Year 2018

Unexpected support for nuclear string model

Nuclear string model (see this) replaces in TGD framework the shell model. Completely unexpected support for nuclear string model emerged from a research published by CLAS Collaboration in Nature (see this). The popular article "Protons May Have Outsize Influence on Properties of Neutron Stars" refers to possible implications for the understanding of neutron stars but my view is that the implications might dramatically modify the prevailing view about nuclei themselves. The abstract of popular article reads as (see this).

"A study conducted by an international consortium called the CLAS Collaboration, made up of 182 members from 42 institutions in 9 countries, has confirmed that increasing the number of neutrons as compared to protons in the atom’s nucleus also increases the average momentum of its protons. The result, reported in the journal Nature, has implications for the dynamics of neutron stars."

The finding is that protons tend to pair with neutrons. If the number of neutrons increases, the probability for the pairing increases too. The binding energy of the pair is liberated as kinetic energy of the pair - rather than becoming kinetic energy of proton as the popular text inaccurately states.

Pairing does not fit with shell model in which proton and neutron shells correlate very weakly. The weakness of proton-neutron correlations in nuclear shell model looks somewhat paradoxical in this sense since - as text books tell to us - it is just the attractive strong interaction between neutron and proton, which gives rise to the nuclear binding.

In TGD based view about nucleus protons and neutrons are connected to nuclear strings with short color flux tubes connecting nucleons so that one obtains what I call nuclear string (see this). These color flux tubes would bind nucleons rather than nuclear force in the conventional sense.

What can one say about correlations between nucleons in nuclear string model? If the nuclear string has low string tension, one expects that nucleons far away from each other are weakly correlated but neighboring nuclei correlate strongly by the presence of the color flux tube connecting them.

Minimization of repulsive Coulomb energy would favor protons with neutrons as nearest neighbors so that pairing would be favored. For instance, one could have n-n-n... near the ends of the nuclear string and -p-n-p-n-... in the middle region and strong correlations and higher kinetic energy. Even more neutrons could be between protons if the nucleus is neutron rich. This could also relate to neutron halo and the fact that the number of neutrons tends to be larger than that of protons. Optimistic could see the experimental finding as a support for nuclear string model.

Color flux tubes can certainly have charge 0 but also charges 1 and -1 are possible since the string has quark and antiquark at its ends giving uubar, ddbar, udbar, dubar with charges 0,0,-1,+1. Proton plus color flux tube with charge -1 would effectively behave as neuron. Could this kind of pseudo neutrons exist in nucleus? Or even more radically: could all neurons in the nucleus be this kind of pseudo neutrons?

The radical view conforms with the model of dark nuclei as dark proton sequences - formed for instance in Pollack effect (see this) - in which some color bonds can become also negatively charged to reduce Coulomb repulsion. Dark nuclei have scaled down binding energy and scaled up size. They can decay to ordinary nuclei liberating almost all ordinary nuclear binding energy: this could explaining "cold fusion" (see this).

See the chapter Nuclear string model.

About the physical interpretation of the velocity parameter in the formula for the gravitational Planck constant

Nottale's formula for the gravitational Planck constant hbar_gr= GMm/v₀ involves parameter v₀ with dimensions of velocity. I have worked with the quantum interpretation of the formula but the physical origin of v₀ - or equivalently the dimensionless parameter β₀=v₀/c (to be used in the sequel) appearing in the formula has remained open hitherto. In the following a possible interpretation based on many-sheeted space-time concept, many-sheeted cosmology, and zero energy ontology (ZEO) is discussed.

A generalization of the Hubble formula β=L/L_H for the cosmic recession velocity, where L_H= c/H is Hubble length and L is radial distance to the object, is suggestive. This interpretation would suggest that some kind of expansion is present. The fact however is that stars, planetary systems, and planets do not seem to participate cosmic expansion. In TGD framework this is interpreted in terms of quantal jerk-wise expansion taking place as relative rapid expansions analogous to atomic transitions or quantum phase transitions. The TGD based variant of Expanding Earth model assumes that during Cambrian explosion the radius of Earth expanded by factor 2.

There are two measures for the size of the system. The M⁴ size L_M⁴ is identifiable as the maximum of the radial M⁴ distance from the tip of CD associated with the center of mass of the system along the light-like geodesic at the boundary of CD. System has also size L_ind defined defined in terms of the induced metric of the space-time surface, which is space-like at the boundary of CD. One has L_ind<L_M⁴. The identification β₀= L_M⁴/L_H<1 does not allow the identification L_H=L_M⁴. L_H would however naturally corresponds to the size of the magnetic body of the system in turn identifiable as the size of CD.

One can deduce an estimate for β0 by approximating the space-time surface near the light-cone boundary as Robertson-Walker cosmology, and expressing the mass density ρ defined as ρ=M/VM4, where VM4=(4π/3) LM43 is the M4 volume of the system. ρ can be expressed as a fraction ε2 of the critical mass density ρcr= 3H2/8π G. This leads to the formula β0= [rS/LM4]1/2 × (1/ε), where rS is Schwartschild radius.

This formula is tested for planetary system and Earth. The dark matter assignable to Earth can be identified as the innermost part of inner core with volume, which is .01 per cent of the volume of Earth. Also the consistency of the Bohr quantization for dark and ordinary matter is discussed and leads to a number theoretical condition on the ratio of the ordinary and dark masses.

See the chapter Quantum Criticality and dark matter or the article About the physical interpretation of the velocity parameter in the formula for the gravitational Planck constant.

An island at which body size shrinks

I encountered in Facebook an article claiming that the bodies of animals shrink at the island of Flores belonging to Indonesia. This news is not Dog's days news (Dog's days news is a direct translation from the finnish synonym for fake news).

Both animals and humans really are claimed to have shrinked in size. The bodies of both hominins (predecessors of humans, humans, ane even elephants) have shrinked at Flores.

1. In 2003, researchers discovered in a mountain cave in the island of Flores fossils of tiny, humanlike individual. It had chimp sized brain and was 90 cm tall. Several villages at the area are inhabited by people with average body height about 1.45 meters.
2. Could the small size of the recent humans at Flores be due to interbreeding between modern humans with Homo Florensiensis (HF) occurred long time ago? The hypothesis could be tested by studying the DNA of HF. Since the estimate age of fossils of HF was 10,000 years, researchers hoped that they could find some DNA to HF. DNA was not found but researchers realized that if HF as interbreeded with humans, this DNA could show itself in DNA of modern humans at Flores. It was found that this DNA can be identified but differs insignificantly from that of modern humans. It was also found that the age of the fossils was about 60,000 years.
3. Therefore it seems that the interbreeding did not cause the reduction in size. The study also showed that at least twice in the ancient history of humans and their relatives arrived as Flores and then grew shorter. This happened also for elephants that arrived to Flores at twice.

1. The hierarchy of Planck constants h_eff=nh₀ (h=6h₀ is a good guess ) assigned with dark matter as phases of ordinary matter and responsible for macroscopic quantum coherence is central in TGD inspired biology . Quantum scales are proportional to or its power (h_eff² for atoms, h_eff for Compton length, and h_eff^{1/2 for cyclotron states).}
2. The value of gravitational Planck constant h_gr (=h_eff) at the flux tubes mediating gravitational interaction could determine the size scale of the animals. Could one consider a local anomaly in which the value of h_gr is reduced and leads to a shrinkage of also body size?
3. h_gr is of form h_gr=GM_Dm/v₀, where v₀ a velocity parameter (see this, this, and this). M_D is a large dark mass of order 10^-4 times the mass of Earth. Gravitational Compton length Λ_gr= h_gr/m=GM/v₀ for a particle with mass m. Λ_gr= h_gr/m does not depend on the mass of the particle - this conforms with Equivalence Principle.

