Could one apply the thermodynamical approach of England in TGD framework?

It turns out possible to gain amazing additional insights about TGD inspired view of life and consciousness by generalizing England's approach discussed in previous posting. Several puzzling co-incidences find an explanation in the thermodynamical framework and the vision about solar system as a living quantum coherent entity gains additional support.

1. The situation considered in England's approach is a system - say biomolecule - in heat bath so that energy is not conserved due the transfer of energy between reactants and heat bath.
   
   
2. The basic equation is equilibrium condition for the reaction i→ f and its time reversal f^*→ i^*. The initial and final state can be almost anything allowing thermodynamical treatment: states of biomolecule or even gene and its mutation. The ratio of the rates for the reaction and its time reversal is given by the ratio of the Boltzmann weights in thermal equilibrium:
   

   R(i→ f)/R(f^*→ i^*)= R , R= e^-(E_i-E_f)/T .
   

   E_i and E_f denote the energies of initial and final state. This formula is claimed to hold true even in non-equilibrium thermodynamics. It is important that the ratio of the rates does not depend at all on various coupling constant parameters. The equilibrium condition must be modified if initial and final states are fermions but it is assumed that states can be described as bosons. Note that in heat bath even fermion number need not be conserved.
   
   

3. If the energy eigenstates are degenerate, the ratio R of Boltzman factors must be modified to include the ratio of state degeneracies
   

   R→ (D(E_i)/D(E_f) × e^-(E_i-E_f)/T .
   

   This generalization is essential in the sequel.
   

   One can imagine two possible reasons for the presence of exponentially large factors compensating Boltzmann weights D(E_i). The first reason is that for h_eff=n× h the presence of n-fold degeneracy due to the n-fold covering of space-time surface reducing to 1-fold covering at its ends at the ends of CD is essential. Second possible reason is that the basic object are magnetic flux tubes modellable as strings with exponentially increasing density of states. These mechanisms could quite well be one and same.
   
   

Consider now the basic idea inspired by this formula in TGD framework.

1. Since magnetic flux tubes are key entities in TGD inspired quantum biology, stringy dynamics suggests itself strongly. The situation thus differs dramatically from the standard biochemical situation because of the presence of dark matter at magnetic flux tubes to which one can assign fermion carrying strings connecting partonic 2-surfaces defining correlates for particles in very general sense.
   
   
2. The key aspect of stringy dynamics is Hagedorn temperature. Slightly below Hagedorn temperature the density of states factor, which increases exponentially, compensates for the Boltzmann factor. Hagedorn temperature is given by
   

   T_Hag = (6^1/2/2π) × (1/α')^1/2 ,
   

   where α' is string tension. In superstring models the value of string tension is huge but in TGD framework the situation is different. As a matter fact, the temperature can be rather small and even in the range of physiological temperatures.
   
   

3. What makes T_Hag so special is that in the equilibrium condition reaction and its reversal can have nearly the same rates. This could have profound consequences for life and even more - make it possible.
   

   In ZEO based quantum measurement theory and theory of consciousness time reversal indeed plays key role: self dies in state function reduction to the opposite boundary of CD and experiences re-incarnation as a time-reversed self. This process is essential element of memory, intentional action, and also remote metabolism, which all rely on negative energy signals travelling to geometric past assignable to time reversed sub-selves (mental images). The above formula suggests that intelligent life emerges near T_Hag, where the time reversed selves are generated with high rate so that system remembers and pre-cognizes geometric future as it sleeps so that memory planned action are possible.
   
   

4. String tension cannot be determined by Planck length as in string models if it is to be important in biology. This is indeed the case in TGD based quantum gravity. The gravitational interaction between partonic 2-surfaces is mediated by fermionic strings connecting them. If string tension were determined by Planck length, only gravitational bound states of size of order Planck length would be possible. The solution of the problem is that the string tension for gravitational flux tubes behaves like 1/h_eff².
   

   In TGD framework string tension can be identified as an effective parameter in the expression of Kähler action as stringy action for preferred extremal strongly suggested by strong form of holography (SH) allowing the description of the situation in terms of fermionic strings and partonic 2-surfaces or in terms of interiors of space-time surfaces and Kähler action. 1/h_eff² dependence can be derived from strong form of holography assuming electric-magnetic duality for Kähler form, and using the fact that the monopoles associated with the ends have same magnetic and electric charges.
   
   

5. The discussion of the analog of Hawking radiation in TGD framework led to an amazing prediction: the TGD counterpart of Hawking
   temperature turns out to be in the case of proton very near to the physiological temperature if the big mass is solar mass (see this). This suggests that the entire solar system should be regarded as quantum coherent living system. This is also suggested by the general vision about EEG. Could Hawking temperature be near to the Hagedorn temperature but below it?
   
   

One can make this vision more detailed.

1. In ZEO the notion of heat bath requires that one considers reactants as subsystems. The basic mathematical entity is the density matrix obtained by tracing over entanglement with environment. The assumption that dark matter is in thermal equilibrium with ordinary matter can be made but is not absolutely crucial. The reactions transforming visible photons to dark photons should take care of the equilibrium. One could even assume that the description applies even in case of the negentropic entanglement since thermodynamical entropy is different from entanglement entropy negative for negentropic entanglement.
   
   
2. In TGD inspired quantum biology one identifies the gravitational Planck constant introduced by Nottale with h_eff=n× h. The idea is simple: as the strength of gravitational interaction becomes so strong that perturbation series fails to converge, a phase transition increasing the Planck constant takes place. h_gr=GMm/v₀= h_eff=n× h implies that v₀/c<1 becomes the parameter defining the perturbative expansion. h_gr is assigned with the flux tubes mediating gravitational interaction and one can say that gravitons propagate along them.
   

