponds to point at which convergence fails.
<OL>
<LI> Discriminant D provides a concrete realization for how the ultrametric distance function emerges.
<LI> d(D) is the number of space-time surfaces with the same D, degeneracy.
<LI> k corresponds naturally to the degree or more generally, maximal degree, of polynomials contributing to sub-WCW. k can be also interpreted as an analogue of inverse temperature. k=1 would correspond to linear polynomials defining trivial algebraic extensions.
</OL>
<LI> p-Adic length scale hypothesis P ≈ p<sup>k</sup>, p=2 or small prime, for preferred ramified primes D=P turns out to be equivalent with the proposal for logarithmic coupling constant evolution for Kähler coupling strength fixed to high degree by number theoretical constraints. Therefore two separate hypotheses fuse to a single one.
</OL>
Consider now the structure of WCW as an analogue of the spin glass energy landscape.
<OL>
<LI> Number theoretically, WCW decomposes to subsets for which a given ramified prime P appears as a prime factor of discriminant D characterizing the polynomial and coding information of ordinary primes that split or are ramified in the extension defined by P(x).
<LI> D=P space-time regions correspond to particles and those with several ramified primes to interaction regions with external particles corresponding to various primes P<sub>i</sub> dividing D: these interaction regions are shared by several regions characterized by P as a factor of D.
<LI> Elementary particles correspond to D=P regions for which one has an especially large number of 4-surfaces with D=P: that is the degeneracy factor d(D) appearing in the analog of Riemann zeta is large so that annealing leads with a high probability to this state. One can say that space-time surfaces define number theoretical analogs of Feynman graphs consisting of particle lines and vertices.
</OL>
In the standard ontology, one can predict scattering rates but particle densities cannot be predicted without further assumptions. In ZEO both can be predicted since there is a complete democracy between particles and particle reactions. Physical event as a superposition of deterministic time evolutions becomes the basic notion and both particles and particle reactions correspond to physical events.
</p><p>
The statistical model represents the probabilities of physical events within the quantization volume defined by CD. Particle characterized by D=P and corresponds to a scattering event with a single incoming and outgoing particle, and the statistical model predicts the densities of various particles as probabilities of D=P events. Genuine particle reaction corresponds to D= ∏ P<sub>i</sub> and the model gives the probabilities of observing these events within CD.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">Finite Fields and TGD</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/finitefieldsTGD.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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-90804842155648126852022-11-14T22:54:00.004-08:002022-11-14T22:54:57.180-08:00Could the exotic smooth structures have a physical interpretation in the TGD framework?
The exotic smooth structures appearing for 4-D manifolds, even R<sup>4</sup>, challenges both the classical GRT and quantum GRT based on path integral approach. They could also cause problems in the TGD framework. I have already considered the possibility that the exotics could be eliminated by what could be called holography of smoothness meaning that the smooth structure for the boundary dictates it for the entire 4-surface. One can however argue that the atlas of charts for 3-D boundary cannot define uniquely the atlas of charges for 4-D surface.
</p><p>
In the TGD framework, exotic smooth structures could also have a physical interpretation. As noticed, the failure of the standard smooth structure can be thought to occur at a point set of dimension zero and correspond to a set of point defects in condensed matter physics. This could have a deep physical meaning.
<OL>
<LI> The space-time surfaces in H=M<sup>4</sup>× CP<sub>2</sub> are images of 4-D surfaces of M<sup>8</sup> by M<sup>8</sup>-H-duality. The proposal is that they reduce to minimal surfaces analogous to soap films spanned by frames. Regions of both Minkowskian and Euclidean signature are predicted and the latter correspond to wormhole contacts represented by CP<sub>2</sub> type extremals. The boundary between the Minkowskian and Euclidean region is a light-like 3-surface representing the orbit of partonic 2-surface identified as wormhole throat carrying fermionic lines as boundaries of string world sheets connecting orbits of partonic 2-surfaces.
<LI> These fermionic lines are counterparts of the lines of ordinary Feynman graphs, and have ends at the partonic 2-surfaces located at the light-like boundaries of CD and in the interior of the space-time surface. The partonic surfaces, actually a pair of them as opposite throats of wormhole contact, in the interior define topological vertices, at which light-like partonic orbits meet along their ends.
<LI> These points should be somehow special. Number theoretically they should correspond points with coordinates in an extension of rationals for a polynomial P defining 4-surface in H and space-time surface in H by M<sup>8</sup>-H duality. What comes first in mind is that the throats touch each other at these points so that the distance between Minkowskian space-time sheets vanishes. This is analogous to singularities of Fermi surface encountered in topological condensed matter physics: the energy bands touch each other. In TGD, the partonic 2-surfaces at the mass shells of M<sup>4</sup> defined by the roots of P are indeed analogs of Fermi surfaces at the level of M<sup>4</sup>⊂ M<sup>8</sup>, having interpretation as analog of momentum space.
</p><p>
Could these points correspond to the defects of the standard smooth structure in X<sup>4</sup>? Note that the branching at the partonic 2-surface defining a topological vertex implies the local failure of the manifold property. Note that the vertices of an ordinary Feynman diagram imply that it is not a smooth 1-manifold.