   The estimate of this article gives Λ_gr= 2πM _D/v₀= 2.9× r_S(E)$, where the Schwartshild radius of Earth is $r_S(E)=2GM_E=.9$ mm. This gives Λ_gr= 2.6 mm, which corresponds to p-adic length scale L(k=187). Brain contains neuron blobs with this size scale. The size scale of organism is expected to be some not too large multiple of this scale.

   Could one think that v₀ at Flores is larger than normally and reduces the value of Λ_gr so that the size for the gravitational part of the magnetic body of any organism shrinks, and that this gradually leads to a reduction of the size of the biological body. Second possibility is that the value of dark mass M_D is at Flores smaller than elsewhere: one would have a dark analogy of ordinary local gravitational anomaly. The reduction of h_gr should be rather large so that the first option looks more plausible.

Badly behaving photons again

I wrote about two years ago about strange halving of the unit of angular momentum for photons. The article had title Badly behaving photons and space-time as 4-surface).

Now I encountered a popular article (see this) telling about this strange halving of photon angular momentum unit two years after writing the above comments. I found nothing new but my immediate reaction was that the finding could be seen as a direct proof for h_eff=nh₀ hierarchy, where h₀ is the minimal value of Planck constants, which need not be ordinary Planck constant h as I have often assumed in previous writings.

Various arguments indeed support for h=6h₀. This hypothesis would explain the strange findings about hydrogen atom having what Mills calls hydrino states having larger binding energy than normal hydrogen atom (see this): the increase of the binding energy would follow from the proportionality of the binding energy to 1/h_eff². For n₀=6→ n<6 the binding energy is scale up as (n/6)². The values of n=1,2,3 dividing n are preferred. Second argument supporting h=6h₀ comes from the model for the color vision (see this).

What is the interpretation of the ordinary photon angular momentum for n=n₀= 6? Quantization for angular momentum as multiples of hbar₀ reads as l= l₀hbar₀= (l₀/6)hbar, l₀=1,2... so that fractional angular momenta are possible. l₀=6 gives the ordinary quantization for which the wave function has same value for all 6 sheets of the covering. l₀=3 gives the claimed half-quantization.

See the chapter Quantum Criticality and dark matter or the article Badly behaving photons and space-time as 4-surface.

Two new findings related to high Tc super-conductivity

I learned simultaneously about two findings related to high Tc super-conductivity leading to a proposal of a general mechanism of bio-control in which small signal can serve as a control knob inducing phase transition producing macroscopically quantum coherent large h_eff phases in living matter.

High Tc superconductivity at room temperature and pressure

Indian physicists Kumar Thapa and Anshu Pandey have found evidence for superconductivity at ambient (room) temperature and pressure in nanostructures (see this). There are also earlier claims about room temperature superconductivity that I have discussed in my writings.

Here is part of the abstract of their article.

We report the observation of superconductivity at ambient temperature and pressure conditions in films and pellets of a nanostructured material that is composed of silver particles embedded into a gold matrix. Specifically, we observe that upon cooling below 236 K at ambient pressures, the resistance of sample films drops below 10-4 Ohm, being limited by instrument sensitivity. Further, below the transition temperature, samples become strongly diamagnetic, with volume susceptibilities as low as -0.056. We further describe methods to tune the transition to temperatures higher than room temperature.

During years I have developed a TGD based model of high Tc superconductivity and of bio-superconductivity (see this and this).

Dark matter is identified as phases of ordinary matter with non-standard value h_eff/h=n of Planck constant (see this) (h=6h₀ is the most plausible option). Charge carriers are h_eff/h₀=n dark macroscopically quantum coherent phases of ordinary charge carriers at magnetic flux tubes along which the supra current can flow. The only source of dissipation relates to the transfer of ordinary particles to flux tubes involving also phase transition changing the value of h_eff.

This superconductivity is essential also for microtubules exhibit signatures for the generation of this kind of phase at critical frequencies of AC voltages serving as a metabolic energy feed providing for charged particles the needed energy that they have in h_eff/h₀=n phase.

Large h_eff phases with same parameters than ordinary phase have typically energies large than ordinary phase. For instance. Atomic binding energies scale like 1/h_eff² and cyclotron energies and harmonic oscillator energies quite generally like h_eff. Free particle in box is however quantum critical in the sense that the energy scale E= hbar_eff²/2mL² does not depend on the h_eff if one has L∝ h_eff. At space-time level this is true quite generally for external (free) particles identified as minimal 4-surfaces. Quantum criticality means independence on various coupling parameters.

What is interesting is that Ag and Au have single valence electron. The obvious guess would be that valence electrons become dark and form Cooper pairs in the transition to superconductivity. What is interesting that the basic claim of a layman researcher David Hudson is that ORMEs or mono-atomic elements as he calls them include also Gold. These claims are not of course taken seriously by academic researchers. In the language of quantum physics the claim is that ORMEs behave like macroscopic quantum systems. I decided to play with the thought that the claims are correct and this hypothesis served later one of the motivations for the hypothesis about dark matter as large h_eff phases: this hypothesis follows from adelic physics (see this), which is a number theoretical generalization of ordinary real number based physics.

TGD explanation of high Tc superconductivity and its biological applications strongly suggest that a feed of "metabolic" energy is a prerequisite of high Tc superconductivity quite generally. The natural question is whether experimenters might have found something suggesting that the external energy feed - usually seen as a prerequisite for self-organization - is involved with high Tc superconductivity. During same day I got FB link to another interesting finding related to high Tc superconductivity in cuprates and suggesting positive answer to this question!

Transition to high Tc superconductivity involves positive feedback

The discovery of positive feedback in the transition to hight Tc superconductivity is described in the popular article " Physicists find clues to the origins of high-temperature superconductivity" (see this). Haoxian Li et al at the University of Colorado at Boulder and the Ecole Polytechnique Federale de Lausanne have published a paper on their experimental results obtained by using ARPES (Angle Resolved Photoemission Spectroscopy) in Nature Communications (see this).

The article reports the discovery of a positive feedback loop that greatly enhances the superconductivity of cupra superconductors. The abstract of the article is here.

Strong diffusive or incoherent electronic correlations are the signature of the strange-metal normal state of the cuprate superconductors, with these correlations considered to be undressed or removed in the superconducting state. A critical question is if these correlations are responsible for the high-temperature superconductivity. Here, utilizing a development in the analysis of angle-resolved photoemission data, we show that the strange-metal correlations don’t simply disappear in the superconducting state, but are instead converted into a strongly renormalized coherent state, with stronger normal state correlations leading to stronger superconducting state renormalization. This conversion begins well above Tc at the onset of superconducting fluctuations and it greatly increases the number of states that can pair. Therefore, there is positive feedback––the superconductive pairing creates the conversion that in turn strengthens the pairing. Although such positive feedback should enhance a conventional pairing mechanism, it could potentially also sustain an electronic pairing mechanism.

The explanation of the positive feedback in TGD TGD framework could be following. The formation of dark electrons requires "metabolic" energy. The combination of dark electrons to Cooper pairs however liberates energy. If the liberated energy is larger than the energy needed to transform electron to its dark variant it can transform more electrons to dark state so that one obtains a spontaneous transition to high Tc superconductivity. The condition for positive feedback could serve as a criterion in the search for materials allowing high Tc superconductivity.

