Three atmospheric puzzles with a common solution

The motivation of this a posting came from a popular article telling about the theory of Earle Williams and colleagues explaining so called D-region ledge below 80 km. The mystery is that are no free electrons in lower atmosphere: one application is to radio communications. Radio waves propagate in ionosphere like in wave guide but not in lower atmosphere which is insulator.

I decided to look whether TGD inspired new physics might tell something interesting about the problem but the conclusion was negative. This search process ended as I realized that the model of Williams and colleagues might elegantly explain also two other poorly understood phenomena related to Earth's atmosphere.

1. Consider first D-region ledge. The incoming solar UV radiation generates free electrons, mostly by ionization of nitric oxide NO by kicking away the unpaired electron. This happens in the entire atmosphere. The electron density however goes to practically zero at lower heights and during night-time D-region disappears entirely. As a consequence, atmosphere is rather poor conductor of electricity. The idea of the article is that the dust generated as small meteors burn in the atmosphere into small dust particles, which then bind the free electrons generated by UV radiation and then gradually fall down to ground.
   
   
2. The stability of Earth's electric field is second mystery. Earth is negatively charged generating so called fair weather potential giving rise to electric field about 100-300 V/m at the surface of Earth and going to zero at heights about 1000 km. We do not understand the reason for why Earth is negatively charged.
   

   Even worse, a simple estimate using the value of electric field and estimate for ionic conductivity shows that it should take only a time of about 500 seconds for this negative charge to be lost by positive ionic currents from ionosphere (see this)! How Earth can preserve its negative charge? What mechanism prevents these currents from flowing or compensates them with opposite currents? Thunderstorms and electric clouds have been proposed as mechanisms bringing negative charge to Earth. But this only shifts the problem to that of understanding how electric clouds and thunder are generated.
   

   The model explaining D-region ledge could solve also this problem. There would be an ohmic positive ion current to earth and small ohmic electron current upwards in Earth's electric field. But besides this there would be downwards "gravitational" current of negatively charged dust particles compensating the ohmic current in equilibrium! Electrons could drift upwards to D-region from ground but could travel down as free travellers of dust particles!
   

   In purely plasma physical mood one would neglect gravitation altogether since the ratio mg/qE of gravitational and electric forces would be about 10^-12 for electron. For dust particles with low enough ratio Q/m ratio one cannot neglect gravitation! Note that dust particles with critical Q/m ratio for which electric and gravitational forces compensate each other could remain stationary in atmosphere. The critical radio would be of order 10^-9. From this one can estimate the critical charge of say water droplet, bacterium, or levitating meditator;-).
   
   

3. The origin of electric clouds and thunder storms is a third mystery. In the regions with thunder clouds at heights about 10 km the electric field can become about 10³ V/m and lightnings are generated when the strengths becomes large than that required by di-electric breakdown in air. Between thunder clouds and Earth the electric field usually changes its sign. We do not really understand how the large negative charge of thunder cloud and positive charge at the surface of Earth below it are generated.
   

   The model of D-region ledge suggests also a mechanism for the generation of thunder clouds. The electrically charged dust stucks cloud to like dust to water or ice so that the cloud becomes electrically charged. Since the dust does not reach ground and positive ionic current reaches it, the local electric field of Earth changes sign and eventually reaches the value needed for di-electric breakdown.
   
   

4. Lightnings are found to have a strange feature: the energies of electrons can be relativistic and gamma rays are observed. This does not fit with the standard view. For this I have proposed explanation in terms of dark electrons travelling along magnetic flux tubes without dissipation and thus accelerating to to relativistic energies of order 10⁵, one fifth of electron mass. Dark matter in TGD sense is indeed at criticality and the criticality corresponds now to the dielectric breakdown.
   My first thought was that this model suitably extended might throw light also to the above three mysteries but I soon realized that standard physics is enough: the magnetic flux tubes containing dark ions and electrons represent a small effect.
   

Addition: 11 months later an email that I received concerning this post led to an alternative explanation in the spirit of TGD. This relies on new results in the understanding of h_eff/h=n hierarchy gained during the last year.

1. Ionization in biosystems could be understood being as due to the transitions increasing the value of n for unpaired valence electrons of atom so that atoms are ionized at physiological temperatures. The reason is that the binding energy scale of atom proportional to 1/n² reduces below the thermal energy so that dark atoms cease to be stable at physiological temperatures and lose their valence electrons.
   
   
2. One could apply this idea also to the ionization of NO molecules in D region ledge below 80 km. UV radiation from Sun can induce ionization of electrons in the valence bonds of NO to produce NO₊. What if the ionization of NO molecules in D region ledge below 80 km creates mostly dark and thus invisible electrons. Why these electrons would be mostly dark or why they would transform to dark electrons?
   
   
3. Different values of n correspond to different quantum phases of matter. Could the ordinary wisdom about thermodynamical systems such as ferromagnet or Bose-Einstein condensates allow a generalization to the recent situation? Could the rate for ordinary electron produced in ionization to tranform to dark electron increase in the presence of dark phase. Could dark electrons form a Bose-Einstein condensate of electron Cooper pairs at magnetic flux tubes "eating" the electrons formed in the ionization of NO.
   
   

For a summary of earlier postings see Links to the latest progress in TGD.

Mechanism for the transfer of genetic information from soma cells to germ cells

There was a highly interesting popular article No Sex Required: Body Cells Transfer Genetic Info Directly Into Sperm Cells, Amazing Study Finds summarizing the findings discussed in the article Soma-to-Germline Transmission of RNA in Mice Xenografted with Human Tumour Cells: Possible Transport by Exosomes.

The abstract of the article gives for a professional a readable summary.

Mendelian laws provide the universal founding paradigm for the mechanism of genetic inheritance through which characters are segregated and assorted. In recent years, however, parallel with the rapid growth of epigenetic studies, cases of inheritance deviating from Mendelian patterns have emerged. Growing studies underscore phenotypic variations and increased risk of pathologies that are transgenerationally inherited in a non-Mendelian fashion in the absence of any classically identifiable mutation or predisposing genetic lesion in the genome of individuals who develop the disease. Non-Mendelian inheritance is most often transmitted through the germline in consequence of primary events occurring in somatic cells, implying soma-to-germline transmission of information. While studies of sperm cells suggest that epigenetic variations can potentially underlie phenotypic alterations across generations, no instance of transmission of DNA- or RNA-mediated information from somatic to germ cells has been reported as yet.

To address these issues, we have now generated a mouse model xenografted with human melanoma cells stably expressing EGFP-encoding plasmid. We find that EGFP RNA is released from the xenografted human cells into the bloodstream and eventually in spermatozoa of the mice. Tumor-released EGFP RNA is associated with an extracellular fraction processed for exosome purification and expressing exosomal markers, in all steps of the process, from the xenografted cancer cells to the spermatozoa of the recipient animals, strongly suggesting that exosomes are the carriers of a flow of information from somatic cells to gametes. Together, these results indicate that somatic RNA is transferred to sperm cells, which can therefore act as the final recipients of somatic cell-derived information.

Some background is needed to understand this rather technical summary.

1. Darwinism has dominated biology since Darwin. The rules of classical Mendelian inheritance conform with the Darwinian view and can be reduced to genetic level. Various traits are inherited genetically by sexual reproduction and genome would change during lifetime only through mutations. Genome changes exremely slowly by random changes for offspring from which selection pressures choose the survivors.
   

   Lamarckian view in turn assumed that the external circumstances experienced by organism leave a trace, which can be inherited but it could not be formulated in terms of modern molecular biology whereas the Darwinian dogma could be formulated in terms of Weissman's genetic barrier. Information flows from germ cells to soma but never in opposite direction. If it would do so, the soma interacting with environment could transfer information to germ cells and the experiences during lifetime could leave inheritable trace to germ cells.
   

   An analogous dogma is that information is always transcribed from DNA to RNA to proteins but never in opposite direction. It is now known that this takes place in case of viruses and retroviruses: there are so called jumping genes which can also make copies of themselves. 5 per cent of human genome conists of endogenous retroviruses capable of doing the same. The huge genome of maize is due to this kind of proces.
   
   

2. The development epigenetics has started to shatter the belief on Wessimann's genetic barrier. Gene expression is not fixed by genome alone and can be change even when genes are unaffected. Silencing of genes by DNA methylation and histone modification allow to modify gene expression. Silencing is essentially a locking of gene preventing its expression by transcription followed by translation.
   

   It is now known that epigenetic changes in the gene expression can be inherited. The mechanisms are still poorly understood. What seems however clear the genome is more like a slowly changing hardware and gene expression or whatever is behind it is the software and programs can change very rapidly by just adding or deleting comment signs in the code. A deeper understanding of this software is needed.
   
   

3. Epigenetic inheritance requires that genetic information is transferred from soma cells to germ cells. If only DNA or RNA are capable of representing genetic information, then DNA or RNA must be transferred from soma cells to germ cells. No instance of direct DNA or RNA mediated information from soma to germ cells had been observed before
   the above mentioned experiments. One can of course challenge the assumption about DNA and RNA as the only representations of genetic information.
   
   

The basic idea of the experiment was simple. Use a marker for RNA by using plasmids (DNA strands not belonging to chromosomes) genetically engineered to code for a marker protein making itself visible by fluoresence. Then one just follows the fate of these proteins generated in soma cells and looks whether they end up inside germ cells and how this happens.

