BCS super conductivity at almost room temperature

Towards the end of year 2018 I learned about the discovery of BCS type (ordinary) superconductivity at temperature warmer than that at North Pole (see this). The compound in question was Lantanium hydride LaH₁₀. Mihail Eremets and his colleagues found that it BCSame superconducting at temperate -23 C and high pressure 170 GPa about 1.6 million times the atmospheric pressure (see this).

The popular article proposed an intuitive explanation of BCS superconductivity, which was new to me and deserves to be summarized here. Cooper pairs would surf on sound waves. The position would correspond to a constant phase for the wave and the velocity of motion would be the phase velocity of the sound wave. The intensity of sound wave would be either maximum or minimum corresponding to a vanishing force on Cooper pair. One would have equilibrium position changing adiabatically, which would conform with the absence of dissipation.

This picture would conform with the general TGD based vision inspired by Sheldrakes's findings and claims related to morphic resonance (see this) , and by the conjectured general properties of preferred extremals of the variational principle implied by twistor lift of TGD (see this). The experimental discovery is of course in flagrant conflict with the predictions of the BCS theory. As the popular article tells, before the work of Eremets et al the maximum critical temperature was thought to be something like 40 K corresponding to -233 C.

The TGD based view is that Cooper pairs have members (electrons) at parallel flux tubes with opposite directions of magnetic flux and spin and have non-standard value of Planck constant h_eff= n× h₀= n× h/6 (see this and this), which is higher than the ordinary value, so that Cooper pairs can be stable at higher temperatures. The flux tubes would have contacts with the atoms of the lattice so that they would experience the sound oscillations and electrons could surf at the flux tubes.

The mechanism binding electrons to Cooper pair should be a variant of that in BCS model. The exchange of phonons generates an attractive interaction between electrons leading to the formation of the Cooper pair. The intuitive picture is that the electrons of the Cooper pair can be thought of lying on a mattress and creating a dip towards which the other electron tends to move. The interaction of the flux tubes with the lattice oscillations inducing magnetic oscillations should generate this kind of interaction between electrons at flux tubes and induce a formation of a Cooper pair.

Isotope effect is the crucial test: the gap energy and therefore critical temperature are proportional the oscillation frequency ω_D of the lattice (Debye frequency) proportional to 1/M^1/2 of the mass M of the molecule in question and decreases with the mass of the molecule. One has lantanium-hydroxide, and can use an isotope of hydrogen to reduce the Debye frequency. The gap energy was found to change in the expected manner.

Can TGD inspired model explain the isotope effect and the anomalously high value of Debye energy? The naive order of magnitude estimate for the gap energy is of form E_gap= x× hbar_effω_D, x a numerical factor. The larger the value of h_eff= n× h₀= n× h/6, the larger the gap energy. Unless the high pressure increases ω_D dramatically, the critical temperature 250 K would require n/6∼ T_cr/T_max(BCS)∼ 250/40∼ 6. For this value the cyclotron energy E_c= h_efff_c is much below thermal energy for magnetic fields even in Tesla range so that the binding energy must be due to the interaction with phonons.

The high pressure is needed to keep lattice rigid enough at high temperatures so that indeed oscillates rather than "flowing". I do not see how this could prevent flux tube mechanism from working. Neither do I know, whether high pressure could somehow increase the value of Debye frequency to get the large value of critical temperature. Unfortunately, the high pressure (170 GPa) makes this kind of high Tc superconductors unpractical.

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

Articles and other material related to TGD.

Intelligent blackholes

Thanks for Nikolina Benedikovic for kindly providing an interesting link and for arousing my curiosity. In the link one learns that Leonard Susskind has admitted that superstrings do not provide a theory of everything. This is actually not a mindblowing surprise since very few can claim that the news about the death of superstring theory would be premature. Congratulations in any case to Susskind: for a celebrated super string guru it requires courage to change one's mind publicly. I will not discuss in the following the tragic fate of superstrings. Life must continue despite the death of superstring theory and there are much more interesting ideas to consider.

Susskind is promoting an idea about growing blackholes increasing their volume as the swallow matter around them (see this). The idea is that the volume of the blackhole measures the complexity of the blackhole and from this its not long way to the idea that information - may be conscious information (I must admit that I cannot imagine any other kind of information) - is in question.

Some quantum information theorists find this idea attractive. Quantum information theoretic ideas find a natural place also in TGD. Magnetic flux tubes would naturally serving as space-time correlates for entanglement (the p-adic variants of entanglement entropy can be negative and would serve as measures of conscious information) and this leads to the idea about tensor networks formed by the flux tubes (see this). So called strong form of holography states that 2-D objects - string world sheets and partonic 2-surfaces as sub-manifolds of space-time surfaces carry the information about space-time surface and quantum states. M⁸-M⁴ ×CP₂ correspondence would realize quantum information theoretic ideas at even deeper level and would mean that discrete finite set of data would code for the given space-time surface as preferred extremal.

In TGD Universe long cosmic strings thickened to flux tubes would be key players in the formation of galaxies and would contain galaxies as tangles along them. These tangles would contain sub-tangles having interpretation as stars and even planets could be such tangles.

I just wrote an article describing a model of quasars (see this) based on this idea. In this model quasars need not be blackholes in GRT sense but have structure including magnetic moment (blackhole has no hair), an empty disk around it created by the magnetic propeller effect caused by radial Lorentz force, a luminous ring and accretion disk, and so called Elvis structure involving outwards flow of matter. One could call them quasi- blackholes - I will later explain why.

1. Matter would not fall in blackhole but magnetic and volume energy in the interior would transform to ordinary matter and mean thickening of the flux tubes forming a configuration analogous to flow lines of dipole magnetic fields by looping. Think of formation of dipole field by going around flux line replaced by flux tube, returning and continuing along another flux line/tube.
   
   
2. The dipole part of the structure would be cylindrical volume in which flux tubes would form structure consisting analogous to a coil in which one makes n₂ ≈ 10⁷ (G_N = R²/n₂h₀) windings in CP₂ direction and continues in different position in M⁴ and repeats the same. This is like having a collection of coils in M₄ but each in CP₂ direction. This collection of coils would fill the dipole cylinder having the case of quasar studied a radius smaller than the Schwartshild radius r_S ≈ 5×10⁹ km but with the same order of magnitude. The wire from given coil would continue as a field line of the magnetic dipole field and return back at opposite end of dipole cylinder and return along it to opposite pole. The total number of loops in the collection of n₁ dipole coils with n₂ windings in CP₂ direction is n₁ ×n₂.
   
   
3. What is unexpected that although the volume contribution to action assignable to cosmological constant is positive as it must be, the energy is negative (I have checked this many times but cannot find mistake)! Could the expansion of flux tubes liberating ordinary and dark matter particles (in TGD sense) as analog of the decay of inflaton field continue without limit? At certain flux tube radius the total energy becomes zero - this corresponds roughly to a biological length scale about 1 mm for the value of cosmological constant in the length scale of the observed universe (see this). Could the string tension become negative so that ordinary matter could be created without limit? It is quite possible that preferred extremal property prevents negative values of string tension but I have not found a good argument for this.
   

   Remark: Note that the twistor lift of TGD allows to consider entire hierarchy of cosmological constants behaving like 1/L(k)², where L(k) is p-adic length scale corresponding to p≈ 2^k.
   
   

4. Cosmological expansion would naturally relate to the thickening of the flux tubes, and one can also consider the possibility that the long cosmic string gets more and more looped (dipole field gets more and more loops) so that the quasi-blackhole would increase in size by swallowing more and more of long cosmic string spaghetti to the dipole region and transforming it to the loops of dipole magnetic field.
   
