How the fourth phase of water discovered by Pollack is formed?

The fourth phase of Pollack is new phase of water whose existence is demonstrated convincingly by Pollack. This phase might be behing various other phases of water - such as ordered water, the Brown gas, etc... claimed by free energy researchers.

1. The fourth phase is formed in the experiments of Pollack in a system consisting of water bounded by gel phase and the new phase itself is gel like. It consists of negatively charged regions of thickness, which can be as thick as 200 micrometers and even thicker exclusion zones (EZs) have been reported. "EZ" comes from the observation that the negatively charged regions exclude some atoms, ions, and molecules. The stoichiometry of EZ is H_1.5O meaning that there hydrogen bonded pairs of H₂O molecules with one proton kicked away.
   
   
2. Where do the protons go? TGD proposal is that it becomes dark proton at the flux tubes outside the exclusion zone. This generates nanoscopic or even macroscopic quantum phase. DNA double strands with negative charge would represent an example of this kind of phase with 2 negative charges per base pair. Cell is negatively charged and would also represent an example about fourth phase inside cell. In TGD inspired prebiology protocells would be formed by the bubbles of fourth phase of water as I have proposed in the article "More Precise TGD Based View about Quantum Biology and Prebiotic Evolution". One ends up with a rather detailed model of prebiotic evolution involving also clay minerals known as phyllosilicates.
   
   
3. irradiation of water using IR photons with energies in the range of metabolic energy quanta - nominal value is about .5 eV) - generates fourth phase. This suggests that metabolic energy might be used to generate them around DNA strands for instance.
   

   Also microwave radiation in the range of few GHz generates fourth phase and many other mechanisms have been suggested. Microwaves also generate the burning of water which might therefore also involve the formation of EZs and microwave frequenzies affect strongly microtubules (see this and this). It seems that the energy feed is the key concept. Maybe a spontaenously occurring self-organization process induced by a feed of energy is in question.
   
   

How the fourth phase is formed? I have considered several alternative answers.

1. Physicist del Giudice has proposed the existence of coherence domains of size of order 1 micrometer in water. The proposal would be that coherence domains of water containing water molecules with one O-H bond per two molecules at criticality for splitting so that metabolic energy quantum can split it and kick the proton out as dark proton. The problem is how to achieve the almost ionization in such a manner that highly regular H_1.5 stochiometry is obtained.
   
   
2. I have also proposed that so called water clathrates might be involved and serve at least as seeds for the generation of fourth phase of water. Water clathrates can be see as cages containing hydrogen-bonded water - forming a crystal structure analogous to ice. Maybe fourth phase involving also hydrogen bonds between two water molecules before the loss of proton could be formed from clathrates by a phase transition liberating the dark protons.
   
   

I have not considered earlier a proposal inspired by the fact that the sequences of dark protons at dark magnetic flux tubes outside the fourth phase can be regarded as dark nuclei.

1. Dark nuclei are characterized by dark binding energy. If the dark binding energy scales like Coulomb energy it behaves like 1/size scale and thus like 1/h_eff. The model for dark genetic code as dark proton sequences generated as DNA becomes negatively charged by the generaton of fourth phase of water around it suggests that the size of dark protons is of order nanometer. This implies that the dark nuclear binding energy is in the UV region. Just the energy about 5 eV needed to kick O-H bond near criticality against splitting by a small energy dose such as metabolic energy quantum.
   
   
2. Could it be that the formation of EZs proceeds as a chain reaction, that is dark nuclear fusion? If so the basic entities of life - EZs - would be generated spontaneously as Negentropy Maximization Principle indeed predicts! Note that this involves also formation of dark nucleus analogs of DNA, RNA, aminoacids and realization of genetic code! As dark proton is added to a growing dark proton sequence, a (dark or) ordinary photon with energy about 5 eV is liberated as binding energy and could (transform to ordinary photon and) kick new O-H bond near near criticality or over it and external IR radiation at metabolic energy takes care of the rest. If the system is near criticality, many other manners to get it over the border can be imagined. Just a feed of energy generating IR radiation is enough.
   
   
3. The resulting dark nuclei can be transform to ordinary nuclei. and this would give rise to ordinary cold fusion (see "Biological transmutations, and their applications in chemistry, physics, biology, ecology, medicine, nutrition, agriculture, geology" by Kervran and "The secret life of plants" by Tompkins and Bird). Biofusion of nuclei of biologically important ions such as Ca in living matter has been reported. Also in systems in which hydrolysis splits water to yield hydrogen gas, the same phenomenon is reported. For instance, Kanarev and Mizuno report cold fusion in this kind of systems. The explanation would be in terms of fourth phase of water: in the splitting of water not only hydrogen atoms but also dark protons and dark nuclei would be formed.
   
   

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

Are the zeros of Riemann zeta number theoretically universal?

I have already posted the following piece of text as part of earlier posting. Since the outcome of simple argument leads to very powerful statement about number theoretic anatomy of
the zeros of Riemann zeta, I thought that it would be approriate to represent it separately.

Dyson's comment about Fourier transform of Riemann Zeta is very interesting concerning Number Theoretic Universality (NTU) for Riemann zeta.

1. The numerical calculation of Fourier transform for the distribution of the imaginary parts iy of zeros s=1/2+iy of zeta shows that it is concentrated at discrete set of frequencies coming as log(pⁿ), p prime. This translates to the statement that the zeros of zeta form a 1-dimensional quasicrystal, a discrete structure Fourier spectrum by definition is also discrete (this of course holds for ordinary crystals as a special case). Also the logarithms of powers of primes would form a quasicrystal, which is very interesting from the point of view of p-adic length scale hypothesis. Primes label the "energies" of elementary fermions and bosons in arithmetic number theory, whose repeated second quantization gives rise to the hierarchy of infinite primes. The energies for general states are logarithms of integers.
   
   
2. Powers pⁿ label the points of quasicrystal defined by points log(pⁿ) and Riemann zeta has interpretation as partition function for boson case with this spectrum. Could pⁿ label also the points of the dual lattice defined by iy?
   
   
3. The existence of Fourier transform for points log(p_iⁿ) for any vector y_a requires p_i^iy_a to be a root of unity. This could define the sense in which zeros of zeta are universal. This condition also guarantees that the factor n^-1/2-iy appearing in zeta at critical line are number theoretically universal (p^1/2 is problematic for Q_p: the problem might be solved by eliminating from p-adic analog of zeta the factor 1-p^-s.
   
   
   1. One obtains for the pair (p_i,s_a) the condition log(p_i)y_a= q_ia2π, where q_ia is a rational number. Dividing the conditions for (i,a) and (j,a) gives
      

      p_i= p_j^q_ia/q_ja
      

      for every zero s_a so that the ratios q_ia/q_ja do not depend on s_a. Since the exponent is rational number one obtains p_i^M= p_j^N for some integers, which cannot be true.
      
      

   2. Dividing the conditions for (i,a) and (i,b) one obtains
      

      y_a/y_b= q_ia/q_ib
      

      so that the ratios q_ia/q_ib do not depend on p_i. The ratios of the imaginary parts of zeta would be therefore rational number which is very strong prediction and zeros could be mapped by scaling y_a/y₁ where y₁ is the zero which smallest imaginary part to rationals.
      