More technically: mouse model was xenografted with human melanoma cells stably expessing EGFP-coding plasmid (expressed in a manner possibly evoking emotions: human melanoma cancer tissue was implanted in mouse). EGFP-RNA is released from xenografted human cells to blood. One just looks whether it eventually ends up to the sperm cells of mice and tries to identify the transfer mechanism. Only transfer to sperm cells was studied. One might expect that the transfer of RNA can happen also to ovum. I guess that the sperm cells are easier to study.

What was observed?

1. The transfer of RNA from soma cells to sperm cells was indeed found to occur. The transferred RNA can in turn induce epigenetic effects in germ cells known to be inherited by a mechanisms, which however remain poorly understood. Epigenetic mechanisms seem to be involved in the cases considered so that DNA is not changed, only its expression.
   
   
2. The transfer mechanism was identified. The transferred RNA is contained by exosomes analogous to synaptic vesicles transferring neurotransmitters from presynaptic to postsynaptic cell. Transfer of RNA takes place via fusion of the membranes just like transfer of neurotransmitters. Maybe genetic engineering using exosomes or analogous structures to transfer the needed material to cells has been tried.
   
   

The implications of the findings are dramatic but already implied by the earlier work in epigenetics. What is important that Lamarckian view can be now defended by a concrete genetic mechanism. Lamarckism implies that the time scale of inheritance becomes the time scale for the appearence of a new generation. Nutrition, environment, lifestyle and even meditation and similar practices, are already now known to affect gene expression on daily basis: we are not victims of genetic determinism and are epigenetically responsible for our own well-being. Epigenetic information can be transferred also to germ cells so that we responsible also for the well-being of our children. Our children suffer our sins and share our sufferings.

The precise mechanism of inheritance of epigenetic modifications is poorly understood. For instance, it is known that alleles (variants of game gene) can express themselves differently: this would be due to epigenetics. One allele can also induce other allele to express in the same manner. Somekind of "social pressure" like interaction seems to be involved.

TGD suggests the notion of magnetic body and cyclotron resonance as this interaction. The DNA of offspring get tuned to the DNA of mother during pregnancy and this gives to epigenetic inheritance. Various epigenetic mechanisms such as methylation and histone modification could affect cyclotron frequencies besides purely geometric modifications of DNA and locking at the level of gene could be accompanied kicking out of tune at the level of magnetic body. These aspects are discussed in earlier blog posting and the article Magnetic body, bio-harmonies, morphogenesis, and epigenetics.

Bacteria behave like spin system: Why?

In Physorg there was an interesting article titled Bacteria streaming through a lattice behave like electrons in a magnetic material. The popular article tells arbout article by Dunkel et al with title Ferromagnetic and antiferromagnetic order in bacterial vortex lattices. The following summarizes what has been studied and observed.

1. The researchers have studied a square lattice of about 100 wells with well radius below 50 microns and well depth about 18 microns. The wells are connected by thin channels. Also triangular lattice has been studied.
   
   
2. Below a critical radius about 35 microns an ordered flow is generated. The flow involves interior flow and edge flow in opposite direction consisting of single bacterium layer. One can understand this from angular momentum conservation. The coherence of this flow is however surprising. If one believes that each bacterium in principle chooses its swimming direction, one must understand what forces bacteria to select the same swimming direction.
   
   
3. Below a critical radius of channel about d=4 microns the flow directions in the neighboring wells are opposite for the square lattice. One has superposition of lattice and its dual with opposite flow directions. In the case of triangular lattice analogous cituation is encountered. In this situation there is no flow between the wells but there is an interaction. The minimization of dissipative losses requires minimization of velocity gradients inside channels. made possible by same local flow direction for the edge currents of neighboring wells.
   
   
4. Above the critical radius the flow changes its character. The flows synchronize and the interior flows rotate in the same direction as do also edge flows which occur also between the neighboring channels and give rise to closed flows around the boundaries of square like regions behind wells having larger scale. This flow pattern is consistent with angular momentum conservation: the angular momenta of lattice and its dual cancel each other.
   
   
5. The phase transition is analogous to that from antiferromagnetism to ferromagnetism. The total angular momenta of bacteria, their colonies, are analogous to spins. The situation can be modelled as 2-D Ising model consisting of lattice of spins with nearest neighbor interactions. Usually the spins are assigned with electrons but now they are assigned with bacteria.
   
   

This raises interesting questions. Bacteria swim by using flagellae. They can decide the swimming direction and control it by controlling the flagellae. Bacteria are living organisms and have a free will. Why would bacterium colory behave like quantal many-spin system. What happens when the swimming direction becomes same for the bacteria inside single well: does the colony become an entity with collective consciousness and do bacteria obey "social pressure". Does this happen also for the colony formed by these colonies in transition to ferromagnetism like state?

If one takes TGD inspired quantum biology as starting point, one can represent more concrete questions and possible answers to them.

1. Magnetic body (MB) controls the biological body (BB) be it organism or part of it. MB contains dark matter as cyclotron Bose-Einstein condensates of bosonic ions. Pairs of parallel flux tubes could also contain members of Cooper pairs whose spin depends on whether the magnetic fields at flux tubes are parallel or antiparallel.
   
   
2. What could be the mechanism of control? MB is assumed to send dark photon signals from MB to biological body
   to control it and an attractive idea is that control is by angular momentum conservation. Since the angular momentum transfer involve is due to a phase transition analogous to the change of the direction of magnetization or generation of magnetization the angular momentum transfer is large irrespective of the value of unit of angular momentum for dark photon (see discussion below). This large angular momentum could be transformed to angular momentum of ordinary matter and in recent case be responsible for generating the rotational motion of bacterium or larger unit.
   

   The transfer of dark photons induced by a phase transition changing the direction of dark magnetization might thus induce a large transfer of angular momentum to BB and generate macroscopic rotation. If this were the case the rotational state of dark MB of bacterium would serve as a template for bacterium.
   

   The bacterium colony associated with the well below critical size would correspond to super-organism having MB whose rotational state could serve as template for the bacterial MBs in turn serving as a similar template for the bacteria.
   
   
   

3. If the net angular momenta of MB and corresponding BB (bacterium, well colony, colony of these) vanish separately, the model is consistent with the model of the article in which local considerations determine the rotational directions. In this case the MBs of well colonies would behave like spins with nearest neighbor interactions.
   

   One can also consider the possibility that at quantum criticality long range quantum fluctuations occur and the local equilibrium conditions do not hold true. Even more, the net angular momenta of MB and BB would cancel each other but would not necessarily separately. This would imply apparent non-conservation of angular momentum at the level of bacterium colony at criticality and might allow to find experimental support for the notion of magnetic body. The proof of MB carrying dark matter as a concept would be very much like that of neutrino the existence of which was deduced from apparenent energy non-conservation in beta decays.
   
   

The model has a problem to worry about. I still am not quite sure whether h_eff/h=n means that that the unit of spin is scaled up by n or that a fractionization of angular momentum by 1/n for single sheet of associated n-fold covering of space-time surface takes place. The control mechanism based on angular momentum conservation could however be at work in both cases. The option assuming fractionization seems to be the realistic one and only this will be considered in the following. Reader can ponder the option assuming scaled up unit of angular momentum (the scaling up of angular momentum of dark photon is not in coherence with the assumption that dark photon has same four-momentum as ordinary photon to which it should be able to transform).

1. Consider first the simplest variant for the effective fractionization of quantum numbers. If one has n-fold covering singular at the boundaries of CD then spin fractionization can be considered such that one has effectively n spin 1/n photons - one per sheet - and the net spin is just the standard spin. This picture fits with the vision that the n-fold covering means that one must make n full 2π turns before turning to the original point at space-time sheet: this allows at space-time surface wave functions with fractional spin which would be many-valued in Minkowski space. Similar fractionization would occur to other quantum numbers such as four-momentum so that net four-momentum would not change. The wavelength of these building bricks of dark photon analogous to Bose-Einstein condensate have frequencies scaled down by factor 1/n.
   

   In this case the direct decay to single ordinary photon interpreted as biophoton is allowed by conservation laws. Of course, also decays to several ordinary photons are possible. The decay to a bunch of n ordinary photons with total momenta 1/n times that of dark photon is possible if the spins of ordinary photons sum up to the spin of dark photon.
   

   The total angular momentum liberated from the cyclotron Bose-Einstein condensate spin could be transferred to spin of ordinary particles, say proton or ion for which the natural scale of orbital angular momentum is much larger (proportional to the rest energy). Simple order of magnitude estimate for orbital angular momentum with respect to the symmetry axis of possibly helical magnetic flux tube shows that in this case the spin could be transformed to angular momentum in the scale of organism and to the motion of organism itself.
   

   Note that dark photon could also decay to a bunch of ordinary photons with momentum scaled down by 1/n since the
   spins of the photons can sum up to spin 1.
   
   

2. A many-sheeted analog of second quantization generalizes the above picture. The n space-time sheets can be labelled by an integer m =1,...,n defining an analog of discrete position variable. One can second quantize the fundamental fermions in this discrete space so that one has not only the ordinary many fermion states with N=0/1 fermions in given mode but also states with fractionization of fermion number and other quantum numbers by q= m/n< 1 in a given mode. This would induce fractionization of bosons identified as fractional many-fermion states.
   