The mechanism could be fundamental in TGD inspired quantum biology. The spontaneous occurrence of the transition would make possible to induce large scale phase transitions by using a very small signal acting therefore as a kind of control knob. For instance, it could apply to bio-superconductivity in TGD sense, and also in the transition of protons to dark proton sequences giving rise to dark analogs of nuclei with a scaled down nuclear binding energy at magnetic flux tubes explaining Pollack effect. This transition could be also essential in TGD based model of "cold fusion" based also on the analog of Pollack effect. It could be also involved with the TGD based model for the finding of macroscopic quantum phase of microtubules induced by AC voltage at critical frequencies (see this).

See the chapter Quantum Criticality and dark matter.

Two different values for the metallicity of Sun and heating of solar corona: two puzzles with a common solution?

Solar corona could be also a seat of dark nucleosynthesis and there are indications that this is the case (see this) . The metallicity of stellar objects gives important information about its size, age, temperature, brightness, etc... The problem is that measurements give two widely different values for the metallicity of Sun depending on how one measures it. One obtains 1.3 per cent from the absorption lines of the radiation from Sun and 1.8 from solar seismic data. Solar neutrinos give also the latter value. What could cause the discrepancy?

Problems do not in general appear alone. There is also a second old problem: what is the origin of the heating of the solar corona. Where does the energy needed for the heating come from?

TGD proposal is based on a model, which emerged initially as a model for "cold fusion" (not really) in terms of dark nucleosynthesis, which produced dark scaled up variants of ordinary nuclei as dark proton sequences with much smaller binding energy. This can happen even in living matter: Pollack effect involving irradiation by IR light of water bounded by gel phase creates negatively charged regions from which part of protons go somewhere. They could go to magnetic flux tubes and form dark nuclei. This could explain the reported transmutations in living matter not taken seriously by academic nuclear physicists.

TGD proposal is that the protons transform to dark proton sequences at magnetic flux tubes with nonstandard value of Planck constant h_eff/h₀=n. Dark nuclei with scaled up size. Dark nuclei can transform to ordinary nuclei by h_eff→ h (h= 6h₀ is the most plausible option) and liberate almost all nuclear binding energy in the process. The outcome would be "cold fusion".

This leads to a vision about pre-stellar evolution. First came the dark nucleosynthesis, which heated the system and eventually led to a temperature at which the ordinary nuclear fusion started. This process could occur also outside stellar cores - say in planet interiors - and a considerable part of nuclei could be created outside star.

A good candidate for the site of dark nucleosynthesis would be solar corona . Dark nucleosynthesis could heat the corona and create metals also here. They would absorb the radiation coming from the solar core and reduce the measured effective metallicity to 1.3 per cent.

See the chapter Cold fusion again or the article Morphogenesis in TGD Universe .

About Comorosan effect in the clustering of RNA II polymerase proteins

The time scales τ equal 5, 10, and 20 seconds appear in the clustering of RNA II polymerase proteins and Mediator proteins (see this and the previous posting). What is intriguing that so called Comorosan effect involves time scale of 5 seconds and its multiples claimed by Comorosan long time ago to be universal time scales in biology. The origin of these time scales has remained more or less a mystery although I have considered several TGD inspired explanations for this time scale is based on the notion of gravitational Planck constant (see this).

One can consider several starting point ideas, which need not be mutually exclusive.

1. The time scales τ associated with RNA II polymerase and perhaps more general bio-catalytic systems could correspond to the durations of processes ending with "big" state function reduction. In zero energy ontology (ZEO) there are two kinds of state function reductions. "Small" reductions - analogs of weak measurements - leave passive boundary of causal diamond (CD) unaffected and thus give rise to self as generalized Zeno effect. The states at the active boundary change by a sequence of unitary time evolutions followed by measurements inducing also time localization of the active boundary of CD. The size of CD increases and gives rise to flow of time defined as the temporal distance between the tips of CD. Large reductions change the roles of the passive and active boundaries and mean death of self. The process with duration of τ could correspond to a life-time of self assignable to CD.

   Remark: It is not quite clear whether CD can disappear and generated from vacuum. In principle this is possible and the generation of mental images as sub-selves and sub-CDs could correspond to this kind of process.

2. I have proposed (see this) that Josephson junctions are formed between reacting molecules in bio-catalysis. These could correspond to the shortened flux tubes . The difference E_J=ZeV of Coulomb energy of Cooper pair over flux tube defining Josephson junction between molecules would correspond to Josephson frequency f_J= 2eV/h_eff. If this frequency corresponds to τ_J= 5 seconds, h_eff should be rather large since E_J is expected to be above thermal energy at physiological temperatures.

   Could Josephson radiation serve as a kind of of synchronizing clock for the state function reductions so that its role would be analogous to that of EEG in case of brain? A more plausible option is that Josephson radiation is a reaction to the presence of cyclotron radiation generated at MB and performing control actions at the biological body (BB) defined in very general sense. In the case of brain dark cyclotron radiation would generate EEG rhythms responsible for control via genome and dark generalized Josephson radiation modulated by nerve pulse patterns would mediate sensory input to the MB at EEG frequencies.

   A good guess is that the energy in question corresponds to Josephson energy for protein through cell membrane acting as Josephson junction and giving to ionic channel or pump. This energy could be universal as therefore same also in the molecular reactions. The flux tubes themselves have universal properties.

3. The hypothesis ℏ_eff= ℏ_gr= GMm/β₀c of Nottale for the value of gravitational Planck constant gives large ℏ. Here v₀=β₀c has dimensions of velocity. For dark cyclotron photons this gives large energy E_c∝ ℏ_gr and for dark Josephson photons small frequency f_J∝ 1/h_gr. Josephson time scale τ_f would be proportional to the mass m of the charged particle and therefore to mass number of ion involved. Cyclotron time scale does not depend on the mass of the charged particle at all and now sub-harmonics of τ_c are natural.

1. If one requires that the multiplies of the time scale 5 seconds are possible, Josephson radiation is favoured since the Josephson time scale proportional to h_gr ∝ m ∝ A, A mass number of ion.

   The problem is that the values A= 2,3,4,5 are not plausible for ordinary nuclei in living matter. Dark nuclei at magnetic flux tubes consisting of dark proton sequences could however have arbitrary number of dark protons and if dark nuclei appear at flux tubes defining Josephson junctions, one would have the desired hierarchy.

2. Although cyclotron frequencies do not have sub-harmonics naturally, MB could adapt to the situation by changing the thickness of its flux tubes and by flux conservation the magnetic field strength to which f_c is proportional to. This would allow MB to produce cyclotron radiation with the same frequency as Josephson radiation and MB and BB would be in resonant coupling.

1. For ℏ_eff= ℏ_gr one has

   r= ℏ_gr/ℏ= GM_Dm/cβ₀= 4.5 × 10¹⁴× (m/m_p) (y/β₀) .

   Here y=M_D/M_E gives the ratio of dark mass M_D to the Earth mass M_E. One can consider 2 favoured values for m corresponding to proton mass m_p and electron mass m_e.

2. E= h_efff gives the concrete relationship f =(E/eV) × 2.4 × 10¹⁴× (h/h_eff) Hz between frequencies and energies. This gives

   x=E/eV = 0.4× r × (f/10¹⁴ Hz) .

3. If the cyclotron frequency f_c=300 Hz of proton for B_end=.2 Gauss corresponds to bio-photon energy of x eV, one obtains the condition

   r=GM_Dm_p/ ℏ β₀≈ .83 × 10¹²x .