   
5. The quasar (and also galactic blackhole candidates and active galactic nuclei) would be extremely intelligent fellows with number theoretical intelligence quotient (number of sheets of the space-time surfaces as covering) about
   

   h_eff/h = n/6= n₁×n₂/6 > GMm(CP₂)/v₀×ℏ = (r_S/R(CP₂))× (1/2β₀),
   

   where one has β₀= v₀/c, where v₀ roughly of the order 10^-3c is a parameter with dimensions of velocity r_S is Schwartschild radius of quasi-blackhole of order 10⁹ km, and R(CP₂) is CP₂ radius of order 10^-32 meters. If this blackhole like structure is indeed cosmic string eater, its complexity and conscious intelligence increases and it would represent the brains of the galaxy as a living organism. This picture clearly resembles the vision of Susskind about blackholes.
   
   

6. This cosmic spaghetti eater has also a time reversed version for which the magnetic propellor effect is in opposite spatial direction: mass consisting of ordinary particles flows to the interior. Could this object be the TGD counterpart of blackhole? Or could one see both these objects as e blackholes dual to each other (maybe as analogs of white holes and blackholes)? The quasar like blackhole would eat cosmic string and its time reversal would swallow from its environment the particle like matter that its time reversed predecessor generated. Could one speak of breathing? Inwards breath and outwards breath would be time reversals of each other. This brings in mind the TGD inspired living cosmology based on zero energy ontology (ZEO) (see this) as analog of Penrose's cyclic cosmology, which dies and re-incarnates with opposite arrow of time again and again.
   
   

A natural question is whether also the ordinary blackholes are quasi-blackholes of either kind. In the fractal Universe of TGD this would look extremely natural.

1. How to understand the fusion of blackholes (or neutron stars, I will however talk only about blackholes in the sequel) to bigger blackhole observed by LIGO if quasi-blackholes are in question? Suppose that the blackholes indeed represent dipole light tangles in cosmic string. If they are associated with the same cosmic string, they collisions would be much more probable than one might expect. One can imagine two extreme cases for the motion of the blackholes. There are two options.
   
   
   1. Tangles plus matter move along string like along highway. The collision would be essentially head on collision.
      
      
   2. Tangles plus matter around them move like almost free particles and string follows: this would however still help the blackholes to find each either. The observed collisions can be modelled as a formation of gravitational bound state in which the blackholes rotate around each other first.
      
      
   The latter option seems to be more natural.
2. Do the observed black-hole like entities correspond to quasar like objects or their time reversals (more like ordinary blackholes). The unexpectedly large masses would suggests that they have not yet lost their mass by thickening as stars usually so that they are analogs of quasars. These objects would be cosmic string eaters and this would also favour the collisions of blackhole like entities associated with the same cosmic string.
   
   
3. This picture would provide a possible explanation for the evidence for gravitational echoes and evidence for magnetic fields in the case of blackholes formed in the fusion of blackholes in LIGO (see this). The echoes would result from the repeated reflection of the radiation from the inner blackhole like region and from the ring bounding the accretion disk.
   

   Note that I have earlier proposed a model of ordinary blackholes in which there would be Schwartschild radius but at some radius below it the space-time surface would become Euclidian. In the recent case the Euclidian regions would be however associated only with wormhole contacts with Euclidian signature of metric bounded by light-like orb its of partonic 2-surfaces and might have sizes of order Compton length scaled up by the value of h_eff/h for dark variants of particle and therefore rather small as compared to blackhole radius.
   
   

See the article TGD view about quasars or the chapter About the Nottale's formula for h_gr and the possibility that Planck length l_P and CP₂ length R are identical giving G= R²/ℏ_eff.

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

Articles and other material related to TGD.

Mice in magnetic fields

I received from Donald Adams a highly interesting link relating to the effects of magnetic field on mice. The claims of the article seem sensational. I do not know whether to trust on the claimed findings since from the viewpoint of TGD inspired quantum biology seem to be too good to be true. I attach a piece of article here reprinted from: Exotic Research Report (V3N1, Jan/Feb/Mar 1999) Magnetism ... A Natural Form of Energy by Walter C. Rawls Jr..

1. How animals dramatically change in relation to magnetic field exposure?

Twelve mice were placed in a cage to be used as controls (untreated). Another twelve mice were placed in a separate cage with exposure to the South pole field of a 2,000 gauss magnet, and the last twelve were put in a cage exposed to the North pole energies of a like magnet. An equal number of males and females were put in each cage. Exposure time was two months.

The untreated control mice behaved and functioned as normal mice. Without exception, the South pole mice slowly became very messy in their housekeeping, their appetites increased, they engaged in sex more, and their offspring were larger than those of the controls. Also, as time passed, they became mentally slow, loosing sensitivity to sound and light changes in the laboratory. Their young were difficult to teach the customary tests; they were lazy, listless, careless and very dirty in appearance.

The North pole mice became very neat and tidy, cleaning themselves frequently. They also became extremely sensitive to any noise or light variations in the laboratory. Their offspring were smaller than those of the controls. They were mentally superior to the controls and out performed the South pole young by several hundred percent in all phases of natural behavior.

The South pole mice were larger, grew faster, matured sooner, and mated continually. They also died earlier than their control counterparts. The North pole mice matured slower and lived 45 to 50 percent longer than the controls. They were also mentally superior to the controls and several hundred percent smarter than the South pole mice. They were much less frequent with sexual behavior than the South pole treated mice and less than the controls.

Rats were the next test subjects, and the results were the same as the findings with the mice. Rabbits and later cats were tested, again the results were the same as with the mice. These experiments are facts of the results of actual controlled experiments and are not theories or ideas. Anyone wishing to do so can reproduce these experiments.

Can we now program man to be more physical or mental, depending on the need of society? Based on our findings from these early experiments, we believe man can be conditioned in a like manner and his life expectancy extended far beyond what is now considered to be his three score and ten years.

Remembering that these tests were conducted on the entire body of the animal, could we by placing the North pole of a magnet directly at the center of the brain of larger animals and voluntary human subjects raise the intelligence and sensitivity?

2. Comments about claimed findings from TGD point of view

If true, these findings provide a direct evidence for the notion of magnetic body (MB) central in TGD inspired theory of consciousness and quantum biology. MB would use biological body as a motor instrument and sensory receptor and serves as an intentional agent. One could understand the findings as being due the loss of the control of the behavior performed by magnetic body as the south directed magnetic field is added. North directed magnetic field seems to have opposite effect.

The fields used are rather strong: the strength is 2 Tesla, by a factor of 10,000 stronger than the endogenous magnetic field B_end=.2 Gauss playing key role in TGD based quantum biology. This field has been assumed to define lower bound for the endogenous magnetic field strengths but it seems that also weak field strengths are possible down to the values where cyclotron energies of dark photons are proportional to h_eff ∝ m (and thus do not depend on mass of the charged particle and are universal) become smaller than thermal energy at physiological temperature.

2.1 Paramagnetic effect as strengthening of the coupling between MB and biological body?

The explanation for the effects could be that paramagnetic effect occurs and depending on the direction of the applied field increases or reduces the coupling of brain to Schumann resonances. The MB of the water and thus of living organisms and of their parts are indeed proposed to entrain with the Schumann resonances of the Earth's magnetic field by resonance coupling. These frequencies would be crucial for the control of biological body by MB.

