Tuesday, March 26, 2024

A simple TGD based model for a spiral galaxy

The origin of the spiral structure of spiral galaxies is one of the poorly understood problems of astrophysics. Independent motions of stars around galaxy in 1/r2 central force leads very rapidly to a loss of original structure since angular velocities behave like ω∝ 1/r2. 1/ρ central forces caused by cosmic string orthogonal to the galactic plane gives ω ∝ 1/ρ. This suggests that there exists some pre-existing spiral structure which is much denser than the surrounding matter. The formation of stars would occur intensely in these regions and the decay of the dark energy of the cosmic string to ordinary matter would also generate stars rotating around the galaxy as effectively free objects. The spiral structure rotates slowly and in a good approximation keeps in shape so that the structure behaves somewhat like a rigid body.

This view differs from the density wave theory (see this) assumes that this structure is dynamically generated and due to self-gravitation. The density wave would be analogous to a traffic jam. The cars entering the traffic jam slow down and the jam is preserved. It can move but with a much slower velocity than the cars. Density wave theory allows us to understand why star formation occurs intensely in the spiral structure with a high density.

TGD suggests that the structure corresponds to a cosmic string, which has thickened to a monopole flux tube and produced ordinary matter.

  1. One possibility is that the galaxy has formed in a topologically unavoidable collising of cosmic string (extremely thin 4-surfaces with 2-D M4 projection). The cosmic string orthogonal to the galactic plane would contain the dark en

    ergy liberated in its thickening and giving rise to part of galactic dark matter and the galactic blackhole would be associated with it. It would create a 1/ρ gravitational expansion explaining the flat velocity spectrum of distant stars. The cosmic string in the galactic plane would in the same way give rise to the galactic matter at the spiral arms and outside the central region. The galactic bar could correspond to a portion of this string.

  2. A simple model for the string world sheet assignable to the string in the galactic plane is as a minimal surface. In the first approximation, one can neglect the gravitational interaction with the second string and see whether it is possible to obtain a static string with a spiral structure with several branches and having a finite size. Th string carries monopole flux and should be closed and one can consider a shape which is flattened square like flux tube, which has changed its shape in the 1/ρ gravitational field of the long string (ω ∝ 1/ρ) and formed a folded structure. The differential rotation tends to lengthen the string and increase its energy. Hence one expects that string tension slows down differential rotation to almost rigid body rotation.
The simplest model is as a minimal stationary string world sheet.
  1. By introducing cylindrical Minkowski coordinates (m0, m1= ρ cos(φ),m2= ρ sin(φ),m3 ) and using (m0=t,φ) as coordinates also for the string world sheet, one can write that ansatz in the form ρ=ρ(t,φ). The metric of M4 in the cylindrical coordinates is mkl&rightleftarrow; (1,-1,-1,-ρ2). The induced metric of X2 in these coordinates has only diagonal components and can be written as

    (gtt=1-ρt2, gφφ=-ρ2φ2) .

  2. For a static ansatz one has ρ= ρ(φ) so that the field equation reduces to an ordinary differential equation for ρ. Rotational invariance allows us to solve the equation as a conservation law for the angular momentum component parallel to the normal of the galactic plane. For as general infinitesimal isometry with Lie algebra generator jAk the conservation of corresponding charge reads as

    α(gαβmkβmkljAl(-g21/2)=0 .

    The conservation laws of momentum and energy hold true and the conservation of angular momentum L3 in direction orthogonal to the galactic plane gives

    gφφρ2(-g2)1/2=1/ρ0 .

    where ρ0 is integration constant. This gives

    xφ= +/- x(1-x2)1/2 , x= ρ/ρ0 .

    From this it is clear that the solution is well-defined only for ρ≤ which suggests that the branches of the spiral must turn back at ρ=ρ0 (x=1).

  3. The differential equation can be solved explicitly: one has

    ∫ dx/(x(1-x2)1/2)= +/- φ +φ0 .

    The integration constant φ0 can be put to zero and the elementary integral using the substitution x= sin(u) gives

    φ= +/- ln[|cos(u)u-u2sin(u) +cot(u)|]

    = +/- ln[|arcsin(x) (1-x2)1/2-arcsin(x)2x +(1-x2)1/2/x|] .

Consider now the general properties of the solution.
  1. The value range of x is [0,1] so that the value ranges of arcsin(x) are [0,π] and its shifts by an integer multiple of 2π. This gives rise to a many-valuedness: arcsinn(x)= arcsin0(x)+ n2π.