<LI> Could the interpretation be that the 4-manifold obtained by removing the partonic 2-surface has exotic smooth structure with the defect of ordinary smooth structure assignable to the partonic 2-surface at its end. The situation would be rather similar to that for the representation of exotic R<sup>4</sup> as a surface in CP<sub>2</sub> with the sphere at infinity removed (see <A HREF="http://arxiv.org/abs/1503.04945v4">this</A>).
<LI> The failure of the cosmic censorship would make possible a pair creation. As explained, the fermionic lines can indeed turn backwards in time by going through the wormhole throat and turn backwards in time. The above picture suggests that this turning occurs only at the singularities at which the partonic throats touch each other. The QFT analog would be as a local vertex for pair creation.
<LI> If all fermions at a given boundary of CD have the same sign of energy, fermions which have returned back to the boundary of CD, should correspond to antifermions without a change in the sign of energy. This would make pair creation without fermionic 4-vertices possible.
</p><p>
If only the total energy has a fixed sign at a given boundary of CD, the returned fermion could have a negative energy and correspond to an annihilation operator. This view is nearer to the QFT picture and the idea that physical states are Galois confined states of virtual fundamental fermions with momentum components, which are algebraic integers. One can also ask whether the reversal of the arrow of time for the fermionic lines could give rise to gravitational quantum computation as proposed <A HREF="http://arxiv.org/abs/1503.04945v4">here</A>.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/intsectform.pdf">Intersection form for 4-manifolds, knots and 2-knots, smooth exotics, and TGD</A>
or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/ratpoints2.pdf">Does M<sup>8</sup> H duality reduce classical TGD to octonionic algebraic geometry?: 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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-30627333408492656632022-11-13T21:52:00.001-08:002022-11-13T21:53:08.237-08:00Could the existence of exotic smooth structures pose problems for TGD?
The article of Gabor Etesi (see <A HREF="https://cutt.ly/2Md7JWP">this</A>) gives a good idea about the physical significance of the existence of exotic smooth structures and how they destroy the cosmic censorship hypothesis (CCH of GRT stating that spacetimes of GRT are globally hyperbolic so that there are no time-like loops.
</p><p>
<B>1. Smooth anomaly</B>
</p><p>
No compact smoothable topological 4-manifold is known, which would allow only a single smooth structure. Even worse, the number of exotics is infinite in every known case! In the case of non-compact smoothable manifolds, which are physically of special interest, there is no obstruction against smoothness and they typically carry an uncountable family of exotic smooth structures.
</p><p>
One can argue that this is a catastrophe for classical general relativity since smoothness is an essential prerequisite for tensory analysis and partial differential equations. This also destroys hopes that the path integral formulation of quantum gravitation, involving path integral over all possible space-time geometries, could make sense. The term anomaly is certainly well-deserved.
</p><p>
Note however that for 3-geometries appearing as basic objects in Wheeler's superspace approach, the situation is different since for D≤3 there is only a single smooth structure. If one has holography, meaning that 3-geometry dictates 4-geometry, it might be possible to avoid the catastrophe.
</p><p>
The failure of the CCH is the basic message of Etesi's article. Any exotic R<sup>4</sup> fails to be globally hyperbolic and Etesi shows that it is possible to construct exact vacuum solutions representing curved space-times which violate the CCH. In other words, GRT is plagued by causal anomalies.
</p><p>
Etesi constructs a vacuum solution of Einstein's equations with a vanishing cosmological constant which is non-flat and could be interpreted as a pure gravitational radiation. This also represents one particular aspect of the energy problem of GRT: solutions with gravitational radiation should not be vacua.
<OL>
<LI> Etesi takes any exotic R<sup>4</sup>, which has the topology of S<sup>3</sup>× R and has an exotic smooth structure, which is not a Cartesian product. Etesi maps maps R<sup>4</sup> to CP<sub>2</sub>, which is obtained from C<sup>2</sup> by gluing CP<sub>1</sub> to it as a maximal ball B<sup>3</sup><sub>r</sub> for which the radial Eguchi-Hanson coordinate approaches infinity: r → &infty;. The exotic smooth structure is induced by this map. The image of the exotic atlas defines atlas. The metric is that of CP<sub>2</sub> but SU(3) does not act as smooth isometries anymore.
<LI> After this Etesi performs Wick rotation to Minkowskian signature and obtains a vacuum solution of Einstein's equations for any exotic smooth structure of R<sup>4</sup>.
</OL>
The question of exotic smoothness is encountered both at the level of embedding space and associated fixed spaces and at the level of space-time surfaces and their 6-D twistor space analogies.
</p><p>
<B>2. Holography of smoothness</B>
</p><p>
In the TGD framework space-time is 4-surface rather than abstract 4-manifold. 4-D general coordinate invariance, assuming that 3-surfaces as generalization of point-like particles are the basic objects, suggests a fully deterministic holography. A small failure of determinism is however possible and expected, and means that space-time surfaces analogous to Bohr orbits become fundamental objects. Could one avoid the smooth anomaly in this framework?