      

   3. The impossible consistency conditions for (i,a) and (j,a) can be avoided if each prime and its powers correspond to its own subset of zeros and these subsets of zeros are disjoint: one would have infinite union of sub-quasicrystals labelled by primes and each p-adic number field would correspond to its own subset of zeros: this might be seen as an abstract analog for the decomposition of rational to powers of primes. This decomposition would be natural if for ordinary complex numbers the contibution in the complement of this set to the Fourier trasform vanishes. The conditions (i,a) and (i,b) require now that the ratios of zeros are rationals only in the subset associated with p_i.
      

For the general option the Fourier transform can be delta function for x=log(p^k) and the set {y_a(p)} contains N_p zeros. The following argument inspires the conjecture that for each p there is an infinite number N_p of zeros y_a(p) satisfying

p^iy_a(p)=u(p)=e^{(r(p)/m(p))i2π} ,

where u(p) is a root of unity that is y_a(p)=2π (m(a)+r(p))/log(p) and forming a subset of a lattice with a lattice constant y₀=2π/log(p), which itself need not be a zero.

In terms of stationary phase approximation the zeros y_a(p) associated with p would have constant stationary phase whereas for y_a(p_i≠ p)) the phase p^iy_a(p_i) would fail to be stationary. The phase e^ixy would be non-stationary also for x≠ log(p^k) as function of y.

1. Assume that for x =qlog(p), q not a rational, the phases e^ixy fail to be roots of unity and are random implying the vanishing/smallness of F(x) .
   
   
2. Assume that for a given p all powers p^iy for y not in {y_a(p)} fail to be roots of unity and are also random so that the contribution of the set y not in {y_a(p)} to F(p) vanishes/is small.
   
   
3. For x= log(p^k/m) the Fourier transform should vanish or be small for m different from 1 (rational roots of primes) and give a non-vanishing contribution for m=1. One has
   

   F(x= log(p^k/m ) =∑_{1≤ n≤ N(p)} e^{[kM(n,p)/mN(n,p)]i2π} .
   

   Obviously one can always choose N(n,p)=N(p).
   
   

4. For the simplest option N(p)=1 one would obtain delta function distribution for x=log(p^k). The sum of the phases associated with y_a(p) and -y_a(p) from the half axes of the critical line would give
   

   F(x= log(pⁿ)) ∝ X(pⁿ)==2cos(n× (r(p)/m(p))× 2π) .
   

   The sign of F would vary.
   
   

5. The rational r(p)/m(p) would characterize given prime (one can require that r(p) and m(p) have no common divisors). F(x) is non-vanishing for all powers x=log(pⁿ) for m(p) odd. For p=2, also m(2)=2 allows to have |X(2ⁿ)|=2. An interesting ad hoc ansatz is m(p)=p or p^s(p). One has periodicity in n with period m(p) that is logarithmic wave. This periodicity serves as a test and in principle allows to deduce the value of r(p)/m(p) from the Fourier transform.
   

What could one conclude from the data (see this)?

1. The first graph gives |F(x=log(p^k| and second graph displays a zoomed up part of |F(x| for small powers of primes in the range [2,19]. For the first graph the eighth peak (p=11) is the largest one but in the zoomed graphs this is not the case. Hence something is wrong or the graphs correspond to different approximations suggesting that one should not take them too seriously.
   

   In any case, the modulus is not constant as function of p^k. For small values of p^k the envelope of the curve decreases and seems to approach constant for large values of p^k (one has x< 15 (e¹⁵≈ 3.3× 10⁶).
   
   

2. According to the first graph | F(x)| decreases for x=klog(p)<8, is largest for small primes, and remains below a fixed maximum for 8<x<15. According to the second graph the amplitude decreases for powers of a given prime (say p=2). Clearly, the small primes and their powers have much larger | F(x)| than large primes.
   
   

There are many possible reasons for this behavior. Most plausible reason is that the sums involved converge slowly and the approximation used is not good. The inclusion of only 10⁴ zeros would show the positions of peaks but would not allow reliable estimate for their intensities.

1. The distribution of zeros could be such that for small primes and their powers the number of zeros is large in the set of 10⁴ zeros considered. This would be the case if the distribution of zeros y_a(p) is fractal and gets "thinner" with p so that the number of contributing zeros scales down with p as a power of p, say 1/p, as suggested by the envelope in the first figure.
   
   
2. The infinite sum, which should vanish, converges only very slowly to zero. Consider the contribution Δ F(p^k,p₁) of zeros not belonging to the class p₁\ne p to F(x=log(p^k)) =∑_pi Δ F(p^k,p_i), which includes also p_i=p. Δ F(p^k,p_i), p≠ p₁ should vanish in exact calculation.
   
   
   1. By the proposed hypothesis this contribution reads as
      

      l Δ F(p,p₁)= ∑_a cos[X(p^k,p₁)(M(a,p₁)+ r(p₁)/m(p₁))2π)t] .

      X(p^k,p₁)=log(p^k)/log(p₁).
      

      Here a labels the zeros associated with p₁. If p^k is "approximately divisible" by p¹ in other words, p^k≈ np₁, the sum over finite number of terms gives a large contribution since interference effects are small, and a large number of terms are needed to give a nearly vanishing contribution suggested by the non-stationarity of the phase. This happens in several situations.
      
      

   2. The number π(x) of primes smaller than x goes asymptotically like π(x) ≈ x/log(x) and prime density approximately like 1/log(x)-1/log(x)² so that the problem is worst for the small primes. The problematic situation is encountered most often for powers p^k of small primes p near larger prime and primes p (also large) near a power of small prime (the envelope of | F(x)| seems to become constant above x∼ 10³).
      
      
   3. The worst situation is encountered for p=2 and p₁=2^k-1 - a Mersenne prime and p₁= 2^2k+1, k≤ 4 - Fermat prime. For (p,p₁)=(2^k,M_k) one encounters X(2^k,M_k)= (log(2^k)/log(2^k-1) factor very near to unity for large Mersennes primes. For (p,p₁)=(M_k,2) one encounters X(M_k,2)= (log(2^k-1)/log(2) ≈ k. Examples of Mersennes and Fermats are (3,2),(5,2),(7,2),(17,2),(31,2), (127,2),(257,2),... Powers 2^k, k=2,3,4,5,7,8,.. are also problematic.
      
      
   4. Also twin primes are problematic since in this case one has factor X(p=p₁+2,p₁)=log(p₁+2)/log(p₁). The region of small primes contains many twin prime pairs: (3,5), (5,7), (11,13), (17,19), (29,31),....
      
      
   These observations suggest that the problems might be understood as resulting from including too small number of zeros.
3. The predicted periodicity of the distribution with respect to the exponent k of p^k is not consistent with the graph for small values of prime unless the periodic m(p) for small primes is large enough. The above mentioned effects can quite well mask the periodicity. If the first graph is taken at face value for small primes, r(p)/m(p) is near zero, and m(p) is so large that the periodicity does not become manifest for small primes. For p=2 this would require m(2)>21 since the largest power 2ⁿ≈ e¹⁵ corresponds to n∼ 21.
   