   Note that the cyclotron energy does not depend on the mass of the charged particle. One obtains for the relation between Josephson energy and Josephson frequency the condition

   x=E_J/eV = 0.4× .83 × 10^-2× (m/m_p)× (xf_J/Hz) , E_J= ZeV .

   One should not confuse eV in ZeV with unit of energy. Note also that the value of Josephson energy does not depend on h_eff so that there is no actual mass dependence involved.

1. For f_J=.2 Hz corresponding to the Comorosan time scale of τ= 5 seconds this would give ZeV= .66x meV. This is above thermal energy E_th= T=27.5 meV at T=25 Celsius for x> 42. For ordinary photon (h_eff= h) proton cyclotron frequency f_c(p) would correspond for x>42 to EUV energy E>42 eV and to wavelength of λ<31 nm.

   The energy scale of Josephson junctions formed by proteins through cell membrane of thickness L(151)=10 nm is slightly above thermal energy, which suggests x≈ 120 allowing to identify L(151)=10 nm as the length scale of the flux tube portion connecting the reactants. This would give E≈ 120 eV - the upper bound of EUV range. For x=120 one would have GM_Em_p y/v₀≈ 10¹⁴ requiring β₀/y≈ 2.2. The earlier estimates (see this) give for the mass M_D the estimate y∼ 2× 10^-4 giving β₀∼ 4.4× 10^-4. This is rather near to β₀= 2^-11∼ m_e/m_p obtained also in the model for the orbits of inner planets as Bohr orbits.

2. For ion with mass number A this would predict τ_A= A× τ_p= A× 5 seconds so that also multiples of the 5 second time scale would appear. These multiples were indeed found by Comoran and appear also in the case of RNA II polymerase.
3. For proton one would thus have 2 biological extremes - EUV energy scale associated with cyclotron radiation and thermal energy scale assignable to Josephson radiation. Both would be assignable to dark photons with h_eff=h_gr with very long wavelength. Dark and ordinary photons of both kind would be able to transform to each other meaning a coupling between very long lengths scales assignable to MB and short wavelengths/time scales assignable to BB.

   The energy scale of dark Josephson photons would be that assignable with junctions of length 10 nm with long wavelengths and energies slightly above E_th at physiological temperature. The EUV energy scale would be 120 eV for dark cyclotron photons of highest energy.

   For lower cyclotron energies suggested by the presence of bio-photons in the range containing visible and UV and obtained for B_end below .2 Gauss, the Josephson photons would have energies ≤ E_th. That the possible values of B_end are below the nominal value B_end=.2 Gauss deduced from the experiments of Blackman does not conform with the earlier ad hoc assumption that B_end represents lower bound. This does not change the earlier conclusions.

   Could the 120 eV energy scale have some physical meaning in TGD framework? The corresponding wavelength for ordinary photons corresponds to the scale L(151)=10 nm which correspond to the thickness of DNA double strand. Dark DNA having dark proton triplets as codons could correspond to either k=149 or k=151. The energetics of Pollack effect suggests that k=149 is realized in water even during prebiotic period (see this).. In the effect discovered by Blackman the ELF photons would transform dark cyclotron photons having h_eff=h_gr and energy about .12 keV. They would induce cyclotron transitions at flux tubes of B_end with thickness of order cell size scale. These states would decay back to previous states and the dark photons transformed to ordinary photons absorbed by ordinary DNA with coil structure with thickness of 10 nm. Kind of standing waves would be formed. These waves could transform to acoustic waves and induce the observed effects. Quite generally, dark cyclotron photons would control the dynamics of ordinary DNA by this mechanism.

   It is indeed natural to assume that B_end corresponds to upper bound since the values of magnetic field are expected to weaken farther from Earth's surface: weakening could correspond to thickening of flux tubes reducing the field intensity by flux conservation. The model for hearing (see this ) requires cyclotron frequencies considerably above proton's cyclotron frequency in B_end=.2 Gauss. This requires that audible frequencies are mapped to electron's cyclotron frequency having upper bound f_c(e) = (m_p/m_e) f_c(p)≈ 6× 10⁵ Hz. This frequency is indeed above the range of audible frequencies even for bats.

To sum up, the model suggests that the idealization of flux tubes as kind of universal Josephson junctions. The model is consistent with bio-photon hypothesis. The constraints on h_gr= GM_Dm/v₀ are consistent with the earlier views and allows to assign Comorosan time scale 5 seconds to proton and nerve pulse time scale to electron as Josephson time scales. This inspires the question whether the dynamics of bio-catalysis and nerve pulse generation be seen as scaled variants of each other at quantum level? This would not be surprising if MB controls the dynamics. The earlier assumption that B_end=0.2 Gauss is minimal value for B_end must be replaced with the assumption that it is maximal value of B_end.

See the chapter Quantum Criticality and dark matter or the article Clustering of RNA polymerase molecules and Comorosan effect.

Why do RNA polymerase molecules cluster?

I received a link to a highly interesting popular article telling about the work of Ibrahim Cisse at MIT and colleagues (see this): at this time about clustering of proteins in the transcription of RNA. Similar clustering has been observed already earlier and interpreted as a phase separation Similar clustering has been observed already earlier and interpreted as a phase separation (see this). Now this interpretation is not proposed by experiments but experimenters say that it is quite possible but they cannot prove it.

I have already earlier discussed the coalescence of proteins into droplets as this kind of process in TGD framework. The basic TGD based ideas is that proteins - and biomolecules in general - are connected by flux tubes characterized by the value of Planck constant h_eff=n× h₀ for the dark particles at the flux tube. The higher the value of n is the larger the energy of given state. For instance, the binding energies of atoms decrease like 1/n². Therefore the formation of the molecular cluster liberates energy usable as metabolic energy.

Remark: h₀ is the minimal value of h_eff. The best guess is that ordinary Planck constant equals to h=6h₀ (see this and this).

TGD view about the findings

Gene control switches - such as RNA II polymerases in the DNA transcription to RNA - are found to form clusters called super-enhancers. Also so called Mediator proteins form clusters. In both cases the number of members is in the range 200-400. The clusters are stable but individual molecules spend very brief time in them. Clusers have average lifetime of 5.1±.4 seconds.

Why the clustering should take place? Why large number of these proteins are present although single one would be enough in the standard picture. In TGD framework one can imagine several explanations. One can imagine at least following reasons.

1. One explanation could relate to non-determinism of state function reduction. The transcription and its initiation should be a deterministic process at the level of single gene. Suppose that the initiation of transcription is one particular outcome of state function reduction. If there is only single RNA II polymerase, which can make only single trial, the changes to initiate the transcription are low. This would be the case if the molecule provides metabolic energy to initiate the process and becomes too "tired" to try again. In nerve pulse transmission there is analogous situation: after the passing of the nerve pulse generation the neuron has dead time period. As a matter of fact, it turns out that the analogy could be much deeper.

   How to achieve the initiation with certainty in this kind of situation? Suppose that the other outcomes do not affect the situation appreciabley. If one particular RNA polymerase fails to initiate it, the others can try. If the number of RNA transcriptase molecule is large enough, the transcription is bound to begin eventually! This is much like in fairy tales about princess and suitors trying to kill the dragon to get the hand of princess. Eventually the penniless swineherd enters the stage.

2. If the initiation of transcription requires large amount of metabolic energy then only some minimal number of N of RNA II polymerase molecules might be able to provide it collectively. The collective formed by N molecules could correspond to a formation of magnetic body with a large value of h_eff=n×h. The molecules would be connected by magnetic flux tubes.
3. If the rate for occurrence is determined by amplitude which is superposition of amplitudes assignable to individual proteins the the rate is proportional to N², N the number of RNA transcriptase molecules.