   Particle with fractional spin cannot decay directly to ordinary particle unless one has m=n: this correspond to the first option. Fractional particles characterized by m/n and (n-m)/n can however fuse to ordinary particle. An attractive additional hypothesis is that the net quantum numbers are integer valued.
   

   I have discussed the possibility of molecular sex: the opposite molecular sexes would have fractional charges summing up to ordinary charges. If magnetic bodies with opposite molecular sexes are paired they have ordinary total quantum numbers and can control ordinary matter by the proposed mechanism based on conservation of angular momentum (or some other charges). Dark matter would serve as template for ordinary matter and dark phase transitions would induce those of visible matter. The proposal that DNA, RNA, tRNA, and amino-acids are accompanied by dark proton sequences (or more general dark nuclei) could realize this picture. DNA double strand could be seen as an outcome of a molecular marriage in this framework! At higher level brain hemispheres might be a seen as a dark matter marriage. This picture can be also seen as emergence of symbols and dynamics based on symbol sequences at the molecular level with molecular marriage making possible very precise selection rules.
   

See the article Bacteria behave like spin systems: Why? or the chapter Criticality and dark matter of "Hyper-finite factors and dark matter hierarchy".

For a summary of earlier postings see Links to the latest progress in TGD.

Quantum phase transitions and 4-D spin glass energy landscape

TGD has led to two descriptions for quantum criticality. The first one relies on the notion of 4-D spin glass degeneracy and emerged already around 1990 when I discovered the unique properties of Kähler action. Second description relies on quantum phases and quantum phase transitions and I have tried to explain my understanding about it above. The attempt to understand how these two approaches relate to each other might provide additional insights.

1. Vacuum degeneracy of Kähler action is certainly a key feature of TGD and distinguishes it from all classical field theories. Small deformations of the vacua probably induced by gluing of magnetic flux tubes (primordially cosmic strings) to these vacuum space-time sheets deforms them slightly and would give rise to TGD Universe analogous to 4-D spin glass. The challenge is to relate this description to the vision provided by quantum phases and quantum phase transitions.
   
   
2. In condensed matter physics one speaks of fractal spin glass energy landscape with free energy minima inside free energy minima. This landscape obeys ultrametric topology: p-adic topologies are ultra metric and this was one of the original motivations for the idea that p-adic physics might be relevant for TGD. Free energy is replaced with the sum of Kähler function - Kähler action of Euclidian space-time regions and imaginary Kähler action from Minkowskian space-time regions.
   
   
3. In the fractal spin glass energy landscape there is an infinite number of minima of free energy. The presence of several degenerate minima leads to what is known as frustration. In TGD framework all the vacuum extremals have the same vanishing action so that there is infinite degeneracy and infinite frustration (also created by the attempt to understand what this might imply physically!). The diffeomorphisms of M⁴ and symplectic transformations of CP₂ map vacuum extremals to each other and acts therefore as gauge symmetries. Symplectic transformations indeed act as U(1) gauge transformations. Besides this each Lagrangian sub-manifold of CP₂ defines its own space of vacuum-extremals as orbit of this symplectic group.
   

   As one deforms vacuum extremals slightly to non-vacuum extremals, classical gravitational energy becomes non-vanishing and Kähler action does not vanish anymore and the above gauge symmetries become dynamical symmetries. This picture serves as a useful guideline in the attempts to physically interpret. In TGD inspired quantum biology gravitation plays indeed fundamental role (gravitational Planck constant h_gr).
   
   

4. Can one identify a quantum counterpart of the degeneracy of extremals? The notion of negentropic entanglement (NE) is cornerstone of TGD. In particular, for maximal negentropic entanglement density matrix is proportional to unit matrix so that states are degenerate in the same sense as the states with same energy in thermodynamics. Energy has Kähler function as analogy now: hence the degeneracy of density matrix could correspond to that for Kähler function. More general NE corresponds to algebraic entanglement probabilities and allows to identify unique basis of eigenstates of density matrix. NE is favored by NMP and serves key element of TGD inspired theory of consciousness.
   

   In standard physics degeneracy of density matrix is extremely rare phenomenon as is also entanglement with algebraic entanglement probabilities. These properties are also extremely unstable. TGD must be somehow special. The vacuum degeneracy of Kähler action indeed distinguishes TGD from quantum field theories, and an attractive idea is that the degeneracy associated with NE relates to that for extremals of Kähler action. This is not enough however: NMP is needed to stabilize NE and this occurs only for dark matter (h_eff/h>1 equals to the dimension of density matrix defining NE).
   

   The strong form of holography takes this idea further: 2-D string world sheets and partonic 2-surfaces are labelled by parameters, which belong to algebraic extension of rationals. This replaces effectively infinite-D WCW with discrete spaces characterized by these extensions and allows to unify real and p-adic physics to adelic physics. This hierarchy of algebraic extensions would be behind various hierarchies of quantum TGD, also the hierarchy of deformations of vacuum extremals.
   
   

5. In 3-D spin glass different phases assignable to the bottoms of potential wells in the fractal spin energy landscape compete. In 4-D spin glass energy of TGD also time evolutions compete, and degeneracy and frustration chacterize also time evolutions. In biology the notions of function and behavior corresponds to temporal patterns: functions and behaviors are fighting for survival rather than only organisms.
   

   At quantum level the temporal patterns would correspond to phase transitions perhaps induced by quantum phase transitions for dark matter at the level of magnetic bodies. Phase transitions changing the value of h_eff would define correlates for "behaviors and the above proposed description could apply to them.
   
   

6. Conformal symmetries (the shorthand "conformal is understood in very general sense here) allow to understand not only quantum phases but also quantum phase transitions at fundamental level and "transitons transforming according to representations of Kac-Moody group or gauge group assignable to the inclusion of hyperfinite factors characterized by the integer m in h_eff(f)= m× h_eff(i) could allow precise quantitative description. Fractal symmetry breaking leads to conformal sub-algebra isomorphic with the original one
   

   What could this symmetry breaking correspond in spin energy landscape? The phase transition increasing the dynamical symmetry leads to a bottom of a smaller well in spin energy landscape. The conformal gauge symmetry is reduced and dynamical symmetry increased, and the system becomes more critical. Indeed, the smaller the potential well, the more prone the system is for being kicked outside the well by quantum fluctuations. The smaller the well, the large the value of h_eff. At space-time level this corresponds to a longer scale. At the level of WCW (4-D spin energy landscape) this corresponds to a shorter scale.
   
   

For backbround see the article the chapter Criticality and dark matter of "Hyper-finite Factors and Dark Matter Hierarchy".

For a summary of earlier postings see Links to the latest progress in TGD.

What's new in TGD inspired view about phase transitions?

The comment of Ulla mentioned Kosterlitz-Thouless phases transition and its infinite order. I am not a condensed matter physicist so that my knowledge and understanding are rather rudimentary and I had to go to Wikipedia. I realized that I have not payed attention to the classification of types of phase transitions, while speaking of quantum criticality. Also the relationship of ZEO inspired description of phase transitions to that of standard positive energy ontology has remained poorly understood. In the following I try to represent various TGD inspired visions about phase transitions and criticality in organized manner and relate them to the standard description.

About thermal and quantum phase transitions

It is good to beging with something concrete. Wikipedia article lists examples about different types of phase transitions. These phase transitions are thermodynamical.

1. In first order phase thermodynamical phase transitions heat is absorbed and phases appear as mixed. Melting of ice and boiling of water represent the basic examples. Breaking of continuous translation symmetry occurs in crystallization and symmetry is smaller at low temperature. One speaks of spontaneous symmetry breaking: thermodynamical fluctuations are not able to destroy the configuration breaking the symmetry.
   
   
2. Second order phase transitions are also called continuous and they also break continuous symmetries. Susceptility diverges, correlation range is infinite, and power-law behaviour applies to correlations. Ferromagnetic, super-conducting, and superfluid transitions are examples. Conformal field theory predics power-law behavior and infinite correlation length. Infinite susceptility means that system is very sensitive to external perturbations. First order phase transition becomes second order transition at critical point. Here the reduction by strong form of holography might make sense for high Tc superconductors at least (they are effectively 2-D).
   
   
3. Infinite order phase transitions are also possible. Kosterlitz-Thouless phase transition occurring in 2-D systems allowing conformal symmetries represents this kind of transition. These phase transitions are continuous but do not break continuous symmetries as usually.
   
   
4. There are also liquid-glass phase transitions. Their existence is hypothetical. The final state depends on the history of transition. Glass state itself is more like an ongoing phase transition rather than phase.
   

These phase transitions are thermal and driven by thermal fluctuations. Also quantum phase transitions are possible.

1. According to the standard definition they are possible only at zero temperature and driven by quantum fluctuations. For instance, gauge coupling strength would be analogous to quantum temperature. This is a natural definition in standard ontology, in which thermodynamics and quantum theory are descriptions at different levels.
   

   Quantum TGD can be seen as a square root of thermodynamics in a well-defined sense and it is possible to speak about quantum phase transitions also at finite temperature if one can identify the temperature like parameter characterizing single particle states as a kind of holographic representations of the ordinary temperature.
   