   Note that this assumption makes sense for any interaction - say in the case of Coulomb interaction in heavy atoms: this assumption is indeed made in the model of leptohadrons (see this) predicting particles colored excitations of leptons lighter the weak bosons: this leads to a contradiction with the decay widths of weak bosons unless the colored leptons are dark. They would be generated in the heavy ion collisions when the situation is critical for overcoming the Coulomb wall.
   

   The cyclotron energy spectrum of dark particles at magnetic flux tubes is proportional to h_gr/m does not depend on particle mass being thus universal. In living matter cyclotron energies are assumed to be in the energy range of bio-photons and thus includes visible and UV energies and this gives a constraint on h_gr if one makes reasonable assumption about strengths of the magnetic fields at the flux tubes (see this). Bio-photons are assumed to be produced in the transformation of dark photons to ordinary photons. Also (gravitational) Compton length is independent on particle mass being equal to L_gr=GM/v₀: this is crucial for macrosopic quantum coherence at gravitational flux tubes.
   
   

3. The basic idea is that Hawking radiation in TGD sense is associated with all magnetic flux tubes mediating gravitational
   interaction between large mass M, say Sun, and small mass m of say elementary particle. How large m can be, must be left open.
   This leads to a generalization of Hawking temperature (see this) assumed to make sense for all astrophysical objects at the flux tubes connecting them to external masses:
   

   T_GR=hbar (GM/R_S² 2π) = hbar/(8 π GM).
   

   For Sun with Schwartschild radius r_S=2GM=3 km one has T_GR= 3.2× 10^-11 eV.
   

   Planck constant is replaced with h_gr=GMm/v₀= h_eff=n× h in the defining formula for Hawking temperature. Since Hawking temperature is proportional to the surface gravity of blackhole, one must replace surface gravity with that at the surface of the astrophysical object with mass M so that radius R_S=2GM of the blackhole is replaced with the actual radius R of the astrophysical object in question. This gives
   

   T_Haw= (m/8 π v₀) ×(R_S/R)² .
   

   The amazing outcome is that for proton the estimate for the resulting temperature for M the solar mass, is 300 K (27 C), somewhat below the room temperature crucial for life!
   

   Could Hagedorn temperature correspond to the highest temperature in which life is possible - something like 313 K (40 C)? Could it be that the critical range of temperatures for life is defined by the interval [T_Haw,T_Hag]? This would require that T_Haw is somewhat smaller T_Hag. Note that Hawking temperature contains the velocity parameter v₀ as a control parameter so that Hawking temperature could be controllable. Of course, also T_Haw=T_Hag can be considered. In this case the temperature of environment would be different from that of dark matter at flux tubes.
   
   

4. The condition T_Haw≤ T_Hag allows to pose an upper bound on the value of the effective string tension
   

   (α')^-1/2≥ (m/4×6^1/2v₀) × (R_S/R) .
   

For details see the article Jeremy England's vision about life and evolution: comparison with TGD approach.

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

Jeremy England's vision about life

We had an intensive discussion with my son-in-law Mikko about the work of Jeremy England. The article of the link is probably the most aggressive hyping I have ever seen but this should not lead to think that a mere hype is in question. There is also another, not so heavily hyped popular article. The material at england lab homepage gives a good view about the work of England for those who cannot tolerate hyping.

England's work is indeed very interesting also from TGD point of view although it is based on standard physics.

Basic ideas of England's theory

I try first to summarize England's vision.

1. Non-equilibrium thermodynamics (NET) is the starting point. NET has been for decades the theoretical framework underlying the attempts to understand living matter using the principles of self-organization theory. Living matter is never an isolated system: dissipation would take it to a totally dead state in this case - nothing would move. Water in the pond when there is no wind, is a good example.
   

   Self-organization requires an external energy feed - gravitational potential energy liberated in water flow in river or electric power feed to the hot plate below a teapot. This energy feed drives the system to a non-stationary state far from a thermal equilibrium state. Dissipation polishes out all details and leads to an asymptotic spatio-temporal self-organization patterns. The flow in a river and convection in the heated teapot. With high enough energy feed chaos emerges: water fall or boiling of tea pot.
   
   

2. The basic hypothesis of England is that evolution means increase in the ability to dissipate. This looks intuitively rather obvious. The evolving system tends to get to a resonance with the energy feed by oscillating with the same frequency so that energy feed becomes maximal and therefore also dissipation. The basic rule is simple: choose the easy option, ride on the wave rather than fighting against it! For instance, the emergence of photosynthesis means that the systems we call plants become very effective in absorbing the energy of sunlight. In this framework essentially all systems are alive to some degree.
   

   Dissipation means generation of entropy. Evolution of life and conscious intelligence would mean maximal effectivenes in the art of producing disorder. Now I am perhaps exaggerating. One should speak about "system's maximal ability to transfer entropy out of it": life is not possible without paper baskets. One could argue that the development of civilization durig last decades demonstrates convincingly that evolution indeed generates systems generating disorder with a maximal rate.
   

   One could argue that the definition is too negative. Living matter is conscious and there is genuine conscious information present. The fact is that evolution involves a continual increase of conscious information: the exponential explosion of science is the best proof for this. England's vision says nothing about it. Something is missing.
   

   It is however quite possible to imagine that the principle of maximal entropy generation is true and that the increase of the ability to produce entropy is implied by some deeper principle allowing to speak about living matter as something tending to increase conscious information resources. To formulate this idea one needs a theory of consciousness, thermodynamics is not enough.
   