    There is an additional double-valuedness due to the fact that one has sin(x+Δ)= sin(x) for Δ=0 and x+Δ = π/2+ arccos(x). At x=π/2 these two roots coincide as comes also clear by looking at the graph of arcsin(x) using the graph of sin(x) in the interval [0,π]. These two branches meet at x=1 which means that single branch turn back.

    In an ideal situation this predicts a spiral with an infinite number of branches labelled by integer n and each branch corresponds to a branch turning back at x=1. An infinitely folded closed cosmic string carrying monopole flux would be in question. The number of branches is for physical reasons finite since otherwise the turning points at the circle x=1 would fill the circle densely.

  2. At the limit x→ 0 (center of the galaxy) the term cot(x) becomes infinite and dominates for finite values of n so that exp(φ) approaches infinity meaning that the the spiral for given n has infinitely many branches near origin and meeting at it. The density of matter becomes very high near the origin. This kind of structure could result in a differential rotation of a string around the cosmic string orthogonal to the galactic plane with angular velocity ω ∝ 1/ρ.

  3. One can look at the situation also at x=1. Here the equation for a given branch turning back at φ=φn reads as

    π/2 - n(n+1/2)4π2= exp(φn) .

    The turning points for branches fill the circles x=1. Of course, only a finite number of branches is physically possible and should correspond to the number of observed branches.

See article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

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

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

Saturday, March 23, 2024

Ionosphere as an analog of neuronal membrane: two new miraculous numerical coincidences

Electric quantum coherence can be considered also in astrophysical scales. Ionosphere, identified the ionized part of the atmosphere, is of a special interest since it corresponds to the electric field in the Earth scale: see the Feynman lectures. Ionization is caused by solar radiation. Also other planets are believed to possess an ionosphere.

Assuming that the surface of Earth and ionosphere define a system analogous to capacitor plates or cell membrane, the ionosphere must have a net positive charge assignable to positive ions. In the article a model for lightning and ball lightning based on the idea that thunderstorms are analogous to nerve pulse patterns for which Pollack effect provides a model (see this), was developed.

  1. The strength of the electric field at the negatively charged surface of Earth E is E=.1-.3 x kV/m, x∈ [.1,.3]. The presence of biological protrusions such as trees can increase the local value of the electric field of Earth by an order of magnitude. The counterpart of the positively charged plate corresponds to the ionosphere, whose lower boundary is at the height h, which varies in the range [80,600] km. The net positive charge of the ionosphere neutralizes the negative charge of the Earth so that the electric field does not extend to higher heights.
  2. The first guess for the electric Compton length is obtained by generalizing the notion of gravitational coupling constant to the electric case as ℏem= Qe/β0, where Q is the total charge of the Earth and the value of β0 could be taken the same as in the gravitational case and β0=1 for Earth and other planets and and β0≈ 2-11 for Sun.
  3. The basic question is whether the entire ionosphere acts as a quantum coherent system or whether electric flux tubes possess electric quantum coherence. The intuitive idea is that the quantum coherence scale in the case of the ionosphere regarded as a capacitor-like system should not be longer than the thickness of the ionosphere varying in the range 60-100 km. The radius d of the electric flux tube is a good first guess for the electric Compton length. Lightnings are analogs of nerve pulses and characterized by a scale of 10-20 km and is a good guess for the quantum coherence length.

    This suggests that the electric Compton for a particle with mass m should be defined as

    Λem(d) = hem/m= (Q(d)e/β0ℏ) × λ ,

    Q(d)= ε0 Eπ d2 ,

    where Q(d)=ε0EEπ d2 is the electric flux associated with the electric flux tube and λ is the Compton length of a charged particle, say electron, electron Cooper pair or proton. The proposal is that it satisfies the consistency condition

    Λem(d) =d .

To get some perspective and to test the idea it is useful to consider capacitors. In this case Λem(d)=d should be smaller than the distance between the capatitor plates.