   

To summarize, the prediction is that for zeros of zeta should divide into disjoint classes {y_a(p)\ labelled by primes such that within the class labelled by p one has p^iy_a(p)=e^{(r(p)/m(p))i2π} so that has y_a(p) = [M(a,p) +r(p)/m(p))] 2π/log(p).

What this speculative picture from the point of view of TGD?

1. A possible formulation for number theoretic universality for the poles of fermionic Riemann zeta ζ_F(s)= ζ(s)/ζ(2s) could be as a condition that is that the exponents p^ks_n(p)/2= p^k/4p^iky_n(p)/2 exist in a number theoretically universal manner for the zeros s_n(p) for given p-adic prime p and for some subset of integers k. If the proposed conditions hold true, exponent reduces p^k/4 requiring that k is a multiple of 4. The number of the non-trivial generating elements of super-symplectic algebra in the monomial creating physical state would be a multiple of 4. These monomials would have real part of conformal weight -1. Conformal confinement suggests that these monomials are products of pairs of generators for which imaginary parts cancel. The conformal weights are however effectively real for the exponents automatically. Could the exponential formulation of the number theoretic universality effectively reduce the generating elements to those with conformal weight -1/4 and make the operators in question hermitian?
   
   
2. Quasi-crystal property might have an application to TGD. The functions of light-like radial coordinate appearing in the generators of supersymplectic algebra could be of form r^s, s zero of zeta or rather, its imaginary part. The eigenstate property with respect to the radial scaling rd/dr is natural by radial conformal invariance.
   

   The idea that arithmetic QFT assignable to infinite primes is behind the scenes in turn suggests light-like momenta assignable to the radial coordinate have energies with the dual spectrum log(pⁿ). This is also suggested by the interpretation of ζ as square root of thermodynamical partition function for boson gas with momentum log(p) and analogous interpretation of ζ_F.
   

   The two spectra would be associated with radial scalings and with light-like translations of light-cone boundary respecting the direction and light-likeness of the light-like radial vector. log(pⁿ) spectrum would be associated with light-like momenta whereas p-adic mass scales would characterize states with thermal mass. Note that generalization of p-adic length scale hypothesis raises the scales defined by pⁿ to a special physical position: this might relate to ideal structure of adeles.
   
   

3. Finite measurement resolution suggests that the approximations of Fourier transforms over the distribution of zeros taking into account only a finite number of zeros might have a physical meaning. This might provide additional understand about the origins of generalized p-adic length scale hypothesis stating that primes p≈ p₁^k, p₁ small prime - say Mersenne primes - have a special physical role.
   
   

See the chapter Unified Number Theoretic Vision of "TGD 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.

Where they are - the gravitational waves?

One hundred years since Einstein proposed gravitational waves as part of his general theory of relativity, an 11-year search performed with CSIRO's Parkes telescope has failed to detect them, casting doubt on our understanding of galaxies and black holes. The work, led by Dr Ryan Shannon (of CSIRO and the International Centre for Radio Astronomy Research), is published today in the journal Science, see the article Gravitational waves from binary supermassive black holes missing in pulsar observations. See also the popular article 11-year cosmic search leads to black hole rethink.

This finding is consistent with TGD view about blackhole like entities ( I wrote 3 blog articles inspired by the most recent Hawking hype: see this, this and this).

In TGD Universe ideal blackhole a space-time region with Euclidian(!) signature of induced metric and horizon would correspond to the light-like 3-surface at which the signature of the metric changes. Ideal blackhole (or rather its surface) would consist solely of dark matter. The large values of gravitational Planck constant h_gr= GMm/v₀, M here is the mass of blackhole and m is the mass of say electron, would be associated with the flux tubes mediating gravitational interaction and gravitational radiation. v₀ is a parameter with dimensions of velocity - some characteristic rotational velocity -say the rotation velocity of blackhole- would be in question.

The quanta of dark gravitational radiation would have much large energies E= h_eff than one would expect on basis of the rotation frequency, which corresponds to a macroscopic time scale. Dark gravitons would arrive as highly energetic particles along flux tubes and could decay to bunches of ordinary low energy gravitons in the detection. These bunches would be bursts rather than continuous background and would be probably interpreted as a noise. I have considered a model for this in here.

See the article TGD view about blackholes and Hawking radiation.

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

Some applications of Number Theoretical Universality

Number theoretic universality (NTU) in the strongest form says that all numbers involved at "basic level" (whatever this means!) of adelic TGD are products of roots of unity and of power of a root of e defining finite-dimensional extensions of p-adic numbers (e^p is ordinary p-adic number). This is extremely powerful physics inspired conjecture with a wide range of possible mathematical applications.

1. For instance, vacuum functional defined as an exponent of Kähler action for preferred externals would be number of this kind. One could define functional integral as adelic operation in all number fields: essentially as sum of exponents of Kähler action for stationary preferred extremals since Gaussian and metric determinants potentially spoiling NTU would cancel each other leaving only the exponent.
   
   
2. The implications of NTU for the zeros of Riemann zeta expected to be closely related to super-symplectic conformal weights will be discussed below.
   
   
3. NTU generalises to all Lie groups. Exponents exp(in_iJⁱ/n) of lie-algebra generators define generalisations of number theoretically universal group elements and generate a discrete subgroup of compact Lie group. Also hyperbolic "phases" based on the roots e^m/n are possible and make possible discretized NTU versions of all Lie-groups expected to play a key role in adelization of TGD.
   

   NTU generalises also to quaternions and octonions and allows to define them as number theoretically universal entities. Note that ordinary p-adic variants of quaternions and octonions do not give rise to a number field: inverse of quaternion can have vanishing p-adic variant of norm squared satisfying ∑_n x_n²=0.
   

   NTU allows to define also the notion of Hilbert space as an adelic notion. The exponents of angles characterising unit vector of Hilbert space would correspond to roots of unity.
   
   

Super-symplectic conformal weights and Riemann zeta

The existence of WCW geometry highly nontrivial already in the case of loop spaces. Maximal group of isometries required and is infinite-dimensional. Super-symplectic algebra is excellent candidate for the isometry algebra. There is also extended conformal algebra associated with δ CD. These algebras have fractal structure. Conformal weights for isomorphic subalgebra n-multiples of those for entire algebra. Infinite hierarchy labelled by integer n>0. Generating conformal weights could be poles of fermionic zeta ζ_F. This demands n>0. Infinite number of generators with different non-vanishing conformal weight with other quantum numbers fixed. For ordinary conformal algebras there are only finite number of generating elements (n=1).

If the radial conformal weights for the generators of g consist of poles of ζ_F, the situation changes. ζ_F is suggested by the observation that fermions are the only fundamental particles in TGD.