</p><p>
The 8-D embedding space topology induces 4-D topology. My first naive intuition was that the 4-D smooth structure, which I believed to be somehow inducible from that of H=M<sup>4</sup>× CP<sub>2</sub>, cannot be exotic so that in TGD physics the exotics could not be realized. But can one really exclude the possibility that the induced smooth structure could be exotic as a 4-D smooth structure?
</p><p>
What does the induction of a differentiable structure really mean? Here my naive expectations turn out to be wrong.
<OL>
<LI> If a sub-manifold S⊂ H can be regarded as an embedding of smooth manifold N to S⊂ H, the embedding N→ S⊂ H induces a smooth structure in S (see <A HREF="https://cutt.ly/tMtvG79">this</A>). The problem is that the smooth structure would not be induced from H but from N and for a given 4-D manifold embedded to H one could also have exotic smooth structures. This induction of smooth structure is of course physically adhoc.
</p><p>
It is not possible to induce the smooth structure from H to sub-manifold. The atlas defining the smooth structure in H cannot define the charts for a sub-manifold (surface). For standard R<sup>4</sup> one has only one atlas.
<LI> Could M<sup>8</sup>-H duality help and holography help? One has holography in M<sup>8</sup> and this induces holography in H. The 3-surfaces X<sup>3</sup> inducing the holography in M<sup>8</sup> are parts of mass shells, which are hyperbolic spaces H<sup>3</sup>⊂ M<sup>4</sup>⊂ M<sup>8</sup>. 3-surfaces X<sup>3</sup> could be even hyperbolic 3-manifolds as unit cells of tessellations of H<sup>3</sup>. These hyperbolic manifolds have unique smooth structures as manifolds with dimension D<4.
<LI> One can ask whether the smooth structure at the boundary of a manifold could dictate that of the manifold uniquely. One could speak of holography for smoothness.
</p><p>
The implication would be that exotic smooth 4-manifold cannot have a boundary. Indeed, R<sup>4</sup> does not have a boundary. Could this theorem generalize so that 3-surfaces as sub-manifolds of mass shells H<sup>3</sup><sub>m</sub> determined by the polynomials defining the 4-surface in M<sup>8</sup> take the role of the boundaries?
</p><p>
The regions of X<sup>4</sup>⊂ M<sup>8</sup> connecting two sub-sequent mass shells would have a unique smooth structure induced by the hyperbolic manifolds H<sup>3</sup> at the ends. These smooth structures are unique by D<4 and cannot be exotic. Smooth holography would determine the smooth structure from that for the boundary of 4-surface.
<LI> However, the holography for smoothness is argued to fail (see <A HREF="https://cutt.ly/3MewYOt">this</A>). Assume a 4-manifold W with 2
different smooth structures. Remove a ball B<sup>4</sup> belonging to an open set U and construct a smooth structure at its boundary S<sup>3</sup>. Assume that this smooth structure can be continued to W. If the continuation is unique, the restrictions of the 2 smooth structures in the complement of B<sup>4</sup> would be equivalent but it is argued that they are not.
</p><p>
The first layman objection is that the two smooth structures of W are equivalent in the complement W-B<sup>3</sup> of an arbitrary small ball B<sup>3</sup>⊂ W but not in the entire W. This would be analogous to coordinate singularity. For instance, a single coordinate chart is enough for a sphere in the complement of an arbitrarily small disk. An exotic smooth structure would be like a local defect in condensed matter physics.
</p><p>
The second layman objection is that smooth structure, unlike topology, cannot be induced from W to W-B<sup>3</sup> but only from W-B<sup>3</sup> to W. If one a smooth structure at the boundary S<sup>3</sup> is chosen, it determines the smooth structure in the interior as standard smooth structure.
<LI> In fact, one could argue that the mere fact the 4-surfaces have boundaries as their ends at the light-like boundaries of CD, implies a unique smooth structure by holography. It is however possible that the mass-shells correspond to discontinuities of derivatives so that the smooth holography decomposes to a piece-wise holography. This would mean that M<sup>8</sup>-H duality is needed.
</OL>
Amazingly, if the holography of smoothness holds true, the avoidance of the smooth exotics requires holography and both number theoretical vision and general coordinate invariance of geometric vision predict the holography in the TGD framework. For higher space-time dimensions D>4 one cannot avoid the exotics. Also the number theoretic vision fails for them.
</p><p>
<B>3. Can embedding space and related spaces have exotic smooth structure?</B>
</p><p>
One can worry about the exotic smooth structures possibly associated with the M<sup>4</sup>, CP<sub>2</sub>, H=M<sup>4</sup>× CP<sub>2</sub>, causal diamond CD=cd× CP<sub>2</sub>, where cd is the intersection of the future and past directed light-cones of M<sup>4</sup>, and with M<sup>8</sup>. One can also worry about the twistor spaces CP<sub>3</sub> <I> resp.</I> SU(3)/U(1)× U(1) associated with M<sup>4</sup> <I> resp.</I> CP<sub>2</sub>.