   

2. The traces of quantum phase transitions are argued to be visible also at finite temperatures if the energy gap
   ℏ×ω is larger than the thermal energy: ℏω>T. In TGD framework Planck constant has a spectrum h_eff/h= n and allows very large values. This allows quantum phase transitions even at room temperature and TGD inspired quantum biology relies crucially on this. What is of special interest that also ordinary thermal phase transitions might be accompanied by quantum phase transitions occurring at the level of magnetic body and perhaps even inducing the ordinary thermal phase transition.
   
   
3. Quantum critical phase transitions occur at critical point and are second order phase transitions so that susceptibility diverges and system is highly sensitive to perturbations and so in wide range around critical temperature (zero in standard theory). Long range fluctuations are generated and this conforms with the TGD vision about the role of large h_eff phases and generalized conformal symmetry: which also implies that the region around criticality is wide (exponentially decaying correlations replaced with power law correlations).
   
   

TGD suggests some examples of quantum phase transition like phenomena.

1. Bose-Einstein (BE) condensate consisting of bosons in same state would represent a typical quantum phase. I have been talking a lot about cyclotron BE condensates at dark magnetic flux tubes. The bosonic particles would be in the same cyclotron state. One can consider also the analogs of Cooper pairs with members at flux tubes of a pair of parallel flux tubes with magnetic fields in same or opposite direction. One member at each tube having spin 1 or zero. This would give rise to high Tc superconductivity.
   
   
2. One natural mechanism of quantum phase transition would be BE condensation to a new single particle state. The rate for an additions of new particle to condensate is proportional to N+1 and disappearance of particle from it to N, where N is the number of particles in condensate. The net rate for BE condensation is difference of these and non-vanishing.
   

   Quantum fluctuations induce phase transition between states of this condensate at criticality. For instance, cyclotron condensate could make a spontaneous phase transition to a lower energy state by a change of cyclotron energy state and energy would be emitted as a dark cyclotron radiation. This kind of dark photon radiation could in turn induce cyclotron transition to a higher cyclotron state at some other flux tube. If NMP holds true it could pose restrictions for the occurrence of transitions since one expects that negentropy is reduced. The transitions should involve negentropy transfer from the system.
   

   The irradiation of cyclotron BE condensate with some cyclotron frequency could explain cyclotron phase transition increasing the energy of the cyclotron state. This kind of transition could explain the effecs of ELF em fields on vertebrate brain in terms of cyclotron phase transition and perhaps serving as a universal communication and control mechanism in the communications of the magnetic body with biological body and other magnetic bodies. The perturbation of microtubules by an oscillating voltage (see this) has been reported by the group of Bandyonophyay to induce what I have interpreted as quantum phase transition (see this).
   

   External energy feed is essential and dark cyclotron radiation or generalized Josephson radiation from cell membrane acting as generalized Josephson junction and propagating along flux tubes could provide it. Cyclotron energy is scaled up by h_eff/h and would be of the order of biophoton energy in TGD inspired model of living matter and considerably above thermal energy at physiological temperature.
   
   

3. Also quantum phase transitions affecting the value of h_eff are possible. When h_eff is reduced and frequency is not changed, energy is liberated and the transition proceeds without external energy feed (NMP might pose restrictions). Another option is increase of h_eff and reduce the frequency in such a manner that that single particle energies are not changed. One can imagine many other possibilities since also p-adic length scale leading to a change of mass scale could change.
   

   The model for cold fusion relies on a process, which is analogous to quantum phase transition. Protons from the exclusion zones (EZs) of Pollack are transferred to dark protons at magnetic flux tubes outside EZ and part of dark protons sequences transform by dark weak decays and dark weak boson exchanges to neutrons so that beta stable dark nuclei are obtained with binding energy much smaller than nuclear binding energy. This could be seen as dark nuclear fusion and quantum analog of the ordinary thermal nuclear fusion. The transformation of dark nuclei to ordinary nuclei by h_eff reducing phase transition would liberate huge energy if allowed by NMP and explain the reported biofusion.
   
   

4. Energetics is clearly an important factor (in ordinary phase transitions for open system thermal energy feed is present). The above considerations assume that ordinary positive energy ontology effectively applies. ZEO allows to consider a more science fictive possibility. In ZEO energy is conserved when one considers single zero energy state as a time evolution of positive energy state. If single particle realizes square root of thermodynamics, one has superposition of zero energy states for which single particle states appear as pairs of positive and negative energy states with various energies: each state in superposition respects energy conservation. In this kind of situation one can consider the possibility that temperature increases and average single particle energy increases. In positive energy ontology this is impossible without energy feed but in ZEO it is not excluded. I do not understand the situation well enough to decide whether some condition could prevent this. Note however that in TGD inspired cosmology energy conservation holds only in given scale (given CD) and apparent energy non-conservation would result by this kind of mechanism.
   
   

Question related to TGD inspired description of phase transitions

The natural questions are for instance following ones.

1. The general classification of thermodynamical phase transitions is in terms of order: the order of the lowest discontinuous derivative of the free energy with respect to some of its arguments. In catastrophe theoretic description one has a hierarchy of criticalities of free energy as function of control variables (also other behavior variables than free energy are possible) and phase transitions with phase transitions corresponding to catastrophe containing catastrophe.... such that the order increases. For intance, for cusp catatrophe one has lambda-shaped critical line and critical point at its tip. Thom's catastrophe theory description is mathematically very attractive but I think that it has problems at experimental side. It indeed applies to flow dynamics defined by a gradient of potential and thermodynamics is something different.
   

   In TGD framework the sum of Kähler function defined by real Kähler action in Euclidian space-time regions and imaginy Kähler action from Minkowskian space-time regions defining a complex quanty replaced free energy. This is in accordance with the vision that quantum TGD can be seen as a complex square root of thermodynamics. Situation is now infinite-dimensional and catastrophe set would be also infinite-D. The hierarchy of isomorphic super-conformal algebras defines an infinite hierarchy of criticalities with levels labelled by Planck constants and catastrophe theoretic description seems to generalize.
   

   Does this general description of phase transitions at the level of dark magnetic body (field body is more general notion but I will talk about magnetic body (MB) in the sequel) allow to understand also thermodynamical phase transitions as being induced from those for dark matter at MB?
   
   

2. Quantum TGD can be formally regarded as a square root of thermodynamics. Does this imply "thermal holography" meaning that single particle states can represent ensemble state as square root of the thermal state of ensemble. Could one unify the notions of thermal and quantum phase transition and include also the phase transitions changing h_eff? Could MB make this possible?
   
   
3. How does the TGD description relate to the standard description? TGD predicts that conformal gauge symmetries correspond to a fractal hierarchy of isomorphic conformal sub-algebras. Only the lowest level with maximal conformal symmetry matters in standard theory. Are the higher "dark" levels something totally new or do they appear in the description of also ordinary phase transitions? What is the precise role of symmetries and symmetry changes in TGD description and is this consistent with standard description. Here the notion of field body is highly suggestive: the dynamics of field body could induce the dynamics of ordinary matter also in phase transitions.
   
   

There is a long list of questions related to various aspects of TGD based description of phase transitions.

1. In TGD framework NMP a applying to single system replaces second law applying to ensemble as fundamental description. Second law follows from the randomness of the state function reduction for ordinary matter and in long length and time scales from the ultimate occurrence of state function reductions to opposite boundary of CD in ensemble. How does this affect the description of phase transitions? NMP has non-trivial implications only for dark matter at MB since it NMP does favors preservation and even generation of negentropic entanlement (NE). Does NMP imply that MB plays a key role in all phase transitions?
   
   
2. Does strong form of holography of TGD reduce all transitions in some sense to this kind of 2-D quantum critical phase transitions at fundamental level? Note that partonic 2-surfaces can be seen as carriers of effective magnetic charges and string world sheets carrying spinor modes accompany magnetic flux tubes. Could underlying conformal gauge symmetry and its change have practical implications for the description of all phase transitions, even 3-D and thermodynamical phase transitions?
   
   
3. Could many-sheetedness of space-time - in particular the associated p-adic length scale hierarchy - be important and could one identify the space-time sheets whose dynamics controls the transition? Could the fundamental description in terms of quantum phase transitions relying on strong form of holography apply to all phase transitions? Could dark phases at MB be the key to the description of also ordinary thermodynamical phase transitions? Could one see dark MB as master and ordinary matter as slave and redue the description of all phase transitions to dark matter level.
   

   Could the change of h_eff for dark matter at field body accompany any phase transition - even thermodynamical - or only quantum critical phase transition at some level in the hierarchy of space-time sheets? Or are also phase transitions involving no change of h_eff possible? Do ordinary phase transitions correspond to these. What is the role of h_eff changing "transitons" and their dynamical symmetries?
   
   

4. The huge vacuum degeneracy of Kähler action implies that any space-time surface with CP₂ projection that is Lagrangian manifold and has therefore dimension not larger than two, is vacuum extremal. The small deformations of these vacuum extremals define preferred extremals. One expects that this vacuum degeneracy implies infinite number of ground states as in the case of spin glass (magnetized system consisting of regions with different direction of magnetization). One can speak of 4-D spin glass. It would seem that the hierarchy of Planck constants labelling different quantum phases and the phase transitions between these phases can be interpreted in terms of 4-D spin glass property? Besides phases one would have also phase transitions having "transitons" as building bricks.
   