Why the direction of external magnetic field does affect the situation? Brain contains magnetic molecules organised in the direction of Earth's magnetic field. The external field would tend increase or reduce the strength of these dipoles and the effect would be enhanced/reduced coupling to Schumann resonances for north/south directed external field. This would strengthen/weaken the communications/control by MB - the higher level intentional agent- and lead to the observed effects.

The frequencies of Schumann resonances indeed correspond to EEG resonance frequencies (see this). Callahan found that in the regions, where Schumann resonances are weak, there is a lot of social disorder so that Schumann resonances seem to be essential also for collective consciousness and well-being. Callahan also found that plants growth faster if the soil is paramagnetic.

2.2 The function of magnetite and other magnetic molecules in brain?

The function of magnetic molecules in brain has remained somewhat a mystery. Certainly they help to navigate but the function might be much deeper. Could magnetic molecules would build a stronger connection to the magnetosphere and magnetic body - could one say that they serve the role of antenna. This would be directly visible in EEG for instance. Resonances would be stronger and communications to and control by MB would be more effective.

Wikipedia article about magnetite tells also about the role of magnetite in brain. The text below contains also my comments.

1. Living organisms can produce magnetite. In humans, magnetite can be found in various parts of the brain including the frontal, parietal, occipital, and temporal lobes, brainstem, cerebellum and basal ganglia. Iron can be found in three forms in the brain – magnetite, hemoglobin (blood) and ferritin (protein), and areas of the brain related to motor function generally contain more iron. Magnetite can be found in the hippocampus associated with information processing, specifically learning and memory.
   

   Comment: If magnetite would serve only for navigation, it would be probably appear only in some special part(s) of brain.
   
   

2. Hemoblogin and ferritin contain iron. Hemoglobin is however only weakly paramagnetic whereas ferritin (protein!) nanoparticles can be superparamagnetic .
   

   Comment: What puts bells ringing is that Callahan found the addition of paramagnetic substances in soil to be beneficial for the plant growth by Callahan.
   
   

3. Magnetite can have toxic effects due to its charge or magnetic nature and its involvement in oxidative stress or the production of free radicals. Research suggests that beta-amyloid plaques and tau proteins associated with neurodegenerative disease (Alzherimer) frequently occur after oxidative stress and the build-up of iron.
   

   Comment: But could the higher level of paramagnetic iron be the reason for Alzheimer or is it due to due to attempt of brain to improve coupling to Schumann resonances and overcome the effects of Alzheimer? Same question has been made also concerning the plaques in axons emerging in Alzheimer (for TGD based model for Alzheimer see this).
   
   

2.3 Magnetic healing at the level of organisms and social structures?

Could one consider artificial strengthening of the coupling of brain to Schumann resonances as magnetic healing of not only biological but also social disorders? Could one just add magnetic molecules to brain? One cannot exclude this kind of possibility and it might be possible to test this with animals.

Many of us are well aware about the worsening situation in our society governed by market economy. Many researchers speak even about a possible collapse of our civilization. Also the strength of the magnetic field of Earth is weakening with a rate of 5 per cent per century (see this). Is this mere accident? It would be interesting to see whether something similar has happened for the local magnetic field during the collapses of the earlier civilizations. If there is a connection, could one imagine improving the situation by magnetic healing?

3. Side remark about spectrum of the strengths of B_end

The endogenous magnetic field B_end is in key role in TGD inspired quantum biology but also other field values than B_end are possible. The range of audible frequencies spanning the range 20 to about 20,000 Hz for humans corresponds to 3 orders of magnitude (10 octaves). Bats hear frequencies up to 200,000. This would give range of 4 orders of magnitude if they were able to hear frequencies down to 20 Hz, they are however able to hear only frequencies above 1 kHz. If also frequencies between 10-20 Hz present in EEG in wake-up state are counted, one obtains 4 orders of magnitude.

The spectrum of the magnetic field strengths has been assumed to correlate directly with the frequencies of heard sounds and to make it possible to map the audible frequencies to the frequencies of dark photon cyclotron radiation with the same frequency communicating the sound signal to MB. Note that dark particles correspond to ordinary particles but with non-standard value of Planck constant h_eff=n× h₀, h= 6× h₀. In the case of EEG the values of n are of the order of 10¹³.

For the most recent view about notion of magnetic body and the role of water entraining to Schumann frequency 60 Hz in the healing of cancer see this.

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

Articles and other material related to TGD.

Quantum theory cannot consistently describe the use of itself: really?

The article "Quantum theory cannot consistently describe the use of itself" of Frauchiger and Renner has created a lot of debate. The title sounds very Gödelian and gives for taste about the abstractness of the problems considered. There is also a popular article in
Quanta Magazine.

The authors claim that the thought experiment shows that the following 3 apparently innocent and obvious assumptions about quantum measurement theory are mutually inconsistent.

1. Quantum theory is universal, which means that agent - I translate it to conscious observer- can analyze second system, even a complex one including other agents, using quantum mechanics.
   
   
2. The predictions made by different agents using quantum theory are not contradictory. This looks trivial but perhaps the point is in the meaning of "prediction".
   
   
3. The outcome of quantum measurement is unique. This looks totally trivial but is not so in Many Worlds interpretation.
   
   

The article has created a lot of criticism and objections. It has been seen as an excellent manner to compare various interpretations of quantum theory and authors indeed do it. The article of Mateus Araujo and blog article of Lubos Motl claim that the article contains a computational error.

It is difficult to believe that authors could have made a computational error since the system is basically very simple and one essentially compares the outcomes of subsequent measurements for a pair of qubits with quantization axes rotated by 45 degrees with respect to those in the first measurements. I would seek the error is at the level of interpretation rather than computation. Authors assume that conscious entities are describable as extremely simple quantum systems (qubits) but simultaneously believe that they are classical entities with memories surviving in the further quantum measurements posed on them.

Scott Aaronson has a lot of fun with the assumption that conscious entities like humans are modelled as qubits.

The thought experiment

Alice and Bob measure their laboratories containing their friends F_A and F_B: the possible outcomes of measurements are specified. Reader can of course argue that measuring laboratories is not possible. Certainly it is not with recent technology but quantum theory does not deny this possibility. There are 4 measurements.

1. F_A measures a qubit - this is popularized as coin toss - and and codes the result to two spin states communicated to F_B as spin states. These are non-orthogonal - this is essential. One can assume that tail correspons to spin UP in z-direction that is state |UP> and and head corresponds to - say - spin UP but in direction making angle of 45 degrees with z-direction. The spin up state in this direction is superposition proportional to |UP> - | DOWN > .
   
   
2. F_B measures the spin in z-direction for the state communicated to him by F_A. The outcome is |UP> for tail but either |UP> or |DOWN> for head.
   

   If F_B observes |DOWN> he can conclude that F_A got head. This is the crucial bit of information and assumed to be stored in memory of agent F_B(whatever memory means!). Even more, F_B is assumed to keep the memory in the sequel under the measurements applied to laboratory by Bob. It is also assumed that all observers have memory surviving futher measurements. This is an implicit assumption and is about consciousness rather than quantum mechanics.
   

   Agents are assumed and to know their QM and be able to apply to it to deduce information about the measurement outcomes of others.
   
   

3. Alice in turn measures the state of her lab containing F_A, and coin. Now the state basis for coin (essentially qubit) is spanned by |OK_A > = |tail P>- | head > and |FAIL_A > = |tail P>+ | head > .
   
   
4. Bob does the same for his lab containing F_B and spin. These states basis are rotated by 45 degrees with respect to those used by F_A and F_B. The state basis is spanned by |OK_B > = |UP>- | DOWN > and |FAIL_B > = |UP> +| DOWN > .
   
