A New Year Gift

TGD is now a very precisely formulated mathematical theory making testable physical predictions: consider as an example only predictions for LHC described in one of the earlier postings. Experimental support from various anomalies is accumulating steadily. The last example was the finding of Martin Grusenick providing additional evidence for the deviations of gravitation in the nearby regions of massive objects from those of Einstein's and Newton's theories. TGD explains the deviation and the explanation led to a further understanding concerning the interpretation of quantum TGD. I had excellent reasons for writing a summary about the developments taken place in TGD during the last year.

I had to give up this plan for a very practical reason. First some background. Virus terror has become more and more painful nuisance during years. Two years ago a friend of friend who is a computer professional saved the situation and also found that there is a computer in Helsinki region bombarding my IP address very intensively. Difficulties began again for about year ago. Only a half year ago I had to stop MATLAB calculations when the program went simply mad. This was the first time when my invisible enemy really forced me to give up a project.

Terror has had also other forms. I am continually updating the .tex files associated with the chapters of the 15 online books at my home page. One especially nasty form of terror has been the replacement of updated tex files with old versions: a very effective manner to destroy my credibility! That this happens is revealed by the fact that I have done some updatings during years such as the replacement of manual lists with automatic ones. Suddenly the file is from the time before the operation (even two years in past!) or from the period of updating so that latex translation stops to an error situation when '\end{enumerate}' or something like that which must be added during updating manually is lacking. There has been also a continual cat and mouse game with files. pdf files mysteriously disappear or the names of tex files are permuted.

The endless testing and comparison to see whether the file at home page is what it is meant to be is alone a horrible stressor. I suffer a blood pressure disease and I must tell that this continual terror has become a real life danger (I tell this with a tiny childish hope that the persons behind this activity might read this, might not be total psychopaths, and might feel mercy towards the poor old man).

In New Year Day my invisible enemy managed to make a real breakthough. Difficulties began at Friday and situation became gradually worse. First WinEdt failed to compile tex to pdf. It took two days to find a solution to the problem. Later it became also impossible to print the pdf files and load them from web. I reinstalled WinEdt, MikTex, Adobe Reader. No help. I changed the firewall program to Norton and learned that many of the program folders of the earlier firewall program were empty. After the re-installation the problems seemed to absent. But the happiness did not last longer than one hour.

Yesterday I learned about Free Registry Fix a program that finds and fixes damaged registers. It found roughly 1000 of them and I thought that the situation was cured. As I sat at the computer this morning I found that problems had returned. I run Free Registry Fix for 4 times under various conditions and found that same number (about hundred) damaged registers appears during the run as is found by it so that the situation is hopeless. From this experiment I can however firmly conclude that the virus damages registers always when computer is on irrespective of whether there are net connections. Virus is tailor made as I have suspected from the beginning. Good to know that I am definitely not a paranoid!

Who could be behind this terror? Ordinary firewall programs detect nothing and the activity is so precisely directed to prevent my work with TGD that a random hacker is probably not in question. A computer professional receiving his salary from computerized violence is a more plausible guess. I have no infrastructure supporting me so that I am an easy prey. I have only some friends who try to help. At this moment the change the operating system to Mac seems to be the only hope to get over the situation. This however costs and I have no money! And I do not of course know how long it takes for my enemy to find his way to the operating system of Mac.

A computer professional tailoring the needed viruses probably takes this only as a interesting programming challenge. The question is who could have the motivation for hiring him. I have been for 32 years a victim of academic terror based on the misuse of academic authority and the question is what could serve as the motivation for initiating a much more concrete terror making my working conditions completely intolerable. What could have induced this last step?

The situation in theoretical physics has become extremely critical. No colleague in his right mind can deny that TGD satisfies the basic criteria for a respectable candidate for a unified theory. Everyone also knows the sad situation of super string models and M-theory - basically the outcome of the silencing of the bottleneck idea that served as the starting point of TGD for 32 years ago and published already around 1982, two years before the super string revolution. It is only a matter of time when the breakthrough of TGD comes since no one can fight endlessly against experimental facts. From the point of view of big audience the breakthrough would be not only a sensation but also a scandal. The treatment that I have received in Finland during these decades is simply something totally incredible taking into account that Finland is a country where cannibalism is criminalized and literacy per cent is quite high. The breakthrough can be postponed by a censorship and blackmailing and trying to make my working conditions completely intolerable. And I would not be totally surprised if some of the fellow human beings with common interests (inducing this little nasty green feeling) would want just a revenge.

So: who is the payer? I do not propose any answer. I just tell what happens and the possible motivations. Reader can use his own heart and brains and facts about the history of science. Also hints for how to get over the hopeless looking situation are well-come.

What one really means with virtual particle?

Massive particles are the basic problem of the twistor program. The twistorialization of massive particles does not seem to be a problem in TGD framework thanks to the possibility to interpret them as massless particles in 8-D sense but the situation has been unsatisfactory for virtual particles (see this).

The ideas possibly allowing to circumvent this problem emerged from a totally unexpected direction (the finding of Martin Grusenick described in previous posting). The TGD inspired explanation of the results together with quantum classical correspondence (see this) led to the proposal that Einstein tensor in space-time regions where the energy density vanishes describes the presence of virtual particles assignable to the exchange of momentum between massive objects. This identification is consistent with Einstein's equations in zero energy ontology and leads to a proposal for a concrete geometric identification of virtual particles in TGD framework.

The basic idea is following. In TGD gauge bosons are identified as wormhole contacts with positive energy fermion and negative energy antifermion at the opposite light-like throats of the contact. The observation is that even if the fermions are on mass shell particles, the sum of their momenta has a continuum of values so that interpretation as a virtual boson makes sense. Free fermions do not correspond to single light-like throat but if the interaction region involves a pair of parallel space-time sheets with distance of order CP₂ length of order 10⁴ Planck lengths, the CP₂ extremal describing fermion has a high probably to touch the second space-time sheet so that topological sum giving rise to second light-like throat is formed. This throat has spherical topology and carries purely bosonic quantum numbers. If on mass shell state with opposite energy is in question, the situation reduces to that for bosons. One can also formulate conditions guaranteing that no new momentum degrees of freedom appear in loops integrals. Since only on mass shell throats are involved one can apply TGD based twistorial description also to virtual particles without any further assumptions.

The detailed explanation of the idea is given by this short article. The reader interested in background can study the chapter Twistors, N=4 Super-Conformal Symmetry, and Quantum TGD of "Towards M-Matrix".

