Tuesday, April 19, 2022

Gravitational fields of Earth and Sun and metabolism

The notion of magnetic body (MB) is central in the TGD inspired quantum biology. There are MBs assignable to electromagnetic and gravitational interactions and even color and electroweak interactions. A considerable progress in the understanding of the role of gravitational MB in metabolism has occurred and I hope that the following summary is reasonably near to the "final" one.

Gravitational magnetic body as a controlling agent and the prediction of two metabolic energy quanta

In the TGD framework magnetic body (MB) would serve as the controlling agent receiving sensory information as a frequency modulated dark Josephson radiation and controlling the cell by using dark cyclotron radiation coming as pulses corresponding to resonant receival of Josephson radiation.

The large value of heff=hgr=GMm/v0 (see this) implies that the dark cyclotron radiation in the EEG range would correspond to visible and UV energies.

The intuitive notion is that MB consists of U-shaped monopole flux tubes extending from the system considered and serving as kinds of tentacles. These flux tubes for two systems can reconnectand form a pair of flux tubes connecting the system if the cyclotron frequencies of the tubes are the same so that cyclotron resonance becomes possible.

In (see this), the question of what the notion of gravitational MB does mean, was considered.

  1. The dark flux tube would be gravitational with heff=hgr. Gravitational flux tubes have lengths, which can be of the order of Earth size scale and the radii of gravitational Bohr orbits define a natural scale form them.
  2. The elongated gravitational flux tubes could correspond to either hydrogen bonds (HBs) or valence bonds (VBs). The loop-like bond could connect nearby atoms just like the ordinary bond. The delocalization of the charge to the flux tube leads to an effectively ionized donor atom.
  3. All values of heff are possible. For electromagnetic flux tubes the values of heff/h are not very large. This picture leads to a view about hydrogen and VBs as bonds having heff/h>1 (see this). Also gravitational variants of hydrogen and VBs are possible. In this case, the proton or electron would be vertically delocalized in the Earth scale so that the donor atom would be effectively ionized. For instance, a phosphate ion could be an effective ion having a gravitational hydrogen bond with the hydrogen of a water molecule.
  4. A gravitational valence bond, connecting a metal atom with an atom with an opposite valence, would lead to effective ionization of the metal atom. For instance, biologically important bosonic ions such as Ca++, Mg++, Fe++ and Zn++ associated with their oxides could correspond to effective ions like this.

    The signature would be a pairing with a neutral oxygen atom by a gravitational valence bond. I have introduced the notion of dark ion to explain the findings of Blackman and others and dark ion could correspond to this kind of pair. Note that the original variant of the model assumed that the entire ion is dark, the later version assumed that the valence electron of free atom is dark, and the model considered here assumes that darkness is a property of bond.

  5. The effective ionization requires energy Δ E to compensate the increment of the gravitational potential energy given by Δ Egr=(≤ Vgr(R)> -Vgr(RE)). Here Egr(R) is gravitational potential energy proton or electron, and RE denotes the radius of Earth, and R is the distance of the point of flux tube from the center of Earth.

    Classical energy conservation suggests that the value of vertical kinetic energy at the surface of Earth is equal to the increment of the gravitational potential energy at the top of the loop. From energy conservation one can estimate the metabolic energy quantum as a liberated kinetic energy in the normal direction equal to the increase of gravitational potential energy. Hence the naive guess could be correct.

  6. The maximal value for Δ Emax for electron Cooper pair (dark Cooper pair is at infinite distance) corresponds to Vgr(RE)= .36 meV to be compared with the energy scale .3 meV defined by the temperature of 3 K microwave background and to the value .4 meV of the miniature potential. This suggests that, in the case of the electron, the reduction of kinetic energy contributes more than 10 per cent to the Δ E.

    For a single dark proton one has Vgr(RE)≈ .34 eV, which is below the nominal value of the metabolic energy currency about .5 eV.