   
5. The 4 possible final states are of form |OK_A > ⊗ |OK_B > , |OK_A > ⊗ |FAIL_B > , |FAIL_A > ⊗ |OK_B > , and |FAIL_A > ⊗ |FAIL_B >
   
   

The authors look what it means if Alice and Bob obtain state |OK_A > ⊗ |OK_B >. This state is obtained in 1/8 of all cases. It is trivial to see that this state contains state |tail > ⊗ |DOWN>. This state is however not a possible outcome in the measurements performed by F_A and F_B since |tail > corresponds to |DOWN> by the construction.

Authors claim that this is a paradox. If F_A and F_B, where just qubits, the authors would not speak of paradox. This kind of measurements have been done for ordinary spins and the predictions of QM have been verified.

There is no paradox if one just regards the systems as spins having no memory or if the memories are possible, they are affected in further measurements. Therefore the paradox must relate to the assumption that the outcomes of ealier measurements by agents F_A and F_B are stored in memory and that these memories are preserved under measurements by Alice and Bob. Since the agents in question have mind consisting of single qubit this assumption leads to a contradiction. There is no conflict between the 3 listed basic assumptions about QM. The paradox results from wrong assumptions about consciousness.

Suppose qubit minds are possible

What if one just for fun assumes that single bit minds are possible? The essential point is that coin⊗F_A, spin⊗F_B and F_A⊗Alice and F_B⊗ Bob represent different conscious entities than F_A, F_B, F_A, Alice and Bob before the state function reduction taking place in measurement in question. WhenX and Y are entangled, it is X⊗Y, which is conscious whereas X and Y are unconscious! This means loss of the memory. The moment of state function reduction producing unentangled product state is moment of consciousness for both X and Y (even for spin!). Hence the information about earlier measurement outcome is destroyed.

For genuine conscious entities the situation is probably different. They can store information about previous measurements so that it is preserved in further quantum measurements involving enanglement and no paradoxes appear. For instance, in the many-sheeted space-time of TGD involving fractal hierarchy of p-adic length scales and scales coming as scales proportional to effective Planck constant the memory storage is possible and biology provides the actual realization. There is also hierarchy of ...selves-subselves-sub-sub-selves.... whre sub-selves of self correspond to its mental images and selves at lower and also higher levels of the hierarchy can store information preserved in the state function reductions.

The view provide by zero energy ontology (ZEO)

In TGD framework ZEO provides some general insights about the notion of memory.

1. Zero energy states provide a generalization of the quantum states as pair of positive and negative energy states with vanishing total quantum numbers assignable to opposite boundaries of CD. Zero energy state can be regarded as superposition of deterministic classical time evolutions connecting initial and final states at boundaries of CD. The motivation for ZEO is that it resolves the basic paradox of quantum measurement theory since state function reduction replacing the superposition of deterministic time evolutions with a new superposition does not break the determinism of any time evolution.
   
   
2. During the lifecycle of self identified as a sequence of what I call small state function reductions (analogs of weak measurements, see Wikipedia), the members of state pairs at the passive boundary of causal diamond (CD) - remain unaffected. One can talk about generalized Zeno effect. The state at passive boundary represents conserved memories. Note that one has hierarchy of CDs inside CDs so that the situation is rather complex.
   
   
3. The states at the at the opposite -active - boundary of CD change. In each unitary evolution the active boundary of CD is de-localized in the moduli space of CDs and the small reduction involves localization in the moduli space of CDs, in particular time localization. The size of CD measured the temporal distance between its dips increases in statistical sense at least and this corresponds to clock time correlating strongly with subjective time defined by the sequence of reductions.
   
   
4. In big state function reduction the role of passive and active states change and CD begins to increase in opposite direction: conscious entity dies and reincarnates as time reversed one. These reductions correspond to the state function reductions occurring in say particle physics experiments and involve drastic change of the quantum state. The memories represented by the state at passive boundary are destroyed and the outcome of the big state function reduction at active boundary represents the new memories.
   
   
5. For minds with size of qubit, the memories would be indeed destroyed and new ones formed. For bigger minds it is quite possible that some sub-...-sub-selves in the hierarchy can preserve the memory and that it can be recalled in the subsequent re-incarnations in the original time direction. Sleep state could correspond at our level of consciousness to temporary death and re-incarnation at opposite time direction. We indeed remember something about yesterday, even previous year! Our mental images also die and re-incarnate and the interpretation would be as medemphychosis at the level of mental images.
   
   

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

Articles and other material related to TGD.

Still about twistor lift of TGD

Twistor lift of TGD led to a dramatic progress in the understanding of TGD but also created problems with previous interpretation. The new element was that Kähler action as analog of Maxwell action was replaced with dimensionally reduced 6-D Kähler action decomposing to 4-D Kähler action and volume term having interpretation in terms of cosmological constant.

Is the negativity of volume energy acceptable?

Twistor lift has the unexpected property that the volume energy is negative if one requires the volume contribution to action be positive. This forces a careful discussion of the situation.

1. One of the predictions was that positive coefficient of the volume term guaranteeing positivity of the action and thus of Kähler function for magnetic flux tube type extremals, led to a negative volume energy if Kähler energy is positive. It seems that one must accept this. It could of course be possible that preferred extremal property does not allow negative total classical energy.
   

   WCW metric must be positive definite. Since it is defined in terms of second partial derivatives of the Kähler function with respect to complex WCW coordinates and their conjugates, the preferred extremals must be completely stable to guarantee that this quadratic form is positive definite. This condition excludes extremals for which this is not the case. There are also other identifications for the preferred extremal property and stability condition would is a obvious additional condition. Note that at quantum criticality the quadratic form would have some vanishing eigenvalues representing zero modes of the WCW metric.
   

   Vacuum functional of WCW is exponent of Kähler function identified as negative of Kähler action for a preferred extremal. The potential problem is that Kähler action contains both electric and magnetic parts and electric part can be negative. For the negative sign of Kähler action the action must remain bounded, otherwise vacuum functional would have arbitrarily large values. This favours the presence of magnetic fields for the preferred extremals and magnetic flux tubes are indeed the basic entities of TGD based physics.
   

   One can ask whether the sign of Kähler action for preferred extremals is same as the overall sign of the diagonalized Kähler metric: this would exclude extremals dominated by Kähler electric part of action or at least force the electric part be so small that WCW metric has the same overall signature everywhere.
   
   

2. What is fascinating that the value of the coefficient of the volume term identified as the value of the empirically deduced value of cosmological constant is such that flux tubes structures with radius of order cell length scale define a fundamental scale above which gravitational binding energy would be higher than magnetic energy and total energy would become negative.
   

   What looks a strange that this could make it possible to generate matter from vacuum endlessly by generating negative gravitational energy. The mere assumption that the classical energy of flux tube cannot be negative looks ad hoc. There could be of course some dynamical restriction coming from preferred extremal property preventing this. Cosmological constant depends also on the extension of rationals and it is quite possible that for instance for canonically imbedded M⁴ with negative energy density the value of Λ vanishes.
   
   

Is the cosmological constant really understood?

The interpretation of the coefficient of the volume term as cosmological constant has been a longstanding interpretational issue and caused many moments of despair during years. The intuitive picture has been that cosmological constant obeys p-adic length scale scale evolution meaning that Λ would behave like 1/L_p²= 1/p≈ 1/2^k.