Mickelson-Morley experiment revisited

The famous Michelson-Morley experiment carried out for about century ago demonstrated that the velocity of light does not depend on the velocity of the source with respect to the receiver and killed the ether hypothesis. This could have led to the discovery of Special Relativity. Reality is not so logical however: actually Einstein ended up with his Special Relativity from the symmetries of Maxwell's equations. Amusingly, for hundred years later Samuli Pentikäinen told me about a Youtube video reporting a modern version of Michelson-Morley experiment by Martin Grusenick in which highly non-trivial results are obtained. If I were a "real" scientists enjoying monthly salary I would not of course pay a slightest attention to this kind of stuff. But I am not a "real" scientists as many of my colleagues are happy to testify (without "":s of course) and have therefore nothing to loose. This gives me the luxury of thinking and I can even try to understand what is involved assuming that the discovery is real.

To my best knowledge there is no written document about the experiment of Martin Grusenick in web but the Youtube video is excellent. The only detail, which might give a reason to suspect that fraud might be in question is when Grusenick states that the mirror used to magnify and reflect the interference pattern to a plywood screen is planar: from the geometry of the arrangement it must be concave and I have the strong impression that this is just a linguistic lapsus.

Addition: Andre K. told that in German video Grusenick uses the expression "einfach" (simple) instead of the counterpart of "planar". Also pronunciation might have led to wrong pattern recognition as I know from my own experience as a person talking very badly broken english;-).

Addition: The change of the distance between beam splitter and mirror in the vertical position might explain the observations in terms of existing physics. A simple estimate however shows that this effect is by a factor of order 10^-3 too small. I am grateful for Samppa for suggesting the estimate.

The reader willing to learn in more detail how Michelson-Morley interferometer works can look very short video sketching how the interference pattern is created. This longer video describes in more detail the principles involved.

I do not bother to transform latex to html since a lot of formulas are involved and automatic translators do not work properly. Instead, I give a link to a pdf file representing the results of Grusenick and their analysis and interpretation in detail.

The results are following.

1. The findings of Grusenick can be understood if the radial component g_rr of the metric of Earth at the Earth's surface deviates from Schwartschild metric by a factor 1+Δ, where Δ is of order Δ ≈10^-4.

2. If one requires that G^tt vanishes for the modification of Schwartshild metric, Δ(r) behaves as Δ(R) R/r outside Earth's surface in good approximation. If the gravitational fields of stars, say Sun, have similar radial component g_rr, the predicted effects on planetary orbits are significant only for elliptic orbits sufficiently near to the surface of the star.

3. In General Relativity the presence of non-vanishing "pressure" terms G^rr, G^θθ, G^φφ in Einstein tensor with a vanishing energy density are difficult to understand. In TGD framework these terms could be due to the sub-manifold constraint forcing the allowed space-time surfaces to be extremals of Kähler action with Einstein equations with energy momentum tensor of matter (not containing the contribution of Kähler action) being satisfied.

4. The effect of the gravitational field of Sun on the interference pattern measured at Earth surface can be visible (fraction of order 10^-2 about the effect of Earth itself) and the experiments indeed demonstrate a diurnal variation of the interference pattern.

5. The extended Michelson-Morley interferometer could provide a new high precision tool to measure the behavior of g_rr as a function of the distance from the Earth and to test the proposed model.

Addition: I am grateful for Frank Pearce for informing me almost year later (20.11. 2010) that he has carried out the Grusenick experiment again. There is small movement of the interference pattern during vertical rotation but nothing comparable to that detected by Grusenick so that the effect is very probably an artifact. An excellent video Vertical Michelson Morley Interferometer Experiment 11 12 2010 about Pearce's version of the experiment can be found here.

For details and background see the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

High Tc super-conductivity in many-sheeted space-time

Mark McWilliams sent me some time ago a link Scientists Detect 'Fingerprint' Of High-temp Superconductivity Above Transition Temperature. What this fingerprint means is that Cooper pairs exists below a critical temperature T_c1 higher than the critical temperature T_c for the onset of the super-conductivity. The finding is surprising but nothing spectacular in a wider perspective. Also the atoms forming Bose-Einstein condensates exists stably above the critical temperature for Bose-Einstein condensation. The finding however suggests what the correct question might be. The reader who has decided to discover the mechanism of high T_c superconductivity could try either or both of the following alternatives.

1. Why quantum coherence for Cooper pairs is possible only below the critical temperature T_c but not in the range (T_c,T_c1)?

2. Why supra currents flow over long distances only below T_c?

I hasten to confess that I am an amateur in the field of high T_c superconductivity. After the idea about the hierarchy of Planck constants emerged for about half decade ago, I could not however resist the temptation to sketch a TGD inspired model for high T_c superconductors with Cooper pairs in large Planck constant phase. The results of the above article suggested that it is a high time to work out the model again.

So I had to start debunking the few years younger me. Not in the usual sense of throwing insults and using dirty rhetoric tricks but going through thoroughly the arguments of the younger colleague in the light of wisdom gained during these years. This process is not easy. I feel deep co-ashame while seeing this fellow to still fall in the sin of using words like 'remarkably' and even 'extremely'! And how badly structured the text of this enthusiasistic and so inpatient young fellow can be! But as a benevolent senior collegue I must tolerate these feelings. After all, these somewhat non-conventional colleagial discussions are the only manner to overcome the problems caused by the lack of the usual communications with colleagues. Sounds somewhat perverse and brings to my mind a prisoner in Stefan Zweig's novel playing chess against himself in order to avoid becoming crazy. In any case, the basic ideas survived the debunking but a lot of unnecessary ad hoc stuff had to be thrown away and the younger me had just to accept the somewhat violent modifications of his manuscript by the older colleague.

So: what did I learn in this process? What distincuishes high T_c cuprate superconductors from BCS type superconductors is that they are quantum critical. What is known that so called stripes ([1], [2]) containing electronic holes and carrying thus positive charge are essential for the existence of Cooper pairs whereas large enough quantum critical fluctuations of stripes are necessary for the onset of super-conductivity. Magnetic fields are usually regarded as enemy of super-conductivity but for spin 1 Cooper pairs magnetic field tends to stabilize the pairs. In high T_c superconductors the breaking of antiferromagnetic disorder induced by the formation of stripes is known to be essential for the formation of Cooper pairs.

In TGD inspired model of bio-superconductivity magnetic flux tubes are the carriers of super-conducting phases consisting of dark variants of ordinary particles characterized by a large value of Planck constant. The natural question is whether this might be the case also in the case of high T_c cuprate super-conductors.