  7. The condition that the end of the vertical gravitational loop travels along a stationary orbit parallel to the plane of rotation of Earth such that the normal velocity of the dark particle vanishes at the top, implies for the tangential velocity vT the condition v2T2R2= GM/R allowing to determine the radius of the orbit as

    R/RE=(rs,Ec2/2ω2)1/3× 1/RE ≈ 3.1 .

    The change of the gravitational potential energy in the transition to an ordinary proton would be Δ E= Δ Egr=.68× Vgr(RE), which would give Δ E=.18 eV. In the dark genetic codons hydrogen bonds appear as triplets. 3 dark protons would give metabolic energy quantum .55 eV. Interestingly, a translocation of 3 protons fuels synthesis of ATP!

  8. For an electron Cooper pair the upper bound for the metabolic energy quantum would be Δ Emax= .33 meV, which is below the miniature potential .4 meV. For the stationary flux tubes one obtains Δ E= .17 meV. Later the evidence for the 'spikes' in fungi (see this) discovered by Adamatsky will be discussed: their amplitude is reported to be in the range .03-2.1 meV which contains Δ E.

    For an electron Cooper pair triplet one would have Δ E= .51 meV consistent with the miniature potential .4 meV. Should one take this seriously? Could also dark electron Cooper pairs organize into triplets like dark protons would do and in this manner define dark genetic code? TGD predicts that genetic code is universal: could also dark electron Cooper pairs define a dark variant of the genetic code?

    Posner molecules [(PO4)-3)]6Ca+29, to be discussed in the sequel, consists of 3 [(PO4)-3)]2Ca+23 acting as a basic unit. This unit could contain 3 electronic Cooper pairs with electronic metabolic energy quantum Δ E= .51 meV. In principle, Cooper pairs can have spin 1 or spin state giving 4 states altogether. Could these states define letters of a dark genetic codon so that the basic unit would define a genetic codon and Posner molecule could correspond to a triplet of genetic codons?

    The TGD view about formation of bound states as Galois singlets (see this) allows us to consider this possibility. For an extension of extensions of ... the Galois group would decompose to a hierarchy of Galois groups actings as normal subgroups. Codons as triplets would be Z3 singlets in both the ordinary and the electronic genetic code. Genes would correspond to larger Galois groups decomposing to normal subgroups. Codon doublets of DNA double strands would be Z2 singlets and triplets of triplets of Posner molecules would be Z3 singlets.

  9. A proper treatment of the situation would require Schrödinger equation for the dark particle at the flux loop. The situation is analogous to a quantum model of the fountain effect of super-fluidity discussed in (see this) in a situation when the gravitational potential can be linearized (WKB approximation).

    One can consider Schödinger equation for hgr idealizing the loop with a 1-D box with gravitational potential GMm/r. The Schrödinger equation reduces in dimensionless variable u= (m/ℏgr)z=2β0 (z/rs), rs= 2GM to

    (-∂u2/2 -β0/u)Ψ= (E/m)Ψ== ε Ψ .

    A possible condition is that the vertical derivative ∂zΨ vanishes at the top of the loop. The metabolic energy quantum equals (GM/RE- ε(v))m and is quantized. The height of the loop could be quantized using the condition that the loop end is stationary with respect to Earth.

If this speculative picture makes sense, quantum gravitation would play a key role in metabolism and genetic code.
  1. The transformation of electrons and protons between ordinary and gravitationally dark states would be a key process of metabolism and biocatalysis. This conforms with the fact that proton and electron exchanges play a key role in biology. For instance, phosphorylation means that the receiving molecule gains phosphate, which can form gravitationally a dark hydrogen bond so that the system becomes metabolically active. This would correspond to the activation in bio-catalysis.
  2. In the same way, in a redox reaction, the electron donor is oxidized and the electron receiver is reduced. Reduced molecule gains the ability to have a gravitationally dark electron, and therefore becomes metabolically active in the electronic sense. Redox reaction would be the electronic counterpart for phosphorylation.
The role of solar gravitational field in metabolism

Also the gravitational field of the Sun could be important in metabolism.