  1. Aluminium capacitors can have a maximum charge of about Q=103 C whereas the maximal charge of a van de Graaff generator is about .14 C. If one assumes d=Λem(d), dC is obtained by scaling as dC/dE= EE/EC . If the capacitor corresponds to a sphere of D=1 mm with charge Q= 103C, the electric field is EC= Q/4πε0D2 at the surface of capacitor and gives for D= 1 m dC= (EE/EC)dE ≈ 10-8 m for EE= 102 V/m.
  2. For a capacitor with capacitance of 1 μF and at voltage 1 V, the charge would be 1 μ C. For β0=1 would have the upper bound Λem,pgr≈ 2.9× 10-3 so that one would have Λem,p ≈ 1.5 × 10-5 m. This gives upper bound for the value of Λem,p since the parameter d must correspond to a solid angle smaller than 4π. Could electronic systems be intelligent and conscious at least on this scale?
The study of the conditions for neuronal axons and DNA strand reveals two numerical miracles.
  1. Neuronal axon is also a capacitor-like system and it is interesting to check what the criterion Λem(d)=d gives in this case. The natural guess for d as quantum coherence length is as the length of the axon idealized as a cylindrical capacitor. Using Q= E× 2π R d and the condition Q(d)e/β0= d one finds that the conditions does not depend on d at all so that it allows all lengths for axons, which is a very nice result from the point of neuroscience.

    The condition however fixes the Compton length of the particle considered. Are there any chances of satisfying this condition for protons or electrons? The condition reads as

    E× 2π Rε0 × (C/e) 4πα = 1/λ .

    Here R is the radius of the axon taken to be R=1 μm. Using E= V/D, where D≈ 10 nm is the thickness of the neuronal membrane and assuming V=.05 V, one obtains E= 5× 106 V/m.

    For β0=1, the estimate for Λe is in a good approximation Λe= 10-12 m to be compared with the actual value Λe=2.4× 10-12 m. The equation d= Λem(d) is fixed apart from a numerical factor of order 1 so that the proposal seems to make sense.

    If one assumes that Cooper pairs of electrons are the charged particles, one obtains Λ2e=1.2× 10-12 m. If one scales down D with a factor 1/2 to 5 nm, one obtains Λe=1.2× 10-12 m, which could be true in absence of superconductivity. The thickness of the cell membrane indeed varies in these limits and is larger for neuronal membranes. One can wonder whether the dynamics is such that the quantity ER stays constant so that the condition remains true.

  2. One can perform the same estimate for DNA strand having the 3 nucleotides per nanometer carrying unit charge. The condition Λem(Qe)ℏΛ/β0= (dn/dl) α× 4π(d/beta0)=d gives

    Λ= (dn/dl)×β0/4πα .

    The condition is satisfied for electron if one assumes β0≈ 2-11: one obtains Λ= 1.5× 10-12 m to be compared with the actual value Λe= 2.42 × 10-12 m. The Compton length for a Cooper pair would be 1 Λ2e= 1.21 × 10-12 m.

These number theoretical miracles mean totally unexpected connections between biochemistry and particle physics and probably myriads of similar connections remain be discovered.

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

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

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

TGD based quantum explanation for the weird properties of Sagittarius A.

Sabine Hosssenfelder tells about the weird properties of the giant blackhole at the center of Milky Way known as Sagittarius A* (briefly SA): see this. SA is located at a distance of 26,700 ly and has mass about 4.1× 1010 solar masses. Its Schwartschild radius rs= 2GM is 1.1× 1011 km. Note that astronomical unit (the distance of the Earth from the Sun) 1.49597870700× 108 km so that SA radius is almost 1000AU. The Schwartschild time Ts= rs/c is 41 s, about 2/3 minutes.

Hossenfelder lists six weird properties of SA.

  1. SA is silent, one might say dead suggesting that no matter is falling inside it. There is however an accretion disk around it.
  2. SA however shows signs of life by emitting periodically X ray flares bursting huge amounts of energy as a radiation. Blackhole should not do this unless it absorbs matter but it is not at all clear whether anything is going inside SA!
  3. SA is rotating extremely rapidly: the period τ of rotation is 10 minutes.
  4. SA possesses a dozen of planet-like objects, so called G-objects, rotating around SA with a velocity which is 60 percent of the maximal rotation velocity allowed by the condition that the rotation velocity inside the blackhole does not exceed the light velocity. How these objects can exist in an extremely hostile environment of the blackhole where the matter from outside should be flowing to the blackhole is a mystery.
  5. There is a blob of matter rotating around SA with a velocity, which is 30 percent of the velocity of light. The object periodically emits ray bursts, which might relate to the mystery of gamma ray bursts.
Could one understand these properties of SA by regarding SA as a blackhole-like object in the TGD sense consisting of a maximally dense flux tube spaghetti which is a quantum system with gravitational Planck constant ℏgr=GM/β0? Could one model SA as a quantum harmonic oscillator in the interior and using gravitational Coulomb potential in the exterior?