1. If the holes at stripes to organize chains consisting of parallel spins they generate dipole magnetic field patterns with long dipole cores, maybe with the length of stripe. Suppose this happens so that stripes or at least portions of them would be 1-D hole ferromagnets: admittedly somewhat esoteric creatures but making mathematical sense.

2. The magnetic flux tubes (in TGD sense!) assignable to these dipole field patterns should accompany stripes and dark Cooper pairs with large Planck constant would reside at these flux tubes.

3. The transversal fluctuations of the flux tubes would be present already below T_c1 and would replace phonons as a mechanism generating the energy gap. Transversal 1-D phonons induced as occillations of lattice atoms would be in question. This could explain BCS type characteristics of high T_c superconductivity.

4. Large enough quantum fluctuations lead to reconnections of flux tubes so that the topology of the resulting network starts to quantum fluctuate. Below T_c the reconnection probability becomes high enough to create so long flux tubes that macroscopic supra currents can flow. This process is a special case of a phenomenon known as percolation: the wetting of sand represents a basic example of this phenomenon. Magnetic percolation provides a beautiful interpretation and perhaps also a generalization of the quantum highway metaphor discussed by Jan Zaanen. In fact, also S=0 zero Cooper pairs could become stable below T_c since their decay to S=1 pairs would become impossible for topological reasons.

I do not want to bore the reader more except by gluing the abstract of the chapter Super-conductivity in Many-Sheeted Space-time of the book "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy" devoted to high T_c superconductivity.

In this chapter a model for high T_c super-conductivity as quantum critical phenomenon is developed. The relies on the notions of quantum criticality, dynamical quantized Planck constant requiring a generalization of the 8-D imbedding space to a book like structure, and many-sheeted space-time. In particular, the notion of magnetic flux tube as a carrier of supra current of central concept.

With a sufficient amount of twisting and weaving these basic ideas one ends up to concrete model for high T_c superconductors as quantum critical superconductors consistent with the qualitative facts that I am personally aware. The following minimal model looks the most realistic option found hitherto.

1. The general idea is that magnetic flux tubes are carriers of supra currents. In anti-ferromagnetic phases these flux tube structures form small closed loops so that the system behaves as an insulator. Some mechanism leading to a formation of long flux tubes must exist. Doping creates holes located around stripes, which become positively charged and attract electrons to the flux tubes.

2. The higher critical temperature T_c1 corresponds to a formation local configurations of parallel spins assigned to the holes of stripes giving rise to a local dipole fields with size scale of the order of the length of the stripe. Conducting electrons form Cooper pairs at the magnetic flux tube structures associated with these dipole fields. The elongated structure of the dipoles favors angular momentum L=2 for the pairs. The presence of magnetic field favors Cooper pairs with spin S=1.

3. Stripes can be seen as 1-D metals with delocalized electrons. The interaction responsible for the energy gap corresponds to the transversal oscillations of the magnetic flux tubes inducing oscillations of the nuclei of the stripe. These transverse phonons have spin and their exchange is a good candidate for the interaction giving rise to a mass gap. This could explain the BCS type aspects of high T_c super-conductivity.

4. Above T_c supra currents are possible only in the length scale of the flux tubes of the dipoles which is of the order of stripe length. The reconnections between neighboring flux tube structures induced by the transverse fluctuations give rise to longer flux tubes structures making possible finite conductivity. These occur with certain temperature dependent probability p(T,L) depending on temperature and distance L between the stripes. By criticality p(T,L) depends on the dimensionless variable x=TL/hbar only: p=p(x). At critical temperature T_c transverse fluctuations have large amplitude and makes p(x_c) so large that very long flux tubes are created and supra currents can run. The phenomenon is completely analogous to percolation.

5. The critical temperature T_c = x_chbar/L is predicted to be proportional to hbar and inversely proportional to L (, which is indeed to be the case). If flux tubes correspond to a large value of hbar, one can understand the high value of T_c. Both Cooper pairs and magnetic flux tube structures represent dark matter in TGD sense.

6. The model allows to interpret the characteristic spectral lines in terms of the excitation energy of the transversal fluctuations and gap energy of the Cooper pair. The observed 50 meV threshold for the onset of photon absorption suggests that below T_c also S=0 Cooper pairs are possible and have gap energy about 9 meV whereas S=1 Cooper pairs would have gap energy about 27 meV. The flux tube model indeed predicts that S=0 Cooper pairs become stable below T_c since they cannot anymore transform to S=1 pairs. Their presence could explain the BCS type aspects of high T_c super-conductivity. The estimate for hbar/hbar₀ = r from critical temperature T_c1 is about r=3 contrary to the original expectations inspired by the model of of living system as a super-conductor suggesting much higher value. An unexpected prediction is that coherence length is actually r times longer than the coherence length predicted by conventional theory so that type I super-conductor could be in question with stripes serving as duals for the defects of type I super-conductor in nearly critical magnetic field replaced now by ferromagnetic phase.

7. TGD predicts preferred values for r=hbar/hbar₀ and the applications to bio-systems favor powers of r=2¹¹. r=2¹¹ predicts that electron Compton length is of order atomic size scale. Bio-superconductivity could involve electrons with r=2²² having size characterized by the thickness of the lipid layer of cell membrane.

At qualitative level the model explains various strange features of high T_c superconductors. One can understand the high value of T_c and ambivalent character of high T_c super conductors, the existence of pseudogap and scalings laws for observables above T_c, the role of stripes and doping and the existence of a critical doping, etc...

References

[1] V. J. Emery, S. A. Kivelson, and J. M. Tranquada (1999), Stripe phases in high-temperature superconductors , Perspective, Vol. 96, Issue 16, 8814-8817, August 3.

[2] J. Zaanen (2006), Superconductivity: Quantum Stripe Search, Nature vol 440, 27 April.

[3] Jan Zaanen (2007), Watching Rush Hour in the World of Electrons. Science vol 315. p. 372.

Dark matter particle was not discovered!

The title of my previous posting was Has dark matter been found?. The answer came in thursday and was Probably not!.

Peter Woit told about the outcome of the experiment. There were two events with the estimated background of .8 events and the probability of observing two or more events is 23 per cent. Therefore the result could be argued to be noise. The experiment was however very useful since it poses an upper bound 7.0×10^-44 cm² for a WIMP of mass 70 GeV at the 90 per cent confidence level. The mass of 70 GeV would maximize the cross section if WIMP corresponds to a dark matter particle. Otherwise the lower bound for mass is 2 GeV: not very informative! The cross section estimate is not absolute but relies on standard model dark matter halos of galaxies based on WIMPs allowing to estimate the density of dark matter particles and their flux to the detector. If one assumes that the density is of same order of magnitude as the density of ordinary particles the upper bound on the cross section is higher.