</p><p>
The key assumption of TGD is that all these structures have maximal isometry groups so that they relate very closely to Lie groups, whose unique smooth structures are expected to determine their smooth structures.
<OL>
<LI> The first sigh of relief is that all Lie groups have the standard smooth structure. In particular, exotic R<sup>4</sup> does not allow translations and Lorentz transformations as isometries. I dare to conclude that also the symmetric spaces like CP<sub>2</sub> and hyperbolic spaces such as H<sup>n</sup>= SO(1,n)/SO(n) are non-exotic since they provide a representation of a Lie group as isometries and the smoothness of the Lie group is inherited. This would mean that the charts for the coset space G/H would be obtained from the charts for G by an identification of the points of charts related by action of subgroup H.
</p><p>
Note that the mass shell H<sup>3</sup>, as any 3-surface, has a unique smooth structure by its dimension.
</p><p>
<LI> Second sigh of relief is that twistor spaces CP<sub>3</sub> and SU(3)/U(1)× U(1) have by their isometries and their coset space structure a standard smooth structure.
</p><p>
In accordance with the vision that the dynamics of fields is geometrized to that of surfaces, the space-time surface is replaced by the analog of twistor space represented by a 6-surface with a structure of S<sup>2</sup> bundle with space-time surface X<sup>4</sup> as a base-space in the 12-D product of twistor spaces of M<sup>4</sup> and CP<sub>2</sub> and by its dimension D=6 can have only the standard smooth structure unless it somehow decomposes to (S<sup>3</sup>× R)× R<sup>2</sup>. Holography of smoothness would prevent this since it has boundaries because X<sup>4</sup> as base space has boundaries at the boundaries of CD.
<LI> cd is an intersection of future and past directed light-cones of M<sup>4</sup>. Future/past directed light-cone could be seen as a subset of M<sup>4</sup> and implies standard smooth structure is possible. Coordinate atlas of M<sup>4</sup> is restricted to cd and one can use Minkowski coordinates also inside the cd. cd could be also seen as a pile of light-cone boundaries S<sup>2</sup>× R<sub>+</sub> and by its dimension S<sup>2</sup>× R allows only one smooth structure.
<LI> M<sup>8</sup> is a subspace of complexified octonions and has the structure of 8-D translation group, which implies standard smooth structure.
</OL>
The conclusion is that continuous symmetries of the geometry dictate standard smoothness at the level of embedding space and related structures.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/intsectform.pdf">Intersection form for 4-manifolds, knots and 2-knots, smooth exotics, and TGD</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/ratpoints2.pdf">Does M<sup>8</sup> H duality reduce classical TGD to octonionic algebraic geometry?: 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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-34153435764026108462022-11-10T20:42:00.010-08:002022-11-11T21:09:00.524-08:00Intersection form for 4-manifolds, knots and 2-knots, smooth exotics, and TGD
Gary Ehlenberger sent a highly interesting commentary related to smooth structures in R<sup>4</sup> discussed in the article of Gompf (see <A HREF="https://cutt.ly/eMracmf">this</A>) and more generally to exotics smoothness discussed from the point of view of mathematical physics in the book of Asselman-Maluga and Brans (see <A HREF="https://cutt.ly/DMu0dYr">this</A>). I am grateful for these links for Gary. The intersection form of 4-manifold (see <A HREF="https://cutt.ly/jMriNdI">this</A>) characterizing partially its 2-homology is a central notion.
</p><p>
<B>The role of intersection forms in TGD</B>
</p><p>
I am not a topologist but I had two good reasons to get interested on intersection forms.
<OL>
<LI> In the TGD framework (see <A HREF="https://tgdtheory.fi/public_html/articles/TGD2021.pdf">this</A>), the intersection form describes the intersections of string world sheets and partonic 2-surfaces and therefore is of direct physical interest (see <A HREF="https://tgdtheory.fi/pdfpool/knotstgd.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/ratpoints2.pdf">this</A>).
<LI> Knots have an important role in TGD. The 1-homology of the knot complement characterizes the knot. Time evolution defines a knot cobordism as a 2-surface consisting of knotted string world sheets and partonic 2-surfaces. A natural guess is that the 2-homology for the 4-D complement of this cobordism characterizes the knot cobordism. Also 2-knots are possible in 4-D space-time and a natural guess is that knot cobordism defines a 2-knot.
</p><p>
The intersection form for the complement for cobordism as a way to classify these two-knots is therefore highly interesting in the TGD framework. One can also ask what the counterpart for the opening of a 1-knot by repeatedly modifying the knot diagram could mean in the case of 2-knots and what its physical meaning could be in the TGD Universe. Could this opening or more general knot-cobordism of 2-knot take place in zero energy ontology (ZEO) (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/zeonew.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/ZEOnumber.pdf">this</A>) as a sequence of discrete quantum jumps leading from the initial 2-knot to the final one.
</OL>
<B>Why exotic smooth structures are not possible in TGD?</B>
</p><p>
The article of Gabor Etesi (see <A HREF="https://cutt.ly/2Md7JWP">this</A>) gives a good idea about the physical significance of the existence of exotic smooth structures (see the <A HREF= "https://cutt.ly/DMu0dYr">book</A> and the <A HREF ="https://cutt.ly/eMracmf">article</A>). They mean a mathematical catastrophe for both classical relativity and for the quantization of general relativity based on path integral formulation.