The reason for why matter is not falling inside SA could be the same as in the case of the hydrogen atom. Quantization would imply that the atom is a quantum system and does not dissipate so that the infrared catastrophe is avoided. Matter around it is at Bohr orbits of a central potential. The first guess would be Coulomb potential but also harmonic oscillator potential or something between these two could be considered.

  1. The quantization of angular momentum gives for a central potential and circular orbits r2ω= nGM/β0. The condition v2/r=ω2r= -d(GM(r)/r) holds true also for a central force. Recall that for the harmonic oscillator this gives ω=1/rs (c=1)and rn= n1/2r1, r1= rs/(2β0)1/2. The constancy of ω means that the system behaves like a rigid body. Note that one has n>0. Note that there is also an S-wave state, which corresponds to n=0 and can be described only by Schrödinger equations or its analog.
  2. For the Coulomb case one obtains ω=2/n3rs and rn= n2agr, agr= rs/2β02. In the interior, r1 ≤ rs requires β0≥ 1/2. In the exterior, agr≥ rs requires β0≤ 21/2 and r1≥ rs. This condition is not however absolutely necessary since the n>1 follows from the condition that the orbital velocity is smaller than c, as will be found. The conditions therefore fix β0 to the range [1/21/2,1/2,1]. The quantization β0=1/n would select β0∈{1/2,1} giving r1= (1,1/21/2)rs for the harmonic oscillator potential and rn∈ {2,1/2}n2rs outside the blackhole.
  3. Orbital velocities are given by vn= 2/nβ02 and vn<c requires n>2/β02, which is true for n> (2,4,8) for β0∈ {1,1/21/2,1/2}. The lowest allowed orbitals have radii (r3=9rs/2,r5= 25rs, r9=162rs).
  4. The inner radius of the accretion disk for which one can find the estimate rinner =30rs (see this). Inside the accretion disk, the harmonic oscillator model could be more appropriate than the Coulomb model. The inner edge of the accretion disk would correspond to (r8=32rs,r6= 36rs, r8=128rs) for β0∈ {1,1/21/2,1/2}. For β0=1/2 the prediction for the radius of the inner edge would be too large and also the prediction for β0=1/21/2 is somewhat too high.
Could one understand the findings about SA in this picture?
  1. The silence of SA would be completely analogous to the quantum silence of atoms. Furthermore, v<c condition would pose strong classical conditions on the allowed orbitals.
  2. The periodically occurring X-ray flares could be analogs of atomic transitions leading to the emission of photons. They could due to the internal excitations of the matter from lower to higher energy state. For β0=1 one has a maximal number of the harmonic oscillator states corresponding to the principal quantum number n=0,1,2 and the n=2 state would correspond to the horizon. Also transition to states which could be modelled as states in Coulomb potential are possible. n=3 Coulomb orbital would be the first allowed state β0=1. The prediction is that the total X-ray energy is quantized.
  3. Could one understand the rotation of SA in terms of the harmonic oscillator model predicting ω= 1/rs giving τ= 2π/rs. The estimated mass of the black hole gives τ= 4.2 minutes. Is the mass estimate for the blackhole too small by a factor of .42 or does the harmonic oscillator model fail?
  4. G-objects could be understood as gravitational analogs of the atomic electrons orbiting SA at radii with small values of n. The orbital radii are predicted to be proportional to n2. The allowed orbitals would correspond to {3≤ n≤ 8, n=5} for β0∈ {1,1/21/2} .
  5. The mysterious blob of matter rotating around SA with velocity v=3c/10 could correspond to a Coulombic Bohr orbit with a small value of n: n=6 orbit gives this value of the velocity for β0=1. For the other options the orbit would belong to the accretion disk.
To sum up, the β0=1 option is selected uniquely by the weird properties of SA.

See the article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

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

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

Tuesday, March 19, 2024

Updated view about the rice experiments of Masaru Emoto

Masaru Emoto has carried to extremely interesting experiments with water at critical point against freezing. Emoto reports is that words expressing emotions are transmitted to water: the expression of positive emotions tend to generate beautiful crystal structures and negative emotions ugly ones. Also music and even pictures are claimed to have similar effects. Emoto has also carried out similar experiments with rice in water at physiological temperature. Rice subjected to words began to ferment and water subject to words expressing negative emotions began to rotten.

