Expanding Earth Model and Pre-Cambrian Era: Part III

I have divided the discussion of Expanding Earth model for pre-Cambrian period in short postings: 5 altogether. In the first posting I discussedd the notions of super-continents, super-oceans, and glaciations during Neoproterozoic period with short coments inspired by R/2 scenario. In second posting I summarized the dominating Snowball model for the climate during Neoproterozoic period in the same spirit. In this posting I will discuss TGD Expanding Earth view about super-continents, super-oceans and glaciations and compares it with Snowball Earth scenario. Fourth posting discusses paleomagnetic tests for R/2 scenario. Fifth posting discusses the Expanding Earth scenario about how life escaped to the underground lakes and seas created during the expansion and returned back in the beginning of Cambrian era.

TGD view about pre-Cambrian period

What is new in TGD based view about pre-Cambrian period is basically due to the R/2 hypothesis (in other words, the radius of Earth was not much more than one half of its recent value during pre-Cambrian period).

1. TGD view about evolution of continents

The hypothesis about the existence of the super-continent Pangea (see this) was inspired by the work of Wegener (see this). The hypothesis about the existence of former super-continents were forced by the correlations with fossil records suggesting connected continent. This is not necessary if the gigantic ocean was absent during R/2 era. The continent Rodinia (see this) could look much like the Rodinia of standard geology except that they formed single connected region with radius R/2.

1. It is possible that there was only single super-continent with widening inland seas all the time until 250 billion Myr. The first option is R increased slowly and that inland lake formed. Rifts could have got wider gradually during this era. If there were land bridges between the continents there would be no need for postulating the cyclic re-formation of super-continent.

2. One can pose many questions about the character of the expansion.
   1. What was the duration of the expansion? Could the expansion have occurred in the time period 750-100 Myr (100 Myr corresponds to the age of dinosaurs with large body size made possible by the reduced gravitation and oxygenation of the atmosphere)? Duration would have been about 650 Myr in this case. Or did it began already at the beginning of Neoproterozoic period (see this) when super-continent Rodinia began to break up? In this case the duration would be about 1 Myr. The estimate based on the quantum model of gravitational radiation predicts that the transition lasted for about 1.1 Gy so that the latter option would be more plausible in this framework.

   2. Did the expansion accelerate as does also cosmic expansion in TGD based universal model for the expansion periods containing only the duration of the expansion period as a parameter (see this) and applying in alls scales? It seems that accelerated expansion is the only sensible option since around 540 Myr the size of Earth should have been rather near to R/2 (perhaps so even at the period of Pangea around 250 My) unless one assumes that super-continent re-formed again.

3. One can also consider the possibility that the continents indeed broke up and reformed again during Cambrian era. One should however have a good physical reason for why this happened. Something must have connected the pieces together and created correlations. Gravitational magnetic flux tubes and phase transitions increasing and reducing Planck constant? Or could it be that the bridges connecting the continents acted like strings inducing oscillation of the distance between continents so that Pangea was surrounded by a large ocean?

4. The formation of the rift (see this) feeding magma from core to the surface would be due to the expansion leading to the formation of fractures. The induced local elevations would be like mountains. As in zipper-rift model ice could have covered these plateaus because the temperature was lower. This is not however essential for TGD based model of glaciations.

5. TGD based variant of Expanding Earth allows subduction but its role could have been small before the Pangeia period if the expansion was accelerating and led only to a relatively small increase of the radius before the Mesozoic period (see this) and continued with an accelerating rate during Mesozoic from 250 Myr to 65 Myr. It is interesting that Mesozoic period begins with the most intensice known extinction of history- so called Permian-Triassic extinction event (see this)- known as Great Dying. About 95 of marine species and 70 percent of terrestrial species became extinct. Maybe genetically determined bio-rhythms could not follow the rapidly changing circadian rhythm. Another explanation for the extinction is the warming of the climate. For this there is indeed support: there is evidence that Antarctica was climate refuge during the extinction (see this). Perhaps both factors were involved and were not independent of each other since rapid expansion might have generated massive methane leakages from underground seas and lakes.

2. TGD based view about evolution of oceans

Continents would have covered most of the area during R/2 era and the covered fraction was slightly smaller than 1/4 of the recent area of Earth. This depends on the area taken by inland seas and polar caps. Nowadays the area covered by continents and inland seas is about 31 per cent so that continental area has increased and would be due to the expansion in vertical direction and deepening of the oceans. The area covered by oceans has increased from a small value to about 70 per cent. Only a small fraction of ocean floor would be subduced in Expanding Earth model. The Proto-Atlantic would have been only a small inland sea. Panthalassic Ocean was inland sea, which expanded to Pacific Ocean during expansion. Pacific Ocean could contain data about ancient ice ages if it was frozen. It however seems that data are consistent with the absence of global glaciation.