  1. At the distance of 1 AU of the Earth, the counterpart of single proton metabolic energy quantum .18 eV would be 2.6 eV, which is in the visible range. For a proton triplet, the energy would be 7.8 eV and in the UV range. This quantum would be realized as a long flux tube directed away from the Sun in the plane of the Earth's orbit and orthogonal to the orbit.
  2. Could the visible solar radiation kick protons to solar gravitational flux tubes and the radiation of photosphere having energy range [.4,.6] eV to the gravitational flux tubes of Earth in photosynthesis? Could the solar part of dark gravitational energy for protons be transformed to ordinary metabolic quanta in metabolism? Note that the feed of the solar radiation energy to flux tubes suggests a modification of the proposed simple model involving only gravitation.
  3. This picture would be true for all Sun-like stars and for planets at the distance of Earth and supports the view that Earth-like planets for Sun-like stars are favourable for life.
Metabolic energy depends on gravitational environment

According to the proposed simple model, bio-chemistry would strongly depend on the local gravitational environment.

  1. For an object with mass M and radius R, the estimated maximal gravitational metabolic energy quantum Emax is scaled up by factor is scaled up by a factor z= (M/ME)× (RE/R). The values of z for Mercury, Venus, Mars, and Moon are (.2,.14,.86,.04). For Venus, which is called the sister planet of Earth, z is not too far from unity.

    For the stationary orbits around an object with radius R1, mass M1, and rotation frequency ω1 the ratio Δ E1/Δ EE of metabolic energy quantum to that for Earth satisfies the scaling formula

    Δ E1/Δ EE = RE/R1 × (1-x1x2x3) ,
    x1= (M1/ME)1/3 ,
    x2=(ωE1)2/3 ,
    x3=RE/R1 .

  2. In the case of the Moon, Emax would be by a factor z= RE/RMoon= .017 smaller than at the surface of Earth. The stationarity condition would require a flux tube orbit radius smaller than the Moon radius. In the case of Venus, the sidereal rotation period is -243.0 days (retrograde): also now the orbit of stationary radius would be smaller than the radius of Venus. This suggests that only the metabolism utilizing the solar gravitational field photosynthesis is possible and would be essentially the same as at the surface of Earth.

  3. In the case of Mars one has ω1E≈ 1 , M1/ME=.1, R1/RE= .533 . This gives Δ E= .24 Δ EE, which for the proton Cooper pair would give .13 eV. Could the solar gravitational field save the space traveller in case of Moon and Mars? The largest distance from Earth is about 1.7 AU and at this distance the maximal value of the solar metabolic energy quantum is scaled down by a factor .59.
Just for fun, one can also look at the situation in Sun.
  1. At the surface of the Sun, one has z≈ 3.0× 102 and the metabolic energy quantum .55 eV for dark proton triplet scales to Δ ESun≈ .16 keV: this is below the threshold for the nuclear fusion and below the temperature of ≈ .23 keV of the solar corona. An interesting question is whether the X-ray radiation arriving to Earth could have some, perhaps even biological, function. TGD indeed predicts that nuclei have excitations in the keV range (see this).
  2. For a dark electron Cooper at solar surface, the upper bound is .08 eV. The temperature of the photosphere corresponds to photon energy of .4-.6 eV, which corresponds to the metabolic energy quantum associated with the Earth's gravitational flux tubes. Could the IR thermal radiation from the photosphere serve as a metabolic energy source?
How does this model relate to the TGD inspired model for Cambrian Explosion (see this and this)?
  1. The TGD explanation for the sudden emergence of new phyla in Cambrian Explosion is that the radius of Earth doubled in CE in rather short time. If the end of flux tube moves along stationary orbit, the scaling formula gives for the metabolic energy quantum before the transition for the dark proton triplet the value Δ Egr=.38 × Δ Egr,max, which gives Δ Egr=.3 eV. This is considerably smaller than .55 eV.
  2. According to Stephen Gould (see the book "Wonderful life" about Burgess Shale Fauna, a large number of the phyla suddenly disappeared. Could this mean that they were not able to adapt to the transition increasing the value of the metabolic energy quantum? On the other hand, a rapid evolution started. Could this relate to the increased sizes of the protonic and electronic metabolic energy quanta? Solar metabolic energy quanta would not have changed.
Do Moon travellers survive in TGD Universe?