This would solve the problems due to the huge value of Λ predicted in GRT approach: the smoothed out behavior of Λ would be Λ∝ 1/a², a light-cone proper time defining cosmic time, and the recent value of Λ - or rather, its value in length scale corresponding to the size scale of the observed Universe - would be extremely small. In the very early Universe - in very short length scales - Λ would be large.

It has however turned out that I have not really understood how this evolution could emerge! Twistor lift seems to allow only a very slow (logarithmic) p-adic length scale evolution of Λ. Is there any cure to this problem?

1. Could one consider the total action for preferred extremals - at least flux tubes - as proportional to effective cosmological constant Λ_eff? Since magnetic energy decreases with the are of string like 1/p≈ 1/2^k, where p defines the transversal length scale of the flux tube, one would have effective p-adic coupling constant evolution of Λ_eff approaching to Λ, which must be extremely small.
   

   The corresponding size scale would correspond to the density of the magnetic energy equal to that of dark energy. Flux tubes with quantized flux would have thickness determined by the length scale defined by the density of dark energy: L∼ ρ_vac^-1/4, ρ_dark= Λ/8π G. ρ_vac∼ 10^-47 GeV⁴ (see this) would give L∼ 1 mm, which would could be interpreted as a biological length scale (maybe even neuronal length scale).
   
   

2. But can Λ be very small? In the simplest picture based on dimensionally reduced 6-D Kähler action this term is not small in comparison with the Kähler action! If the twistor spheres of M⁴ and CP₂ give the same contribution to the induced Kähler form at twistor sphere of X⁴, this term has maximal possible value!
   

   The original discussions treated the volume term and Kähler term in the dimensionally reduced action as independent terms and Λ was chosen freely. This is however not the case since the coefficients of both terms are proportional to 1/α_K²S, where S is the area of the twistor sphere which is same for the twistor spaces of M⁴ and CP₂ if CP₂ size defines the only fundamental length scale. I did not even recognize this mistake.
   
   

The proposed fast p-adic evolution of the cosmological constant would have extremely beautiful consequences. Could the original intuitive picture be wrong, or could the desired p-adic length scale evolution for Λ be possible after all? Could dynamics somehow give it? To see what can happen one must look in more detail the induction of twistor structure.

1. The induction of the twistor structure by dimensional reduction involves the identification of the twistor spheres S² of the geometric twistor spaces T(M⁴)= M⁴× S²(M⁴) and of T_CP2 having S²(CP₂) as fiber space. What this means that one can take the coordinates of say S²(M⁴) as coordinates and imbedding map maps S²(M⁴) to S²(CP₂). The twistor spheres S²(M⁴) and S²(CP₂) have in the minimal scenario same radius R(CP₂) (radius of the geodesic sphere of CP₂. The identification map is unique apart from SO(3) rotation R of either twistor sphere. Could one consider the possibility that R is not trivial and that the induced Kähler forms could almos cancel each other?
   
   
2. The induced Kähler form is sum of the Kähler forms induced from S²(M⁴) and S²(CP₂) and since Kähler forms are same apart from a rotation in the common S² coordinates, one has J_ind = J+R(J), where R denotes the rotation. The sum is J_ind=2J if the relative rotation is trivial and J_ind=0 if R corresponds to a rotation Θ→ Θ+π changing the sign of J= sin(Θ)dΘ ∧dΦ.
   
   
3. Could p-adic length scale evolution for Λ correspond to a sequence of rotations - in the simplest case Θ → Θ + Δ_k Θ taking gradually J from 2J at very short length scales to J=0 corresponding to Δ_∞ Θ=π at very long length scales? A suitable spectrum for Δ_k (Θ) could reproduce the proposal Λ ∝ 2^{-k for Λ.}
   
   
4. One can of course ask whether the resulting induced twistor structure is acceptable. Certainly it is not equivalent with the standard twistor structure. In particular, the condition J²= -g is lost. In the case of induced Kähler form at X⁴ this condition is also lost. For spinor structure the induction guarantees the existence and uniqueness of the spinor structure, and the same applies also to the induced twistor structure being together with the unique properties of twistor spaces of M⁴ and CP₂ the key motivation for the notion.
   
   
5. Could field equations associated with the dimensional reduction allow p-adic length scale evolution in this sense?
   
   
   1. The sum J+R(J) defining the induced Kähler form in S²(X⁴) is covariantly constant since both terms are covariantly constant by the rotational covariance of J.
      
      
   2. The imbeddings of S²(X⁴) as twistor sphere of space-time surface to both spheres are holomorphic since rotations are represented as holomorphic transformations. This in turn implies that the second fundamental form in complex coordinates is a tensor having only components of type (1,1) and (-1,-1) whereas metric and energy momentum tensor have only components of type (1,-1) and (-1,1). Therefore all contractions appearing in field equations vanish identically and S²(X⁴) is minimal surface and Kähler current in S²(X⁴) vanishes since it involves components of the trace of second fundamental form. Field equations are indeed satisfied.
      
      
   3. The solution of field equations becomes a family of space-time surfaces parametrized by the values of the cosmological constant Λ as function of S² coordinates satisfying Λ/8π G = ρ_vac=J∧(*J)(S²). In long length scales the variation range of Λ would become arbitrary small.
      
      
6. If the minimal surface equations solve separately field equations for the volume term and Kähler action everywhere apart from a discrete set of singular points, the cosmological constant affects the space-time dynamics only at these points. The physical interpretation of these points is as seats of fundamental fermions at partonic 2-surface at the ends of light-like 3-surfaces defining their orbits (induced metric changes signature at these 3-surfaces). Fermion orbits would be boundaries of fermionic string world sheets.
   

   One would have family of solutions of field equations but particular value of Λ would make itself visible only at the level of elementary fermions by affecting the values of coupling constants. p-Adic coupling constant evolution would be induced by the p-adic coupling constant evolution for the relative rotations R for the two twistor spheres. Therefore twistor lift would not be mere manner to reproduce cosmological term but determine the dynamics at the level of coupling constant evolution.
   
   

7. What is nice that also Λ=0 option is possible. This would correspond to the variant of TGD involving only Kähler action regarded as TGD before the emergence of twistor lift. Therefore the nice results about cosmology obtained at this limit would not be lost.
   
   

See the article TGD view about quasars or the chapter The Recent View about Twistorialization in TGD Framework of "Towards M-matrix".

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

Articles and other material related to TGD.

What does one really mean with gravitational Planck constant?

There are important questions related to the notion of gravitational Planck constant, to the identification of gravitational constant, and to the general structure of magnetic body. What gravitational Planck constant really is? What the formula for gravitational constant in terms of CP₂ length defining Planck length in TGD does really mean, and is it realistic? What space-time surface as covering space does really mean?

What does one mean with space-time as covering space?

The central idea is that space-time corresponds to n-fold covering for h_eff=n× h₀. It is not however quite clear what this statement does mean.

1. How the many-sheeted space-time corresponds to the space-time of QFT and GRT? QFT-GRT limit of TGD is defined by identifying the gauge potentials as sums of induced gauge potentials over the space-time sheets. Magnetic field is sum over its values for different space-time sheets. For single sheet the field would be extremely small in the present case as will be found.
   
   
2. A central notion associated with the hierarchy of effective Planck constants h_eff/h₀=n giving as a special case ℏ_gr= GMm/v₀ assigned to the flux tubes mediating gravitational interactions. The most general view is that the space-time itself can be regarded as n-sheeted covering space. A more restricted view is that space-time surface can be regarded as n-sheeted covering of M⁴. But why not n-sheeted covering of CP₂? And why not having n=n₁× n₂ such that one has n₁-sheeted covering of CP₂ and n₂-sheeted covering of M⁴ as I indeed proposed for more than decade ago but gave up this notion later and consider only coverings of M⁴? There is indeed nothing preventing the more general coverings.
   