   The process in the case of cluster is indeed reported to to be suprisingly fast as compared to the expectations - something like 20 seconds. The earlier studies have suggests that single RNA polymerase stays at the DNA for minutes to hours. This would be a possible mechanism allowing to speed up bio-catalysis besides the mechanism allowing to find molecules to find by a reduction of h_eff/h= n for the bonds connecting the reactants and the associated liberation of metabolic energy allowing to kick the reactants over the potential wall hindering the reaction.

1. Option I: Molecules could be in a phase analogous to vapour phase and there would be very few flux tube bonds between them. The phase transition would create liquid phase as flux tube loops assignable to molecules would reconnect form flux tube pairs connecting the molecules to a tensor network giving rise to quantum liquid phase. The larger then value of n, the longer the bonds between molecules would be.
2. Option I: The molecules are in the initial state connected by flux tubes and form a kind of liquid phase and the clustering reduces the value of n and therefore the lengths of flux tubes. This would liberate dark energy as metabolic energy going to the initiation of the transcription. One could indeed argue that connectedness in the initial state with large enough value of n is necessary since the protein cluster must have high enough "IQ" to perform intelligent intentional actions.

1. Could floppiness correspond to low string tension assignable to long flux loops with large h_eff/h=n assignable to the building bricks of "floppy" pieces? Could reconnection for these loops give rise to pairs of flux tubes connecting the proteins in the transition to liquid phase? Floppiness could also make possible to scan the enviroment by flux loops for flux loops of other molecules and in case of hit (cyclotron resonance) induce reconnection.
2. In spite of floppiness in this sense, one could have quantum correlations between the internal quantum numbers of the building bricks of the floppy pieces. This would also increase the value of n serving as molecular IQ and provide molecule with higher metabolic energy liberated in the catalysis.

See the chapter Quantum Criticality and dark matter or the article Clustering of RNA polymerase molecules and Comorosan effect.

The discovery of "invisible visible matter" and more detailed view about dark pre-nuclear physics

That 30 per cent of visible matter has remained invisible is not so well-known problem related to dark matter. It is now identified and assigned to the network of filaments in intergalactic space. Reader can consult the popular article "Researchers find last of universe's missing ordinary matter" (see this). The article "Observations of the missing baryons in the warm-hot intergalactic medium" by Nicastro et al (see this) describes the finding at technical level. Note that warm-hot refers to the temperature range 10⁵-10⁶ K.

In TGD framework one can interpret the filament network as as a signature of flux tubes/cosmic string network to which one can assign dark matter and dark energy. The interpretation could be that the "invisible visible" matter emerges from the network of cosmic strings as part of dark energy is transformed to ordinary matter. This is TGD variant of inflationary scenario with inflaton vacuum energy replaced with cosmic strings/flux tubes carrying dark energy and matter.

This inspires more detailed speculations about pre-stellar physics according to TGD. The questions are following. What preceded the formation of stellar cores? What heated the matter to the needed temperatures? The TGD inspired proposal is that it was dark nuclear physics (see the article Cold fusion, low energy nuclear reactions, or dark nuclear synthesis?). Dark nuclei with h_eff=n× h₀ were formed first and these decayed to ordinary nuclei or dark nuclei with smaller value of h_eff=n× h₀ and heated the matter so that ordinary nuclear fusion became possible.

Remark: h₀ is the minimal value of h_eff. The best guess is that ordinary Planck constant equals to h=6h₀ (see this and this).

1. The temperature of the recently detected missing baryonic matter is around 10⁶ K and roughly 1/10:th of the temperature 10⁷ K at solar core. This serves as a valuable guideline.

   I already earlier realized that the temperature at solar core, where fusion occurs happens to be same as the estimated temperature for the binding energy of dark nuclei identified as dark proton sequences with dark nucleon size equal to electron size. The estimate is obtained by scaling down the typical nuclear binding energy for low mass nuclei by the ratio 2^-11 of sizes of ordinary and dark nuclear (electron/proton mass ratio, dark proton has same size as ordinary electron). This led to the idea that nuclear fusion in the solar core creates first dark nuclei, which then decay to ordinary nuclei and liberate essentially all of nuclear binding energy. After that ordinary nuclear fusion at resulting high enough temperature would take the lead.

2. Dark nuclear strings can correspond to several values of h_eff=n× h₀ with size scale scaled up by n. p-Adic length scales L(k)= 2^(k-151)/2L(151), L(151)≈ 10 nm, define favoured values of n as integers in good approximation proportional to 2^k/2. The binding energy scales for dark nuclei is inversely proportional to 1/n (to the inverse of the p-adic length scale). Could 10⁶ K correspond to a p-adic length scale k=137 - atomic length scale of 1 Angstrom?

   Could dark cold fusion start at this temperature and first give rise to "pre-nuclear physics generating dark nuclei as dark proton sequences and with dark nuclear binding energy about . 1 keV with dark nuclei decaying to k=127 dark nuclei with binding energy about 1 keV, and lead to heating of the matter and eventually to cold fusion at k=127 and after than the ordinary fusion? Also the values intermediate in the range [137,127] can be considered as intermediate steps. Note that also k=131 is prime.

3. Interestingly, the temperature at solar corona is about 1 million degrees and by factor 140-150 hotter than the inner solar surface. The heating of solar corona has remained a mystery and the obvious question is whether dark nuclear fusion giving rise to "pre-nuclear" fusion for k=137 generates the energy needed.
4. If this picture makes sense, the standard views about the nuclear history of astrophysical objects stating that the nuclei in stars come from the nuclei from supernovas would change radically. Even planetary cores might be formed by a sequence of dark nuclear fusions ending with ordinary fusion and the iron in the Earth's core could be an outcome of dark nuclear fusion. The temperature at Earth's core is about 6× 10³ K. This corresponds to k=151 in reasonable approximation.

   Remark: What is amusing that the earlier fractal analogy of Earth as cell would make sense in the sense that k=151 corresponds to the p-adic length scale of cell membrane.

   I have also considered the possibility that dark nuclear fusion could have provided metabolic energy for prebiotic lifeforms in underground oceans of Earth and that life came to the surface in Cambrian explosion (see this). The proposal would solve the hen-egg question which came first: metabolism or genetic code since dark proton sequences provide a realization of genetic code (see this).

5. One can imagine also a longer sequence of p-adic length scales starting at lower temperatures and and longer p-adic length scales characterized by integer k for which prime values are the primary candidates. k=139 corresponding to T=.5× 10⁶ K is one possibility. For k= 149 and k=151 (thicknesses for the lipid layer of the cell membrane and cell membrane) one would have T ≈ 2× 10⁴ K and T ≈ 10⁴ K - roughly the temperature at the surface of Sun and biologically important energies E= 2 eV of red light and E=1 eV of infrared light (quite recently it was found that also IR light can serve as metabolic energy in photosynthesis).

   Could dark nuclear fusion process occur at the surface of the Sun? Could one image that the sequence of dark phase transitions proceeding to opposite directions as: k=137 ← 139 ← 149 ← 151→ 149→ 139→ 137→ 131→ 127 between dark nuclear physics corresponding to p-adic length scales L(k) takes place as one proceeds from the surface of the Sun upwards to solar corona and downwards to the core. Of course, also other values of k can be considered: k:s in this sequence are primes: the ends of the warm-hot temperature range 10⁵-10⁶ corresponds roughly to k=143 = 13× 11 and k=137.