</p><p>
The first naive guess was that the exotic smooth structures are not possible in TGD but it turned out that this is not trivially true. The reason is that the smooth structure of the space-time surface is not induced from that of H unlike topology. One could induce smooth structure by assuming it given for the space-time surface so that exotics would be possible. This would however bring an ad hoc element to TGD. This raises the question of how it is induced.
<OL>
<LI> This led to the idea of a holography of smoothness, which means that the smooth structure at the boundary of the manifold determines the smooth structure in the interior. Suppose that the holography of smoothness holds true. In ZEO, space-time surfaces indeed have 3-D ends with a unique smooth structure at the light-like boundaries of the causal diamond CD= cd× CP<sub>2</sub> ⊂ H=M<sup>4</sup>× CP<sub>2</sub>, where cd is defined in terms of the intersection of future and past directed light-cones of M<sup>4</sup>. One could say that the absence of exotics implies that D=4 is the maximal dimension of space-time.
<LI> The differentiable structure for X<sup>4</sup>⊂ M<sup>8</sup>, obtained by the smooth holography, could be induced to X<sup>4</sup>⊂ H by M<sup>8</sup>-H-duality. Second possibility is based on the map of mass shell hyperboloids to light-cone proper time a=constant hyperboloids of H belonging to the space-time surfaces and to a holography applied to these.
<LI> There is however an objection against holography of smoothness (see <A HREF="https://cutt.ly/3MewYOt">this</A>). In the last section of the article, I develop a counter argument against the objection. It states that the exotic smooth structures reduce to the ordinary one in a complement of a set consisting of arbitrarily small balls so that local defects are the condensed matter analogy for an exotic smooth structure.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/intsectform.pdf">Intersection form for 4-manifolds, knots and 2-knots, smooth exotics, and TGD</A>
or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/ratpoints2.pdf">Does M<sup>8</sup>−H duality reduce classical TGD to octonionic algebraic geometry?: 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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-80489933072423102952022-11-05T20:44:00.004-07:002022-12-05T23:32:24.019-08:00Finite Fields and TGD
TGD involves geometric and number theoretic physics as complementary views of physics. Almost all basic number fields: rationals and their algebraic extensions, p-adic number fields and their extensions, reals, complex number fields, quaternions, and octonions play a fundamental role in the number theoretical vision of TGD.
</p><p>
Even a hierarchy of infinite primes and corresponding number fields appears. At the first level of the hierarchy of infinite primes, the integer coefficients of a polynomial Q defining infinite prime have no common prime factors. P=Q hypothesis states that the polynomial P defining space-time surface is identical with a polynomial Q defining infinite prime at the first level of hierarchy.
</p><p>
However, finite fields, which appear naturally as approximations of p-dic number fields, have not yet gained the expected preferred status as atoms of the number theoretic Universe. Also additional constraints on polynomials P are suggested by physical intuition.
</p><p>
Here the notions of prime polynomial and concept of infinite prime come to rescue. Prime polynomial P with prime order n=p and integer coefficients smaller than p can be regarded as a polynomial in a finite field. The proposal is that all physically allowed polynomials are constructible as functional composites of prime polynomials satisfying P=Q condition.
</p><p>
One of the long standing mysteries of TGD is why preferred p-adic primes, characterizing elementary particles and even more general systems, satisfy the p-adic length scale hypothesis. The proposal is that p-adic primes correspond to ramified primes as factors of discriminant D of polynomial P(x). D=P condition reducing discriminant to a single prime is an attractive hypothesis for preferred ramified primes. M<sup>8</sup>-H duality suggests that the exponent exp(K) of Kähler function corresponds to a negative power D<sup>-k</sup>. Spin glass character of WCW suggests that the preferred ramified primes for, say prime polynomials of a given degree, and satisfying D=P, have an especially large degeneracy for certain ramified primes P, which are therefore of a special physical importance.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/finitefieldsTGD.pdf">Finite Fields and TGD</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/finitefieldsTGD.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>Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-42305535862493329102022-11-03T21:53:00.003-07:002022-11-03T21:53:41.597-07:00VO2 can remember like a brain
The following comments were inspired by a popular article
(see <A HREF="https://cutt.ly/lNHzBYa">this</A>) with the title "Scientists accidentally discover a material that can 'remember' like a brain". These materials can remember the history of its physical stimuli. The findings are described in the article "Electrical control of glass-like dynamics in vanadium dioxide for data storage and processing" published in Nature (see see <A HREF="https://cutt.ly/cNHyMMa">this</A>).
</p><p>
The team from the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland did this discovery while researching insulator-metal phase transitions of vanadium dioxide (VO<sub>2</sub>), a compound used in electronics.