   
3. n=n₁× n₂ covering can be illustrated for an electric engineer by considering a coil in very thin 3 dimensional slab having thickness L. The small vertical direction would serve and as analog of CP₂. The remaining 2 large dimensions would serve as analog for M⁴. One could try to construct a coil with n loops in the vertical direction direction but for very large n one would encounter problems since loops would overlap because the thickness of the wire would be larger than available room L/n. There would be some maximum value of n, call it n_max.
   

   One could overcome this limit by using the decomposition n=n₁× n₂ existing if n is prime. In this case one could decompose the coil into n₁ parallel coils in plane having n₂≥ n_max loops in the vertical direction. This provided n₂ is small enough to avoid problems due to finite thickness of the coil. For n prime this does not work but one can of also select n₂ to be maximal and allow the last coil to have less than n₂ loops.
   

   An interesting possibility is that that preferred extremal property implies the decomposition n_gr=n₁× n₂ with nearly maximal value of n₂, which can vary in some limits. Of course, one of the n₂-coverings of M⁴ could be in-complete in the case that n_gr is prime or not divisible by nearly maximal value of n₂. We do not live in ideal Universe, and one can even imagine that the copies of M⁴ covering are not exact copies but that n₂ can vary.
   
   

4. In the case of M⁴× CP₂ space-time sheet would replace single loop of the coil, and the procedure would be very similar. A highly interesting question is whether preferred extremal property favours the option in which one has as analog of n₁ coils n₁ full copies of n₂-fold coverings of M⁴ at different positions in M⁴ and thus defining an n₁ covering of CP₂ in M⁴ direction. These positions of copies need not be close to each other but one could still have quantum coherence and this would be essential in TGD inspired quantum biology.
   

   Number theoretic vision suggests that the sheets could be related by discrete isometries of CP₂ possibly representing the action of Galois group of the extension of rationals defining the adele and since the group is finite sub-group of CP₂, the number of sheets would be finite.
   

   The finite sub-groups of SU(3) are analogous to the finite sub-groups of SU(2) and if they action is genuinely 3-D they correspond to the symmetries of Platonic solids (tetrahedron,cube,octahedron, icosahedron, dodecahedron). Otherwise one obtains symmetries of polygons and the order of group can be arbitrary large. Similar phenomenon is expected now. In fact the values of n₂ could be quantized in terms of dimensions of discrete coset spaces associated with discrete sub-groups of SU(3). This would give rise to a large variation of n₂ and could perhaps explain the large variation of G identified as G= R²(CP₂)/n₂ suggested by the fountain effect of superfluidity.
   
   

5. There are indeed two kinds of values of n: the small values n=h_em/h₀=n_em assigned with flux tubes mediating em interaction and appearing already in condensed matter physics and large values n=h_gr/h₀=n_gr associated with gravitational flux tubes. The small values of n would be naturally associated with coverings of CP₂. The large values n_gr=n₁× n₂ would correspond n₁-fold coverings of CP₂ consisting of complete n₂-fold coverings of M⁴. Note that in this picture one can formally define constants ℏ(M⁴)= n₁ℏ₀ and ℏ(CP₂)= n₂ℏ₀ as proposed for more than decade ago.
   
   

Planck length as CP₂ radius and identification of gravitational constant G

There is also a puzzle related to the identification of gravitational Planck constant. In TGD framework the only theoretically reasonable identification of Planck length is as CP₂ length R(CP₂), which is roughly 10^3.5 times longer than Planck length. Otherwise one must introduce the usual Planck length as separate fundamental length. The proposal was that gravitational constant would be defined as G =R²(CP₂)/ℏ_gr, ℏ_gr≈ 10⁷ℏ. The G indeed varies in un-expectedly wide limits and the fountain effect of superfluidity suggests that the variation can be surprisingly large.

There are however problems.

1. Arbitrary small values of G=R²(CP₂)/ℏ_gr are possible for the values of ℏ_gr appearing in the applications: the values of order n_gr ∼ 10¹³ are encountered in the biological applications. The value range of G is however experimentally rather limited. Something clearly goes wrong with the proposed formula.
   
   
2. Schwartschild radius r_S= 2GM = 2R²(CP₂)M/ℏ_gr would decrease with ℏ_gr. One would expect just the opposite since fundamental quantal length scales should scale like ℏ_gr.
   
   
3. What about Nottale formula ℏ_gr= GMm/v₀? Should one require self-consistency and substitute G= R²(CP₂)/ℏ_gr to it to obtain ℏ_gr=(R²(CP₂)Mm/v₀)^1/2. This formula leads to physically un-acceptable predictions, and I have used in all applications G=G_N corresponding to n_gr∼ 10⁷ as the ratio of squares of CP₂ length and ordinary Planck length.
   
   

Could one interpret the almost constancy of G by assuming that it corresponds to ℏ(CP₂)= n₂ℏ₀, n₂≈ 10⁷ and nearly maximal except possibly in some special situations? For n_gr=n₁× n₂ the covering corresponding to ℏ_gr would be n₁-fold covering of CP₂ formed from n₁ n₂-fold coverings of M⁴. For n_gr=n₁× n₂ the covering would decompose to n₁ disjoint M⁴ coverings and this would also guarantee that the definition of r_S remains the standard one since only the number of M⁴ coverings increases.

If n₂ corresponds to the order of finite subgroup G of SU(3) or number of elements in a coset space G/H of G (itself sub-group for normal sub-group H), one would have very limited number of values of n₂, and it might be possible to understand the fountain effect of superfluidity from the symmetries of CP₂, which would take a role similar to the symmetries associated with Platonic solids. In fact, the smaller value of G in fountain effect would suggest that n₂ in this case is larger than for G_N so that n₂ for G_N would not be maximal.

See the article TGD View about Quasars or the chapter About the Nottale's formula for h_gr and the possibility that Planck length l_P and CP₂ length R are identical giving G= R²/ℏ_eff.

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

Articles and other material related to TGD.

TGD view about quasars

The work of Rudolph Schild and his colleagues Darryl Letier and Stanley Robertson (among others) suggests that quasars are not supermassive blackholes but something else - MECOs, magnetic eternally collapsing objects having no horizon and possessing magnetic moment. Schild et al argue that the same applies to galactic blackhole candidates and active galactic nuclei, perhaps even to ordinary blackholes as Abhas Mitra, the developer of the notion of MECO proposes.

In the sequel TGD inspired view about quasars relying on the general model for how galaxies are generated as the energy of thickened cosmic strings decays to ordinary matter is proposed. Quasars would not be be blackhole like objects but would serve as an analog of the decay of inflaton field producing the galactic matter. The energy of the string like object would replace galactic dark matter and automatically predict a flat velocity spectrum.

TGD is assumed to have standard model and GRT as QFT limit in long length scales. Could MECOs provide this limit? It seems that the answer is negative: MECOs represent still collapsing objects. The energy of inflaton field is replaced with the sum of the magnetic energy of cosmic string and negative volume energy, which both decrease as the thickness of flux tube increases. The liberated energy transforms to ordinary particles and their dark variants in TGD sense. Time reversal of blackhole would be more appropriate interpretation. One can of course ask, whether the blackhole candidates in galactic nuclei are time reversals of quasars in TGD sense.