   It seems that one cannot assign 4-D spin glass dynamics to MB. If magnetic flux tubes are carriers of monopole flux, they cannot be small local deformations of vacuum extremals for which Kähler form vanishes. Hence 4-D spin glass property can be assigned to flux tubes carrying vanishing magnetic flux. Early cosmology suggests that cosmic strings as infinitely flux tubes having 2-D CP₂ projection and carrying monopole flux are deformed to magnetic flux tubes and suffer topological condensation around vacuum extremals and deform them during the TGD counterpart of inflationary period.
   

   Comment: Glass state looks like a transition rather than state and ZEO and 4-D spin glass description would seem to fit naturally to his situation: glass would be a 4-D variant of spin glass. The time scale of transition is long and one might think that h_eff at the space-time sheet "controlling" transition is rather large and also the change of h_eff is large.
   
   

Symmetries and phase transitions

The notion of symmetry is considerably more complex in TGD framework than in standard picture based on positive energy ontology. There are dynamical symmetries of dark matter states located at the boundaries of CD. For space-time sheets describing phase transitions there are also dynamical symmetries but they are different. In standard physics one has just states and their symmetries. Conformal gauge symmetries forming a hierarchy: conformal field theories this symmetry is maximal and the hierarchy is absent.

1. There is importance and very delicate difference between thermal and thermodynamical symmetries. Thermal symmetries are due to thermal equilibrium implying symmetries in statistical sense. Quantal symmetries correspond to representations of symmetry group and are possible if thermal fluctuations do not transform the states of the representations the states of other representation.
   

   Dark dynamical symmetries are quantum symmetries. The breaking of thermal translational symmetry of liquid leads to discrete translational symmetry of crystal having interpretation as quantum symmetry. The generation of continuous thermal translational symmetry from discrete quantum symmetry means loss of quantum symmetry. To my opinion, standard thinking is sloppy here.
   
   

2. For thermodynamical phase transitions temperature reduction induces spontaneous breaking of symmetry: consider only liquid-to-crystal transition. Analogously, in gauge theories the reduction gauge coupling strength leads to spontaneous symmetry breaking: quantum fluctuations combine representation of sub-group to a representation of larger group. It would seem that spontaneous symmetry breaking actually brings in a symmetry and the ubroken symmetry is "thermal" or pure gauge symmetry. QCD serves as an example: as strong coupling strength (analogous to temperature) becomes large confinement occurs and color symmetry becomes pure gauge symmetry.
   
   
3. In TGD the new feature is that there are two kinds of symmetries for dark conformal hierarchies. Symmetries are either pure gauge symmetries or genuine dynamical symmetries affecting the dark state at field body physically. As h_eff increases, the conformal pure gauge symmetry is reduced (the conformal gauge algebra annilating the states becomes smaller) but dynamical symmetry associated with the degrees of freedom above measurement resolution increases. In ordinary conformal theories pure gauge conformal symmetry is always maximal so that this phenomenon does not occur.
   

   The intuitive picture is that the increase of dynamical symmetry induced by the reduction of pure gauge conformal symmetry occurs as temperature is lowered and quantum coherence in longer scales becomes possible. This conforms with the thermodynamical and gauge theory views if pure gauge symmetry is identified as counterpart of symmetry as it is understood in thermodynamics and gauge theories.
   

   The dynamical symmetry of dark matter however increases. This symmetry is something new and would be genuine quantum symmetry in the sense that quantum fluctuations respect the representations of this group. The increase of h_eff indeed implies reduction of Kähler coupling strength analogous to reduction of temperature so that these quantum symmetries can emerge.
   
   

4. There is also a dynamical symmetry associated with phase transitions h_eff(f)=m× h_eff(i) such that m would define the rank of ADE Lie group G classifying states of "transitons". Lie groups with ranks n_i and n_f would be ranks for the Lie group G in the initial and final states. G would correspond to either gauge (not pure gauge) or Kac-Moody symmetry as also for corresponding dynamical symmetry groups associated with phases.
   
   
5. An interesting question relates to Kosterlitz-Thouless Thouless phase transition, which is 2-D and for which symmetry is not changed. Could one interpret it as a phase transition changing h_eff for MB: symmetry group as abstract group would not change although the scale in which acts would change: this is like taking zoom. The dynamical symmetry group assignable to dark matter at flux tubes would however change but remain hidden.
   
   

To sum up, the notion of magnetic (field) body might apply even to the ordinary phase transitions. Dark symmetries - also discrete translational and rotational symmetries - would be assigned with dark MB possibly present also in ordinary phases. The dynamical symmetries of MB would bring a new element to the description. Ordinary phase transitions would be induced by those of MB. This would generalize the vision that MB controls biological body central for TGD view about living matter. In the spirit of slaving hierarchy and TGD inspired vision about quantum biology, ordinary matter would be slave and MB the master and the description of the phase transitions in terms of dynamics of master could be much more simpler than the standard description. This would be a little bit like understanding technical instrument from the knowledge of its function and from control level rather than from the mere physical structure.

For backbround see the article What's new in TGD inspired view about phase transitions? or the chapter Criticality and dark matter of "Hyper-finite Factors and Dark Matter Hierarchy".

For a summary of earlier postings see Links to the latest progress in TGD.

What ZEO can give to the description of criticality?

One should clarify what quantum criticality exactly means in TGD framework. In positive energy ontology the notion of state becomes fuzzy at criticality. It is difficult to assign long range fluctuations and associated quanta with any of the phases co-existent at criticality since they are most naturally associated with the phase change. Hence Zero Energy Ontology (ZEO) might show its power in the description of (quantum) critical phase transitions.

1. Quantum criticality could correspond to zero energy states for which the value of h_eff differs at the opposite boundaries of causal diamond (CD). The space-time surface between boundaries of CD would describe the transition classically. If so, then quanta for long range fluctuations would be genuinely 4-D objects - "transitons" - allowing proper description only in ZEO. This could apply quite generally to the excitations associated with quantum criticality. Living matter is key example of quantum criticality and here "transitons" could be seen as building bricks of behavioral patterns. Maybe it makes sense to speak even about Bose-Einstein condensates of "transitons".
   
   
2. Quantum criticality would be associated with the transition increasing n_eff=h_eff/h by integer factor m or its reversal. Large h_eff phases as such would not be quantum critical as I have sloppily stated in several contexts earlier. n_eff(f) =m × n_eff(i) would correspond to a phase having longer long range correlations as the initial phase. Maybe one could say that at the side of criticality (say the "lower" end of CD) the n_eff(f)=m × n_eff(i) excitations are pure gauge excitations and thus "below measurement resolution" but become real at the other side of criticality (the "upper" end of CD)? The integer m would have clear geometric interpretation: each sheet of n_i-fold coverings defining space-time surface with sheets co-inciding at the other end of CD would be replaced with its m-fold covering. Several replications of this kind or their reversals would be possible.
   
   
3. The formation of m-fold covering could be also interpreted in terms of an inclusion of hyper-finite factors labelled by integer m. This suggests a deep connection with symmetries of dark matter. Generalizing the McKay correspondence between finite subgroups of SU(2) characterizing the inclusions and ADE type Lie groups, the Lie group G characterizing the dynamical gauge group or Kac-Moody group for the inclusion of HFFs characterized by m would have rank given by m (the dimension of Cartan algebra of G).
   

   These groups are expected to be closely related to the inclusions for the fractal hierarchy of isomorphic sub-algebras of super-symplectic subalgebra. h_eff/h=n could label the sub-algebras: the conformal weights of sub-algebra are n-multiples of those of the entire algebra. If the sub-algebra with larger value of n_eff annihilates the states, it effectively acts as normal subgroup and one can say that the coset space of the two super-conformal groups acts either as gauge group or (perhaps more naturally) Kac-Moody group. The inclusion hierarchy would allow to realize all ADE groups as dynamical gauge groups or more plausibly, as Kac-Moody type symmetry groups associated with dark matter and characterizing the degrees of freedom allowed by finite measurement resolution.
   
   

4. If would be natural to assign "transitons" with light-like 3-surfaces representing parton orbits between boundaries of CD. I have indeed proposed that Kac-Moody algebras are associated with parton orbits where super-symplectic algebra and conformal algebra of light-one boundary is associated with the space-like 3-surfaces at the boundaries of CD. This picture would provide a rather detailed view about symmetries of quantum TGD.
   
   

The number-theoretic structure of h_eff reducing transitions is of special interest.

1. A phase characterized by h_eff/h=n_i can make a phase transition only to a phase for which n_f divides n_i. This in principle allows purely physics based method of finding the divisors of very large integers (gravitational Planck constant h_gr =GMm/v₀=h_eff =n× h defines huge integer).
   
   
2. In TGD inspired theory of consciousness a possible application is to a model for how people known as idiot savants unable to understand what the notion of prime means are able to decompose large integers to prime factors (see this). I have proposed that the division to prime factors is a spontaneous process analogous to the splitting of a periodic wave characterized by wave length λ/λ₀=n_i to a wave with wavelength λ/λ₀ =n_f with n_f a divisor of n_i. This process might be completely spontaneous sequence of phase transitions reducing the value of n_eff realized geometrically as the number of sheets of the singular covering defining the space-time sheet and somehow giving rise to a direct sensory percept.
   