I have already earlier discussed a model for the findings of Emoto. In this article I update the model. I will also ask new questions. How emotions are communicated at the fundamental level and how a conscious entity can perceive the emotional state of another conscious entity and possibly affect it? What does emotional intelligence mean? How could one assign a measure of conscious emotional information to the emotional state? How certain sounds or gestures with emotional contents or even pictures can induce emotional response at the fundamenal DNA level?

See the article Updated view about the rice experiments of Masaru Emoto or the chapter Emotions as sensory percepts about the state of magnetic body?.

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

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

Sunday, March 17, 2024

Homomorphic encryption as an elegant manner to save privacy

Sabine Hossenfelder talked about homomorphic encryption, which is an elegant and extremely general algebraic manner to guarantee data privacy (see this). The idea is that the encryption respects the algebraic operations: sums go to sums and products go to products. The processing can be done for the encrypted data without decryption. The outcome is then communicated to the user and decrypted only at this stage. This saves a huge amount of time.

What comes first in mind is Boolean algebra (see this). In this case the homomorphism is truth preserving. The Boolean statement formed as a Boolean algebra element is mapped to the same statement but with images of the statements replacing the original statements. In the set theoretic realization of Boolean algebra this means that unions are mapped to unions and intersections to intersections. In Boolean algebra, the elements are representable as bit sequences and sum and product are done element-wise: one has x2=1 and x+x=0. Ordinary computations can be done by representing integers as bit sequences.

In any computation one must perform a cutoff and the use of finite fields is the neat way to do it. Frobenius homomorphism x→xp in a field of characteristic p maps products to products and, what is non-trivial, also sums to sums since one has (x+y)p= xp+yp. For finite fields F_p the Frobenius homomorphism is trivial but for Fpe, e>1, this is not the case. The inverse is in this case x→x pe-1. These finite fields are induced by algebraic extensions of rational numbers. e corresponds to the dimension of the extension induced by the roots of a polynomial

Frobenius homomorphism extends also to the algebraic extensions of p-adic number fields induced by the extensions of rationals. This would make it possible to perform calculations in extensions and only at the end to perform the approximation replaces the algebraic numbers defining the basis for the extension with rationals. To guess the encryption one must guess the prime that is used and the use of large primes and extensions of p-adic numbers induced by large extensions of rationals could keep the secrecy.

p-Adic number fields are highly suggestive as a computational tool as became clear in p-adic thermodynamics used to calculate elementary particle masses: for p= M127= 2127-1 assignable to electron, the two lowest orders give practically exact result since the higher order corrections are of order 10-76. For p-adic number fields with very large prime p the approximation of p-adic integers as a finite field becomes possible and Frobenius homomorphism could be used. This supports the idea that p-adic physics is ideal for the description of cognition.

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

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

Saturday, March 16, 2024

Direct evidence for the TGD view of quasars

In a new paper in The Astrophysical Journal (see this), JILA Fellow Jason Dexter, graduate student Kirk Long, and other collaborators compared two main theoretical models for emission data for a specific quasar, 3C 273. The title of the popular article is "Unlocking the Quasar Code: Revolutionary Insights From 3C 273".

If the quasar were a blackhole, one would expect two emission peaks. If the galactic disk is at constant temperature, one would expected redshifted emission peak from it. The second peak would come from the matter falling to the blackhole and it would be blueshifted relative to the first peak. Only single peak was observed. Somehow the falling of the matter is prevented to the quasar is prevented. Could the quasar look like a blackhole-like object in its exterior but emit radiation and matter preventing the falling of the matter to it.

This supports the TGD view of quasars as blackhole-like objects are associated with cosmic strings thickened locally to flux tube tangles (see this, this, this and this). The transformation of pieces of cosmic strings to monopole flux tube tangles would liberate the energy characterized by the string tension as ordinary matter and radiation. This process would be the TGD analog of the decay of inflaton field to matter. The gravitational attraction would lead to the formation of the accretion disk but the matter would not fall down to the quasar.

See the article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

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

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

Friday, March 15, 2024

Magnetite produced by traffic as a possible cause of Alzheimer disease

A rather unexpected partial explanation for Alzheimer's disease has been found: magnetite particles, which can be found in urban environments from exhaust gases containing breathing air (see this). I have written earlier about Alzheimer's disease from the TGD point of view (see this). Magnetite particles seem to be found in the hippocampus of those with the disease, which is central to memory. Now it has been found that the exposure of mice to magnetite leads to a generation of Alzheimer disease. The overall important message to the decision makers is that the pollution caused by the traffic in urban environment could be an important cause of Alzheimer disease.