3 dark protons give the nominal value of metabolic quantum. If the naive estimates are taken seriously, terrestrial life might not be possible on Mars and Moon. Humans have however successfully visited the Moon and it is not clear whether the solar gravitational field comes to rescue.

Rather than giving up the idea, it is better to ask what goes wrong with the simplest model. The quasiclassical estimate assumes that the dark charge at the top and bottom of the gravitational flux tube has the same kinetic energy. If the kinetic energy at the top is higher, the value of the metabolic energy quantum increases. This inspires the question whether the reduction of the kinetic energy in the metabolic energy quantum can be neglected.

  1. The simplest model for the particle at gravitational valence bond is as a particle in a box with kinetic energies given by En= n2eff2/mL2, L the length of the loop. If L scales like heff, the kinetic energy does not depend on heff. Therefore the scale of kinetic contribution can be estimated in a molecular length scale.
  2. Could the system adapt to a reduction of the maximal gravitational potential at the surface of the Moon, Mars, or Venus by increasing the average value of n in the superposition of the standing waves having maximum at the top of the valence loop? The system would adapt by increasing the localization of the dark charge at the top of the loop. The reduction of the bond length would mean reduction of the superposition to n=0 wave so that the kinetic energy would be indeed liberated.
Dark gravitational bonds and high energy phosphate bond

How could the somewhat mysterious high energy phosphate bond (HEPB) associated with di-phospates (DP) and tri-phosphates (TP) relate to the gravitationally dark hydrogen bonds (HBs)?

  1. HEPB (see this) is identified as the bond ...--O--... connecting two P atoms in ATP or ADP (see this). Hydrolysis involves also one H2O molecule. The -O-P bond splits inducing the splitting of ATP to ADP and P1. One cannot assign HEPBs to the monophosphates (MPs) associated with DNA so that the splitting of the O-P bond must play an essential role..
  2. It is best to start by listing the facts about ATP→ ADP +Pi+2H+ reaction for which the Wikipedia article (see this) gives both graphical representation and the overall formula for the reaction.

    In the initial state 4 O-atoms of ATP have a visible negative charge. The simplest assumption is that all ions O- actually correspond to gravitationally hydrogen bonded O...H pairs with a delocalized proton charge so one should use the notation O"-". O- would be replaced with O...H-O-H such that the HB carries a gravitationally dark proton delocalized in even astrophysical scale. The negative charge would be only effective and associated with OH"-" rather than being a real negative charge of O-. The same assumption is natural also for ADP and AMP. This would define the meaning of organic phosphates. In the final state both Pi and ADP have visible charge -3 to give a total visible charge -6.

    2H+ in the final state guarantees the conservation of the visible charge in the reaction.

  3. The P(O"-")2 of the third phosphate transforms to an inorganic phosphate Pi. A natural interpretation is that the gravitationally dark protons become ordinary ones. This explains 2H+ in the final state. This reaction would liberate part of the metabolic energy.
  4. One H2O molecule is used in the reaction. The natural assumption is that one hydrogen of H2O has a dark gravitational HB with the oxygen appearing in O-P of (O"-"2P=O)-O-P... so that it one has O"-" visible charge -1. The bond ...P-O-...H becomes the effective oxygen ion of ...P-O"-" of Pi so that Pi would not be completely inorganic. The remaining OH of the water molecule becomes one O"-" of P of ADP. Also this reaction can liberate metabolic energy.
See the article Quantum gravitation and quantum biology in TGD Universe or the chapter with the same title.

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

Articles and other material related to TGD.

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