Did animal mitochondrial evolution have a long period of stagnation?

I encountered an interesting popular article telling about findings challenging Darwin's evolutionary theory. The original article of Stoeckle and Thaler is here.

The conclusion of the article is that almost all animals, 9 out of 10 animal species on Earth today, including humans, would have emerged about 100,000 200,000 years ago. According to Wikipedia all animals are assumed to have emerged about 650 million years ago from a common ancestor. Cambrian explosion began around 542 million years ago. According to Wikipedia Homo Sapiens would have emerged 300,000-800,000 years ago.

On basis of Darwin's theory based on survival of the fittest and adaptation to a new environment, one would expect that the species such as ants and humans with large populations distributed around the globe become genetically more diverse over time than the species living in the same environment. The study of so called neutral mutations not relevant for survival and assumed to occur with some constant rate however finds that this is not the case. The study of so called mitochondrial DNA barcodes across 100,000 species showed that the variation of neutral mutations became very small about 100,000-200,00 years ago. One could say that the evolution differentiating between them began (or effectively began) after this time. As if mitochondrial clocks for these species would have been reset to zero at that time as the article states it This is taken as a support for the conclusion that all animals emerged about the same time as humans.

The proposal of (at least ) the writer of popular article is that the life was almost wiped out by a great catastrophe and extraterrestrials could have helped to start the new beginning. This brings in mind Noah's Ark scenario. But can one argue that humans and the other animals emerged at that time: were they only survivors from a catastrophe. One can also argue that the rate of mitochondrial mutations increased dramatically for some reason at that time.

Could one think that great evolutionary leap initiating the differentiation of mitochondrial genomes at that time and that before it the differentiation was very slow for some reason? Why this change would have occurred simultaneously in almost all animals? Something should have happened to the mitochondria and what kind of external evolutionary pressure could have caused it?

1. To me the idea about ETs performing large scale genetic engineering does not sound very convincing. That only a small fraction of animals survived the catastrophe sounds more plausible idea. Was it great flood? One can argue that animals living in water would have survived in this case. Could some cosmic event such as nearby supernova have produced radiation killing most animals? But is mass extinction really necessary? Could some evolutionary pressure without extinction caused the apparent resetting of mitochondrial clock?
2. In TGD based quantum biology the great leaps could be caused by quantum criticality perhaps induced by some evolutionary pressure due to some kind of catastrophe. The value of h_eff=nh₀ (h₀ is the minimal value of Planck constant) - kind of IQ in very general sense - in some part of mitochondria could have increased and also its value would have fluctuated. Did a new longer length scale relevant to the functioning of mitochondrias emerge? Did the mitochondrial size increase? Here I meet the boundaries of my knowledge about evolutionary biology!
3. Forget for a moment the possibility of mass extinction. Could the rate of mutations, in particular the rate of neutral mutations, have increased as a response to evolutionary pressure? Just the increased ability to change helps to survive. This rate would become high at quantum criticality due to the presence of large quantum fluctuations (variations of h_eff). If the mitochondria were far from quantum quantum criticality before the catastrophe, the rate of mutations would have been very slow. Animal kingdom would have lived a period of stagnation. The emerging quantum criticality - forced by a catastrophe but not involving an extinction - could have increased the rate dramatically.

The experiments of Masaru Emoto with emotional imprinting of water

Sini Kunnas sent a link to a video telling about experiments of Masaru Emoto (see this) with water, which is at criticality with respect to freezing and then frozen. Emoto reports is that words expressing emotions are transmitted to water: positive emotions tend to generate beautiful crystal structures and negative emotions ugly ones. Also music and even pictures are claimed to have similar effects. Emoto has also carried out similar experiments with rice in water. Rice subjected to words began to ferment and water subject to words expressing negative emotions began to rotten.

Remark: Fermentation is a metabolic process consuming sugar in absence of oxygen. Metabolism is a basic signature of life so that at least in this aspect the water+rice system would become alive. The words expressing positive emotions or even music would serve as a signal "waking up" the system.

One could define genuine skeptic as a person who challenges existing beliefs and pseudo-skeptic (PS in the sequel) as a person challenging - usually denying - everything challenging the mainstream beliefs. The reception of the claims of Emoto is a representative example about the extremely hostile reactions of PSs as aggressive watchdogs of materialistic science towards anything that challenges their belief system. The psychology behind this attitude is same as behind religious and political fanatism.

I must emphasize that I see myself as a thinker and regard myself as a skeptic in the old-fashioned sense of the word challenging the prevailing world view rather than phenomena challenging the prevailing world view. I do not want to be classified as believer or non-believer. The fact is that if TGD inspired theory of consciousness and quantum biology describes reality, a revolution in the world view is unavoidable. Therefore it is natural to consider the working hypothesis that the effects are real and see what the TGD based explanation for them could be.

The Wikipedia article about Masaru Emoto (see this) provides a good summary of the experiments of Emoto and provides a lot of links so that I will give here only a brief sketch. According to the article Emoto believed that water was a "blueprint for our reality" and that emotional "energies" and "vibrations" could change the physical structure of water. The water crystallization experiments of Emoto consisted of exposing water in glasses to different words, pictures or music, and then freezing and examining the aesthetic properties of the resulting crystals with microscopic photography. Emoto made the claim that water exposed to positive speech and thoughts would result in visually "pleasing" crystals being formed when that water was frozen, and that negative intention would yield "ugly" crystal formations.

In 2008, Emoto and collaborators published and article titled "Double-Blind Test of the Effects of Distant Intention on Water Crystal Formation" about his about experiments with water in the Journal of Scientific Exploration, a peer reviewed scientific journal of the Society for Scientific Explorations (see this). The work was performed by Masaru Emoto and Takashige Kizu of Emoto’s own IHM General Institute, along with Dean Radin and Nancy Lund of the Institute of Noetic Sciences, which is on Stephen Barrett's Quackwatch (see this) blacklist of questionable organizations. PSs are the modern jesuits and for jesuits the end justifies the means.

Emoto has also carried experiments with rice samples in water. There are 3 samples. First sample "hears" words with positive emotional meaning, second sample words with negative emotional meaning, and the third sample serving as a control sample. Emoto reports (see this) that the rice subjected to words with positive emotional content began to ferment whereas water subject to words expressing negative emotions began to rotten. The control sample also began to rotten but not so fast.

In the article The experiments of Masaru Emoto with emotional imprinting of water I will consider the working hypothesis that the effects are real, and develop an explanation based on TGD inspired quantum biology. The basic ingredients of the model are following: magnetic body (MB) carrying dark matter as h_eff/h=n phases of ordinary matter; communications between MB and biological body (BB) using dark photons able to transform to ordinary photons identifiable as bio-photons; the special properties of water explained in TGD framework by assuming dark component of water implying that criticality for freezing involves also quantum criticality, and the realization of genetic code and counterparts of the basic bio-molecules as dark proton sequences and as 3-chords consisting of light or sound providing a universal language allowing universal manner to express emotions in terms of bio-harmony realized as music of light or sound. The entanglement of water sample and the subject person (with MBs included) realized as flux tube connections would give rise to a larger conscious entity expressing emotions via language realized in terms of basic biomolecules in a universal manner by utilizing genetic code realized in terms of both dark proton sequences and music of light of light and sound.

See the chapter Dark Nuclear Physics and Condensed Matter or the article The experiments of Masaru Emoto with emotional imprinting of water.

How molecules in cells "find" one another and organize into structures?