3. Model for glaciations

In TGD framework single super continent covering most of Earth becomes the counterpart of Rodinia (see this). The hypothetical oceans are replaced with inland seas and polar caps. The super-continent covering most of Earth absorbs less solar heat than tropical oceans so that glaciations become more probable. Snowball Earth is replaced with a series of ordinary glaciations proceeding from poles since the places at Equator were near North Pole. There is no need for the glaciations to progress to the equator. The rifting for the counterpart of Rodinia is consistent with the formation of fractures due to the expansion of Earth. The reduction of gravitational binding energy due to the increase of the radius requires feed of energy and this could be one reason for the cooling and initiation of the glaciation.

There are several questions which must be answered if one wants to gain a more detailed understanding.

1. How does R/2 model modify the view about glaciations? Very probably there was a frozen polar cap. Snowball Earth could be replaced with ordinary glaciations proceeding from North and South Pole.

2. How does the predicted 3+3 hour diurnal cycle modify the ordinary picture? Certainly 3-hour day reduces the amplitude of the diurnal temperature variations. Could this period have left genetic traces to the mono-cellulars, say biological clocks with this period?

3. How does the predicted four times stronger surface gravity affect the glaciation process? Could strong gravity leave detectable signatures such as anomalously strong effects on the shape of surface of Earth or deeper signatures about the motion of ice.

There are also questions related to the energetics of the expansion.

1. The expansion required energy and could have induce glaciations in this manner. Energy conservation would hold for the total mechanical and gravitational energy of Earth given by

   E=L²/2I -kGM²/R<0 .

   Here L is the conserved angular momentum L = Iω and ω increases from 1/4<ω_now to <ω_now during the expansion. The moment of inertia I is of order of magnitude I≈MR² and k is a numerical constant not too far from unity. The kinetic energy is actually negligible as compared to the gravitational potential energy. The reduction of the gravitational binding energy requires a compensating energy, which could come both from Earth interior or from the Earth's surface. Both effects would induce a cooling possibly inducing glaciations.

2. One expects that in the initial stages of the expansion there was just an expansion. This meant stretching requiring also energy. The formation of rifts leading to the formation of oceans as magma flowed out would have started already in the beginning of Proterozoic period. Eventually fractures were formed and in TGD framework one might expect that the distribution of fractures could have been fractal. A considerable fraction of fractures was probably volcanoes so that CO₂ begun to leak to the atmosphere and local 'oasis' were formed. Also hot springs liberating heat energy from Earth crust could have been formed as in Island. The pockets inside Earth increased in size and were filled with water. Life started to escaped to the walls of the fractures and to the water pockets. Also the recent oceans can be seen as widened cracks which transformed to the expanding sea floors whereas continents did not expand. As the continental crust ceased to expand no heat was needed for the expansion and this together with increased CO₂ content of atmosphere would explain why there was no further glaciations and heating of the Earth. At this period the flow of the magma from Earth core provided the energy needed to compensate the reduction of gravitational energy.

3. It must be emphasized that TGD variant of Expanding Earth theory is not in conflict with tectonic plate theory. It explains the formation of tectonic plates and the formation of magma flow from rifts giving also rise to subduction and this theory is therefore a natural extension of the tectonic plate theory to times before the expansion ceased.

4. Estimate for the duration of the transition changing gravitational Planck constant

The reader without background in quantum physics and TGD can skip this section developing an estimate for the duration of the transition changing Planck constant and inducing the scaling of the radius of Earth by a factor two. The estimate is about 1.1 Gy. It must be emphasized that the estimate is not first principle calculation and relies strongly on quantum classical correspondence.

The duration of the quantum transition inducing the expansion of the gravitational space-time sheet of Earth and thus of Earth itself by a factor two can be estimated by using the same general formula as used to estimate the power of gravitational radiation emitted in a transition in which gravitational Planck constant assignable to star-planet system is reduced (see this).

1. The value of gravitational Planck constant characterizing the gravitational field body of Earth is GM²/v₀, where the velocity parameter v₀ < 1 (c=1) is expected to be larger than v₀ ≈ 2^-11 characterizing Sun-Earth system.

2. Assuming a constant mass density for Earth the gravitational potential energy of Earth is given by

   V=(M/2)× ω²r² , ω= (6GM/R³)^1/2 .

   As far as radial oscillations are considered, the system is mathematically equivalent with a harmonic oscillator with mass M. The energies for the radial oscillations are quantized as E = (n+1/2)hbar_grω.

3. The radii of Bohr quantized orbits for the harmonic oscillator scale like hbar^1/2 so that hbar→ 4hbar is needed to obtain R→ 2R rather than hbar→ 2hbar as the naive Compton length argument would suggest. This requires the scaling v₀→ v₀/4. The change of the ground state energy in this quantum transition is

   V=(M/2)× ω²r² , ω= (6GM/R³)^1/2 .

   ΔE= (1/2)×(hbar_gr,f×ω_f -hbar_gr,i×ω_i) ,

   hbar_gr,f=4×hbar_gr,i=4GMm/v_0,i ,

   ω_i= 2^3/2 ω_f =2^3/2(6GM/R_f³)^1/2 .

   R_f=R denotes the recent radius of Earth.