1. Riemann Zeta ζ(s)= ∏_p(1/(1-p^-s) identifiable formally as a partition function ζ_B(s) of arithmetic boson gas with bosons with energy log(p) and temperature 1/s= 1/(1/2+iy) should be replaced with that of arithmetic fermionic gas given in the product representation by ζ_F(s) =∏_p (1+p^-s) so that the identity ζ_B(s))/ζ_F(s) =ζ_B(2s) follows. This gives
   

   ζ_B(s)/ζ_B(2s) .
   

   ζ_F(s) has zeros at zeros s_n of ζ (s) and at the pole s=1/2 of zeta(2s). ζ_F(s) has poles at zeros s_n/2 of ζ(2s) and at pole s=1 of ζ(s).
   

   The spectrum of 1/T would be for the generators of algebra {(-1/2+iy)/2, n>0, -1}. In p-adic thermodynamics the p-adic temperature is 1/T=1/n and corresponds to "trivial" poles of ζ_F. Complex values of temperature does not make sense in ordinary thermodynamics. In ZEO quantum theory can be regarded as a square root of thermodynamics and complex temperature parameter makes sense.
   
   

2. If the spectrum of conformal weights of generators of algebra (not the entire algebra!) corresponds to poles serving as analogs of propagator poles, it consists of the "trivial" conformal h=n>0- the standard spectrum with h=0 assignable to massless particles excluded - and "non-trivial" h=-1/4+iy/2. There is also a pole at h=-1.
   

   Both the non-trivial pole with real part h_R= -1/4 and the pole h=-1 correspond to tachyons. I have earlier proposed conformal confinement meaning that the total conformal weight for the state is real. If so, one obtains for a conformally confined two-particle states corresponding to conjugate non-trivial zeros in minimal situation h_R= -1/2 assignable to N-S representation.
   

   In p-adic mass calculations ground state conformal weight must be -5/2. The negative fermion ground state weight could explain why the ground state conformal weight must be tachyonic -5/2. With the required 5 tensor factors one would indeed obtain this with minimal conformal confinement. In fact, arbitrarily large tachyonic conformal weight is possible but physical state should always have conformal weights h>0.
   
   

3. h=0 is not possible for generators, which reminds of Higgs mechanism for which the naive ground states corresponds to tachyonic Higgs. h=0 conformally confined massless states are necessarily composites obtained by applying the generators of Kac-Moody algebra or super-symplectic algebra to the ground state. This is the case according to p-adic mass calculations, and would suggest that the negative ground state conformal weight can be associated with super-symplectic algebra and the remaining contribution comes from ordinary super-conformal generators. Hadronic masses whose origin is poorly understood could come from super-symplectic degrees of freedom. There is no need for p-adic thermodynamics in super-symplectic degrees of freedom.
   
   

Are the zeros of Riemann zeta number theoretically universal?

Dyson's comment about Fourier transform of Riemann Zeta is very interesting concerning NTU for Riemann zeta.

1. The numerical calculation of Fourier transform for the distribution of the imaginary parts iy of zeros s=1/2+iy of zeta shows that it is concentrated at discrete set of frequencies coming as log(pⁿ), p prime. This translates to the statement that the zeros of zeta form a 1-dimensional quasicrystal, a discrete structure Fourier spectrum by definition is also discrete (this of course holds for ordinary crystals as a special case). Also the logarithms of powers of primes would form a quasicrystal, which is very interesting from the point of view of p-adic length scale hypothesis. Primes label the "energies" of elementary fermions and bosons in arithmetic number theory, whose repeated second quantization gives rise to the hierarchy of infinite primes. The energies for general states are logarithms of integers.
   
   
2. Powers pⁿ label the points of quasicrystal defined by points log(pⁿ) and Riemann zeta has interpretation as partition function for boson case with this spectrum. Could pⁿ label also the points of the dual lattice defined by iy?
   
   
3. The existence of Fourier transform for points log(p_iⁿ) for any vector y_a requires p_i^iy_a to be a root of unity. This could define the sense in which zeros of zeta are universal. This condition also guarantees that the factor n^-1/2-iy appearing in zeta at critical line are number theoretically universal (p^1/2 is problematic for Q_p: the problem might be solved by eliminating from p-adic analog of zeta the factor 1-p^-s.
   
   1. One obtains for the pair (p_i,s_a) the condition log(p_i)y_a= q_ia2π, where q_ia is a rational number. Dividing the conditions for (i,a) and (j,a) gives
      

      p_i= p_j^q_ia/q_ja
      

      for every zero s_a so that the ratios q_ia/q_ja do not depend on s_a. Since the exponent is rational number one obtains p_i^M= p_j^N for some integers, which cannot be true.
      
      

   2. Dividing the conditions for (i,a) and (i,b) one obtains
      

      y_a/y_b= q_ia/q_ib
      

      so that the ratios q_ia/q_ib do not depend on p_i. The ratios of the imaginary parts of zeta would be therefore rational number which is very strong prediction and zeros could be mapped by scaling y_a/y₁ where y₁ is the zero which smallest imaginary part to rationals.
      
      

   3. The impossible consistency conditions for (i,a) and (j,a) can be avoided if each prime and its powers correspond to its own subset of zeros and these subsets of zeros are disjoint: one would have infinite union of sub-quasicrystals labelled by primes and each p-adic number field would correspond to its own subset of zeros: this might be seen as an abstract analog for the decomposition of rational to powers of primes. This decomposition would be natural if for ordinary complex numbers the contibution in the complement of this set to the Fourier trasform vanishes. The conditions (i,a) and (i,b) require now that the ratios of zeros are rationals only in the subset associated with p_i.
      

For the general option the Fourier transform can be delta function for x=log(p^k) and the
set {y_a(p)} contains N_p zeros. The following argument inspires the conjecture that
for each p there is an infinite number N_p of zeros y_a(p) satisfying

p^iy_a(p)=u(p)=e^{(r(p)/m(p))i2π} ,

where u(p) is a root of unity that is y_a(p)=2π (m(a)+r(p))/log(p) and forming a subset of a lattice
with a lattice constant y₀=2π/log(p), which itself need not be a zero.

In terms of stationary phase approximation the zeros y_a(p) associated with p would have constant stationary phase whereas for y_a(p_i≠ p)) the phase p^iy_a(p_i) would fail to be stationary. The phase e^ixy would be non-stationary also for x≠ log(p^k) as function of y.

1. Assume that for x =qlog(p), q not a rational, the phases e^ixy fail to be roots of unity and are random implying the vanishing/smallness of F(x) .
   
   
2. Assume that for a given p all powers p^iy for y not in {y_a(p)} fail to be roots of unity and are also random so that the contribution of the set y not in {y_a(p)} to F(p) vanishes/is small.
   
   
3. For x= log(p^k/m) the Fourier transform should vanish or be small for m different from 1 (rational roots of primes) and give a non-vanishing contribution for m=1. One has
   

   F(x= log(p^k/m ) =∑_{1≤ n≤ N(p)} e^{[kM(n,p)/mN(n,p)]i2π} .
   

   Obviously one can always choose N(n,p)=N(p).
   