Tommaso Dorigo gives a nice summary about the implications of the finding in this posting SUSY more unlikely by the new CDMS II results. The SUSY afficionados identifying WIMP as neutralino could experience unpleasant sensations in their stomach since this identification eats a considerable fraction of the parameter space of SUSYs. Tommaso Dorigo created the impression that the experiment poses limits on SUSY parameters as such: this is of course not true. Even the believers on neutralino dark matter have no reason to get worried about funding: there are LOTs of parameter space left.

What does TGD say about the results. For few months ago I still believed that TGD does not predict space-time supersymmetry but the progress in the understanding of the mathematical structure of the theory forced me to turn up my coat (see this). The resulting super-symmetry shares a lot with standard SUSY but differs in some aspects dramatically from it. In TGD framework neutralino is not responsible for dark matter and its density is expected to be much lower than in dark matter scenarios -of the same of order of magnitude as the densities of other particles. The irony is that if neutralino corresponds to dark matter in TGD sense (has large Planck constant and therefore lives at different page of the Big Book whose pages are partially characterized by the values of Planck constant than we do), its detection requires that it leaks to our page. This reduces the detection probability further!

In TGD framework the most plausible interpretation of WIMPs (not identified as dark matter) would be as neutralinos (see this). If one takes seriously the anomalous eeγγ +missing transverse energy event detected for 15 years ago by CDF, one can deduce from the kinematics of this event the masses of the superpartners of electron, Higgs, and Z⁰ using p-adic length scale hypothesis and the assumption that SUSY breaking at the level of mass spectrum means only different p-adic mass scales for the members of SUSY multiplet. The masses are 131 GeV (just at the upper bound allowed kinematically), 45.6 GeV, and 91.2 GeV (Z⁰ mass) respectively. My hope was that they might have detected 45.6 GeV higgsino but this hope was unrealistic from TGD point of view suggesting much lower flux of these particles.

Addition: In New Scientist there is an article titled 2010 preview: Will a neutralino steal Higgs's thunder? about the possibility that LHC might discover neutralino before Higgs. Also Lubos Motl mentions this possibility. If the mixing between neutralinos is absent and SUSY breaking takes place only via the choice of the p-adic mass scale, Higgsino with 45.6 GeV mass would be the neutralino and its discovery would indirectly prove also the existence of Higgs in TGD Universe. Do not forget the 45.6 GeV;-)!

Has dark matter particle been found?

Both Jester and that Lubos tell about rumours that weakly interacting massive particle (WIMP) has been detected in CDMS (Cryogenic Dark Matter Detector).

The detectors of WIMPs are located deep underground to eliminate most of the cosmic rays and ideally leave only weakly interacting particles (electrons and gamma rays remain in the signal). Lubos had a link to a Youtube video about an audiovisual simulation of the events. The video translates the events to musical tones and light and the musical outcome is very "syncopic". Probably the jazzy character is the product of my own brain doing its best to build familiar patterns from the raw sensory data. The outcome is rather "melodic" due to the proper choice of notes chosen to represent data about position of event.

In standard scenario WIMP is identified as a dark matter particle.

1. What comes in mind in TGD framework first is sneutrino (for TGD view about super-symmetry see this, this, this, and also this.). Probably the detection mechanism involves interactions with nucleons so that the detector is not able to detect sneutrinos however (see below). Sneutrino need not be dark in TGD sense (non-standard value of hbar) if its mass is so large that intermediate gauge bosons cannot decay to it. Otherwise darkness in the sense of non-standard value of hbar at space-time sheets at which the particle is stable is forced by the decay widths of weak gauge bosons, which does not allow other than known light particles as decay products of weak gauge bosons. Neutrino masses are predicted by the p-adic mass calculations apart from p-adic mass scale and the analog of CKM mixing. The mass of sneutrino would be half octave of the corresponding neutrino mass if SUSY is broken only via the selection of the p-adic mass scale. Unfortunately, neutrino masses (that is topological mixing matrix for neutrinos with different genera determining the counterpart of CKM mixing matrix) are not very well known.

2. From the discussion in Lubos blog I learned that the most plausible candidate for the WIMP is neutralino, the lightest super-symmetric particle. It would be the counterpart of photon, Z⁰ boson, or Higgs or their mixture. In this posting I told that an old anomalous event scattering event giving indications for supersymmetry fixes via the p-adic length scale hypothesis the masses of some super-symmetric particles and it is interesting to see whether the prediction is correct! The masses of selectron, higgsino, and Z⁰-gluino are predicted to be 131 GeV, 45.6 GeV, and 91.2 GeV (Z⁰ mass) respectively so that higgsino with 45.6 GeV mass should be in question.

For a background see the chapter p-Adic Mass Calculations: New Physics of the book "p-Adic Length Scale Hypothesis And Dark Matter Hierarchy".

Long length scale limit of TGD as General Relativity with sub-manifold constraint

What is the precise relationship of the long length scale limit of TGD to General Relativity as a description of gravitational interactions? On basis of physical intuition it is clear that Einstein's equations hold true for the matter topologically condensed around vacuum extremals of Kähler action and that energy momentum tensor can be described as average description for small deformations of vacuum extremals. The question is what happens in the case of non-vacuum extremals. Does a simple variational principle leading to Einstein's equations at long length scale limit exist and allow to identify the solutions as extremals of Kähler action?

The answer to the question is affirmative. It has been clear from the beginning that TGD in long length scales as a theory of gravitational interactions is General Relativity with a sub-manifold constraint. The problem is to formulate this statement so that extremals of Kähler action are consistent with Einstein's equations. This requires basic wisdom about sub-manifold geometry and about variational principles and boils dow to two and half pages of formulas difficult to transform to html. Interested reader can click this to see the details.

This could be also a good exercise in the noble art of debunking: the average debunker does not understand anything about contents but it seems that he cannot avoid saying something about it. How to debunk convincingly in this kind of situation? This is a real challenge in bad rhetorics. But only for an advanced debunker. Novices should develop their skills with simpler targets such as entire life work. After all, a life work consisting of about 15.000 pages is much easier to debunk than two and half pages of text because one can make "general statements" and avoid comments about content.