   

3. England has a further idea. The evolution life is not climbing to Mount Everest but coming down from it. Life emerges spontaneously. This is definitely in conflict with the standard wisdom, in particular with the thermodynamical belief on thermal death of the Universe as all gradients disappear. Darwinian evolution would be a special case of a more general phenomenon, which could be called dissipation driven adaptation (DDA). I made a head-on-collision with this principle in totally different framework by starting from quantum criticality of TGD: if took time to fully realize that indeed: evolution could be seen as a sequence of phase transitions breaking in which certain infinite-dimensional symmetry was spontaneously broken to become just the same symmetry but in longer scale!
   

   Standard thermodynamics predicts the heat death of the Universe as all gradients gradually disappear. This prediction is problematic for England's argument suggesting that differentiation occurs instead of homogenization. Here the standard view about space-time might be quite too simplistic to overcome the objection. In TGD many-sheeted space-time comes in rescue.
   

   Here is an example about England's argumentation. It seems intuitively clear that replication increases entropy (it is not however clear whether just the splitting into pieces is even more effective manner to increase entropy!). This would suggest that DDA forces the emergence of replication. Very effective dissipators able to replicate, would increase the total effectiveness in dissipation and be the winners. The proposal to be tested is that bacterial mutations , which are best replicators are also best dissipators.
   
   

What is missing from England's theory?

What is missing from England's theory? The answer is same as the answer to the question what is missing from standard physics.

1. What is conscious observer - self?
   

   Observer, which remains outsider to the physical world in the recent day physics - both classical and quantum. Hence one does not have a theory of consciousness and cannot speak about conscious information. Thermodynamics gives only the notion of entropy as a measure for the ignorance.
   

   Therefore there is a long list of questions that England's theory does not address. What are the physical correlates of attention, sensory perception, cognition, emotions relating closely to information, etc.? Is there some variational principle behing concious existence, and does it imply evolution? Could second law and DDA be seen as consequences of this variational principle ?
   

   England does not say much about quantum theory since he talks only about thermodynamics but his hypothesis is consistent with quantum theory. The restriction to thermodynamics allows only statistical description and notions like
   macroscopic quantum coherence are left outside.
   
   

2. What is life?
   

   Again one has a long list of questions.
   

   What it is to be alive? What distinguishes between living and inanimate systems. What it is to die? How general phenomenon evolution is: does it apply to all matter? Also notions like self-preservation and death are present only implicitly in an example about a population of wine glasses whose members might gradually evolve to survive in an environment populated by opera sopranos.
   

   One can make also other kinds of questions. What really happens in replication? What is behind genetic code? Etc...
   

   England is a spiritual person and has made clear that the gulf between science and spirituality is something which bothers him . England even has the courage to use the word "God". Therefore it sounds somewhat paradoxical that England avoids using the concepts related to consciousness and life. This is however the only option if one does not want to lose academic respectability.
   
   

How England's theory relates to TGD?

It is interesting to see whether England's vision is consistent with TGD inspired theory of consciousness, which can be also seen as a generalization of quantum measurement theory achieved by bringing the observer part of the quantum physical world. In TGD framework several new principles are introduced and they relate to the new physics implied by the new view about space-time.

1. The new physics involves a generalization of quantum theory by introducing a hierarchy of Planck constants h_eff =n×h with various quantal length and time scales are proportional to h_eff. h_eff hierarchy predicts a hierarchy of quantum coherent systems with increasing size scale and time span of memory and planned action. h_eff defining a kind of intelligence quotient labels the levels of a hierarchy of conscious entities.
   

   h_eff hierachy labels actually a fractal hierarchy of quantum criticalities: a convenient analogy is a ball at a top of ball at the top..... The quantum phase transitions inreasing h_eff occur spontaneously: this
   is the TGD counterpart for the spontaneous evolution in England's theory. Dark matter is what makes system alive and intelligent and thermodynamical approach can describe only what we see at the level of visible matter.
   
   

2. Second key notion is zero energy ontology (ZEO). Physical states are replaced by events, one might say. Event
   is a pair of states: initial state and final state. In ZEO these states correspond to states with opposite total
   conserved quantum numbers: positive and negative energy states. This guarantees that ZEO based quantum theory is consistent with the fundamental conservation laws and laws of physics as we understand them although it allows non-determinism and free will. Positive and negative energy states are localized at opposite boundaries of a causal diamond (CD). Penrose diagram - diamond symbol - is a good visualization and enough for getting the idea.
   

   State function reduction (SFR) is what happens in quantum measurement. The first SFR leads to a state which is one in a set of states determined once measurement is characterized. One can only predict the probabilities of various outcomes. Repeated quantum measurements leave the state as such. This is Zeno effect - watched kettle does not boil.
   

   In ZEO something new emerges. The SFR can be performed at either boundary of CD. SFR can occur several times at the same boundary so that the state at it does not change. The state at the opposite boundary however changes - one can speak of the analog of unitary time evolution - and the second boundary also moves farther away. CD therefore increases and the temporal distance between its tips does so also.
   

   The interpretation is as follows. The sequence of reductions at fixed bounary corresponds to a conscious entity, self. Self experiences the sequence of state function reductions as a flow of time. Sensory experience and thoughts, emotions, etc.. induced by it come from the moving boundary of CD. The constant unchanging part of self which meditators try to experience corresponds to the static boundary - the kettle that does not boil.
   

   Self dies in the first reduction to the opposite boundary of CD. Self however re-incarnates. The boundaries of self change their roles and the geometric time identified as distance between the tips of CD increases now in opposite direction. Time-reversed self is generated.
   
   

3. Negentropy Maximization Principle (NMP) stating roughly that the information content of consciousness is maximal. Weak form of NMP states that self has free will and can choose also non-maximal negentropy gain. The basic principle of ethics would be "Increase negentropy". p-Adic mathematics is needed to construct a measure for conscious information and the notion of negentropic entanglement (NE) emerges naturally as algebraic entanglement.
   