The writing of the article led also to a considerable understanding of two key aspects of TGD. The understanding of twistor lift and p-adic evolution of cosmological constant improved considerably. Also the understanding of gravitational Planck constant and the notion of space-time as a covering space became much more detailed in turn allowing much more refined view about the anatomy of magnetic body.

See the article TGD View about Quasars
or the chapter About the Nottale's formula for h_gr and the possibility that Planck length l_P and CP₂ length R are identical giving G= R²/ℏ_eff.

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

Articles and other material related to TGD.

Twistor lift for 2-D objects

TGD involves also 2-D objects - partonic 2-surfaces and string world sheets in an essential manner and strong form of holography (SH) states that these objects carry the information about quantum states. This does not mean that the dynamics would reduce to that for string like objects since it is essential that these objects are sub-manifolds of space-time surface. String world sheets carry induced spinor fields and it seems that these are crucial for understanding elementary particles. There are several questions to be answered.

1. Are fermionic fields localized to 2-surfaces? The generalization superconformal symmetry fixing both the bosonic and fermion parts of the action requires that also the interior of space-time carries induced spinor field. Their interpretation is not quite clear: could they perhaps give rise to a supersymmetry? The condition of super-symmetry fixes the analog of massless Dirac action uniquely for both string world sheets and interior of space-time surface. The situation is not clear for the partonic 2-surfaces, which are in special role physically in zero energy ontology (ZEO). There is an infinite number of conserved super currents associated with the modes of the modified Dirac operator defining fermionic super generators. This leads to quantum classical correspondence stating that the eigenvalues of Cartan generators for the fermionic representations of Noether charges are equal to corresponding classical Noether charges defined by the space-time dynamics.
   
   
2. A long-standing question has been whether stringlike objects and partonic 2-surfaces are fundamental dynamical objects or whether they emerge only at the level of effective action. M⁸-H duality states that space-time surfaces M⁸ picture are associative in the sense that either tangent or normal space of space-time surface at any vpoint is associative and therefore quaternionic.
   

   Number theoretic vision suggests that also 2-D objects are fundamental. In number theoretic vision also commutative sub-manifolds of space-time surfaces having induced quaternionic structure reducing to commutative (complex) structure are very natural. Either the tangent space or normal space of 2-surface can be commutative and this gives rise to string world sheets and partonic 2-surfaces as duals of each other just as space-time surfaces have regions for which either tangent spaces or normal spaces are associative (these correspond to regions of space-time with Minkowskian resp. Euclidian signatures of the induced metric). The reduction of the theory to mere string theory is not possible since partonic two surfaces have commutative normal space (partonic 2-surfaces) as part of the tangent space of space-time surface.
   
   

3. What action one should assign with the 2-D objects. The action should be assigned to string world sheets and partonic 2-surfaces representing vertices but the assignent of action with partonic 2-surfaces at the ends of CD does not look natural since they are in the role of initial values. The first guess for the action is as area action. Fermionic action would be fixed uniquely in terms of modified gamma matrices reducing to induced gamma matrices.
   

   Also space-time surfaces in the simplest scenario are minimal surfaces except for a discrete set of singular points at which there is energy transfer between Kähler action and volume term. Something similar is expected also in 2-D case: there must also second part in the action and transfer of Noether changes between the two parts in this set of points.
   

   These points have an identification as point-like particles carrying fermion number and located at partonic 2-surfaces at boundaries of causal diamond (CD) or defining topological vertices so that a classical space-time correlates for twistor diagrams emerge.
   

   Since particles in twistor approaches are associated with the ends of string boundaries at the ends of light-like orbits of partonic 2-surfaces at boundaries of causal diamond (CD), the exceptional points for both space-time surface and string world sheet would correspond to the intersections of string world sheets and partonic 2-surfaces defining also counterparts of vertices.
   
   

Twistor lift provides a first principle approach to the action assignable to the 2-D surfaces.

1. The simplest possibility is that one has also now a Kähler action but now for 4-D space-time surface in the product of twistor spaces of M⁴ and CP₂ dimensional reduced to Cartesian product of twistor sphere S² and 2-D surface representing string world sheet. The assigment of action to partonic 2-surface at the boundary of CD or 2-D generalization of vertex does not look feasible. 4-D Kähler action would be dimensionally reduced to 2-D form and area term.
   
   
2. Field equations contain two terms coming from the variation with respect to the induced metric and Kähler form respectively. The terms coming from the variation with respect to metric vanishes for minimal surfaces since energy momentum tensor is proportional to the induced metric. The term coming from the variation with respect to induced Kähler form need not vanish for minimal surfaces unless there are additional conditions.
   

   The term is of the same form as in 4-D case, which case this term vanishes for holomorphic solutions and also for all known extremals, and there are excellent reasons that this is true also in 2-D case. It therefore seems that minimal surfaces are in question except for discrete set of points as in 4-D case: this conforms with universality forced by quantum criticality stating that Kähler coupling constant disappears from dynamics except in this discrete set of points.
   

   In accordance with SH, this set of points at which minimal surface property fails would define also the correponding points for space-time surface itself. This singularity could mean breakdown of holomorphy, perhaps analogs of poles for analytic functions are in question. One cannot of course exclude the possibility that the boundaries of string world sheets defining orbits of fundamental fermions are analogous to cuts for holomorphic functions.
   
   

3. 2-D minimal surfaces in space-time are also minimal surfaces in imbedding space since the induction from space-time to 2-surface can be also thought of as an induction from imbedding space. SH suggest that space-time as 4-D surface is determined by fixing the 2-D minimal surfaces and finding space-time surface containing them. This space-time surface need not always exist, and one of the key ideas about cognition is that in p-adic case the possibility of p-adic pseudo-constants allows the existence of p-adic space-time surfaces always but that in real case this is not always the case: what is imaginable is not necessarily realizable.
   

   At the level of M⁸ the condition that the coefficients of a polynomial determining the space-time surface are in extension of rationals is very powerful condition and might prevent the extension. As a matter fact, SH becomes at the level of M⁸ even stronger: discrete set of points naturally identifiable as the set of singular points and thus poles of analytic function basically would determine the space-time surface. If fermion lines correspond to cuts, this super-strong form of SH would weaken. For polynomials considerws here cuts are however not possible and they should be generated in the map from H to M⁴× CP₂.
   
   

For details and background see the article Some Questions Related to the Twistor Lift of TGD or the chapter of "Towards M-matrix" with the same title.

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

Articles and other material related to TGD.

Interpretation of the experiments of Montagnier et al

One can make the model of MB more detailed by applying it the experiments of Montagnier et al discussed already earlier from TGD viewpoint (see this). I have developed in collaboration with Peter Gariaev a model for analogous observations by this group (see this).

Consider first a very rough sketch of the experiments.

1. A fragment of DNA was amplified by PCR. It was diluted to say 10^-6 by adding pure water and found to generate EMS at ULF frequency range .5-3 kHz. Call this sample A.
   
   
2. Dilution was put in mu-mental container, which does not allow ULF radiation to get out. In its vicinity another tube, call it B, containing pure water was placed. The water content of each tube was filtered through 450 nm and 20 nm filters. Filtering does not allow particles with size smaller than 20 nm to go through. The samples were diluted to 10^-15 by adding pure water. During each dilution a mechanical agitation of water by generating a vortex was performed.
   
   
3. Copper solenoid producing 7 Hz current was added around the samples. Eventually EMS was found in both A and B. In B there was primer, DNA polymerase, and free nucleotides but not the template complementary strand as in ordinary polymerase chain reaction.
   
   

The TGD interpretation for what happened in sample A would be following.