<OL>
<LI> PhD student Mohammad Samizadeh Nikoo was trying to figure out how long it takes for VO<sub>2</sub> to make a phase transition from insulating to conducting phase under "incubation" by a stimulation by a radio frequency pulse of 10 μs duration and voltage amplitude V= 2.1 V. Note that the Wikipedia article talks about semiconductor-metal transition. The voltage pulse indeed acted like a voltage in a semiconductor.
<LI> As the current heated the sample it caused a local phase transition to metallic state in VO<sub>2</sub>. The induced current moved across the material, following a path until it exited on the other side. A conducting filament connecting the ends of the device was generated by a percolation type process.
<LI> Once the current had passed, the material exhibited an insulating state but after incubation time t<sub>inc</sub>, which was t<sub>inc</sub>∼ .1 μs for the first pulse, it became conducting. This state lasted at least 10,000 seconds.
</p><p>
After applying a second electrical current during the experiment, it was observed that t<sub>inc</sub> appeared to be directly related to its history and was shorter than for the first incubation period .1 μs. The VO<sub>2</sub> seemed to remember the first phase transition and anticipate the next. One could say that the system learned from experience.
</OL>
Before trying to understand the finding in the TGD framework, it is good to list some basic facts about vanadium and vanadium-oxide VO<sub>2</sub> or Vanadium(IV) oxide (see <A HREF="https://cutt.ly/yNHhahk">this</A>).
<OL>
<LI> Vanadium is a transition metal, which has valence shells d<sup>3</sup>s<sup>2</sup>. It is known that the valence electrons of transition metals can mysteriously disappear, for instance in heating (see <A HREF="https://www.nature.com/articles/s41467-017-00946-1">this</A>). The TGD interpretation (see <A HREF="https://tgdtheory.fi/pdfpool/qcritdark3.pdf">this</A>) would be that heating provides energy making it possible to transform ordinary valence electrons to dark valence electrons with a higher value of h<sub>eff</sub> and higher energy. In the recent case, the voltage pulses could have the same effect.
<LI> VO<sub>2</sub> forms a solid lattice of V<sup>4+</sup> ions. There are two lattice forms: the monoclinic semiconductor below T<sub>c</sub>=340 K and the tetragonal metallic form above T<sub>c</sub>. In the monoclinic form, the V<sup>4+</sup> ions form pairs along the c axis, leading to alternate short and long V-V distances of 2.65 Angström and 3.12 Angström. In the tetragonal form, the V-V distance is 2.96 Angström. Therefore size of the unit cell for the monoclinic form is 2 times larger than for the tetragonal form. At T<sub>c</sub> IMT takes place. The optical band gap of VO<sub>2</sub> in the low-temperature monoclinic phase is about 0.7 eV.
<LI> Remarkably, the metallic VO<sub>2</sub> contradicts the Wiedemann Franz law, which states that the ratio of the electronic contribution of the thermal conductivity (κ) to the electrical conductivity (σ) of a metal is proportional to the temperature. The thermal conductivity that could be attributed to electron movement was 10 per cent of the amount predicted by the Wiedemann Franz law. That the conductivity is 10 times higher than expected, suggests that the mechanism of conductivity is not the usual one.
</p><p>
Semiconductor property below T<sub>c</sub> suggests that a local phase transition modifying the lattice structure from monoclinic to tetragonal takes place at the current path in the incubation.
</OL>
One can try to understand the chemistry and unconventional conductivity of VO<sub>2</sub> in the TGD framework.
<OL>
<LI> Vanadium could give 4 valence electrons to O<sub>2</sub>: 3 electrons d<sup>3</sup>:sta and one from s<sup>2</sup>. In the TGD Universe, the second electron from s<sup>2</sup> could become dark and go to the bond between V<sup>4+</sup> ions in the VO<sub>2</sub> lattice and take the role of conduction electron.
<LI> This could explain the non-conventional character of conductivity. In the semiconductor phase, an electric voltage pulse or some other perturbation, such as impurity atoms or heating, can provide the energy needed to increase the value of h<sub>eff</sub>. Electric conductivity could be due to the transformation of electrons to dark electrons possibly forming Cooper pairs at the flux tube pairs connecting V<sup>4+</sub> ions or their pairs. The current would run along the flux tubes as a dark current.
<LI> In a semi-conducting (insulating) state, the flux tube pairs connecting V<sup>4+</sup> ions would be relatively short. The voltage pulse inducing a local metallic state could provide the energy needed to increase h<sub>eff</sub> and thus the quantum coherence scale. This would be accompanied by a reconnection of the short flux tube pairs to longer flux tube pairs serving as bridges along which the dark current could run.
</p><p>
One can also consider U-shaped closed flux tubes associated with V<sup>4+</sup> ions or ion pairs, which reconnect in IMT to longer flux tubes. The mechanism would be very similar to that proposed for the transition to high temperature superconductivity (see <A HREF="https://tgdtheory.fi/pdfpool/biosupercondI.pdf">this</A>, <A HREF="https://tgdtheory.fi/pdfpool/biosupercondII.pdf">this</A>, and <A HREF="https://tgdtheory.fi/pdfpool/SCBerryTGD.pdf">this</A>).
</OL>
Experimenters suggest a glass type behavior.