   

4. For the simplest option N(p)=1 one would obtain delta function distribution for x=log(p^k). The sum of the phases associated with y_a(p) and -y_a(p) from the half axes of the critical line would give
   

   F(x= log(pⁿ)) ∝ X(pⁿ)==2cos(n× (r(p)/m(p))× 2π) .
   

   The sign of F would vary.
   
   

5. The rational r(p)/m(p) would characterize given prime (one can require that r(p) and m(p) have no common divisors). F(x) is non-vanishing for all powers x=log(pⁿ) for m(p) odd. For p=2, also m(2)=2 allows to have |X(2ⁿ)|=2. An interesting ad hoc ansatz is m(p)=p or p^s(p). One has periodicity in n with period m(p) that is logarithmic wave. This periodicity serves as a test and in principle allows to deduce the value of r(p)/m(p) from the Fourier transform.
   
   

What could one conclude from the data (see this)?

1. The first graph gives |F(x=log(p^k| and second graph displays a zoomed up part of |F(x| for small powers of primes in the range [2,19]. For the first graph the eighth peak (p=11) is the largest one but in the zoomed graphs this is not the case. Hence something is wrong or the graphs correspond to different approximations suggesting that one should not take them too seriously.
   

   In any case, the modulus is not constant as function of p^k. For small values of p^k the envelope of the curve decreases and seems to approach constant for large values of p^k (one has x< 15 (e¹⁵≈ 3.3× 10⁶).
   
   

2. According to the first graph | F(x)| decreases for x=klog(p)<8, is largest for small primes, and remains below a fixed maximum for 8<x<15. According to the second graph the amplitude decreases for powers of a given prime (say p=2). Clearly, the small primes and their powers have much larger | F(x)| than large primes.
   
   

There are many possible reasons for this behavior. Most plausible reason is that the sums involved converge slowly and the approximation used is not good. The inclusion of only 10⁴ zeros would show the positions of peaks but would not allow reliable estimate for their intensities.

1. The distribution of zeros could be such that for small primes and their powers the number of zeros is large in the set of 10⁴ zeros considered. This would be the case if the distribution of zeros y_a(p) is fractal and gets "thinner" with p so that the number of contributing zeros scales down with p as a power of p, say 1/p, as suggested by the envelope in the first figure.
   
   
2. The infinite sum, which should vanish, converges only very slowly to zero. Consider the contribution Δ F(p^k,p₁) of zeros not belonging to the class p₁≠ p to F(x=log(p^k)) =∑_pi Δ F(p^k,p_i), which includes also p_i=p. Δ F(p^k,p_i), p≠ p₁ should vanish in exact calculation.
   
   
   1. By the proposed hypothesis this contribution reads as
      

      l Δ F(p,p₁)= ∑_a cos[X(p^k,p₁)(M(a,p₁)+ r(p₁)/m(p₁))2π)t] .

      X(p^k,p₁)=log(p^k)/log(p₁).
      

      Here a labels the zeros associated with p₁. If p^k is "approximately divisible" by p¹ in other words, p^k≈ np₁, the sum over finite number of terms gives a large contribution since interference effects are small, and a large number of terms are needed to give a nearly vanishing contribution suggested by the non-stationarity of the phase. This happens in several situations.
      
      

   2. The number π(x) of primes smaller than x goes asymptotically like π(x) ≈ x/log(x) and prime density approximately like 1/log(x)-1/log(x)² so that the problem is worst for the small primes. The problematic situation is encountered most often for powers p^k of small primes p near larger prime and primes p (also large) near a power of small prime (the envelope of | F(x)| seems to become constant above x∼ 10³).
      
      
   3. The worst situation is encountered for p=2 and p₁=2^k-1 - a Mersenne prime and p₁= 2^2k+1, k≤ 4 - Fermat prime. For (p,p₁)=(2^k,M_k) one encounters X(2^k,M_k)= (log(2^k)/log(2^k-1) factor very near to unity for large Mersennes primes. For (p,p₁)=(M_k,2) one encounters X(M_k,2)= (log(2^k-1)/log(2) ≈ k. Examples of Mersennes and Fermats are (3,2),(5,2),(7,2),(17,2),(31,2), (127,2),(257,2),... Powers 2^k, k=2,3,4,5,7,8,.. are also problematic.
      
      
   4. Also twin primes are problematic since in this case one has factor X(p=p₁+2,p₁)=log(p₁+2)/log(p₁). The region of small primes contains many twin prime pairs: (3,5), (5,7), (11,13), (17,19), (29,31),....
      
      
   These observations suggest that the problems might be understood as resulting from including too small number of zeros.
3. The predicted periodicity of the distribution with respect to the exponent k of p^k is not consistent with the graph for small values of prime unless the periodic m(p) for small primes is large enough. The above mentioned effects can quite well mask the periodicity. If the first graph is taken at face value for small primes, r(p)/m(p) is near zero, and m(p) is so large that the periodicity does not become manifest for small primes. For p=2 this would require m(2)>21 since the largest power 2ⁿ≈ e¹⁵ corresponds to n∼ 21.
   
   

To summarize, the prediction is that for zeros of zeta should divide into disjoint classes {y_a(p)\ labelled by primes such that within the class labelled by p one has p^iy_a(p)=e^{(r(p)/m(p))i2π} so that has y_a(p) = [M(a,p) +r(p)/m(p))] 2π/log(p).

What this speculative picture from the point of view of TGD?

1. A possible formulation for number theoretic universality for the poles of fermionic Riemann zeta ζ_F(s)= ζ(s)/ζ(2s) could be as a condition that is that the exponents p^ks_n(p)/2= p^k/4p^iky_n(p)/2 exist in a number theoretically universal manner for the zeros s_n(p) for given p-adic prime p and for some subset of integers k. If the proposed conditions hold true, exponent reduces p^k/4 requiring that k is a multiple of 4. The number of the non-trivial generating elements of super-symplectic algebra in the monomial creating physical state would be a multiple of 4. These monomials would have real part of conformal weight -1. Conformal confinement suggests that these monomials are products of pairs of generators for which imaginary parts cancel. The conformal weights are however effectively real for the exponents automatically. Could the exponential formulation of the number theoretic universality effectively reduce the generating elements to those with conformal weight -1/4 and make the operators in question hermitian?
   
   
2. Quasi-crystal property might have an application to TGD. The functions of light-like radial coordinate appearing in the generators of supersymplectic algebra could be of form r^s, s zero of zeta or rather, its imaginary part. The eigenstate property with respect to the radial scaling rd/dr is natural by radial conformal invariance.
   

   The idea that arithmetic QFT assignable to infinite primes is behind the scenes in turn suggests light-like momenta assignable to the radial coordinate have energies with the dual spectrum log(pⁿ). This is also suggested by the interpretation of ζ as square root of thermodynamical partition function for boson gas with momentum log(p) and analogous interpretation of ζ_F.
   

   The two spectra would be associated with radial scalings and with light-like translations of light-cone boundary respecting the direction and light-likeness of the light-like radial vector. log(pⁿ) spectrum would be associated with light-like momenta whereas p-adic mass scales would characterize states with thermal mass. Note that generalization of p-adic length scale hypothesis raises the scales defined by pⁿ to a special physical position: this might relate to ideal structure of adeles.
   