   

For backbround see the article the chapter Criticality and dark matter of "Hyper-finite Factors and Dark Matter Hierarchy".

For a summary of earlier postings see Links to the latest progress in TGD.

E8 symmetry, harmony, and genetic code

Bee gave in Facebook a link to an article about a connection between icosahedron and E₈ root system (see this). The article (I have seen an article about the same idea earlier but forgotten it!) is very interesting.

The article talks about a connection between icosahedron and E₈ root system. Icosahedral group has 120 elements and its double covering 2× 120=240 elements. Remarkably, E₈ root system has 240 roots. E₈ Lie algebra is 248 complex-dimensional contains also the 8 commuting generators of Cartan algebra besides roots: it is essential that the fundamental representation of E₈ co-incides with its adjoint representation. The double covering group of icosahedral group acts as the Weyl group E₈. A further crucial point is that the Clifford algebra in dimension D=3 is 8-D.

One starts from the symmetries of 3-D icosahedron and ends up with 4-D root system F₄ assignable to Lie group and also to E₈ root system. E₈ defines a lattice in 8-D Euclidian space: what is intriguing that dimensions 3,4, 8 fundamental in TGD emerge. To me this looks fascinating - the reasons will be explained below.

What I might have understood

I try to explain what I have possibly understood.

1. The notion of root system is introduced. The negatives of roots are also roots but not other multiples. Root system is crystallographic if it allows a subset of roots (so called simple roots) such that all roots are expressible as combinations of these simple roots with coefficients having the same sign. Crystallographic root systems are special: they correspond to the fundamental weights of some Lie algebra. In this case the roots can be identified essentially as the quantum numbers of fundamental representations from which all other representations are obtained as tensor products. Root systems allow reflections as symmetries taking root system to itself. This symmetry group is known as Coxeter group and generalizes Weyl group. Both H₃ and H₄ are Coxeter groups but not Weyl groups.
   
   
2. 3-D root systems known as Platonic roots systems (A₃, B₃, H₃) assignable to the symmetries of tetrahedron, octahedron (or cube), and icosahedron (or dodecahedron) are constructed. The root systems consist of 3 suitably chosen unit vectors with square equal to 1 (square of reflection equals to one) and the Clifford algebra elements generated by them by standard Clifford algebra product. The resulting set has a structure of discrete group and is generated by reflections in hyper-planes defined by the roots just as Weyl group does. This group acts also on spinors and one obtains a double covering SU(2) of rotation group SO(3) and its discrete subgroups doubling the number of elements. Platonic symmetries correspond to the Coxeter groups for a "Platonic root system" generated by 3 unit vectors defining the basis of 3-D Clifford algebra. H₃ is not associated with any Lie algebra but A₃ and B₃ are.
   

   Pinors (spinors) correspond to products of arbitrary/even number of Clifford algebra elements. They mean something else than usually a bein identified as elements of the Clifford algebra acting and being acted on from left or right by multiplication so that they always behave like spin 1/2 objects since only the left(right)-most spin is counted. The automorphisms involve both right and left multiplication reducing to SO(3) action and see the entire spin of the Clifford algebra element.
   
   

3. The 3-D root systems (A₃, B₃, H₃) are shown to allow an extension to 4-D root systems known as (D₄, F₄, H₄) in terms of 3-D spinors. D₄ and F₄ are root systems of Lie algebras (see this). F₄ corresponds to non-simply-laced Lie group related to octonions. H₄ is not a root system of any Lie algebra.
   

   
   

4. The observation that the dimension of Clifford algebra of 3-D space is 2³=8 and thus allows imbedding of at most 8-D root system must have inspired the idea that it might be possible to construct the root system of E₈ in 8-D Clifford algebra from 240 pinors of the double covering the 120 icosahedral reflections. Platonic solids would be behind all exceptional symmetry groups since E₆ and E₇ are subgroups of E₈ and the construction should give their root systems also as low-dimensional root systems.
   
   

Mc Kay correspondence

The article explains also McKay correspondence stating that the finite subgroups of rotation group SU(2) correspond to simply laced affine algebras assignable with ADE Lie groups.

1. One considers the irreducible representations of a finite subgroup of the rotation group. Let the number of non-trivial representations be m so that by counting also the trivial representation one has m+1 irreps altogether. In the Dynkin diagram of affine algebra of group with m-D Cartan algebra the trivial representation corresponds to the added node. One decomposes the tensor product of given irrep with the spin 2 representation into direct sum of irreps and constructs a diagram in which the node associated with the irrep is connected to those nodes for which corresponding representation appears in the direct sum. One can say that going between the connected nodes corresponds to forming a tensor product with the fundamental representation. It would be interesting to know what happens if one constructs analogous diagrams by considering finite subgroups of arbitrary Lie group and forming tensor products with the fundamental representation.
   
   
2. The surprising outcome is that the resulting diagram corresponds to a Dynkin diagram of affine (Kac-Moody) algebra of ADE group with Cartan algebra, whose dimension is m. Cartan algebra elements correspond to tensor powers of fundamental representation: can one build any physical picture from this? For m= 6,7,8 one obtains E₆, E₇, E₈. The result of the article implies that these 3 Lie-groups correspond to basis of 3 3-D unit identified as units of Clifford algebra: could this identification have some concrete meaning as preferred non-orthogonal 3-basis?
   
   
3. McKay correspondence emerges also for inclusions of hyper-finite factors of type II₁. The integer m characterizing the index of inclusion corresponds to the dimensions of Cartan algebra for ADE type Lie group. The inclusions of hyperfinite factors (HFFs) are characterized by integer m≥3 giving the dimension of Cartan algebra of ADE Lie groups (there are also C, F and G type Lie groups). m= 6,7,8 corresponds to exceptional groups E₆, E₇, E₈ on one hand and to the discrete symmetry groups of tetrahedron, octahedron, icosahedron on the other hand acting as symmetries of corresponding 3-D non-crystallographic systems and not allowing interpretation as Weyl group of Lie group.
   
   

Connection with the model of harmony

These findings become really exciting from TGD point of view when one recalls that the model for bioharmony ( for 12-note harmonies central in classical music in general relies on icosahedral geometry. Bioharmonies would add something to the information content of the genetic code: DNA codons consisting of 3 letters A,T,C,G would correspond to 3-chords defining given harmony realized as dark photon 3-chords and maybe also in terms of ordinary audible 3-chords. This kind of harmonies would be roughly triplets of 3 basic harmonies and there would be 256 of them (the number depends on counting criteria). The harmonies could serve as correlates for moods and emotional states in very general sense: even biomolecules could have "moods". This new information should be seen in biology. For instance, different alleles of same gene are known to have different phenotypes: could they correspond to different harmonies? In epigenetics the harmonies could serve as a central notion and allow to realize the conjectured epigenetic code and histone code. Magnetic body and dark matter at them would be of course the essential additional element.

The inspiring observations are that icosahedron has 12 vertices - the number of notes in 12-note harmony and 20 faces- the number of amino-acids and that DNA codons consist of three letters - the notes of 3-chord.

1. Given harmony would be defined by a particular representation of Pythagorean 12-note scale represented as self-non-intersecting path (Hamiltonian cycle) connecting the neighboring vertices of icosahedron and going through all 12 vertices. One assumes that neighboring vertices differ by one quint (frequency scaling by factor 3/2): quint scale indeed gives full octave when one projects to the basic octave. One obtains several realizations (in the sense of not being related by isometry of icosahedron) of 12-note scale. These realizations are characterized by symmetry groups mapping the chords of harmony to chords of the same harmony. These symmetry groups are subgroups of the icosahedral group: Z₆, Z₄, and two variants of Z₂ (generated by rotation of π and by reflection) appear. Each Hamiltonian cycle defines a particular notion of harmony with allowed 3-chords identified by the 20 triangles of icosahedron.
   

   
   

2. Pythagoras is trying to whisper me an unpleasant message: the quint cycle does not quite close! This is true. Musicologists have been suffering for two millenia of this problem. One must introduce 13th note differing only slightly from some note in the quint cycle. At geometrical level one must introduce tetrahedron besides icosahedron - only four notes and four chords and gluing along one side to icosahedron gives only one note more. One can keep tetrahedron also as disjoint from icosahedron as it turns out: this would give 4-note harmony with 4 chords something much simpler that 12- note harmony.
   

   
   

3. The really astonishing discovery was that one can understand genetic code in this framework. First one takes three different types of 20-chord harmonies with group Z₆, Z₄, and Z₂ defined by Hamiltonian cycles: this can be done in many different maners (there are 256 of them). One has 20+20+20 chords and one finds that they correspond nicely to 20+20+20=60 DNA codons: DNA codons coding for a given amino-acid correspond to the orbit of the triangle assigned with the amino-acid under the symmetry group of harmony in question.
   

   The problem is that there are 64 codons, not 60. The introduction of tetrahedron brings however 4 additional codons and gives 64 codons altogether. One can map the resulting 64 chord harmony to icosahedron with 20 triangles (aminoacids) and the degeneracies (number of DNA codons coding for given amino-acid in vertebrate code) come out correctly! Even the two additional troublesome amino-acids Pyl and Sec appearing in Nature and the presence of two variants of genetic code (relating to two kinds of Z₂ subgroups) can be understood.
   