The relationship between TGD and GRT is described in the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

About the noble art of debunking

The reason why I got the stimulus to write about the art of debunking was that TGD was just debunked by a couple of fellows this morning: it was the fastest debunking that I have experienced since it took just half an hour. A friend of mine who still had some illusions about the intellectual honesty of scientists told to his physicist friends about TGD. The first response was somewhat irritated "Does TGD predict the perihelion shift of Mercury?" "Does TGD predict lense effect?". God Grief! I responded patiently and gave a brief summary about what is common between TGD and how the theories differ plus a long list of further reading.

This was too much: these fellows got really angry. Am I really thinking that they would bother to read this stuff?! The response was what one might guess it to be. The text is just word salad, there are no calculations, calculations are not detailed enough, and in any case: TGD does not predict anything new. The response carefully avoided any mention to contents since this would have necessitated some reading. The fellows of course argued that they had read the whole stuff. This would have been quite an achievement: 5 chapters of formula rich text during half an hour during morning hours when people have often also some other things to do!

Well, for a layman it is difficult to believe what kind of idiots are spending taxpayer's money as scientists. It has been difficult also for me. In ordinary job person with these ethical standards would end up to jail within few years.

This debunking experience was really not anything new to me. The academic world of Finland is the Promised Land for intellectually lazy mediocrits whose academic profile does not include much more than the standard arrogance plus the skills in the art of debunking. It would be of course naive to think that the situation is not much better elsewhere.

Of course, every academic person worth of his salary must be able to debunk. I have learned during these years the basic rules of the art of debunking as a victim and I am ready to admit that I have not tested these rules in practice. Despite the lack of personal experimentation I think that I can safely share the wisdom about the tricks of the trade publicly so that any novice can by direct experimental work to get convinced that the rules really work. Here they are.

1. Select the victim to be below you in the hierarchy. The best choice is someone who has no institutional shielding. A good tip: exercise with TGD!

2. The innocent novice might think that it might be necessary to do a lot of work by learning what the intended victim has done. This is not at all necessary! If you necessary want to see some trouble, read some abstract or introduction. Basically it is enough to know the branch of science that the victim is working on and perhaps some rough idea about what he is suggesting. Some cautiousness is however required: Lubos debunked TGD by claiming that the theory exists inside my head only. Lubos had not bothered to visit my home page to see that there is 15 books of detailed documentations. Avoiding this kind of blunders requires only a minimum amount of preliminary work.

3. The innocent novice might also worry about how he can develop detailed arguments if he knows nothing about the stuff to be debunked. No problem! The whole point is that you do not say anything about contents!! "General arguments" are much easier and actually optimal to create the illusion that you have a profound knowledge about the subject matter, and see immediately that something is wrong (you need not specify what this "something" is!). Laconic comments create also an expression that you are a little bit inpatient of being forced to waste your precious time by commenting this kind of trash. If you necessarily want to take risks by saying something about contents be very very cautious: this is not for beginners since there is always the danger that your reveal that you have not actually read the material. Check at least that it is theoretically possible that you have read the material so that you do not make the same blunder as the physicist friends of my friend this morning.

Simple! Isn't it! But keep in mind the Golden Rule of debunking: say never anything about contents!! To make the idea concrete I give some general arguments which bite always. The text is just word salad! There are no calculations! Calculations are not sufficiently detailed! Logical deductions are circular! There are no clear principles! The author has misunderstood even elementary general principles! The theory does not predict anything new! Difficult to understand what the author is aiming at and what his motivations are! If the idea would have something in it, it would have been discovered long ago! And so on... The innocent novice can get rid of his innocence by developing similar arguments as an exercise.

Expanding Earth Theory and Pre-Cambrian Era: Part V

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 the third posting I dicussed TGD Expanding Earth view about super-continents, super-oceans and glaciations and compares it with Snowball Earth scenario. Fourth posting was devoted to paleomagnetic tests for R/2 scenario. This posting will discuss 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.

Did life go underground during pre-Cambrian era?

The basic idea of Expanding Earth model is that the life developed in underground seas and emerged to the surface of Earth in Cambrian explosion. The series of pre-Cambrian glaciations explains why the life escaped underground and how the underground seas were formed.

1. If one believes that the reduction of gravitational binding energy was responsible the cooling, then the expansion of Earth could have begun at the same time as Sturtian glaciation (see this). On the other hand, the TGD estimate for the duration of the expansion period giving 1.1 Gyr, suggests that the breakup of the Rodinia, which began in the beginning of Proterozoic period corresponds to the beginning of the expansion. The simplest assumption is that the radius of R at the beginning of Cambrian period was not yet much larger than R/2 and continued to increase during Cambrian period and ended up around 100 My, when dinosaurs and other big animals had emerged (possibly as a response to the reduction of gravity). This means that there were land bridges connecting the separate continents.

2. One must explain the scarcity of fossils during pre-Cambrian era. If the more primitive life forms at the surface of Earth did not have hard cells and left no fossils one can understand the absence of highly evolved fossils before Cambrian explosion (see this). If life-forms emerged cracks and underground seas there would be no fossils at the surface of Earth. In the case of volcanoes dead organisms would have ended to gone to the bottom of the water containing volcano and burned away.

3. The expansion had formed the underground pockets and fractures made possible for the water to flow from the surface to the pockets. Life would have evolved in fractures and pockets. The first multicellular fossils appeared during Ediacaran period (segmented worms, fronds, disks, or immobile bags) (see this) and have little resemblance to recent life forms and their relationship with Cambrian life forms is also unclear. Ediacaran life forms could have migrated from the fractures and Cambrian fossils from from the underground seas and lakes. The highly evolved life-forms in Cambrian explosion could have emerged from underground seas through fractures.

One can make also questions about the underground life.

1. The obvious question concerns the sources of metabolic energy in underground seas. In absence of solar radiation photosynthesis was not possible plants were absent. The lowest levels in the metabolic hierarchy would have received their metabolic energy from the thermal or chemical energy of Earth crust or from volcanoes. The basic distinction between plants and animals might be that the primitive forms of plants developed at the surface of Earth and those of animals in underground seas.

2. At first it seems strange that the Cambrian life-forms had eyes although there was no solar radiation in the underground seas. This is actually not a problem. These life-forms had excellent reasons for possessing eyes and in absence of sun-light the life forms had to invent lamp. Indeed, many life forms in deep sea and sea trenches produce their own light (see this). It would be interesting to try to identify from Cambrian fossils the body parts which could have served as the light source.

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

Expanding Earth Model and Pre-Cambrian Era: Part IV

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 the third posting I dicussed TGD Expanding Earth view about super-continents, super-oceans and glaciations and compares it with Snowball Earth scenario. This posting is devoted to paleomagnetic tests for R/2 scenario. Fifth posting will discuss 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.