   The negentropy to which NMP refers is not the negative of thermodynamical entropy describing lack of information of outsider about state of system. This negentropy characterizes the conscious information assignable to
   negentropic entanglement (NE) characterized by algebraic entanglement coefficients with measure identified as a number theoretic variant of Shannon entropy. Hence NMP is consistent with the second law implied by the mere
   non-determinism of SFR.
   

   NMP demands that self during sequence of reductions at the same boundary generates maximum negentropy gain at the changing CD boundary. If self fails, it dies and re-incarnates (in a reduction to the opposite CD boundary more negentropy is generated). Selves do not want to die and usually they do not believe on re-incarnation, and therefore do their best to avoid what they see as a mere death. This is the origin of self-preservation. Self must collect negentropy somehow: gathering negentropic sub-selves (mental images) is a manner to achieve this. Plants achieve this by photosynthesis, which means generation of negentropy and storage of it to various biomolecules. Animals are not so saintly and simply eat plants and even other animals. We are negentropy thieves all.
   

   Re-incarnation also means increase of h_eff and getting to higher level in hierarchy and occurs unavoidably. As in England's theory, evolution occurs spontaneously: it is not climbing to Mount Everest but just dropping down.
   
   

4. England says "Some things we consider inanimate actually may already be 'alive'." This conforms with TGD view. Even elementary particles could have self: it is however not clear whether their SFR sequences contain more that one reduction to a fixed boundary - necessary for having a sense about the flow of time. Elementary particles would even cognize: in adelic physics every system has both real and p-adic space-time surfaces as its correlates. It can even happen that system has only p-adic space-time correlates but not the real one: this kind of systems would be only imaginations of real system! This is one of the most fascinating implications of strong form of holography which follows from strong form of General Coordinate Invariance forced by the new view about space-time.
   

   Clearly the notion of evolution generalizes from biological context to entire physics in TGD. One can speak about
   p-adic evolution and evolution as increase of h_eff. The most abstract formulation is number theoretical:
   evolutioncorresponds to the increase of the complexity of extension of rationals to which the parameters characterizing space-time surfaces belong to.
   
   

5. Does DDA emerge in TGD framework? NMP demands a lot of SFRs - also at the level of visible matter. The non-determimism of SFR alone means a loss of knowledge about the state of system and an increase of thermodynamical entropy so that living systems would generate entropy very effectively also in TGD Universe at the level of visible matter. If one believes that second law and NET imply DDA as England argues, then also TGD implies it at the level of visible matter. For dark matter the situation is different, since the outcome of SFR is not not random anymore. Seen from TGD perspective England's vision misses what is essential for life - the generation of phases of matter identifiable as the mysterious dark matter.
   
   
6. England talks about God. In a theory of consciousness predicting infinite self hierarchy, it is easy to assign the attribute "divine" to the levels of consciousness above given level of hierarchy. Personally I have nothing against calling the Entire Universe "God".
   

   One could give NMP the role of God. For strong form of NMP SFR would be almost deterministic except for ordinary matter for which entanglement is not algebraic and is therefore entropic: the universe would the best possible one in dark sectors and the worst one in the visible matter sector - Heaven and Hell! Weak form of NMP makes possible even more effective generation of negentropy than its strong form but allows self to make also stupid things and even SFRs with a vanishing negentropy gain: the outcome is state with no entanglement (system is in very literal sense alone in this state). The world in dark matter sectors is not anymore the best possible one but can become better and does so in statistical sense.
   
   

7. Replication is a crucial aspect of being alive. England argues that DDA allows to understand its emergence but does not tell about its mechanism. In TGD framework replication can be understood as an analog of particle decay - say photon emission by electron. This requires however a new notion: magnetic body. In Maxwell's theory one cannot assign any field identity to a physical system but TGD view about space-time forces to assign to a given system its field/magnetic body. The replication occurs primarily at the level of magnetic body carrying dark matter as large h_eff phases. Magnetic body replicates and ordinary visible matter self-organizates around the resulting copies of it. The dynamics of dark matter would induce also DNA replication, transcription and mRNA translation, and there are some indications that it is indeed "dark DNA" (dark proton sequences having DNA, RNA, amino-acids, and tRNA as biochemical counterparts), which determines what happens in transcription.
   
   

For details see the article Jeremy England's vision about life and evolution: comparison with TGD approach.

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

Quantum criticality and protein folding

In Thinking Allowed Original there was a link to a new observation about protein folding process. During folding some proteins hold single building blocks in shapes that were thought to be impossible to find in stable form. Stable shapes contained some parts, which were trapped like mosquitos in amber.

A concrete TGD based model relies on the general ideas of TGD inspired quantum biology.

1. Biomolecules containing aromatic rings play a fundamental role. All DNA nucleotides contain them and there are 4 proteins, which also have them. trp and phe are of special importance and form a pair structurally analogous to a base pair in DNA strand. The rings are assumed to carry the analog of supra current and be in or at least be able to make transition to a state with large h_eff. The delocalization of electron pairs in aromatic ring could be a signature of h_eff/h>1.
   
   
2. trp-phe pairing would be responsible for information molecule-receptor pairing. Information molecule and receptor would be at the ends of flux tubes serving as communication lines, and the attachment of info molecule to receptor would fuse the two flux tubes to longer one. After that communication would become possible as dark photon signals and dark supra currents. Formation of info molecule-receptor complex would be like clicking icon generating a connection between computers in net. Info molecules would generate the communication channels - they would not be the signals. This is the distinction from standard neuroscience.
   
