About the energetics of the proposed compression and expansion of Earth

One should also understand the energetics of compression and expansion. Under what conditions these transitions are possible? Gravitational and atomic binding energies are involved. Gravitational binding energies per atom are proportional to the ratio r_s/R_P for the planet. The binding energy liberated in the transition k=139→ 137 is independent of planetary parameters. In the case of Earth, this transition should provide the energy making possible formation of the Moon and the proposed formation of Rydberg atoms making possible large scale quantum coherence.

One can ask whether the transition is possible for all planets and whether the Earth and Venus, with almost the same value of r_s/r_P, are in a special position. For large values of r_s/r_P the electric binding energy needed for the formation of a moon might be too large. r_s/r_P is indeed large for Jupiter and Saturn which suggests that the transition k=139→ 137 essential for the emergence of life and for the formation of the Moon cannot reduce the radius by factor 1/2. The mechanism for the formation of moons must be different. For small values of r_s/r_P electromagnetic binding energy would be more than needed. A rough estimate for r_s/R is as r_s/R∼ (R/R_E)² (r_s(E)/r_E) and decreases with the size of the object.

Consider next estimates for the changes of the gravitational and electric binding energies per atom. For simplicity, restrict the consideration to the case of the Earth first.

1. The gravitational binding energy per atom with mass number A increases in the transition R_E→ R_E/2.

   Δ E_gr=(r_s/2R_E) A m_p ∼ A × 3.14 ~eV .

2. The change Δ E_B of the binding energy in the transition k=139→ 137 can be estimated by using the expression for the ground state binding energy of atom with nuclear charge Z for k=139 assigned for ordinary atoms

   E_B(139)= Z² ×α_em²/8m_e ∼ Z² ×13.6 eV .

   One has E_B(137)= 4E_B(139) so that the increase of the binding energy is

   Δ E_B= 3E_B(139)∼ 3Z² ×13.6 ~eV .

   From Z≤ A/2 one has

   Δ E_B≤ A²× (3/4)× 13.6 ∼ ~eV

3. The condition Δ E_gr= Δ E_B gives a lower bound A≥ .3 .

   This condition is true for all atoms in the case of Earth and there is also surplus energy to throw out a layer forming the Moon.

For a general planet, the lower bound for A scales as the ratio x_P=(r_s/r_P)/(r_s/R_E). The values of x_P for Venus Mercury and Mars (.85,0.14 .20). It has been proposed that Venus has had a moon but has lost it. Also the nearness of the Sun is unfavourable for having a moon. The formation of the moon could have led to a compression of the Venus and if the life evolved in the interior it would not have survived at the surface after the expansion since the atmosphere (95 percent CO₂ and 3.5 percent nitrogen) has temperature of 467 ^_ºC and pressure, which is 93 times that on the Earth.

For the gas giants Jupiter resp. Saturnus with ratio x_J∼ 29.0 resp. x_s∼ 10 the lower bound for A is 7.7 resp. 3.3. Moon resp. Titan has x_J∼ .07 resp. x_T∼ .056.

See the article Could the notions of quantum geology and quantum biology make sense? 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.