Paleo-magnetic data and Expanding Earth model

Paleomagnetic data from pre-Cambrian period might allow to test R/2 hypothesis. This data could in principle help to trace out the time development R(t) from R/2 to R if the non-dipole contribution to magnetic field depends on R(t).

1. About paleo-magnetism

Paleomagnetism (see this) provides quantitative methods to determine the latitude at which the sample of sedimentary rock was originally. Magnetic longitude cannot be determined because of rotational symmetry so that other information sources must be used. There are several methods allowing to deduce the direction and also the magnitude of the local magnetic field and from this the position of the sample during the time the sample was formed.

1. Below the Curie point thermal remanent magnetization is preserved in basalts of the ocean crust and not affected by the later magnetic fields unless they are too strong. This allows to deduced detail maps from continental drifting and polar wander maps after 250 Myr (Pangea period). During pre-Cambrian period the ocean floors of hypothetical oceans would have disappeared by subduction. In R/2 model there are no oceans: only inland seas.

2. In the second process magnetic grains in sediments may align with the magnetic field during or soon after deposition; this is known as detrital remnant magnetization (DRM). If the magnetization is acquired as the grains are deposited, the result is a depositional detrital remnant magnetization (dDRM); if it is acquired soon after deposition, it is a post-depositional detrital remnant magnetization (pDRM).

3. In the third process magnetic grains may be deposited from a circulating solution, or be formed during chemical reactions, and may record the direction of the magnetic field at the time of mineral formation. The field is said to be recorded by chemical remnant magnetization (CRM). The mineral recording the field commonly is hematite, another iron oxide. Red-beds, clastic sedimentary rocks (such as sandstones) that are red primarily because of hematite formation during or after sedimentary diagenesis, may have useful CRM signatures, and magnetostratigraphy (see this) can be based on such signatures. Snowball model predicts that nothing came to the bottoms of big oceans! How can we know that they existed at all!

During pre-Cambrian era the application of paleomagnetic methods (see this) is much more difficult.

1. Reliable paleomagnetic data range up to 250 My, the period of Pangaea, and magnetization direction serves as a reliable information carrier allowing detailed polar wander maps. During pre-Cambrian era one cannot use polar wander maps and the polarity of the magnetic field is unknown. Therefore theoretical assumptions are needed including hypothetical super-continents, hypothetical oceans, and continental drift and plate tectonics. All this is on shaky grounds since no direct information about super-continents and ancient oceans exists. R/2 model suggests that continental drift and plate tectonics have not been significant factors before the expansion period when only inland seas and polar ice caps were present. Measurements have been however carried out about magnetization for pre-Cambrian sediments at continents recently and gives information about the strength of the magnetic field (see this): the overall magnitude of the magnetic field is same as nowadays.

2. At Precambrian period the orientation of iron rich materials can serve as a record. The original records can be destroyed by various mechanisms (diagenesis). Also the orientations of the sediments can change in geological time scales.

3. Tens of thousands of reversals of the magnetic polarity (see this) have occurred during Earth's history. There have been long periods of stability and periods with a high frequency of reversals. The average duration of glaciation is around one Myr. The determination of the polarity of B possible by using samples from different points.

4. Mountain building orogeny (see this) releases hot water as a byproduct. This water can circulate in rocks thousands of kilometers and can reset the magnetic signature. The formation of fractures during the expansion of Earth could have released hot water having the same effect.

2. Could paleomagnetic data kill or prove R/2 model?

The first question is how one might kill R/2 model using data from pre-Cambrian era. Paleomagnetic data could do the job.

1. Remanent magnetization is proportional to the value of magnetic field causing it in weak magnetic fields. Therefore the magnetization in principle gives information about the magnetic fields that prevailed in early times.

2. Suppose that the currents generating the magnetic field can be idealized to conserved surface currents K around cylindrical surfaces of radius r and height h scaled down to to r/2 and h/2 and that the value of K is not affected in the process. With this assumptions the magnetic moment behaves μ ~ I r²h→ μ/8. A continuous current vortices with j = k/r, which is ir-rotational outside the symmetry axis, produce a similar result if the radius of the vortices scales as r→ r/2. Since dipole magnetic field scales as 1/r³ and is scaled up by a factor 8 in R→ R/2, the scalings compensate and the dipole magnetic fields at surface do not allow to distinguish between the two options. Non-dipole contributions might allow to make the distinction.

3. The group led by Lauri J. Pesonen in Helsinki University (see this) has studied paleomagnetic fields at pre-Cambrian era. The summary of results is a curve at the home page of the group and shows that the scale of the magnetic during pre-Cambrian era is same as nowadays. On the other hand, the recent thesis by Johanna Salminen- one of the group members- reports abnormally high values of magnetization in Pre-Cambrian intrusions and impact structures in both Fennoscandia and South Africa (see this). No explanation for these values has been found but it is probably not the large value of primary magnetization.

Another manner to do test the R/2 model is by comparing the signs of the magnetizations at magnetic equator and poles. They should be of opposite sign for dipole field. The polarity of magnetic field varies and there are no pre-Cambrian polar wander maps. One can deduce from the condition B_r/rB_θ = 2cot(θ) holding true for dipole field the azimutal distance Δθ along the direction of the measured magnetic field to the pole along geodesic circle in the direction of the tangential component of B. One cannot however tell the sign of Δθ, in other words whether a given pre-Cambrian sample belongs to Norther or Southern magnetic hemisphere. There are however statistical methods allowing to estimate the actual pole position using samples from several positions (for an excellent summary see (see this).

For instance, if the magnetic field is in North-South direction during Rodinian period (see this), standard model would predict that the sign at the Equator is opposite to that at South Pole. In R/2 model the sample would be actually near North Pole and polarizations would have same sign. The sign of magnetization at apparent southern latitude around 45 degrees would have been opposite to that at South pole which is in conflict with dipole field character. Maybe the global study of magnetization directions when magnetic field was approximately in North-South direction could allow to find which option is correct. Also the dependence of the strength of the magnetic field as function of θ could reveal whether R/2 model works or not. The testing requires precise dating and position determination of the samples and a detailed model for the TGD counterpart of Rodinia and its construction requires a specialist.

If the expansion continued after 250 Myr with an accelerating rate and Earth radius was still considerably below its recent value, the comparison of pole wandering charts deduced from ocean floor paleomagnetic data at faraway locations might allow to show that the hypothesis about dipole field is not globally consistent for R option. Even information about the time evolution of the radius could be deduced from the requirement of global consistency.