   

What could the interpretation of the icosahedral symmetry?

An open problem is the proper interpretation of the icosahedral symmetry.

1. A reasonable looking guess would be that it quite concretely corresponds to a symmetry of some biomolecule: both icosahedral or dodecahedral geometry give rise to icosahedral symmetry. There are a lot of biomolecules with icosahedral symmetry, such as clathrate molecules at the axonal ends and viruses. Note that dodecahedral scale has 20 notes - this might make sense for Eastern harmonies - and 12 chords and there is only single dodecahedral Hamiltonian path found already by Hamilton and thus only single harmony. Duality between East and West might exist if there is mapping of icosahedral notes and to dodecahedral 5-chords and dodecahedral notes to icosahedral 3-chords and different notions of harmony are mapped to different notions of melody - whatever the latter might mean!).
   
   
2. A more abstract approach tries to combine the above described pieces of wisdom together. The dynamical gauge group E₈ (or Kac-Moody group) emerging for m=8 inclusion of HFFs is closely related to the inclusions for the fractal hierarchy of isomorphic sub-algebras of super-symplectic subalgebra. h_eff/h=n could label the sub-algebras: the conformal weights of sub-algebra are be n-multiples of those of the entire algebra.
   

   The integers n_i resp. n_f for included resp. including super conformal sub-algebra would be naturally related by n_f= m× n_i. m=8 would correspond to icosahedral inclusion and E₈ would be the dynamical gauge group characterizing dark gauge degrees of freedom. The inclusion hierarchy would allow to realize all ADE groups as dynamical gauge groups or more plausibly, as Kac-Moody type symmetry groups associated with dark matter and characterizing the degrees of freedom allowed by finite measurement resolution.
   

   
   

3. E₈ as dynamical gauge group or Kac-Moody group would result from the super-symplectic group by dividing it with its subgroup representing degrees of freedom below measurement resolution. E₈ could be the symmetry group of dark living matter. Bioharmonies as products of three fundamental harmonies could relate directly to the hierarchies of Planck constants and various generalized super-conformal symmetries of TGD! This convergence of totally different theory threads would be really nice!
   
   

Experimental indications for dynamical E₈ symmetry

Lubos (thanks to Ulla for the link to the posting of Lubos) has written posting about experimental finding of E₈ symmetry emerging near the quantum critical point of Ising chain at quantum criticality at zero temperature. Here is the abstract :

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E₈ Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi–one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

Phase transition leads from ferromagnetic to paramagnetic phase and spin excitations as pairs of kinks are replaced with spin flips (shortest possible pair of kinks and loss of the ferromagnetic order). In attempts to interpret the situation in TGD context, one must however remember that dynamical E₈ is also predicted by standard physics so that one must be cautious in order to not draw too optimistic conclusions.

In TGD framework h_eff/h> 1 phases or phase transitions between them are associated with quantum criticality and it is encouraging that the system discussed is quantum critical and 1-dimensional.

1. The large value of h_eff would be associated with dark magnetic body assignable to the magnetic fields accompanying the E₈ "mesons". Zero temperature is not a prerequisite of quantum criticality in TGD framework.
   
   
2. One should clarify what quantum criticality exactly means in TGD framework. In positive energy ontology the notion of state becomes fuzzy at criticality. For instance, it is difficult to assign the above described "mesons" with either ferromagnetic or paramagnetic phase since they are most naturally associated with the phase change. Hence Zero Energy Ontology (ZEO) might show its power in the description of (quantum) critical phase transitions.
   

   Quantum criticality could correspond to zero energy states for which the value of h_eff differs at the opposite boundaries of causal diamond (CD). Space-time surface between boundaries of CD would describe the transition classically. If so, then E₈ "mesons" would be genuinely 4-D objects - "transitons" - allowing proper description only in ZEO. This could apply quite generally to the excitations associated with quantum criticality. Living matter is key example of quantum criticality and here "transitons" could be seen as building bricks of behavioral patterns. Maybe it makes sense to speak even about Bose-Einstein condensates of "transitons".
   

   The finding suggests that quantum criticality is associated with the transition increasing n_eff by factor m=8 or its reversal - maybe the standard value n_eff(i) =1. n_eff(f) =8 could correspond to the ferromagnetic phase having long range correlations. Could one could say that at the side of criticality (say the "lower" end of CD) the n_eff(f)=8 excitations are pure gauge excitations and thus "below measurement resolution" but become real at the other side of criticality (the "upper" end of CD)?
   
   

3. The 8 "mesons" associated with spin excitations naturally correspond to the generators of the Cartan algebra of E₈. If the "mesons" belong to the fundamental (= adjoint) representation of E₈, one would expect 120+120 additional particles with non-vanishing E₈ charges. Why only Cartan algebra? Is the reasons that Cartan algebra is in preferred role in the representations of Kac-Moody algebras in that charged Kac-Moody generators can be constructed from Cartan algebra generators by standard construction used also in string models. Could this explain why one expects only 8 "mesons". Are charged "mesons" labelled by the elements of double covering of icosahedral group more difficult to excite?
   
   

For the pdf version of the article see E₈ symmetry, harmony, and genetic code.

For a summary of earlier postings see Links to the latest progress in TGD.

Should we start to bury free will?

Bee wrote in here blog about free will with the title "Free will is dead-lets bury it". I see free will as quintessence of life and very much alive: I would feel like a murderer while trying to bury. I had to ask several times whether the beginning of the article was meant to be irony since later Bee gave link to her article The Free Will Function in which she proposed a model of free will but without any reference to metaphysics, which she obviously regarded as something non-scientific. Bee should decide whether free will exists or not;-). In any case, the somewhat arrogant tone of the article got me alittle bit irritated since I worked for last 25 years to develop quantum theory of consciousness and this theory is actually extension of quantum measurement theory proposing to solve its problems.

Since I have written so much about TGD inspired theory of consciousness and free will (not competely free of course) and I have so many other things to discuss, my decision was "No comments". I was indeed happy that Lubos saw the trouble of writing a nice and reasonably polite blog article about the issue of free will from the point of view of quantum measurement theory. Lubos wrote more recently a not so polite further article about the same topic suggesting also free will at elementary particlle level. I find the politicial attitudes of Lubos weird and also his superstring fanatism looks strange to me but I had to agree with most what he wrote about free will.

The reason why I am not at all eager to start burying free will is following. Theoretical physics is basically as an attempt to understand our conscious experiences, in particular the regularities of conscious experience expressed in terms of laws of physics. Unfortunately, theoretical physicists have been so busy with their calculations that they have forgotten what theoretical physics basically is about: too many of them have degenerated to blind appliers of algorithms defining their specialization. They have forgotten that they experience free will directly. Anyone trying to pretend that she has no free will and that her experiencs are just epiphenomena without any causal power, demonstrates in the first traffic lights that she is faking. We are continually making mental simulations of "What if...", which probably involve free will in virtual world - kind of scaled down world representing external world. Without these simulations we would not survive. The belief in free will is so deeply rooted in language that it is practically impossible to speak or write without using concepts with relate to conscious experience and free will.

Lubos discusses several issues in his postings.

1. The outcome of quantum measurement is non-deterministic and random as one looks the outcomes of quantum measurements for an ensemble of similar systems. This neither implies free will at the level of measured systems nor excludes it: we do not know whether individual system experiences free will or not in state function (assuming conscious experiences are completely private: an assumption that TGD forces to challenge - sharing of mental images is predicted to be possible).
   
   
2. Free will theorem is what forces free will in quantum measurement theory: the conscious entity performing quantum measurents must have free will to choose the observables measured. Without this assumption one cannot speak about quantum measurement theory. This does not mean that the decision to make certain quantum measurement could be state function reduction at higher abstraction level but it could be. The question of course is "What these abstraction levels could be physically and mathematically?". Bee does not believe in free will and has proposed something that she calls superdeterminism presumably trying to make state function reductions in some sense deterministic: I could not make any sense of this idea.
   
   
3. In order to speak about free will at more detailed level one must have some idea what experiencer - "me" - is. This leads to further questions. For instance, there seems to be intentional, goal directed free will: does it reduce it to free will as a passive selection betwen given options as would occur if free will corresponds to state function reduction. A flood of questions emerges once the taboo is broken and the consclusion is that one should construct nothing less than a theory of consciousness to answer them.
   
   

There were many points, which Lubos did not discuss but which from TGD point of view are central.

1. Free will theorem leaves many things open. State function reduction is in conflict with the determinism of unitary time evolution. Unless one is ready to give up completely the notion of reality and do without ontology one must be ready to modify the existing beliefs about time: more precisely, about the relationship between geometric time appearing in field equations and subjective time which could more or less correspond to a sequence of state function reductions. Usually these times are identified.
   
   Copenhagenist option is to give up ontology and leave only epistemology would mean that we can have only knowledge represented by wave function. Knowledge is however about something and if we give up ontologizing altogether there is no objective reality! The neglect of this problem is to my opinion the greatest blunder of last century in theoretical physics. Taking it seriously could have led to revolution for long time ago.
   
   
2. To avoid the logical contradiction without becoming Copenhagenist, one must accept two causalities: causality of free will and of field equations. Since causality involves time there must be two different notions of time: subjective time associated with the sequence o state function reductions and geometric time associated with field equations. Quantum jumps should replace the entire determistic time evolution with a new one: not just break the deterministic evolution in some time interval. Geomeric causality would be respected.
   