The title of the popular article How molecules in cells 'find' one another and organize into structures expresses an old problem of biology. Now the group led by Amy S. Gladfelter has made experimental progress in this problem. The work has been published in Science (see this).

It is reported that RNA molecules recognize each other to condense into the same droplet due to the specific 3D shapes that the molecules assume. Molecules with complementary base pairing can find each other and only similar RNAs condense on same droplet. This brings in mind DNA replication, transcription and translation. Furthermore, the same proteins that form liquid droplets in healthy cells, solidify in diseases like neurodegenerative disorders.

Some kind of phase transition is involved with the process but what brings the molecules together remains still a mystery. The TGD based solution of this mystery is one of the first applications of the notion of many-sheeted space-time in biology, and relies on the notion of magnetic flux tubes connecting molecules to form networks.

Consider first TGD based model about condensed and living matter. As a matter fact, the core of this model applies in all scales. What is new is there are not only particles but also bonds connecting them. In TGD they are flux tubes which can carry dark particles with nonstandard value h_eff/h=n of Planck constant. In ER-EPR approach in fashion they would be wormholes connecting distance space-time regions. In this case the problem is instability: wormholes pinch and split. In TGD monopole magnetic flux takes care of the stability topologically.

The flux tube networks occur in all scales but especially important are biological length scales.

1. In chemistry the flux tubes are associated with valence bonds and hydrogen bonds (see this). In biology genetic code would be realized as dark nuclei formed by sequences of dark protons at magnetic flux tubes. Also RNA, amino-acids, and even tRNA could have dark counterparts of this kind (see this). Dark variants of biomolecules would serve as templates for their ordinary variants also at the level of dynamics. Biochemistry would be shadow dynamics dictated to high degree by the dark matter at flux tubes.
2. Dark valence bonds can have quite long length and the outcome is entangled tensor net (see this). These neuronal nets serve as correlates for cognitive mental images in brain (see this) emotional mental images in body (see this). Dark photons propagating along flux tubes (more precisely topological light rays parallel to them) would be the fundamental communication mechanism (see this). Transmitters and nerve pulses would only change the connectedness properties of these nets.

1. Reconnection of flux tubes serves is the first basic mechanism in the dynamics of flux tube networks and would give among other things rise to neural nets. The connection between neurons would correspond basically to flux tube pair which can split by reconnection. Also two flux tube pairs can reconnect forming Y shaped structures. Flux tube pairs could be quite generally associated with long dark hydrogen bonds scaled up by h_eff/h=n from their ordinary lengths. Flux tube pairs would carry besides dark protons also supra phases formed by the lone electron pairs associated quite generally with hydrogen bonding atoms. Also dark ions could appear at flux tubes.

   Biomolecules would have flux loops continually scanning the environment and reconnecting if they meet another flux loop. This however requires that magnetic field strengths are same at the two loops so that a resonance is achieved at level of dark photon communications. This makes possible recognition by cyclotron frequency spectrum serving as signature of the magnetic body of the molecule.

   Water memory (see this) would rely on this recognition mechanism based on cyclotron frequencies and also immune system would use it at basic level (here one cannot avoid saying something about homeopathy although I know that this spoils the day of the skeptic: the same mechanism would be involved also with it). For instance, dark DNA strand accompanying ordinary DNA and dark RNA molecules find each other by this mechanism (see this). Same applies to other reactions such as replication and translation .

2. Shortening of the flux tubes h_eff/h reducing phase transition is second basic mechanism explaining how biomolecules can find each other in dense molecular soup. It is essential that the magnetic fields at flux tubes are nearly the same for the reconnection to form. A more refined model for the shortening involves two steps: reconnection of flux tubes leading to a formation of flux tube pair between molecules and shortening by h_eff/h reducing phase transition.

1. I just wrote an article (see this) about a solution of two old problems of hydrothermodynamics: the behavior of liquid-gas system in the critical region not consistent with the predictions of statistical mechanics (known already at times of Maxwell!) and the behavior of water above freezing point and in freezing. Dark flux tubes carrying dark protons and possibly electronic Cooper pairs made from so called lone electron pairs characterizing atoms forming hydrogen bonds.
2. The phase transition from gas to liquid occurs when the number of flux tubes per molecule is high enough. At criticality both phases are in mechanical equilibrium - same pressure. Most interestingly, in solidification the large h_eff flux tubes transform to ordinary ones and liberate energy: this explains anomalously high latent heats of water and ammonia. The loss of large h_eff flux tubes however reduces "IQ" of the system.

1. Sol-gel transition would correspond to this kind of biological phase transitions. Protein folding (see this) - kind of freezing of protein making it biologically inactive - and unfolding would be second basic example of this transition. The freezing would involve formation of flux tube bonds between points of linear protein and assignable to hydrogen bonds. External perturbations induce melting of the proteins and they become biologically active as the value of h_eff/h=n characterizing their maximal possible entanglement negentropy content (molecular IQ) increases. External perturbation feeds in energy acting as metabolic energy. I have called this period molecular summer.
2. Solidification of proteins reducing is reported to be associated with diseases such neurodegenerative disorders. In TGD picture this would reduce the molecular IQ since the ability of system to generate negentropy would be reduced when h_eff for the flux tubes decreases to its ordinary value. What brings molecules together is not understood and TGD provides the explanation as h_eff reducing phase transition for flux tube pairs.

See the chapter Quantum Criticality and Dark Matter.

Maxwell's lever rule and expansion of water in freezing: two poorly understood phenomena

The view about condensed matter as a network with nodes identifiable as molecules and bonds as flux tubes is one of the basic predictions of TGD and obviously means a radical modification of the existing picture. In the sequel two old anomalies of standard physics are explained in this conceptual framework. The first anomaly was known already at the time of Maxwell. In critical region for gas liquid-phase transition van der Waals equation of state fails. Empirically the pressure in critical region depends only on temperature and is independent on molecular volume whereas van der Waals predicting cusp catastrophe type behavior predicts this dependence. This problem is quite general and plagues all analytical models based on statistical mechanics.

Maxwell's area rule and lever rule is the proposed modification of van der Waals in critical region. There are two phases corresponding to liquid and gas in the same pressure and the proportions of the phases vary so that the volume varies.

The lever rule used for metal allows allows to explain the mixture but requires that there are two "elements" involved. What the second "element" is in the case of liquid-gas system is poorly understood. TGD suggests the identification of the second "element" as magnetic flux tubes connecting the molecules. Their number per molecule varies and above critical number a phase transition to liquid phase would take place.

Second old problem relates to the numerous anomalies of water (see the web pages of Martin Chaplin). I have discussed these anomalies from TGD viewpoint in (see this). The most well-known anomalies relate to the behavior near freezing point. Below 4 degrees Celsius water expands rather than contracts as temperature is lowered. Also in the freezing an expansion takes place.

A general TGD based explanation for the anomalies of water would be the presence of also dark phases with non-standard value of Planck constant h_eff/h=n (see this). Combining this idea with the above proposal this would mean that flux tubes associated with hydrogen bonds can have also non-standard value of Planck constant in which case the flux tube length scales like n. The reduction of n would shorten long flexible flux tubes to short and rigid ones. This reduce the motility of molecules and also force them nearer to each other. This would create empty volume and lead to an increase of volume per molecule as temperature is lowered.

Quite generally, the energy for particles with non-standard value of Planck constant is higher than for ordinary ones (see this). In freezing all dark flux tubes would transform to ordinary ones and the surplus energy would be liberated so that the latent heat should be anomalously high for all molecules forming hydrogen bonds. Indeed, for both water and NH₃ having hydrogen bonds the latent heat is anomalously high. Hydrogen bonding is possible if molecules have atoms with lone electron pairs (electrons are not assignable to valence bonds). Lone electron pairs could form Cooper pairs at flux tube pairs assignable to hydrogen bonds and carrying the dark proton. Therefore also high T_c superconductivity could be possible.