   

3. Finite measurement resolution suggests that the approximations of Fourier transforms over the distribution of zeros taking into account only a finite number of zeros might have a physical meaning. This might provide additional understand about the origins of generalized p-adic length scale hypothesis stating that primes p≈ p₁^k, p₁ small prime - say Mersenne primes - have a special physical role.
   
   

See the chapter Unified Number Theoretic Vision of "TGD 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.

"Invisible magnetic fields" as dark magnetic fields

A further victory for the notion of dark magnetic fields: scientstists create a "portal" that conceals electromagnetic fields (see this). The popular article talks about wormholes and invisible magnetic fields. A couple of comments about the official terminology are in order.

"Wormhole" is translation of "flux tube carrying monopole current". Since TGD is "bad" science, "wormhole" is the correct wording although it does not have much to do with reality. Similar practice is applied by stringy people when they speak of wormholes connecting blackholes. The original TGD terminology talks about partonic 2-surfaces and magnetic flux tubes but again: this is "bad" science. Reader can invent an appropriate translation for "bad".

"Invisible magnetic field" translates to "dark magnetic field carrying monopole flux". Dark magnetic fields give rise to one of the basic differences between TGD and Maxwellian theory. These magnetic fluxes can exist without generating currents. This makes them especially important in early cosmology since they explain the long range magnetic fields having no explanation in standard cosmology. Super-conductivity is second application and central in TGD inspired quantum biology.

What is fantastic that technology based on TGD is now being created without a slightest idea that it is technology based on TGD (really;-)?- sorry for my alter ego, which does not understand the importance of political correctness). Experimenters have now created a magnetic field for which flux travels from position to another as invisible flux. The idea is to use flux, which propagates radially from point (in good approximation) through a spherical super-conductor and is forced to run along dark flux tubes by Meissner effect.

Indeed, in TGD based model of super-conductor the supracurrents flow along dark flux tubes as dark Cooper pairs through super-conductor (see the earlier posting). Since magnetic field cannot penerate on super-conductor they travel along dark flux tubes carrying magnetic monopole fluxes and supra currents.

One of the applications is to guide magnetic fluxes to desired positions in MRI. Precisely targeted communication and control in general. This is one of the basic ideas of TGD inspired quantum biology.

See the chapter Criticality and dark matter.

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

Macroscopically quantum coherent fluid dynamics at criticality?

Evidence for the hierarchy of Planck constants implying macroscopic quantum coherence in quantum critical systems is rapidly accumulating. Also people having the courage to refer to TGD in their articles are gradually emerging. The most recent fluid dynamics experiment providing this kind of evidence is performed by Yves Couder and Emmanuel Fort (see for instance the article Single particle diffraction in macroscopic scale). Mathematician John W. M. Bush has commented these findings in the Proceedings of National Academy of Sciences and the article provides references to a series of papers by Couder and collaborators.

The system studied consist of a tray containing water at a surface, which is oscillating. The intensity of vibration is just below the critical value inducing so called Faraday waves at the surface of water. Although the water surface is calm, water droplet begins to bounce and generates waves propagating along the water surface - "walkers". Walkers behave like classical particles at Bohr orbits. As they pass through a pair of slits they behave they choose random slit but several experiments produce interference pattern. Walkers exhibit an effect analogous to quantum tunneling and even the analogs of quantum mechanical bound states of walkers realized as circular orbits emerge as the water tray rotates!

The proposed interpretation of the findings is in terms of Bohm's theory. Personally I find it very difficult to believe in this since Bohm's theory has profound mathematical difficulties. Bohm's theory was inspired by Einstein's belief on classical determinism and the idea that quantum non-determinism is not actual but reduces to the presence of hidden variables. Unfortunately, this idea led to no progress.

TGD is analogous to Bohm's theory in that classical theory is exact but quantum theory is now only an exact classical correlate: there is no attempt to eliminate quantum non-determinism. Quantum jumps are between superpositions of entire classical time evolutions rather than their time=constant snapshots: this solves the basic paradox of Copenhagen interpretation. A more refined formulation is in terms of zero energy ontology, which in turn forces to generalize quantum measurement theory to a theory of consciousness.

Macroscopic quantum coherence associated with the behavior of droplets bouncing on the surface of water is suggested by the experiments. For instance, quantum measurement theory seems to apply to the behavior of single droplet as it passes through slit. In TGD the prerequisite for macroscopic quantum coherence would be quantum criticality at which large h_eff=n×h is possible. There indeed is an external oscillation of the tray containing water with an amplitude just below the criticality for the generation of Faraday waves at the surface of water. Quantum classical correspondence states that the quantum behavior should have a classical correlate. The basic structure of classical TGD is that of hydrodynamics in the sense that dynamics reduces to conservation laws plus conditions expressing the vanishing of an infinite number of so called super-symplectic charges - the conditions guarantee strong form of holography and express quantum criticality. The generic solution of classical field equations could reduce to Frobenius integrability conditions guaranteing that the conserved isometry currents are integrable and thus define global coordinates varying along the flow lines.

One should be of course very cautious. For ordinary Schrödinger equation the system is closed. Now the system is open. This is not a problem if the only function of external vibration is to induce quantum criticality. The experiment brings in mind the old vision of Frölich about external vibrations as induced of what looks like quantum coherence. In TGD framework this coherence would be forced coherence at the level of visible matter but the oscillation itself would correspond to genuine macroscopic quantum coherence and large value of h_eff. A standard example are penduli, which gradually start to oscillate in unisono in presence of weak synchronizing signal. In brain neurons would start to oscillator synchronously by the presence of dark photons with large h_eff.

See the chapter Criticality and dark matter of of "Hyperfinite factors and dark matter hierarchy".

See the chapter Criticality and dark matter.

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

Algebraic universality and the value of Kähler coupling strength

With the development of the vision about number theoretically universal view about functional integration in WCW , a concrete vision about the exponent of Kähler action in Euclidian and Minkowskian space-time regions. The basic requirement is that exponent of Kähler action belongs to an algebraic extension of rationals and therefore to that of p-adic numbers and does not depend on the ordinary p-adic numbers at all - this at least for sufficiently large primes p. Functional integral would reduce in Euclidian regions to a sum over maxima since the troublesome Gaussian determinants that could spoil number theoretic universality are cancelled by the metric determinant for WCW.

The adelically exceptional properties of Neper number e, Kähler metric of WCW, and strong form of holography posing extremely strong constraints on preferred extremals, could make this possible. In Minkowskian regions the exponent of imaginary Kähler action would be root of unity. In Euclidian space-time regions expressible as power of some root of e which is is unique in sense that e^p is ordinary p-adic number so that e is p-adically an algebraic number - p:th root of e^p.

These conditions give conditions on Kähler coupling strength α_K= g_K²/4π (hbar=1)) identifiable as an analog of critical temperature. Quantum criticality of TGD would thus make possible number theoretical universality (or vice versa).

1. In Euclidian regions the natural starting point is CP₂ vacuum extremal for which the maximum value of Kähler action is
   

   S_K= π²/2g_K²= π/8α_K .
   

