Did the proposed Expansion of Earth during Cambrian Explosion lead to the formation of Moon?

The discussions related to the Expanding Earth hypothesis stimulated interesting questions. How planets and Moons would have been born in TGD-based astrophysics and could the formation of Moon relate to the Expanding Earth hypothesis (see for instance this) and whether the gradual growth of Moon's orbit could relate to it.

During the last year, I wrote two articles about the birth of stars and planets and also moons in TGD Universe last year (see this and this).

The first basic idea is the fractality of TGD-based cosmology, which follows from the TGD view of space-time as a 4-D surface in H=M⁴× CP₂. Another key idea is the replacement of a smooth continuous cosmic expansion with a sequence of fast explosions.

1. The scaled down versions of Big Bang would occur on different scales. For example, a star would produce shells of mass ejected in an explosion that would condense into planets.
2. The planets could also do the same and this would lead to the birth of shells, from these the rings would be born and from these the Moons would be born.

The Cambrian explosion is also an explosion. The composition of the Moon is the same as that of the Earth. The crazy question that comes to mind (I can already hear my colleague's snoring laughter in my ears) is whether the Moon was born this way but .5 Gy ago (instead of 4.5 Gy), in the Cambrian explosion. This of course does not exclude the possibility that Moon was formed in a similar explosion for 4.5 billion years ago.

Can the Cambrian option be ruled out by comparing the ages of the Earth's Moon? Radiometric age determinations give the matter making up the Earth and the Moon (so not the Earth or the Moon itself!!) age estimates of 4.543 Gy and 4.46 Gy, i.e. an age difference of 80 million years.

1. The age of the material composing Moon has been deduced from the radioactive decay of Zirconium and in the latest determination it increased by 40 million years. This inaccuracy is of the same order as the difference in the ages of the substances! So can the Moon be matter of the same age as the Earth? You can also critically ask why the Moon's and Earth's matter would be of different ages when the composition is the same? The most natural explanation is that the substance is the same and therefore of the same age.
2. Radioactive age determinations would therefore not rule out the hypothesis of the formation of the Moon in the Cambrian explosion. In such an explosion, a layer with a thickness of about 6 km would have been thrown out and taken with it both the life on the surface and the fossils if there were any! .5 billion years old fossils would be products of underground life!

Is there any empirical evidence that the age of the Moon cannot be on the order of .5 billion years. Is there any evidence for the explosive origin of the Moon? Could one compare Theia hypothesis and the two variants of TGD proposal? Could the dynamics of the Moon-Earth system help here?

1. It is known that the distance of the Moon from the Earth increases slowly: v=3.78 cm per year (see this). Could the recent rate for the increase of the orbital radius be interpreted in terms of cosmic expansion? The Hubble constant is about H= 70 km/sMpc, where parsec (pc) is 3.26 ly. This gives for the cosmic recession velocity of Moon v(now)= HR≈ 2.8 cm/y. This is 74 per cent of the observed velocity of increase for the orbital radius. This suggests that the velocity due to the explosion has gradually decreased and is approaching the cosmic recession velocity (, which increases linearly with the distance: this effect has been observed but surprisingly, has not been interpreted in terms of the cosmic recession velocity!).

   Could the deviation v-v(now) be a remnant of the rapid increase in the orbital radius associated with the Cambrian explosion?

2. If Moon was born in about .5 billion years ago and the velocity would have been constant v= 3.78 cm/y, the Moon would have reached a distance of about 1.9× 10⁷ m, which is about 2.97R_E (three Earth radii) from the Earth and much smaller than R=60R_E so that the speed should have been significantly faster at the beginning.
3. If the Moon was born in such an explosion 4.5 Gy ago, the same rough estimate assuming constant velocity v= 3.78 cm/y would give for the distance of the Moon R=26.7 R_E, R_E=6,357 km. This is roughly by a factor 1/2 smaller than the recent distance R=60R_E of the Moon. This option looks more reasonable than the Cambrian option.

   Cosmic expansion cannot explain the increase of the Moon's orbital radius. One would have dR/dt= HR giving the estimate R(t)= R_Eexp(v(now)t/R) and R(now)=eR_E , which is consierably smaller than R= 60R_E.

4. Could Theia hypothesis explain the growth of the distance of the Moon's to its recent in terms of the recoil momentum gained by the evaporated fragment giving rise to the Moon? This should have made the orbit elliptic. The orbit of the Moon is slightly elliptic: the eccentricity is .055 (see this). One should also understand the mechanism, which distributed the remaining matter evenly along the surface of the Earth.

   What is intriguing from the TGD point of view is that the radius of Earth could have increased by a factor 2 in the collision with Theia. This would explain the findings motivating the Expanding Earth hypothesis if the continents were formed already in the collision with the Theia.

See the article Expanding Earth Hypothesis and Pre-Cambrian Earth 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.