See the chapter Quantum Criticality and Dark Matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy" or the article Maxwell's lever rule and expansion of water in freezing: two poorly understood phenomena.

Superfluids dissipate!

People in Aalto University - located in Finland by the way - are doing excellent work: there is full reason to be proud! I learned from the most recent experimental discovery by people working in Aalto University from Karl Stonjek. The title of the popular article is Friction found where there should be none—in superfluids near absolute zero.

In rotating superfluid one has vortices and they should not dissipate. The researchers of Aalto University however observed dissipation: the finding by J. Mäkinen et al is published in Phys Rev B. Dissipation means that they lose energy to environment. How could one explain this?

What comes in mind for an inhabitant of TGD Universe, is the hierarchy of Planck constants h_eff =n×h labelling a hierarchy of dark matters as phases of ordinary matter. The reduction of Planck constant h_eff liberates energy in a phase transition like manner giving rise to dissipation. This kind of burst like liberation of energy is mentioned in the popular article ("glitches" in neutron stars). I have already earlier proposed an explanation of fountain effect of superfluidity in which superfluid flow seems to defy gravity. The explanation is in terms of large value of h_eff implying delocalization of superfluid particles in long length scale (see this).

Remark: Quite generally, binding energies are reduced as function of h_eff/h= n. One has 1/n² proportionality for atomic binding energies so that atomic energies defined as rest energy minus binding energy indeed increase with n. Interestingly, dimension 3 of space is unique in this respect. Harmonic oscillator energy and cyclotron energies are in turn proportional to n. The value of n for molecular valence bonds depends on n and the binding energies of valence bonds decrease as the valence of the atom with larger valence increases. One can say that the valence bonds involving atom at the right end of the row of the periodic table carry metabolic energy. This is indeed the case as one finds by looking the chemistry of nutrient molecules.

The burst of energy would correspond to a reduction of n at the flux tubes associated with the superfluid. Could the vortices decompose to smaller vortices with a smaller radius, maybe proportional to n? I have proposed similar mechanism of dissipation in ordinary fluids for more than two decades ago. Could also ordinary fluids involve hierarchy of Planck constants and could they dissipate in the same manner?

In biology liberation of metabolic energy - say in motor action - would take place in this kind of "glitch". It would reduce h_eff resources and thus the ability to generate negentropy: this leads to smaller negentropy resources and one gets tired and thinking becomes fuzzy.

See the chapter Quantum criticality and dark matter.

Condensed matter simulation of 4-D quantum Hall effect from TGD point of view

There is an interesting experimental work related to the condensed matter simulation of physics in space-times with D=4 spatial dimensions meaning that one would have D=1+4=5-dimensional space-time (see this and this). What is simulated is 4-D quantum Hall effect (QHE). In M-theory D= 1+4-dimensional branes would have 4 spatial dimensions and also 4-D QH would be possible so that the simulation allows to study this speculative higher-D physics but of course does not prove that 4 spatial dimensions are there.

In this article I try to understand the simulation, discuss the question whether 4 spatial dimensions and even 4+1 dimensions are possible in TGD framework in some sense, and also consider the general idea of the simulation higher-D physics using 4-D physics. This possibility is suggested by the fact that it is possible to imagine higher-dimensional spaces and physics: maybe this ability requires simulation of high-D physics using 4-D physics.

See the chapter Quantum Hall effect and Hierarchy of Planck Constants or the article Condensed matter simulation of 4-D quantum Hall effect from TGD point of view.

Exciton-polariton Bose-Einstein condensate at room temperature and heff hierarchy

Ulla gave in my blog a link to a very interesting work about Bose-Einstein condensation of quasi-particles known as exciton-polaritons. The popular article tells about a research article published in Nature by IBM scientists.

Bose-Einstein condensation happens for exciton-polaritons at room temperature, this temperature is four orders of magnitude higher than the corresponding temperature for crystals. This puts bells ringing. Could h_eff/h=n be involved?

One learns from Wikipedia that exciton-polaritons are electron hole pairs- photons kick electron to higher energy state and exciton is created.These quasiparticles would form a Bose-Einstein condensate with large number of particles in ground state. The critical temperature corresponds to the divergence of Boltzmann factor given by Bose-Einstein statistics.

1. The energy of excitons must be of order thermal energy at room temperature: IR photons are in question. Membrane potential happens to corresponds to this energy. That the material is organic, might be of relevance. Living matter involves various Bose-Einstein condensate and one can consider also excitons.

   As noticed the critical temperature is surprisingly high. For crystal BECs it is of order .01 K. Now by a factor 30,000 times higher!

2. Does the large value of h_eff =n×h visible make the critical temperature so high?

   Here I must look at Wikipedia for BEC of quasiparticles. Unfortunately the formula for n^1/3 is copied from source and contains several errors. Dimensions are completely wrong.

   It should read n^1/3= (ℏ)^-1 (m_effkT_cr)^x, x= 1/2.

   [not x=-1/2 and 1/ℏ rather than ℏ as in Wikipedia formula. This is usual: it would important to have Wikipedia contributors who understand at least something about what they are copying from various sources].

3. The correct formula for critical temperature T_cr reads as

   T_cr= (dn/dV)^y ℏ²/m_eff , y=2/3.

   [T_cr replaces T_c and y=2/3 replaces y=2 in Wikipedia formula. Note that in Wikipedia formula dn/dV is denoted by n reserved now for h_eff=n×h].

4. In TGD one can generalize by replacing ℏ with ℏ_eff=n ×ℏ so that one has

   T_cr→ n²T_cr .

   Critical temperature would behave like n² and the high critical temperature (room temperature) could be understood. In crystals the critical temperature is very low but in organic matter a large value of n≈ 100 could change the situation. n≈ 100 would scale up the atomic scale of 1 Angstrom as a coherence length of valence electron orbitals to cell membrane thickness about 10 nm. There would be one dark electron-hole pair per volume taken by dark valence electron: this would look reasonable.

Is this possible?

1. Fermi energy E is given by almost identical formula but with factor 1/2 appearing on the right hand side. Using the density dn_e/dV for electrons instead of dn/dV gives an upper bound for T_cr ≤ 2E_F. E_F varies in the range 2-10 eV. The actual values of T_cr in crystals is of order 10^-6 eV so that the density of quasi particles must be very small for crystals: dn_cryst/dV≈ 10^-9dn_e/dV .
2. For crystal the size scale L_cryst of the volume taken by quasiparticle would be 10^-3 times larger than that taken by electron, which varies in the range 10^1/3-10^2/3 Angstroms giving the range (220-460) nm for L_cryst.
3. On the other hand, the thickness of the plastic layer is L_layer= 35 nm, roughly 10 times smaller than L_cryst. One can argue that L_plast ≈ L_layer is a natural order of magnitude for L_cryst for quasiparticle in plastic layer. If so, the density of quasiparticles is roughly 10³ times higher than for crystals. The (dn/dV)²-proportionality of T_cr would give the factor T_cr,plast≈ 10⁶ T_cr,cryst so that there would be no need for non-standard value of h_eff!

   But is the assumption L_plast ≈ L_layer really justified in standard physics framework? Why this would be the case? What would make the dirty plastic different from super pure crystal?

For background see the chapter Criticality and dark matter.

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