4. From the estimate for the power of gravitational radiation in similar transition the estimate for the duration τ of the quantum transition is

   τ= a(v_0,iv_0,f)^-k/2×(hbar_gr,i+hbar_gr,f)/2ΔE = a2^-kv_0,f^-k×(1+r)/(rω_f-ω_i) , r=hbar_f/hbar_i=4 .

   The average of Planck constants associated with the initial and final states and geometric mean of the parameters v_0i and v_0f is dictated by time reversal invariance. The exponent k is chosen to be same as that obtained for from the condition that that the ratio of the power to the classical radiation power emitted in the transition between planetary Bohr orbits does not depend on v₀ (quantum classical correspondence). This gives k=5. The condition that the power of gravitational radiation from Hulse-Taylor binary is same as the power predicted by the classical formula (quantum classical correspondence) gives a=.75.

5. The explicit expression for τ reads as

   τ= K× av_0,f^-5× (R/2GM)^1/2×R/c,

   K=5× 2^-7× (2+2^1/2)/3^1/2 .

6. The basic data are M_Sun = 332900 M (mass of Sun using Earth's mass as unit) and the mnemonic r_S,Sun=2GM_Sun = 2.95×10³ m: together with R = 6371×10³ m these data allow a convenient estimation of R/2GM. For k=10 and a=.75 this gives t = 1.17 Gyr. This is twice the estimate obtained by requiring that the transition begins at about 750 Myr (the beginning of Sturtian glaciation) and ends around 100 My (the age of gigantic animals whose evolution would be favored by the reduction of surface gravity). The estimate would suggest that the quantum transition began already around 1.1 Gyr, which in the accuracy used corresponds to the beginning of Neoproterozoic at 1 Gyr (see this). The breaking of super-continent Rodinia indeed began already at this time.

7. Note that the value of v_0f for the gravitational field body of Earth as it is now would be v_0f=2^-10 to be compared with v₀ ≈ 2^-11 for Sun-Earth gravitational field body.

5. Snowball Earth from TGD point of view

In TGD framework the main justification for Snowball Earth disappears since the samples believed to be from Equator would be from North pole and glaciation could be initiated from pole caps. Consider next in more detail the evidence for Snowball Earth from TGD point of view.

1. Low latitude glacial deposits, glacial sediments at tropical latitudes, tropical tillites, etc. providing support for snowball Earth (see this) would be near North pole of at Northern latitudes. Ordinary glaciations proceeding from poles would explain the findings (see this). If total glaciations were present, a rough scaling suggests that the evidence from them should be found from southern latitudes around 45 degrees in the standard model framework.

   The testable prediction is that the evidence for glaciations in ice-ball Earth framework should be found only below Equator and near South Pole. This finding would be of course extremely weird and would strongly favor R/2 option. Interestingly, in Southern Brasil all indicators for glaciations are absent (see (see this) and references therein). This region belonged to Godwana continent and there is evidence that its location was at middle latitudes at Southern Hemisphere.

2. Banded iron formations (see this) are regarded as evidence for Snowball Earth and occur at tropical levels (near North Pole in R/2 model). Iron dissolved in anoxic ocean would have become in a contact with photosynthetically produced oxygen and implied the formation of iron-oxide. The iron formation would have been produced at the tipping points of anoxic and oxygenated ocean. One can consider also an explanation in terms of deep inland seas, which become stagnant and anoxic near the sea floor.

   In TGD framework sea floor near North Pole could contain banded iron formations. This would explain also why the banded iron formations are rather rare. The oxygen could have come also from underground after the formation of cracks and led to the oxygenation of inland seas from bottom. The assumption that oxygenation took place already during the first glaciation, could explain why banded iron formations are absent during the second glaciation.

3. Calcium carbonate deposits (see this) have ¹³C signature (per cent for the depletion of ¹³ isotope and large for organic material) is consistent with that for mantle meaning abiotic origin. The explanation of Calcium carbonate deposits in TGD framework could be the same as in Snowball Earth model. Atmospheric CO₂ could come from the volcanoes and react with the silicates during the ice-free periods to form calcium carbonate which then formed the deposits. CO₂ could have also biological origin and come from the underground life at the walls of the expanding fractures/volcanoes or in underground seas or lakes. In this case also methane is expected. This option would predict ¹³C signature characteristic for organic matter. Also this kind of signatures have been observed and support ordinary glaciations. Also rapid fluctuations of the signature from positive to negative take place and might have signatures of temporary melting induced organic contribution to the calcium carbonate.

4. Iridium anomaly (see this) is located at the base of Calcium Carbonate deposits. In Snowball Earth model Iridium deposits derive from the Iridium of cosmic rays arriving at the frozen ice surface. As the ice melts, Iridium deposits are formed. In R/2 model the condensation of Iridium would proceed through the same mechanism. The possible problem is whether the time is long enough for the development of noticeable deposits. Near poles (Equator and South pole in standard model) this could be the case.

For details see the new chapter Expanding Earth Model and Pre-Cambrian Evolution of Continents, Climate, and Life of "Genes and Memes".