The brain needs metabolic energy. Hemoglobin is central to the supply of metabolic energy because it binds oxygen. Could it be thought that Alzheimer's is at least partially related to a lack of metabolic energy in the hippocampus? In the sequel I will consider this explanation in the TGD framework.

Short digression to TGD view of metabolism

Oxygen molecules O2 bind to iron atoms in hemoglobin (see this) that already have a valence bond with 5 nitrogen atoms and a bond is created where Fe has received 5 electrons and a sixth from oxygen molecule O2. So Fe behaves the opposite of what you would expect and hemoglobin is very unusual chemically!

Phosphate O=PO3, or more precisely phosphate ion O=P(O-)3), which also plays a central role in metabolism, also breaks the rules: instead of accepting 3 valence electrons, it gives up 5 electrons to oxygen atoms.

Could the TGD view of quantum biology help to understand what is involved. Dark protons created by the Pollack effect provide a basic control tool of quantum biochemistry in TGD. Could they be involved now. Consider first the so-called high energy phosphate bond, which is one of the mysteries of biochemistry.

  1. Why the electrons in the valence bonds prefer to be close to P in the phosphate ion? For phosphate one would expect just the opposite. The negative charge of 3 oxygens could explain why electrons tend to be nearer to P.
  2. The TGD based view of metabolism allows to consider a new physics explanation in which O=P(O-)3 is actually a "dark" variant of neutral O=P(OH)3 in which 3 protons of OH have become dark (in the TGD sense) by Pollack effect, which has kicked 3 protons to monopole flux tubes of the gravitational magnetic body of phosphate to such a large distance that the resulting dark OH looks like OH-, that is negatively charged. Charge separation between the biological body and magnetic body would have occurred. This requires metabolic energy basically provided by the solar radiation. One could see the dark phosphate as a temporary metabolic energy storage and the energy would be liberated when ATP transforms to ADP.
Could this kind of model apply also to the Fe binding with 5 N atoms in haemoglobin by valence bonds such that, contrary to naive expectations, electrons tend to be closer to Fe than N atoms? Can one imagine a mechanism giving an effective negative charge to the N atoms or the heme protein and to O-O?
  1. In this case there are no protons as in the case of phosphate ions. The water environment however contains protons and pH as a negative logarithm of the proton concentration measures their concentration. pH=7 corresponds to pure water in which H+ and OH- concentrations are the same. The hint comes from the fact that small pH, which corresponds to a high proton concentration, is known to be favourable for the binding of oxygen to the heme group.
  2. Could dark protons be involved and what is the relationship between dark proton fraction and pH? Could pH measure the concentration of dark protons as I have asked?
  3. Could the transformation of ordinary protons to dark protons at the gravitational MB of the heme protein induce a negative charge due to OH- ions associated with the heme protein and could this favour the transfer of electrons towards Fe? Could the second O of O-O form a hydrogen bond with H such that the proton of the hydrogen bond becomes dark and makes O effectively negatively charged?

What the effect of magnetite could be?

Magnetite particles, .5 micrometers in size, consist of Fe3O4 molecules containing iron and oxygen. According to Wikipedia, magnetite appears as crystals and obeys the chemical formula Fe2+(Fe3+)2(O-2)4. The electronic configuration is [Ar] 3d6 4s2 and 3 Fe ions have donated besides the s electrons also one electron to oxygen.

Could it happen that somehow the oxygen absorption capacity of hemoglobin would decrease, that the amount of hemoglobin would decrease, or that oxygen would bind to the magnetite molecules on the surface of the magnetite particle? For example, could you think that some of the O2 molecules bind to Fe3O4 molecules instead of hemoglobin at the surface of the magnetite. Carbon monoxide is dangerous because it binds to the heme. Could it be that also the magnetite crystals do the same or rather could heme bind to them (thanks for Shamoon Ahmed for proposing this more reasonable looking option).