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

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".

Expanding Earth Model and Pre-Cambrian Era: Part II

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 this posting I will discuss the dominating Snowball model for the climate during Neoproterozoic period in the same spirit. Third posting discussed 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.

Snowball Earth model for the glaciation during pre-Cambrian era

Snowball Earth (see this, this, and this) is recently the leading model for the glaciations (see this) during Proterozoic era. The term is actually somewhat misleading: Iceball Earth would more to the point. Slushball earth (see this) is a variant of Snowball Earth which does not assume total freezing near equator.

The history behind the Snowball Earth concept is roughly following (see this).

1. Mawson studied the Neoproterozoic stratigraphy of South Australia and identified extensive glacial sediments and speculated with the possibility of global glaciation. He did not know anything about continental drift hypothesis and plate tectonic theory and thought that the ancient position of Australia was the same as it is today. Continent drifting hypothesis however explained the finding as sediments deposited at the higher latitudes the hypothesis was forgotten.

2. Later Harland suggested on basis of geomagnetic data that glacial tillites (see this) in Svalbard and Greenland were deposited at tropical latitudes. In TGD framework with with R® R/2 these tillites would have been at higher latitudes towards North Pole.

3. The facts are that Sun was 6 per cent fainter at that time and glaciations are known to occur. The question is whether they were global and long-lasting or a sequence of short-lasting possibly local glaciations. The Russian climatologist Budyko constructed a model based on energy balance and found that it is possible to have a global glaciation if the ice sheets proceeded enough from polar regions (to about 30 degree latitude). The model was based on the increased reflectiveness (albedo) of the Earth's surface due to the ice covering giving rise to positive feedback loop. Budyko did not believe that global glaciation had occurred since the model offered no way to escape eternal glaciation.

4. Kirschwink introduced the term Snowball Earth, which is actually misleading. Iceball Earth would be more to to the point. He found that the so called banded iron formations are consistent with a global glaciation. He also proposed a mechanism for melting the snowball. The accumulation of CO₂ from volcanoes would have caused ultra-greenhouse effect causing warming of the atmosphere and melting of the ice.

5. Slushball Earth (see this) differs from Snowball Earth in that that only a thin ice cover or even its absence near equator is assumed. The model allows to explain various findings in conflict with Snowball Earth, such as the evidence for the presence of melt-water basins.

6. Zipper rift model (see this) assumes that there was a sequence of glaciations rather similar to the glaciations that have occurred later. The model assumes that the rifts (see this) of the super-continent Rodinia occurred simultaneously with glaciations. The associated tectonic uplift led to the formation of high plateaus hosting the glaciers. The iron band formation can be be assigned with inland seas allowing complex chemistries and anoxicity near the sea floor.

1. The basic ideas of the Snowball Earth model

Snowball Earth (see this, this and this) differs from ordinary glaciations in that only oceans are frozen whereas in the ordinary glaciation land mass is covered by ice. The basic ideas of the snowball Earth relate to the mechanism initiating the global freezing and melting.

1. The glaciation would have been initiated by some event, say a creation of super-volcano. Also astrophysical mechanism might be involved. Somewhat paradoxically, tropical continents during cryogenian period (see this) are needed for the initiation because they reflect the solar radiation more effectively than tropical oceans.

2. The positive ice-albedo feedback is an essential concept: the more ice the larger the fraction of the radiation reflected back so that the more ice is generated. If the glaciation proceeds over a critical latitude about 30 degrees positive feedback forces a global glaciation.

3. The problem of the model is how to get rid of the glaciation. The proposal of Kirschvink was that the accumulation of CO₂ from volcanoes could have led to a global super-warming. The time scale for CO₂ emissions is measured in millions of years. The needed atmospheric concentration of CO₂ is by a factor 350 higher than the recent concentration. Due the ice cover the CO₂ could not be absorbed to the siliceous rocks and concentration would increase. The melting of the ice meant higher absorbtion of heat by uncovered land. Positive feedback loop was at work again but in different direction.

2. Evidence for and objections against Snowball Earth

Wikipedia article about Snowball Earth (see this) discusses both evidence for and objections against Snowball Earth. Low latitude sediments at tropical latitudes and tropical tillites at Equatorial latitudes provide strong piece of evidence for Snowball Earth. Calcium carbonate deposits having ¹³C signature (per cent for the depletion of ¹³ isotope and large for organic material) consistent with that for mantle meaning abiotic origin is second evidence. Iridium anomaly located at the base of Calcium Carbonate deposits is third piece of evidence. The evidence for Snowball Earth will be discussed in more detail later since it is convenient to relate the evidence to R/2 model for glaciations.

1. Paleomagnetic data (see this) used to the dating of sediments assuming tectonic plane theory and super-continent drifting might be misleading. No pole wandering maps exist and the polarity of the magnetic field must be deduced by statistical methods. The primary magnetization could have been reset and the orientation of the magnetic minerals could have changed from the original one. It is also possible that magnetic field patterns were not dipolar. Also the assumption of hypothetical super-continents and oceans brings in uncertainties. In R/2 model of course the determination of the positions changes completely.

2. Carbon isotope ratios are not what they should be. There are rapid variations of ¹²C/¹³C ratio with organic origin. Suggests that freezing and melting followed each other in rapid succession. In standard framework this would suggest Slushball Earth meaning ice-free and ice-thin regions around the equator and hydrological cycles. In R/2 model the regions at Equator are near North Pole and the explanation would be in terms of ordinary glaciations.

3. The distribution of isotopes of element Boron suggest variations of pH of oceans. The explanation is in terms of buildup of carbon dioxide in atmosphere dissolved into oceans/seas. In R/2 model a sequence of glaciations would explain the findings.

4. Banded iron formations providing support for the model are actually rather rare and absent during Marinoan glaciation.

5. Wave-formed ripples, far-traveled ice-rafted debris and indicators of photosynthetic activity, can be found throughout sediments dating from the 'Snowball Earth' periods. This serves a evidence open-water deposits. In snow-ball model these could be 'oases' of melt-water but computer simulations suggest that large areas of oceans would have left ice-free. in R/2 model these would be signatures of ordinary glaciations.

6. Paleomagnetic data have led to the conclusion that Australia was at Equator. In R/2 model it would have been near North Pole. Namibia was also thought to be near Equator (see this). Indirect arguments forced the conclusion that it at 75 degree Southern latitude. In R/2 model this corresponds to 60 degrees Southern latitude and ordinary glaciation proceeding from South Pole is a natural explanation and ordinary glaciation would be in question in both cases.