   
3. All quantum critical phenomena involve generation of large h_eff phases. Folding emerges or disappears at quantum criticality (QC) possible in certain temperature range of width about 40 K and depending on pH. The flux tubes associated with phe and trp containing aromatic rings carrying "supra current" would become dark (either h→ h_eff or h_eff> h increases) and thus much longer and reconnect temporarily and force phe and trp in a close contact after the reverse transition inducing shortening. This is a general mechanism making biomolecules able to find each other in what looks like molecular soup in the eyes of standard biochemist. The contacts between amino-acids phe and trp formed in this manner are structurally identical with the hydrogen bonding between members of DNA base pairs and they would fix the final folding pattern to high degree.
   

There was also a link to very interesting article about possible topological phenomena related to protein folding. Authors are Henrik and Jakob Bohr (akin to the Great Niels Bohr?) and Sören Brunak.

The article is very easy to read and explains the basic topological concepts like winding in a simple manner. The proposal is that the excitation of so called wringing modes of proteins are involved in the generation and disappearance of the protein folding. Excitation of wringing modes twisting the protein (think about how one wrings water from a wetted cloth) would make the protein folding state cold denatured unstable and transform in to stable folded (F) state. In the same manner their excitation would transform hot denatured (HD) stable state to folded state. Wringing modes could be excited by radiation.

In TGD framework the folding phase diagram CD-F-HD could be understood also in terms of quantum criticality (QC). Perhaps the simplest option is that the transitions CD-F and HD-F involve a generation of critical states leading to a generation of long range correlations (large h_eff) inducing the folding pattern. Absorption of photons to wringing modes would induce the criticality and the folding would proceed by the mechanism discussed above.

For background see the chapter More Precise TGD Based View about Quantum Biology and Prebiotic Evolution or article with the same title.

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

Further progress in the number theoretic anatomy of zeros of zeta

I wrote for some time ago an article about number theoretical universality (NTU) in TGD framework and ended up with the conjecture that the non-trivial zeros of zeta can be divided into classes C(p) labelled by primes p such that for zeros y in given class C(p) the phases p^iy are roots of unity. The impulse leading to the idea came from an argument of Dyson referring to the evidence that the Fourier transform for the locus of non-trivial zeros of zeta is a distribution concentrated on powers of primes.

There is a very interesting blog post by Mumford , which led to a much more precise formulation of the idea and improved view about the Fourier transform hypothesis: the Fourier transform must be defined for all zeros, not only the non-trivial ones and trivial zeros give a background term allowing to understand better the properties of the Fourier transform.

Mumford essentially begins from Riemann's "explicit formula" in von Mangoldt's form.

∑_p∑_{n≥ 1} log(p)δ_pⁿ(x)= 1- ∑_k x^s_k-1 - 1/x(x²-1) ,

where p denotes prime and s_k a non-trivial zero of zeta. The left hand side represents the distribution associated with powers of primes. The right hand side contains sum over cosines

∑_k x^s_k-1= 2∑_k cos(log(x)y_k)/x^1/2 ,

where y_k ithe imaginary part of non-trivial zero . Apart from the factor x^-1/2 this is the just Fourier transform over the distribution of zeros.

There is also a slowly varying term 1-1/x(x²-1), which has interpretation as the analog of the Fourier transform term but sum over trivial zeros of zeta at s=-2n, n>0. The entire expression is analogous to a "Fourier transform" over the distribution of all zeros.

Therefore the distribution for powers of primes is expressible as "Fourier transform" over the distribution of both trivial and non-trivial zeros rather than only non-trivial zeros as suggested by numerical data to which Dyson referred to). Trivial zeros give a slowly varying background term large for small values of argument x (poles at x=0 and x=1 - note that also p=0 and p=1 appear effectively as primes) so that the peaks of the distribution are higher for small primes.

The question was how can one obtain this kind of delta function distribution concentrated on powers of primes from a sum over terms cos(log(x)y_k) appearing in the Fourier transform of the distribution of zeros. Consider x=pⁿ. One must get a constructive interference. Stationary phase approximation is in terms of which physicist thinks. The argument was that a destructive interference occurs for given x=pⁿ for those zeros for which cosine does not correspond to a real part of root of unity as one sums over such y_k: random phase approximation gives more or less zero. To get something nontrivial y_k must be proportional to 2π× n(y_k)/log(p) in class C(p) to which y_k belongs. If the number of these y_k:s in C(p) is infinite, one obtains delta function in good approximation by destructive interference for other values of argument x.

The guess that the number of zeros in C(p) is infinite is encouraged by the behaviors of the densities of primes one hand and zeros of zeta on the other hand. The number of primes smaller than real number x goes like

π(x)=#(primes <x)∼ x/log(x)

in the sense of distribution. The number of zeros along critical line goes like

#(zeros <t) = (t/2π) × log(t/2π)

in the same sense. If the real axis and critical line have same metric measure then one can say that the number of zeros in interval T per number of primes in interval T behaves roughly like

#(zeros<T)/#(primes<T) =log(T/2π)×log(T)/2π

so that at the limit of T→ ∞ the number of zeros associated with given prime is infinite. This asumption of course makes the argument a poor man's argument only.

See the chapter Unified Number Theoretic Vision of "Physics as Generalized Number Theory" or the article Could one realize number theoretical universality for functional integral?.

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

How did life evolve during pre-Cambrian period?

The formulation of a more detailed TGD inspired vision about how life might have evolved in TGD Universe during pre-Cambrian era is a fascinating challenge. In Cambrian explosion relatively rapid expansion of Earth size by a factor of 2 assumed in TGD version of Expanding Earth model. TGD indeed predicts that cosmic expansion takes place in given scale as rapid jerks rather than continuously as in ordinary cosmology. The key ingredients besides standard facts are TGD inspired interpretation for Cambrian Explosion (CE) (see this and this), of dark matter as large h_eff phases (see this), and the notion of magnetic flux tubes. These provide TGD view about Pollack's Exclusion Zones (EZs, as key factors in the evolution of life.