<OL>
<LI> Spin glass corresponds to the existence of a very large number of free energy minima in the energy landscape implying breaking of ergodicity. A system consisting of regions with varying direction of magnetization is the basic example of spin glass. In the recent case, decomposition to metallic and insulating regions could define the spin glass.
<LI> TGD predicts the possibility of spin glass type behavior and leads to a model for spin glasses (see <A HREF="https://tgdtheory.fi/public_html/articles/sg.pdf">this</A>). The quantum counterpart of spin glass behavior would be realized in terms of monopole flux tube structures (magnetic bodies) carrying dark phases of the radinary particles such as electrons serving as current carries in the metallic phase.The length of the flux tube pair would be one critical parameter near T<sub>c</sub>. Quantum criticality against the change of h<sub>eff</sub> increasing the length of the flux tube pair by reconnection would make the system very sensitive to perturbations.
<LI> These phases are highly sensitive to external perturbations and represent in TGD inspired theory of consciousness higher levels with longer quantum coherence scale and number theoretical complexity measured by the dimension n= h<sub>eff</sub>/h<sub>0</sub> of the extension having interpretation as a kind of IQ. These phases would receive sensory information from lower levels of the hierarchy with smaller values of n and control them.
</p><p>
The large number of free energy minima as a correlate for number theoretical complexity would make possible the representation of "sensory" information as "memories".
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcondmatshort.pdf">TGD and Condensed Matter</A> or the <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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-80482581945167907012022-11-02T22:53:00.003-07:002022-11-02T22:53:41.751-07:00More anomalies related to the standard model of galaxy formation
Various anomalies associated with the ΛCDM model assuming that dark matter forms halos and with the general view of galaxy formation have been accumulating rapidly during years. The MOND model assumes no dark mass but modifies Newton's law of gravitation and is inconsistent with the Equivalence Principle. In TGD, the halo is replaced with a cosmic string and the Equivalence Principle and Newtonian gravitation survive. Both MOND and TGD can handle these anomalies because there is no dark mass halo.
</p><p>
In this article, three new anomalies disfavoring ΛCDM but consistent with MOND and TGD are discussed. There are too many thin disk galaxies, dwarf galaxies do not have dark matter halos, and tidal tails associated with star clusters are asymmetric.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/galanomalies.pdf">More anomalies related to the standard model of galaxy formation</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.<Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-28856582355045269222022-11-02T05:19:00.005-07:002022-11-02T22:56:46.344-07:00Too many thin disk galaxies
The title of the article "Breaking Cosmology: Too Many Disk Galaxies – “A Significant Discrepancy Between Prediction and Reality” (see <A HREF="https://cutt.ly/LNPTtYp">this</A>) describes quite well the situation in the cosmology. The views of the dynamics of galaxies seem to be wrong.
</p><p>
In the current study (see <A HREF="https://iopscience.iop.org/article/10.3847/1538-4357/ac46ac">this</A>, Pavel Kroupa’s doctoral student, Moritz Haslbauer, led an international research group to investigate the evolution of the universe using the latest supercomputer simulations. The calculations are based on the Standard Model of Cosmology; they show which galaxies should have formed by today if this theory were correct. The researchers then compared their results with what is currently probably the most accurate observational data of the real Universe visible from Earth.
</p><p>
It is found that the fraction of disk galaxies is much larger than predicted. This suggests that the morphology of disk galaxies is very slowly changing and mergers of galaxies, favoured by dark matter halos, are not so important as though in the dynamics of galaxies. The cold dark matter scenario predicts spherical halos, which does not fit well with the large fraction of disk galaxies. The MOND approach is favored because there are no dark matter halos favoring spherical galaxies and mergers.
</p><p>
In the TGD framework (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>), dark matter or rather, dark energy would be associated with what I call cosmic strings so that halos are absent. Cosmic strings are extremely massive and create a 1/ρ transversal gravitational field, which explains the flat velocity spectrum of distant stars automatically.
</p><p>
The orbits of stars are helical since there is free motion in the direction of a long string. This strongly favors the formation of disk galaxies with the plane of the disk orthogonal to the string and correlation between the normals of the disks along the long cosmic string. In accordance with the findings, the concentration of matter at the galactic plane is very natural in the TGD framework.
</p><p>
The intersections of the string-like objects moving at 3-surface are topologically unavoidable and one can ask whether the galaxies are formed as two cosmic string intersect and the resulting perturbation induces their thickening leading to the transformation of the dark energy of the cosmic string to ordinary matter. This would be an analogy for the decay of an inflaton field to ordinary matter.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/galanomalies.pdf">More anomalies related to the standard model of galaxy formation</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>.
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<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.<Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-87407875615856013182022-10-31T22:48:00.002-07:002022-10-31T22:50:09.413-07:00The asymmetry of tidal tails as a support for the TGD view of dark matter
The most recent puzzling discovery related to the galactic dynamics is that for certain star clusters associated with tidal tails there is an asymmetry with respect to the direction of the motion along the tail (see <A HREF="https://arxiv.org/abs/2210.13472">this</A>). The trailing tail directed to the galactic nucleus is thin and the leading tail is thick and there are many more stars in it. Stars also tend to leak out along the direction of motion along the tail. One would not expect this kind of asymmetry in the Newtonian theory since the contribution of the ordinary galactic matter to the gravitational potential possibly causing the asymmetry is rather small.