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

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

Wednesday, March 13, 2024

About the problem of two Hubble constants

The usual formulation of the problem of two Hubble constants is that the value of the Hubble constant seems to be increasing with time. There is no convincing explanation for this. But is this the correct way to formulate the problem? In the TGD framework one can start from the following ideas discussed already earlier (see this).
  1. Would it be better to say that the measurements in short scales give slightly larger results for H0 than those in long scales? Scale does not appear as a fundamental notion neither in general relativity nor in the standard model. The notion of fractal relies on the notion but has not found the way to fundamental physics. Suppose that the notion of scale is accepted: could one say that Hubble constant does not change with time but is length scale dependent. The number theoretic vision of TGD brings brings in two length scale hierarchies: p-adic length scales Lp and dark length scale hierarchies Lp(dark)=nLp, where one has heff=nh0 of effective Planck constants with n defining the dimension of an extension of rationals. These hierarchies are closely related since p corresponds to a ramified prime (most naturally the largest one) for a polynomial defining an extension with dimension n.
  2. I have already earlier considered the possibility that the measurements in our local neighborhood (short scales) give rise to a slightly larger Hubble constant? Is our galactic environment somehow special?
Consider first the length scale hierarchies.
  1. The geometric view of TGD replaces Einsteinian space-times with 4-surfaces in H=M4\times CP2. Space-time decomposes to space-time sheets and closed monopole flux tubes connecting distant regions and radiation arrives along these. The radiation would arrive from distant regions along long closed monopole flux tubes, whose length scale is LH. They have thickness d and length LH. d is the geometric mean d=(lPLH)1/2 of Planck length LP and length LH. d is of about 10-4 meters and size scale of a large neuron. It is somewhat surprising that biology and cosmology seem to meet each other.
  2. The number theoretic view of TGD is dual to the geometric view and predicts a hierarchy of primary p-adic length scales Lp ∝ p1/2 and secondary p-adic length scales L2,p =p1/2Lp. p-Adic length scale hypothesis states that p-adic length scales Lp correspond to primes near the power of 2: p ≈ 2k. p-adic primes p correspond to so-called ramified primes for a polynomial defining some extension of rationals via its roots.

    One can also identify dark p-adic length scales

    Lp(dark) =nLp ,

    where n=heff/h0 corresponds to a dimension of extension of rationals serving as a measure for evolutionary level. heff labels the phases of ordinary matter behaving like dark matter explain the missing baryonic matter (galactic dark matter corresponds to the dark energy assignable to monopole flux tubes).

  3. p-Adic length scales would characterize the size scales of the space-time sheets. The Hubble constant H0 has dimensions of the inverse of length so that the inverse of the Hubble constant LH∝ 1/H0 characterizes the size of the horizon as a cosmic scale. One can define entire hierarchy of analogs of LH assignable to space-time sheets of various sizes but this does not solve the problem since one has H0 ∝ 1/Lp and varies very fast with the p-adic scale coming as a power of 2 if p-adic length scale hypothesis is assumed. Something else is involved.
One can also try to understand also the possible local variation of H0 by starting from the TGD analog of inflation theory. In inflation theory temperature fluctuations of CMB are essential.
  1. The average value of heff is < heff>=h but there are fluctuations of heff and quantum biology relies on very large but very rare fluctuations of heff. Fluctuations are local and one has <Lp(dark)> = <heff/h0> Lp. This average value can vary. In particular, this is the case for the p-adic length scale Lp,2 (Lp,2(dark)=nL2,p), which defining Hubble length LH and H0 for the first (second) option.
  2. Critical mass density is given by 3H02/8πG. The critical mass density is slightly larger in the local environment or in short scales. As already found, for the first option the fluctuations of the critical mass density are proportional to δ n/n and for the second option to -δ n/n. For the first (second) option the experimentally determined Hubble constant increases when n increases (decreases). The typical fluctuation would be δ heff/h ∼ 10-5. What is remarkable is that it is correctly predicted if the integer n decomposes to a product n1=n2 of nearly identical or identical integers.

    For the first option, the fluctuation δ heff/heff=δn/n in our local environment would be positive and considerably larger than on the average, of order 10-2 rather than 10-5. heff measures the number theoretic evolutionary level of the system, which suggests that the larger value of <heff> could reflect the higher evolutionary level of our local environment. For the second option the variation would correspond to δn/n≤ 0 implying lower level of evolution and does not look flattering from the human perspective. Does this allow us to say that this option is implausible?

    The fluctuation of heff around h would mean that the quantum mechanical energy scales of various systems determined by <heff>=h vary slightly in cosmological scales. Could the reduction of the energy scales due to smaller value of heff for systems at very long distance be distinguished from the reduction caused by the redshift. Since the transition energies depend on powers of Planck constant in a state dependent manner, the redshifts for the same cosmic distance would be apparently different. Could this be tested? Could the variation of heff be visible in the transition energies associated with the cold spot?