   The condition reads S_K=q =m/n if one allows roots of e in the extension. If one requires minimal extension of involving only e and its powers one would have S_K=n. One obtains
   

   1/α_K= 8q/π ,
   

   where the rational q=m/n can also reduce to integer. One cannot exclude the possibiity that q depends on the algebraic extension of rationals defining the adele in question.
   

   For CP₂ type extremals the value of p-adic prime should be larger than p_min=53. One can consider a situation in which large number of CP₂ type vacuum extremals contribute and in this case the condition would be more stringent. The condition that the action for CP₂ extremal is smaller than 2 gives
   

   1/α_K≤ 16/π ≈ 5.09 .
   

   It seems there is lower bound for the p-adic prime assignable to a given space-time surface inside CD suggesting that p-adic prime is larger than 53× N, where N is particle number.
   

   This bound has not practical significance. In condensed matter particle number is proportional to (L/a)³ - the volume divided by atomic volume. On basis p-adic mass calculations p-adic prime can be estimated to be of order (L/R)². Here a is atomic size of about 10 Angstroms and R CP₂ "radius. Using R≈ 10⁴ L_Planck this gives as upper bound for the size L of condensed matter blob a completely super-astronomical distance L≤ a³/R² ∼ 10²⁵ ly to be compared with the distance of about 10¹⁰ ly travelled by light during the lifetime of the Universe. For a blackhole of radius r_S= 2GM with p∼ (2GM/R)² and consisting of particles with mass above M≈ hbar/R one would obtain the rough estimate M>(27/2)× 10^-12m_Planck ∼ 13.5× 10³ TeV trivially satisfied.
   
   

2. The physically motivated expectation from earlier arguments - not necessarily consistent with the recent ones - is that the value α_K is quite near to fine structure constant at electron length scale: α_K≈ α_em≈ 137.035999074(44).
   

   The latter condition gives n=54=2× 3³ and 1/α_K≈ 137.51. The deviation from the fine structure constant is Δ α/α= 3× 10^-3 -- .3 per cent. For n=53 one obtains 1/α_K= 134.96 with error of 1.5 per cent. For n=55 one obtains 1/α_K= 150.06 with error of 2.2 per cent. Is the relatively good prediction could be a mere accident or there is something deeper involved?
   
   

What about Minkowskian regions? It is difficult to say anything definite. For cosmic string like objects the action is non-vanishing but proportional to the area A of the string like object and the conditions would give quantization of the area. The area of geodesic sphere of CP₂ is proportional to π. If the value of g_K is same for Minkowskian and Euclidian regions, g_K²∝ π² implies S_K ∝ A/R²π so that A/R²∝ π² is required.

This approach leads to different algebraic structure of α_K than the earlier arguments.

1. α_K is rational multiple of π so that g_K² is proportional to π². At the level of quantum TGD the theory is completely integrable by the definition of WCW integration(!) and there are no radiative corrections in WCW integration. Hence α_K does not appear in vertices and therefore does not produce any problems in p-adic sectors.
   
   
2. This approach is consistent with the proposed formula relating gravitational constant and p-adic length scale. G/L_p² for p=M₁₂₇ would be rational power of e now and number theoretically universally. A good guess is that G does not depend on p. As found this could be achieved also if the volume of CP₂ type extremal depends on p so that the formula holds for all primes. α_K could also depend on algebraic extension of rationals to guarantee the independence of G on p. Note that preferred p-adic primes correspond to ramified primes of the extension so that extensions are labelled by collections of ramified primes, and the ramimified prime corresponding to gravitonic space-time sheets should appear in the formula for G/L_p².
   
   
3. Also the speculative scenario for coupling constant evolution could remain as such. Could the p-adic coupling constant evolution for the gauge coupling strengths be due to the breaking of number theoretical universality bringing in dependence on p? This would require mapping of p-adic coupling strength to their real counterparts and the variant of canonical identification used is not unique.
   
   
4. A more attractive possibility is that coupling constants are algebraically universal (no dependence on number field). Even the value of α_K, although number theoretically universal, could depend on the algebraic extension of rationals defining the adele. In this case coupling constant evolution would reflect the evolution assignable to the increasing complexity of algebraic extension of rationals. The dependence of coupling constants on p-adic prime would be induced by the fact that so called ramified primes are physically favored and characterize the algebraic extension of rationals used.
   
   
5. One must also remember that the running coupling constants are associated with QFT limit of TGD obtained by lumping the sheets of many-sheeted space-time to single region of Minkowski space. Coupling constant evolution would emerge at this limit. Whether this evolution reflects number theoretical evolution as function of algebraic extension of rationals, is an interesting question.
   
   

See the chapter Coupling Constant Evolution in Quantum TGD and 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.

Could one realize number theoretical universality for functional integral?

Number theoretical vision relies on the notion of number theoretical universality (NTU). In fermionic sector NTU is necessary: one cannot speak about real and p-adic fermions as separate entities and fermionic anti-commutation relations are indeed number theoretically universal.

By supersymmetry NTU should apply also to functional integral over WCW (or its sector defined by given causal diamond CD) involved with the definition of scattering amplitudes. The expression for the integral should make sense in all number fields simultaneously. At first this condition looks horrible but the Kähler structure of WCW and the identification of vacuum functional as exponent of Kähler function, and the unique adelic properties of Neper number e give excellent hopes about NTU and also predict the general forms of the functional integral and of the value spectrum of Kähler action for preferred extremals.

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.

The effects of psychedelics as a key to the understanding of remote mental interactions?

There is a book about psychedelics titled as "Inner paths to outer space: Journies to Alien Worlds through Psychedelics and Other Spiritual Technics" written by Rick Strassman, Slawek Wojtowicz, Luis Eduardo Luna and Ede Frecska (see this). The basic message of the book is that psychedelics might make possible instantaneous remote communications with distant parts of the Universe. The basic objection is that light velocity sets stringent limits on classical communications. Second objection is that the communications require huge amount of energy unless they are precisely targeted. The third objection is that quantum coherence in very long, even astrophysical scales is required. In TGD framework this argument does not apply.

In Zero Energy Ontology (ZEO) communications in both directions of geometric time are possible and kind of time-like zig-zag curves make possible apparent superluminal velocities. Negentropic quantum entanglement provides second manner to share mental images, say sensory information remotely. The proposed model leads to a general idea that the attachment of information molecules such as neurotransmitters and psychedelics to a receptor as a manner to induce a remote connection involving transfer of dark potons signals in both directions of geometric time to arbitrarily long distances. The formation of magnetic flux tube contact is a prerequisite for the connection having interpretation as direct attention or sense of presence. One can see living organisms as systems continually trying to build this kind of connections created by a reconnection of U-shaped flux tubes serving as magnetic tentacles. Dark matter as a hierarchy of phases with arbitrary large value of Planck constants guarantees quantum coherence in arbitrary long scales.

The natural TGD inspired hypothesis about what happens at the level of brain to be discussed in sequel in detail goes as follows.