I have gathered useful links from web to build a more detailed version of TGD vision and it is perhaps appropriate to give a list of some useful links - they appear also as references. These links might help reader considerably in getting touch about the problems involved and reader can easily find more.

1. Data related to Mars
   
   Two generations of windblown sediments on Mars
   Sedimentary Mars
   Liquid flows in Mars today: NASA confirms evidenc:
   
   
2. Metabolism
   
   Microbial metabolism
   Electron transport chain
   Metal-eating microbes in African lake could solve mystery of the planet's iron deposits
   
   
3. When did photosythesis emerge?
   Ancient rocks record first evidence for photosynthesis that made oxygen
   Cyanobacteria:
   
   
4. When did oxygenation really occur?
   Great Oxygenation Event
   Mass-Independent Sulfur Isotopic Compositions in Stratospheric Volcanic Eruptions
   Neoarchean carbonate-associated sulfate records positive Δ³³S anomalies
   Great Oxidation Event "a misnomer"
   
   An Oxygen-poor "Boring" Ocean Challenged Evolution of Early Life
   
   
5. The role of iron
   Evidence for a persistently iron-rich ocean changes views on Earth's early history
   
   

1. What happened before Cambrian explosion?

The story about evolution of life is constructed from empirical findings based on certain geological, chemical, and isotope signatures. The study of sediment rocks makes possible reasonably reliable age determinations but involves assumptions about the rate of sedimentation. Water, ice, acids, salt, plants, animals, and changes in temperature contribute to weathering and cause erosion involves water, ice, snow, wind, waves and gravity as agents and leads to sedimentation. Also organic material forms sediments both on land and at ocean floors.

Isotope ratios serve as signatures since they are different in inanimate and living matter because those for living matter reflect those in atmosphere and are affected by cosmic rays. The concentrations of various elements are important signatures: mention only oxygen, nitrogen, sulphur compounds such as sulphide, hydrogen sulphide. and sulphate iron, and molybden.

The story involves great uncertainties and should not be taken only as a story. In the following TGD view about how life evolved before Cambrian Explosion (CE) about .6 gy ago is summarized. The Pre-Cambrian part of TGD inspired story differs dramatically from the official narrative since only lakes would have been present whereas official story assumes oceans and continents. Earth would have very much like Mars before CE - even its radius would have been essentially same (half of the recent radius of Earth). This suggests that Mars could teach us a lot about the period before CE. The deviations seem to explain its paradoxical looking aspects of the standard story.

1. Life according to TGD evolved in underground oceans and at the surface of Earth containing lakes but no oceans. The lifeforms at the surface of Earth were prokaryotes whereas the life in underground oceans consisted of relatively complex photo-synthesizing eukaryotes.
   
   
2. The recent data from Mars gives an idea what the situation at Earth was during CE since the radius of Earth at that time was very nearly same as that of Mars now. There is evidence for sedimentation and for water near to and even at the surface provided quite recently. The life at the surface of Earth before CE consisted mainly of prokaryotes and very simple mono-cellular eukaryotes and something like this is expected at the surface of Mars now.
   
   
3. Already around 3.5 gy ago prokaryotes using sulphate as energy metabolite were present. Photo-synthesizing cyanobacteria emerged about 3.2 gy ago. They became later the plasmids of plant cells responsible for photo-synthesis. The problem of the standard story is that this did not lead to oxygenation of the hypothetic oceans and rapid evolution of eukaryotes and multi-cellulars.

   In standard vision one can explain the absence of oxygen based life in hypothetic oceans by the presence of oxygen sinks. It is known that the ancient oceans (shallow oceans, lakes, or ponds in TGD) were oxygen poor and iron rich. The data about Mars - the red planet because of
   iron rusting - makes possible to test the feasibility of this hypothesis. The oxygen produced by the cyanobacteria was used to the formation of rusted iron layers giving rise to iron ores. For 1.8 gy ago the formation of rusted iron layers ceased. A possible explanation is that all iron was used. The ores could have been also generated by bacteria using iron as metabolite and transforming it to iron oxide. There are however now iron ores after 1-8 gy: did these bacteria lose the fight for survival?
   

   In TGD Earth atmosphere remained oxygen poor since the small lakes could not produce enough oxygen to induce the oxygenation of the atmosphere. The lakes however gained gradually oxygen. First it went to the oxidation of iron.
   
   

4. A general belief has been that about 2.4 gy ago Great Oxidation Event (GOE) occurred. The basic evidence for GEO is from volcano eruptions, which seem to have produced anomalously small amount of sulphur after 2.4 gy. The reason would have been the formation of sulphate SO₄ from atmospheric oxygen and sulphur emanating from volcano.
   

   This evidence has been however challenged by measuring sulphur anomalies for recent volcanic eruptions. Their sign varies in time scale of month changing from positive to negative. It is quite possible that GOE is an illusion.
   
   

5. There is also problem related to to the "boring period" 1.8-.8 gy. It seems that the hypothetic oceans remained still oxygen poor and iron rich. It has been also suggested that the boring period continued up to CE: the first animals after CE could have oxygenated Earth's oceans. In TGD Universe GOE is indeed illusion for the simple reason that oceans did not exist! Life was boring at the surface of Earth from 3.5 gy to .6 gy.
   
   
6. Life would have evolved in underground seas containing oxygenated water, probably already 3.2 gy ago, and making possible photo-synthesis and cellular respiration. Animal cells formed by eukaryotes with nucleus carrying genome with prokaryotes, which later became mitochondria. Plant cells emerged when these eukaryotes engulfed also cyanobacteria, which made photo-synthesis possible. The highly developed eukaryotes were burst to the surface as the radius of Earth increased by a factor two in geologically short time scale. Oceans containing oxygen rich water were formed. CE can be equated with GOE in TGD picture.
   