1. As explained ordinary DNA strand is paired with dark DNA strand for which dark proton triplets at flux tube parallel to ordinary DNA strand represent the codons. This is analog of pairing of DNA strand and its conjugate.
   
   
2. The cyclotron transitions of dark protons (possibly also those changing the direction of spin) generate the ULF radiation as classical em fields accompanied dark photons transformed to ordinary photons. The energies of dark photons are given by E= h_grf and should be above thermal energy at physiological temperatures. The transformations of dark photons to ordinary photons give rise to bio-photons with energies in visible and UV, and possibly also below this range.
   
   
3. Dilution eliminated ordinary DNA from A but left some dark DNA strands to the water. This is nothing but the phantom DNA phenomenon discovered by Gariaev and collaborators. In case of water memory one has phantoms of bio-active molecules. I have applied TGD also to other experimental findings and ideas by Gariaev et al. In particular there are articles written in collaboration about the TGD realization of identification of DNA as hologram and about DNA remote replication analogous to what happens in Montagnier's experiments (see this).
   
   
4. The interpretation of the agitation carried out also in the preparation of homeopathic remedies is that it provided metabolic energy needed to generate large h_eff. Quite generally, the energy of dark variant is larger than that of ordinary state: for instance, cyclotron energy is proportional to h_eff and atomic binding energies to 1/h_eff² so that metabolic energy is needed.
   

   The analogy with ordinary DNA and the idea that DNA replication is a shadow of the replication of dark DNA suggests that dark DNA replicated and a population of dark DNA mimicking ordinary DNA was generated in the diluted water sample A. More generally, water would perform mimicry of bio-active molecule by using dark protons at its magnetic body to generate the cyclotron frequency spectrum of the molecule. An interesting possibility is that dark proton sequences - dark nuclei - perform this mimicry.
   
   

5. The general model suggests that dark DNA generate transversal flux tubes at transversal sheets going through it. One could start by saying loosely that dark photon cyclotron radiation propagated along these flux tubes to the pure water sample, where there was flux tube receiving this radiation. But what the precise meaning of this statement could be, becomes more clear in the following.
   
   

What happened in the pure water sample?

1. Dark photon radiation at ULF frequencies should have caused the generation of dark DNA strands also in pure water sample. The water in the pure water sample mimicked the dark photon radiation by the basic homeopathic mechanism and generated dark DNA strands with transversal flux tubes at transversal flux sheets carrying magnetic fields corresponding to the cyclotron frequencies of dark DNA nucleotides.
   
   
2. Did a pairing of dark DNA in A and its conjugate in B analogous to the pairing of DNA and its conjugate take place? As in the ordinary DNA pairing the pairing would be favored by the minimization of interaction energy. The flux tubes connecting the members of the pair would be like stretched hydrogen bonds between DNA strand and its conjugate so that it would be very long, of order cyclotron wavelength of proton in the magnetic field of flux tube. TGD indeed predicts that hydrogen bonds have length spectrum corresponding to various values of h_eff. In this case however rather small values are involved. Now the values would be very large by h_eff=h_gr.
   
   
3. Did the transversal flux tubes attach to the dark DNA flux tubes directly and have length of the order of distance between samples? Or did the flux tubes from water sample combine to many-sheeted gravitational flux tube with length of the order of cyclotron frequency of proton? The latter option is favored.
   

   The dark photons assignable to the frequency range .5-3 kHz should have energies above thermal energy at physiological temperature in order to have physiological effects. This requires h_eff≥ 6× 10¹⁰: f=.5 kHz would correspond to a thermal energy of photon for most probable wavelength about 10 μm.
   

   A reasonable estimate for the length of the flux tubes involved comes from the cyclotron wavelength of proton. The cyclotron frequency .5-3.0 kHz for proton requires magnetic field about .3 -2.0 Gauss somewhat stronger than B_end=.2 Gauss (B_E=.5 Gauss). The cyclotron wavelength would be in the range .1-.6 Mm (Earth radius is 6.4 Mm) so that the analogs of hydrogen bonds would be very long!
   
   

4. The generation of ordinary DNA strands in this sample would have been by the analog of DNA - dark DNA pairing that should occur in standard biology. The DNA fragment in pure water sample was reproduced as if the complementary strand would have been present.
   
   
5. As already explained, the dark protons are at single sheeted ordinary flux tubes accompanying DNA. n_gr flux tubes from various positions would combine n_gr-sheeted flux tube with same M⁴ projection as ordinary flux tube: they were on top of each other in M⁴× CP₂. Why the protons deserved to be called dark is that the proton sequences at n_gr separate flux tubes form single quantum coherent many-proton states somewhat analogous to Bose-Einstein condensate. Cyclotron energy is therefore naturally n_gr times the cyclotron energy of single state. This is essentially quantum non-locality made possible by the locality at the gravitational flux tube quantum controlling the system. Also dark photons having n_gr-fold energy non-local many-photon states with one photon at each flux tube with same energy and momentum.
   
   
6. Also 7 Hz frequency is necessary for the effect to occur. A natural guess is that this frequency is related to Schumann resonances (see this), which are associated with collective oscillations in the Earth's magnetic field in the cavity bounded by Earth's surface and ionosphere in which em waves cannot propagate. Schumann resonances dominate the frequency spectrum from 3 Hz to 60 Hz - a considerable part of EEG - and there are distinct peaks at frequencies resonance 7.81, 14.3, 20.8, 27.3 and 33.8 Hz.
   

   In the linear model Schumann resonances treating atmosphere as vacuum Schumann resonance frequencies f_n= (n(n+1))^1/2c/2π R_E are determined by the geometry alone with lowest resonance at 7.41 Hz for R_E= 6371 km. The finite conductivity of atmosphere lowers the propagation velocity of light and the frequencies are reduced. This can bring the resonance frequency 7.81 Hz nearer to 7 Hz, and there is of course also the continuum besides the resonance peaks.
   

   In TGD picture the quasi-continuum would relate to the many-sheetedness of the space-time surface making it possible for light to propagate along large number of flux tube paths so that the effective light-velocity would vary. A more precise model give also a resonance at 4.11 Hz. This resonance frequency however varies due to the several factors.
   

   The interpretation of Schumann resonances 7.81, 14.3, 20.8, 27.3 and 33.8 Hz and higher resonances as resonance frequencies of EEG is highly attractive. At higher frequencies the resonances appear approximately with 6.5 Hz intervals. Next resonance would be at 40.3 Hz, which is the familiar thalamo-cortical resonance frequency to which consciousness was once assigned. 8:th partial wave has resonance frequency 60 Hz which happens to be the frequency appearing in the experiments of Li and Heroux. 4 Hz frequency in turn is theta resonance frequency in EEG.
   

   This supports the view that water entrains to Schumann frequencies by tuning to cyclotron frequencies by varying the thickness of flux tubes of its MB so that the coupling of living matter to the oscillations of Earth's magnetic field would play fundamental role in biology and neuroscience. The testable prediction is the correlation of EEG with the local Schumann resonance spectrum of Earth independent of individual.
   

   Dr. Phil Callahan claims on basis of intensive experimental work that there is a tendency of political strifes and wars to concentrate on regions where Schumann resonances are weak. In the proposed picture this would not be surprising. The reduction in the level of consciousness would imply strifes and wars at the level of society and cancer at the level of cell community.
   
   

For details see the article Could Cancer be a Disease of Magnetic Body? by Dana Flavin and me or alternatively the chapter of "Biosystems as Conscious holograms" with the same title.

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

Articles and other material related to TGD.