   But how subjective and geometric time relate? They are not identical: subjective time is irreversible and has no future whereas geometric time is reversible and has both future and past. They are however not independent: subjective time can be measured by using clocks telling about the flow of geometric time. Why the flow of subjective time seems to correspond to movement of geometric time= constant surface towards geometric future at least approximately (memories might correspond to multitime experiences with inputs from geometric recent and past)?
   
   

3. Does state function reduction correspond to experience of free will at the level of measurement system? How this system could experience continuous flow of time if each state function reduction implies violent change. Could it be that Zeno effect or something more general makes possible experienced flow of subjective time. In standard quantum measurement theory repeated measurements to not change the state: could they give in a more general theory rise to the experience about flow of time. What the measurement of new observales causing dramatic state function reduction to a new eigenstate basis does mean: could the conscious existence of system end? Does the repetition of new kind of measurement give rise to re-incarnation of consciousness entity in some sense?
   
   
4. The intuitive view is that self -"me" - corresponds to something separate from the environment. Could self correspond to a system having no entanglement with the external world? In standard quantum theory this cannot be true. Interactions generate entanglement continually. One the other hand, self as an entity experiencing flow of time receives continually sensory input and already this seems to imply that it cannot remain unentangled. It seems that something is badly wrong in the standard ontology. Is quantum system something more than we have thought it to be? If it represents conscious entity, it should have two components of experience: the experience about unchanging self defining personal identity and the experiences induced by the sensory input.
   
   
5. The prevailing belief is that quantum effects are important only in short scales and in macroscopic scales quantum effects give only rise to statistical behaviour describable by kinetic equations. If one wants to understand
   human consciousness in terms of quantum theory, this seems to mean that macroscopic quantum coherence is possible. But this does not seem to be the case according to the standard quantum theory. Planck constant is too small. To obtain macroscopic quantum coherence much large Planck constant would be needed. Could it be that Planck constant has a spectrum of values?
   

   Usually new idea solves many problems and the problem of dark matter is certainly one of the biggest problems of modern physics. Could dark matter correspond to matter with non-standard value(s) of Planck constant? TGD based answer to this leading question is "Yes!". The levels in the fractal hierarchies of sub-algebras super-conformal algebras associated with quantum TGD are labelled by Planck constant and the identification is as dark matter hierarchy playing crucial role in living systems.
   
   

6. In principle quantum measurement can be carried out for any system. Does this mean that consciousness and free will are universal phenomena appearing in all scales? Physical systems form a hierarchy: do also conscious entities define hierarchy so that the notion of collective consciousness and consciousness even at elementary particle length scales would make sense.
   
   
7. Living matter is different. Is it different because it is more intelligent and can affect the environment and receive information from it? What is behind intelligence? Conscious information, one might call it negentropy, certainly relates to intelligence and cognition and the question is what negentropy is physically and mathematically. Here standard physics cannot help: the notion of Shannon entropy is all that it can give. How the mathematical formalism of standard physics could be generalized so that it could talk about negentropy?
   
   
8. A theory of consciousness is needed. This theory should be a generalization of quantum measurement theory. Indeed, the basic problem of quantum measurement theory is that observer remains outsider. Observations induce state function reductions but observer itself still remains a mystery. Observer - self - should emerge from the generalization of the quantum measurement theory. The first question concerns the variational principle for the dynamics of consciousness. Since information is so essential for consciousness, the optimist wanting to live in the best possible world someday might postulate that the variational principle must guarantee that the information gain of conscious experience is maximal in each state function reduction: every reduction creates a slightly better world. This boils down to Negentropy Maximization Principle. NMP would be analogous to second law but would state formally just the opposite. How do thermodynamical entropy and negentropy relate and can they be mutually consistent?
   
   

There are many challenges and TGD suggest how to meet them.

1. One must generalize ontology in order to solve the contradiction between deterministic time evolution and evolution by state function reductions. One must understand the notion of subjective time and its relationship to the geometric time. The new ontology must allow to understand selves as something unchanged in some aspects and continually changing in some other aspects. Self as Zeno effect must allow the change due to the sensory input giving rise to the flow of subjective time.
   

   In TGD framework the answer is Zero Energy Ontology (ZEO). The concept of quantum state is generalized. States are now analogs for physical events characterized by initial and final quantum state that is pairs of positive and negative energy states. The conserved quantum numbers of the members are opposite so that zero energy states can be created from vacuum. This is a radical generalization of the physicalist world of view but entirely consistent with conservation laws: there is no need to give laws of physics in order to have free will. Positive and negative energy parts of the zero energy states can be assigned to opposite light-like boundaries of causal diamonds (CDs), which are intersections of future and past directed light-cones multipled by CP₂. CDs form a fractal scale hierarchy. They can be seen as imbedding space correlates for the 4-D perceptive fields of selves.
   
   

2. One must generalize standard quantum measurement theory to a theory of consciousnes. Negentropy Maximization Principle or something akin to it should be consistent with the standard rules of quantum measurement theory and possibly generalize them. In particular, NMP should tell which observables are measured in given entangled situation. The density matrix defined by the entanglement is the unique candidate for the universal observable. All systems could be said to give rise to quantum measurements. NMP must decide how long the self "lives": self lives as long as repeated state function reductions at the same boundary give the maximal negentropy gain.
   

   State function reductions occur at either boundary of CD as long as they produce maximal negentropy gain. If the reduction at opposite boundary produces larger negentropy gain, it occurs. Self dies and re-incarnates as time reversed self. During repeated state function reductions at same boundary the part of state at that boundary and boundary itself remains unafffected (this corresponds to unchanging part of self) whereas the state at opposite boundary changes and the bounary also shifts outwards. The increase of the distance between the tips of CD corresponds to the flow of geometric time and gives precise meaning for the ageing of self.
   

   The totally unexpected prediction is that life is not just a brief spark in cosmic darkness. This particular life is only one in a sequence of lives: the next life will be lived at the opposite boundary of personal CD to opposite direction of geometric time. The negentropy gained during his life will be usable as possibly unconscious knowledge during the next life. What our next life will be depends how much we gather negentropic resources for the next life. We can also make moral choices since NMP in its weak form leaves us freedom to make also bad choices or especially negentropic choices. Thus we can make also choices, which do not yield optimal negentropy gain. By allowing sin NMP also makes possible really big negentropy gains: NMP is like venture capitalist in this sense. In statistical sense there is however an evolution as increase of the negentropic sources of the Universe. Crime is part of being alive: living creatures are fighting desperately for NE and a clever but inmoral manner to gain it is to eat other living beings.
   
   

3. One must have a mathematical definition of negentropy. When negentropic entanglement (NE) is possible and what is the measure for the negentropy? Shannon entropy is the natural starting point and p-adic generalization of Shannon entropy might fit the bill: it is well defined for algebraic entanglement probabilities belonging to the algebraic extension of rationals defining also the extensions of varius various p-adic number fields). This requires a generalization of real physics from physics of matter to that of matter and cognition and this demands new mathematics.
   

   Cognition could correspond to entire hierarchy of p-adic physics assignable to various p-adic number fields and their extensions. Combining all these physics together one obtains something that one might call adelic physics and number theoretic constraints give powerful conditions on physics in various number fields: p-adic physics - cognition- should provide representations of real physics - material world. What I call algebraic universality and strong form of holography could realize this principle.
   

   The possibility of NE implies that the reduction does not always lead to an unentangled state but can generate NE. Living systems would be systems generating NE and biological evolution could be seen as a gradual generation of negentropic resources - I have called them Akashic Records.
   

   What is important that entanglement negentropy and thermodynamical entropy are not negatives of each other. Hence NMP is not in conflict with the second law but predicts it for the ordinary matter as a consequence of non-determinism of state function reduction. It is however true that large entropic recources realized as a large number of states with the same energy makes possible both large thermodynamical entropy and NE with large negentropy.
   
   

4. What makes possible macroscopic quantum coherence? An answer to this question has been already proposed: hierarchy of dark matters realized as large h_eff phases. These phases are associated with quantum criticality for which generalized conformal symmetries provide mathematical realization. Large value of h_eff makes possible long range correlations and also space-time correlates for the non-determinism of the critical systems. Living matter represents key example of quantum critical system involving dark matter in an essential manner.
   
   

To summarize, the inclusion of free will to physics requires extension of quantum measurement theory to a theory of consciousness. ZEO provides a new ontology in which the sequence of quantum jumps can be regarded as a sequence of recreations of the universe as 4-D sense, as superpositions of time evolutions. ZEO provides also the generalization of state function reduction concept: life is generalized Zeno effect and the first state function reduction to the opposite boundary of CD means the death of self and re-incarnation at the opposite boundary of CD. NMP is the variational principle of consciousness and the notion of NE is possible if one extends quantum physics to adelic physics with cognition described in terms of p-adic physics. Evolution emerges as a continual re-creation of the quantum Universe in 4-D sense increasing negentropic recources of the Universe. One can understand Darwinian fight for survival as fight for negentropic resources forced by the demands of NMP: produce (or steal!) negentropy of perish.

For the pdf version of the article see Should we start burying free will.

For a summary of earlier postings see Links to the latest progress in TGD.