   Plants are divided into green and red algae, a small group of fresh water monocellulars glaucophytes, and land plants. Land plants must have emerged after CE. Red algae are multi-cellulars (corals are representative example). Also green algae can be multi-cellulars and land plants are thought to have developed from them. An interesting question is whether multi-cellular plants and animals emerged already before CE as the findings would suggest.
   
   

The basic objection against this vision is that photo-synthesis is not possible underground. Did photo-synthesis occur in shallow lakes storing chemical energy transferred to the underground seas. This does not seem a plausible option but cannot be excluded. The volcanoes and hydrothermal vents bring water from underground. The water contains ground water and ordinary sea water, which ended underground in various manners, and also magmatic component. The geothermal vents and most volcanoes are however associated with the regions were tectonic plates meet and should not have existed before CE.

TGD inspired model for Pollack's exclusion zones (EZs) suggests a solution of the problem. The formation of these negatively charged regions of water is induced by solar radiation, IR radiation at energies which correspond to metabolic energy quantum, and also at energies corresponding to THz frequency. TGD based model proposes that the protons from EZ becomes large h_eff protons at magnetic flux tubes associated with EZ. These flux tubes could be quite long and extend to the underground oceans. Dark photons with energy spectrum containing that of bio-photons could travel along these flux tubes. This suggests that solar radiation transforms partially to dark photons, which travel along flux tubes to the underground sea and transform to ordinary photons caught by photo-synthesizing cells.

Interestingly, also the temperature of Earth is such that thermal radiation would be in visible region and one cannot exclude the possibility that dark photons emerge also from this source. This would make possible also cell respiration and oxygen rich water.

Skeptic is of course wondering whether the flux tubes were long enough.

1. The basic idea about dark matter residing at magnetic flux tubes emerged in TGD from Blackman's findings about quantal looking effects of ELF em fields on vertebrate brain by assigning them to cyclotron frequencies Ca⁺⁺ ions in endogenous magnetic field B_end= .2 Gauss, which is by a factor 2/5 weaker than the recent magnetic field of Earth and assigning large non-standard value of Planck constant to the flux tubes so that the energies of ELF quanta are above thermal energies.
   
   
2. The value of magnetic field at flux tubes of "personal" magnetic bodies of organisms have B_end in its value spectrum. B_end could be conserved in evolution somewhat like the salinity of ancient (underground) ocean. The flux tubes of B_end would have transformed the photons of solar radiation to dark cyclotron photons allowing them to travel to underground sea and transform back to ordinary photons to be absorbed by pre-plant cells. I have proposed that a similar mechanism is at work in biological body and could explain the reported ability of some people to survive without any obvious metabolic energy feed.
   
   

2. How the cellular life could have evolved before CE?

In the following I summarize what looks the most plausible view about evolution of life in TGD framework. I represent first basic classification to make reading easier.

2.1 Basic classification of lifeforms

Lifeforms are classified into prokarioties (no cell nucleus) and eukaryotes (cell nucleus).

1. Prokaryotes are mono-cellular and have no separate cell nucleus. They are divided into bacteria and archea. Bacteria do not have genome but only circular DNA strand and usually accompanied by an almost palindrome. Archea have also genes. Cyanobacteria are simplest photo-synthetizing cells: these prokaryotes have been engulfed by eukaryotes to form plant cells containing them as plasmids. Plant cells contain also mitochondria believed also to be ancient prokaryotes which have been "eaten" by eukaryotes. Plants cells contain both mitochondria and plastids whereas animal cells contain only mitochondria.
   
   
2. Eukaryotes have cell nucleus containing the genome. Eukaryotes divide into three kingdoms: animals, plants, and fungi. Fungi can be said to be between animals and plants: they do not perform photo-synthesis but have cell walls.
   
   

2.2 Prokaryote-eukaryote distinction

From the existing data one can conclude that during pre-Cambrian period only prokaryotes existed at the at surface of earth - presumably in small lakes in TGD Universe and ocean floors in standard Universe. The first photo-synthetizing prokaryotes - cyanobacteria - emerged about 3.2 gy ago and their predecessors where prokaryotes extracting metabolic energy from sulphate. Cyanobacteria are able to survive in practically any imaginable environment:

Cyanobacteria are arguably the most successful group of microorganisms on earth. They are the most genetically diverse; they occupy a broad range of habitats across all latitudes, widespread in freshwater, marine, and terrestrial ecosystems, and they are found in the most extreme niches such as hot springs, salt works, and hypersaline bays. Photoautotrophic, oxygen-producing cyanobacteria created the conditions in the planet's early atmosphere that directed the evolution of aerobic metabolism and eukaryotic photo-synthesis. Cyanobacteria fulfil vital ecological functions in the world's oceans, being important contributors to global carbon and nitrogen budgets.

It is therefore natural to assume that cyanobacteria migrated to underground ocean through pores and fractures at the floor of lakes. They would have fused with pre-eukaryotes having only cell nucleus but no metabolic machinery to become chloroplasts. This would have given rise to the first eukaryotes able to perform photo-synthesis. The primitive cells prokaryotes defining pre-mitochondria would have also fused with these pre-eukaryotes so that both pre-plant and pre-animal cells wold have emerged. Why there is no evidence for the existence of pre-mitochondria as independent cells at the surface of Earth? Did they emerge first underground oceans, where photo-synthesis was not possible and disappeared in the fusion with pre-eukaryotes and therefore left no trace about their existence on the surface of Earth?