7. There is evidence for the continental ice cover does not fit with Snowball Earth predicts that there should be no continental ice-cover. The reason is that freezing of the ocean means that there is no evaporation from oceans and no water circulation so that ice-cover cannot develop on continents. There is considerable evidence that continents were covered by thick ice (see this). This suggests ordinary glaciations possible in R/2 model.

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

Expanding Earth Theory and Pre-Cambrian Era: Part I

I already had a short posting about pre-Cambrian evolution in light of Expanding Earth hypothesis. Because of the profound implications of the hypothesis I decided to represent the model as short postings in the hope that it might find the response that it certainly would deserve.

Expanding Earth hypothesis is by no means not new. It was proposed by (see this) and I learned about it from the video animations of (see this and this) demonstrating that the continents fit nicely to form a single continent covering entire Earth if the radius is one half of the recent radius. What TGD has to give is a new physics justification for Expanding Earth hypothesis: cosmic expansion is replaced with a sequence of fast expansion periods increasing the value of Planck constant and these transitions occur in all scales.

If Expanding Earth hypothesis is correct it forces to modify dramatically the view about pre-Cambrian period. The super-continent theory could be replaced by much simpler theory and it might be possible to give up the assumption about hypothetical super continents and super oceans. The view about glaciations (see this) must be modified dramatically. Concerning the evolution of life the natural hypothesis is that it escaped to the underground seas formed as a consequence of expansion during pre-Cambrian era and returned back to the surface in Cambrian Explosion.

I have divided the discussion in short postings: 5 altogether. In the first posting I will discuss the notions of super-continents, super-oceans, and glaciations during Neoproterozoic period with short coments inspired by R/2 scenario. Next posting will discuss the dominating Snowball model for the climate during Neoproterozoic period in the same spirit. Third posting discussed 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.

Super-continents, super-oceans, and glaciations during Neoproterozoic period

1. Super-continent theory

Super-continent theory assumes a cyclic formation of hypothetical super continents (see this). Rodinia (see this), Pannotia (see this), and Pangea (see this) might have preceded by earlier super-continents. The period would be roughly 250 Myr.

1. The super-continent Rodinia (see this) is assumed to have existed during interval: 1100-750 Myr. 750 Myr ago Rodinia rifted into three continents: Proto-Laurasia which broke up and eventually reformed to form Laurasia (North America and Asia), the continental craton of Congo (part of Africa), and Gondwana (now southern hemisphere plus India).

2. Pannotia (see this) existed during time interval 600-540 Myr. Pannotia rifted in the beginning of Cambrian era to Laurentia (North America), Baltica, Siberia and Gondwana (see the illustration of Pannotia).

3. Wegener (see this) ended up to postulate that super-continent Pangea should have existed about 250 Myr ago (see this). The support for its existence is rather strong since tectonic plate model and paleo-magnetic methods allows to trace the drift of the tectonic plates.

One can criticize the cyclic model. The concentration of land mass to Southern Hemisphere during Rodinia period does not look very probable event. The cyclically occurring formation of connected land mass surrounded by much larger ocean looks even less probable unless one can develop some very good physical mechanism forcing this. The basic motivation for super-continent theory are various correlations between distant parts of Earth which would cannot be understood otherwise. In R/2 model the the continents would have been quite near to each other during the expansion and the notion of cyclic formation of super-continents becomes un-necessary since land bridges between the continents could explain the correlations. There would have been just single super-continent all the time.

2. Standard view about oceans

In the standard model the total area covered by oceans has reduced since pre-Cambrian era due to the increase of the continental cover, which is nowadays 29 per cent. Oceans cover the remaining 71 per cent with Antarctica and Arctica included. The evolution of Oceans in standard model requires the introduction of hypothetical oceans which left no trace about their existence (subduction mechanism provides perhaps too convenient trash bin for hypothetical theoretical constructs).

1. Proto-Atlantic Ocean was introduced to explain some contradictions with Wegener's Pangea model allowing to conclude which parts at opposite sides of Atlantic Ocean had been in contact. Proto-Atlantic Ocean closed as Pangea formed and opened again in slightly different manner to form Atlantic Ocean. This process implied mixing of older pieces of the continents and explained the contradictions. Large inland sea is a natural counterpart of the Proto-Atlantic Ocean in R/2 option.

2. Mirovia (see this) was the super-ocean surrounding Rodinia. It transformed to Pan-African Ocean surrounding Pannotia. Pan-African ocean was then closed so that the ocean floor of Mirovia disappeared by subduction and left no signs about its existence.

3. In the rifting (see this) of Pannotia Panthalassic ocean (see this) emerged and was the predecessor of the Pacific ocean.

The presence of super-oceans is forced by the assumption that the radius of Earth was the recent one during the pre-Cambrian era plus the local data related to the evolution of continents. The questionable aspect is that these oceans did not leave any direct trace about their existence. In R/2 model there is no need for these super-oceans except possibly the counterpart of Panthalassic Ocean (see this).

3. Glaciations during Neoproterozoic period

Glaciations dominated the Neoproterozoic period (see this) between 1-.542 billion years. The period is divided into Tonian (see this), Cryogenian (see this), and Ediacaran periods (see this). The most severe glaciations occurred during Cryogenian period.

It is believed that during Cryogenian period (see this) two worldwide glaciations -Sturtian and Marinoan glaciations- took place. This involves extrapolation of continental drift model and plate tectonics theory. Also hypothesis about hypothetical super-continents is needed so that one must take these beliefs with some skepticism. In R/2 model the world wide glaciations are replaced with ordinary glaciations proceeding from poles.

1. Sturtian glaciation occurred 750-700 Myr. The breakup of Rodinia is believed to have occurred at this time. One can wonder whether there is a correlation between these events. R/2 model suggest that the energy needed to compensate the reduction of gravitational energy in expansion could have caused the cooling.

2. Marinoan (Varanger) glaciation ended around 635 Myr ago.

Deposits of glacial tillites (see this) at low latitudes serve as support for the claim that these glaciations were world wide. In R/2 model Equator corresponds to North pole in TGD framework where Rodinia covered entire Earth and the interpretation would as ordinary glaciations.

After the end of Marinoan glaciation followed Ediacaran period during 635-542 Myr (see this). The first multicellular fossils appeared at this time. Their relationship to Cambrian fossils is unclear. The standard interpretation for the small number of fossils in pre-Cambrian period is that hard shells needed for fossilization were not yet developed. The problem is that these shells should have developed almost instantaneously in Cambrian explosion.

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