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MOND theory (see <A HREF="https://cutt.ly/GNTzBPr">this</A>) is reported to explain the finding satisfactorily.
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<LI> The tidal tails of the star cluster are directed towards (leading tail) and outwards from it (trailing tail). The standard explanation is that gravitational forces produce them as a purely gravitational effect. These tails can be however often thin and long, which has raised suspicions concerning this explanation.
<LI> MOND hypothesis assumes that gravitational acceleration starts to transform above some critical radius from 1/r<sup>2</sup> form to 1/r form. This applies to galaxies and star clusters modelled as a point-like object. This idea is realized in terms of a non-linear variant of the Poisson equation by introducing a coefficient μ(a/a<sub>0</sub>) depending on the ratio a/a<sub>0</sub> of the strength of gravitational acceleration a expressible as gradient of the gravitational potential. a<sub>0</sub> is the critical acceleration appearing as a fundamental constant in the MOND model. μ approaches unity at large accelerations and a linear function of a/a<sub>0</sub> at small accelerations. Note that MOND violates the Equivalence Principle.
<LI> For MOND, the effective gravitational potential of the galactic nucleus becomes logarithmic. Therefore the outwards escape velocity in the trailing tail is higher than the inwards escape velocity in the leading tail so that the stars tend to be reflected back from the trailing tail. This would cause tidal asymmetry implying that the tail directed to the galactic nucleus contains more stars than the outwards tail. The MOND model uses the effective gravitational mass of the galaxy to model the situation in a quasi-Newtonian way.
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TGD allows us to consider both the variant of the MOND model. The model provides also a possible explanation for the formation of the star cluster itself.
<OL>
<LI> In the TGD framework, cosmic strings are expected to form a network (see <a HREF= "https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>, <a HREF= "https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>, and <a HREF= "https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>). In particular, one can assign to the tidal tails a cosmic string oriented towards the galactic nucleus, call it L<sub>t</sub> to distinguish it from the long cosmic string along L along which galaxies are located. The thickening of a long string and the associated formation of a tangle generates ordinary matter as the dark energy of the string transforms to ordinary matter. This is the TGD counterpart for the transformation of the energy of an inflaton field to ordinary matter.
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This process can occur for both the galactic string L and L<sub>t</sub>. In the first case it would give rise to galaxies along L and in the case of L<sub>t</sub> to the formation of star clusters. Unlike in MOND, the gravitation remains Newtonian and the Equivalence Principle is satisfied in TGD.
<LI> The long cosmic string L along which the galaxies are located gives an additive logarithmic contribution to the total gravitational potential of the galaxy. This contribution explains the flat velocity spectrum of distant stars.
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At some critical distance, the contribution of L begins to dominate over the contribution of ordinary matter. The critical acceleration of the MOND model is replaced with the value of acceleration at which this occurs. In contrast to MOND, this acceleration is not a universal constant and depends on the mass of the visible part of the galaxy. TGD predicts a preferred plane for the galaxy and free motion in the direction of the cosmic string orthogonal to it. Also the absence of dark matter halo is predicted.
<LI> Concerning the formation of the tidal tails, the simplest TGD based model is very much the same as the MOND model except that one has 2-D logarithmic gravitational potential of string rather than modification of the ordinary 3-D gravitational potential of the galaxy. Therefore TGD allows a very similar model at qualitative level.
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One can however challenge the assumption that the mechanism is purely gravitational.
<OL>
<LI> The tidal tails tend to have a linear structure. Could they correspond to linear structures, long strings or tentacles extending towards the galactic nucleus? Could the formation of star clusters itself be a process, which is analogous to the formation of galaxies as a thickening of cosmic string leading to formation of a flux tube tangle?
<LI> Why more stars at the rear end rather than the frontal end of the moving star cluster? Could one have a phase transition transforming dark energy to matter proceeding along the cosmic L<sub>t</sub> string rather than a star cluster moving? Dark energy would burn to ordinary matter
and give rise to the star cluster.
<LI> The burning could proceed in both directions or in a single direction only. If the burning proceeds outwards from the galactic nucleus, the star formation is just beginning at the trailing end. In the leading end, the tangle formed by cosmic string has expanded and stretched due to the reduction of string tension. This could explain the asymmetry between trailing and leading ends at least partially.
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If the burning proceeds both outwards and inwards, only the MOND type explanation remains.
<LI> Second asymmetry is that the stars tend to leak out along the direction of motion. The gravitational field of the galaxy containing the logarithmic contribution explains this at least partially. Long cosmic string L<sub>t</sub> creates a transversal gravitational field and this could strengthen this tendency. The motion along L<sub>t</sub> is free so that the stars tend to leak out from the system along the direction of L<sub>t</sub>.
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See the chapter <a HREF= "https://tgdtheory.fi/pdfpool/astro.pdf">TGD and Astrophysics</A>.
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For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0