Both photo-synthesis and cell respiration involve so called electron transport chain (ETC) as a basic structural element. It is associated with any membrane structure and in photo-synthesis it captures the energy of photon and in cell respiration it catches the biochemical energy which could be emitted as photon so that the fundamental mechanism is the same. This suggests that cell respiration emerged as a modification of photo-synthesis a the level of prokaryotes first. Before the emergence of mitochondria and plastids ETC associated with pre-eukaryote membrane would have served the role of mitochondria or plastid. Using business language, mitochondria and plastids meant "outsourcing" of photosynthesis and cellular respiration.

For background see the chapter More Precise TGD Based View about Quantum Biology and Prebiotic Evolution or article with the same title. See also the article About evolution before Cambrian Explosion.

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

Neil Turok about recent depressing situation in theoretical physics

Neil Turok is one of the very few theoreticians, whose existence raises hopes that we might get over the stagnation period of theoretical physics lasted for four decades now. It relies basically on sloppy thinking initiated with the advent of GUTs and amplified via the emergence of SUSY, superstring models and eventually M-theory. Loop gravity starting from naive canonical quantization attempt of general relativity is also a representative example of this sloppy thinking and naive belief that it is possible to understand Nature without considering deep metaphysical questions.

The outcome is endless variety of extremely contrived "models" and "effective theories" creating the illusion of understanding and most importantly: huge amounts of curriculum vitae is generated. Academic theoretical physics has become very much like playing the market.

The standard excuse for the failure of the theories is that there is no data, we need a bigger accelerator, gravitation is so extremely weak interaction, we cannot detect dark matter, etc... The fact is that there is more than enough refined experimental data challenging existing physics in all length scales - condensed matter, biology,..., even astrophysics in solar system.

The problems are on the theory side and due to reductionistic dogmatism and the refusal to see physics from a wider perspective including also biology and consciousness. The extremely narrow professional specialization optimal for the career building is one stumbling block. The professional arrogance of theoreticians enjoying monthly salary combined with unforeseen conformism is second problem. Typical theoretician simply refuses to touch in anything not published in so called respected journal and is even proud of this narrow mindedness and calls it professionalism!

Turok does not hesitate to articulate the truth known by many people in the field.

"Our existing theories are too contrived, arbitrary, ad hoc,” Turok complains. “I think we could be on the verge of the next big revolution in theory. It will be inspired by the data, by the failure of traditional paradigms. It will change our view of the universe.”"

I cannot but agree (and even have some rather detailed ideas about what this revolution might be;-)). But we must patiently wait until the lost generations get retired.

See the article To Explain the Universe, Physics Needs a Revolution in Scientific American.

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

Do neurons have their private genomes?

Genetics is experiencing a revolution as the information technology has made possible new research methods and old dogmas must be given up. Before continuing, thanks for Ulla for giving links (see this and this) explaining the results of the article discussed in more detail: this led to a correction of some misunderstandings. See also this for a background.

It has been discovered that brain cells have a mosaic like distribution of genomes (see this, this, and this). In standard framework this mosaic should be created by random mutations.

The mechanism of mutation is reported to involve transcription rather than DNA replication. The mutation would take place for DNA when its is copied to RNA after opening of the DNA double strand. The mutations would have occurred during the period when neurons replicate and the mutation history can be read by studying the distributions of changes in the genome.

This brings in mind the finding that "knockout", that is removing a part of gene does not affect transcription (see the earlier blog posting). This suggests that the dark DNA is not changed in these modifications and mRNA is determined by the dark DNA, which would serve as a template for transcription rather than ordinary DNA. If this were the case also for neurons, the mutations of neuronal genes should not affect the gene transcription at all, and there would be no negative (or positive) effects on brain function. This seems too conservative. The mutations should have some rmore active role.

One can consider also different interpretation. The mutations of DNA could be induced by the dark DNA. As dark DNA changes, ordinary DNA associated with it is forced to change too - sooner or later. Especially so when the genome is in a state in which mutations can take place easily. Neurons during to replication stage could have such quantum critical genomes.

Evolution would not be mere selection by a survival of random mutations by external environment in the time scale much longer than lifetime of individual - but a controlled process, which can occur in time scale shorter than lifetime and differently inside parts of say brain. This is what the idea TGD inspired biology suggests. The modified DNA could be dark DNA and and serve as template for transcription and also induce transformation of ordinary DNA associated with it.

Whether this change can be transferred to the germ cells to be transferred to the offspring remains of course an open question. One can imagine that dark DNA strands (magnetic flux tubes) can penetrate germ cells and replace the earlier dark DNA sections and induce change of ordinary DNA. Or is a more delicate mechanism involving dark photons in question. With inspiration coming from the findings reported by Peter Gariaev I have proposed a model of remote DNA replication suggesting that DNA can be replicated remotely if the needed nucleotides are present: the information about DNA could be transferred as dark photons, which can be transformed to ordinary photons identified as
bio-photons. Could Lysenko have been at least partially right despite that he was a swindler
basing his views on ideology?

In any case, TGD inspired biology allows to imagine a controlled evolution of DNA in analogy to that what occurs in R&D departments of modern technological organizations. The notion of dark DNA suggests that biological systems indeed have a "R&D department" in which new variants of DNA studied as "dark DNA" sequences realised as dark proton sequences - same about dark RNA, and amino-acids and even tRNA. The possibility to transcribe RNA from dark DNA would mean that the testing can be carried in real life situations.

There indeed exists evidence that traumatic - and thus highly emotional - memories may be passed down through generations in genome . Could the modifications of brain DNA represent long term memories as the above described experiment suggests? Could the memories be transferred to the germ cells using the mechanism sketched above?

For background see the new chapter Dark matter, quantum gravity, and prebiotic evolution or the article "Direct Evidence for Dark DNA?!".

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