  3. The large fluctuation in the local neighbourhood also implies a large fluctuation of the temperature of the cosmic microwave background: one should have δT/T ≈ δn/n≈ δ H0/H0. Could one test this proposal?
See the article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

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

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

Herbig Haro objects from the TGD point of view

The Youtube posting "The James Webb Space Telescope Has Just Made an Incredible Discovery about Our Sun! Birth of Sun"!" (see this) tells about Herbit Haro object HH211 located at a distance 1000 light years about which JWQST has provides a picture (I hope that the sensationalistic tone of the title does not irritate too much: it seems that we must learn to tolerate this style).

Herbig Haro luminous objects are associated with very young stars, protostars. Typically they involve a pair of opposite jets containing streams of matter flowing with a very high speed of several hundred km/s. The jets interact with the surrounding matter and generate luminous regions. HH211 was the object studied by JWT. The jets were found to contain CO, SiO, H2.

Herbig Haro objects provide information about the very early states of star formation. As a matter of fact, the protostar stage still remains rather mysterious since the study of these objects is very challenging already because their distances are so large. The standard wisdom is that stars are born, evolve and explode as supernovae and that the remnants of supernovae provide the material for future stars so that the portion of heavy elements in their nuclei should gradually increase. The finding that the abundances of elements seem to depend only weakly on cosmic time seems to be in conflict with these findings and forces us to ask whether the vision about the protostars should be modified. Also JWT found that the galaxies in the very young Universe can look like the Milky Way and could have element abundances of recent galaxies which challenges this belief.

The association of the jets to Herbig Haro objects conforms with the idea that cosmic strings or monopole flux tubes formed from them are involved with the formation of a star. One can consider two options for how the star formation proceeds in the TGD Universe.

  1. The seed for the star formation comes from the transformation of dark energy associated with the cosmic string or monopole flux tube to ordinary matter (it could also correspond to a large heff phase and behave like dark matter and. explain the missing baryonic matter). By the conservation of the magnetic flux the magnetic energy density per unit length of the monopole flux tube behaves like 1/S and decreases rapidly with its transversal area. The volume energy density increases like area but its growth is compensated by the phase transition reducing the value of the analog of cosmological constant Λ so that on the average this contribution behaves as a function of the p-adic length scale. In the same way as magnetic energy per unit length. The energy liberated from the process is however rather small except for almost cosmic strings and this process might apply only to the formation of first generation stars.
  2. The second option is that the process is analogous to "cold fusion" interpreted in the TGD framework as dark fusion (see this, this and this) in which ordinary matter, say protons and perhaps even heavier nuclei, are transformed to dark protons at the monopole flux tubes having much larger Compton length (proportional to heff) that ordinary protons or nuclei. If the nuclear binding energy scales like 1/heff for dark nuclei nuclear potential wall, is rather low and the dark fusion can take place at rather low temperatures. The dark nuclei would then transform to ordinary nuclei and liberate almost all of their ordinary nuclear binding energy, which would lead to a heating which would eventually ignite the ordinary nuclear fusion at the stellar core. Heavier nuclei could be formed already at this stage rather than in supernova explosions. This kind of process could occur also at the planetary level and produce heavier elements outside the stellar cores.

    This process in general requires energy feed to increase the value of heff. In living matter the Pollack effect would transform ordinary protons to dark protons. The energy could come from solar radiation or from the formation of molecules, whose binding energy would be used to increase heff (see this). This process could lead to the formation of molecules observed also in the jets from HH211. Of course, also the gravitational binding energy liberated as the matter condenses around the seed liberates and could be used to generate dark nuclei. This would also raise the temperature helping to initiate dark fusion. The presence of the dark fusion and the generation of heavy elements already at this stage distinguishes between this view and the standard picture.

    The flux tube needed in the process would correspond to a long thickened monopole flux tube parallel to the rotation axis of the emerging star. Stars would be connected to networks by these flux tubes forming quantum coherent structures (see this). This would explain the correlations between very distant stars difficult to understand in the standard astrophysics. The jets of the Herbig Haro object parallel to the rotation axis would reveal the presence of these flux tubes. The translational motion of matter along a helical flux tube would generate angular momentum. They would make possible the transfer of the surplus angular momentum, which would otherwise make the protostar unstable. By angular momentum conservation, the gain of the angular momentum by the protostar could involve generation of opposite angular momentum assignable to the dark monopole flux tubes.

See the article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

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

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