1. Psychedelics bind to the same receptors as the neurotransmitters with similar aromatic rings (weaker assumption is that neurotransmitters in question possess aromatic rings). This is presumably consistent with the standard explanation of the effect of classical psychedelics as a modification of serotonin uptake. This binding replaces the flux tube connection via neurotransmitter to some part of the personal magnetic body with a connection via psychedelic to some other system, which might be even in outer space. A communication line is created making among other things possible remote sensory experiences.
   

   Magnetic fields extending to arbitrary large distances in Maxwell's theory are replaced with flux tubes in TGD framework. The magnetic bodies of psychedelics would carry very weak magnetic fields and would have very large h_eff - maybe serving as a kind of intelligence quotient.
   
   

2. This would be like replacing the connection to the nearby computer server with a connection to a server at the other side of the globe. This would affect the usual function of transmitter and possibly induce negative side effects. Clearly, TGD inspired hypothesis gives for the psychedelics much more active role than standard hypothesis.
   
   
3. Phychedelics can be classified into two groups depending on whether they contain derivative of amino-acid trp with two aromatic rings or phe with one aromatic ring. Also DNA nucleotide resp. its conjugate have 2 resp. 1 similar aromatic rings. This suggests that the coupling between information molecule and receptor is universal and same as the coupling between the two bases in DNA double strand and consists of hydrogen bonds. This hypothesis is testable since it requires that the trp:s/phe:s of the information molecule can be brought to same positions as phe:s/trp:s in the receptor. If also protein folding relies on this coupling, one might be able to predict the folding to a high degree.
   
   
4. A highly suggestive idea is that molecules with aromatic rings are fundamental conscious entities at the level of molecular biology, and that more complex conscious entities are created from them by reconnection of flux tubes. DNA/RNA sequences and microtubules would be basic examples about this architecture of consciousness. If so, protein folding would be dictated by the formation trp-phe contacts giving rise to larger conscious entities.
   
   

See the chapter Meditation, Mind-Body Medicine and Placebo: TGD point of view of "TGD Based View about Consciousness, Living Matter, and Remote Mental Interactions" or the revised article Psychedelic induced experiences as key to the understanding of the connection between magnetic body and information molecules?.

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

First indications for the breaking of lepton universality due to the higher weak boson generations

Lepton and quark universality of weak interactions is basic tenet of the standard model. Now the first indications for the breaking of this symmetry have been found.

1. Lubos tells that LHCb has released a preprint with title Measurement of the ratio of branching ratios (Bbar₀→ Dbar ^*+ τ ν_τ)/ (Bbar₀→ Dbar^*+ μ ν_μ). The news is that the measured branching ratio is is about 33 per cent instead of 25 percent determined by mass ratios if standard model is correct. The outcome differs by 2.1 standard deviations from the prediction so that it might be a statistical fluke.
   
   
2. There are also indications for second Bbar⁰ anomaly (see this). B mesons have to long and short-lived variants oscillating to their antiparticles and back - this relates to CP breaking. The surprise is that the second B meson - I could not figure out was it short- or long-lived - prefers to decay to eν instead of μnu;.
   
   
3. There are also indications for the breaking of universality (see this) from B⁺ → K⁺e⁺ e^- and B⁺ → K⁺ μ⁺mu;^- decays.
   

In TGD framework my first - and wrong - guess for an explanation was CKM mixing for leptons. TGD predicts that also leptons should suffer CKM mixing induced by the different mixings of topologies of the partonic 2-surfaces assignable to charged and neutral leptons. The experimental result would give valuable information about the values of leptonic CKM matrix. What new this brings is that the decays of W bosons to lepton pairs involve the mixing matrix and CKM matrix whose deviation from unit matrix brings effects anomalous in standard model framework.

The origin of the mixing would be topological - usually it is postulated in completely ad hoc manner for fermion fields. Particles correspond to partonic 2-surfaces- actually several of them but in the case of fermions the standard model quantum numbers can be assigned to one of the partonic surfaces so that its topology becomes especially relevant. The topology of this partonic 2- surface at the end of causal diamond (CD) is characterized by its genus - the number of handles attached to sphere - and by its conformal equivalene class characterized by conformal moduli.

Electron and its muon correspond to spherical topology before mixing, muon and its neutrino to torus before mixing etc. Leptons are modelled assuming conformal invariance meaning that the leptons have wave functions - elementary particle vacuum functionals - in the moduli space of conformal equivalence classes known as Teichmueller space.

Contrary to the naive expection mixing alone does not explain the experimental finding. Taking into account mass corrections, the rates should be same to different charged leptons since neutrinos are not identified. That mixing does not have any implications follows from the unitary of the CKM matrix.

The next trial is based on the prediction of 3 generations of weak bosons suggested by TGD.

1. TGD based explanation of family replication phenomenon in terms of genus-generation correspondence forces to ask whether gauge bosons identifiable as pairs of fermion and antifermion at opposite throats of wormhole contact could have bosonic counterpart for family replication. Dynamical SU(3) assignable to three lowest fermion generations/genera labelled by the genus of partonic 2-surface (wormhole throat) means that fermions are combinatorially SU(3) triplets. Could 2.9 TeV state - if it would exist - correspond to this kind of state in the tensor product of triplet and antitriplet? The mass of the state should depend besides p-adic mass scale also on the structure of SU(3) state so that the mass would be different. This difference should be very small.
   
   
2. Dynamical SU(3) could be broken so that wormhole contacts with different genera for the throats would be more massive than those with the same genera. This would give SU(3) singlet and two neutral states, which are analogs of η′ and η and π⁰ in Gell-Mann's quark model. The masses of the analogs of η and π⁰ and the the analog of η′, which I have identified as standard weak boson would have different masses. But how large is the mass difference?
   
   
3. These 3 states are expected to have identical mass for the same p-adic mass scale, if the mass comes mostly from the analog of hadronic string tension assignable to magnetic flux tube. connecting the two wormhole contacts associates with any elementary particle in TGD framework (this is forced by the condition that the flux tube carrying monopole flux is closed and makes a very flattened square shaped structure with the long sides of the square at different space-time sheets). p-Adic thermodynamics would give a very small contribution genus dependent contribution to mass if p-adic temperature is T=1/2 as one must assume for gauge bosons (T=1 for fermions). Hence 2.95 TeV state for which there are some indications could indeed correspond to second Z generation. W should have
   similar state at 2.5 TeV.
   

The orthogonality of the 3 weak bosons implies that their charge matrices are orthogonal. As a consequence, the higher generations of weak bosons do not have universal couplings to leptons and quarks. The breaking of universality implies a small breaking of universality in weak decays of hadrons due to the presence of virtual M_G,79 boson decaying to lepton pair. These anomalies should be seen both in the weak decays of hadrons producing Lν pairs via the decay of virtual W or its partner W_G,79 and via the decay of virtual Z or its partner Z_g,79 to L⁺ L^-. Also γ_G,79 could be involved.

This could explain the three anomalies associated with the neutral B mesons, which are analogs of neutral K mesons having long- and short-lived variants.

1. The two anomalies involving W bosons could be understood if some fraction of decays takes place via the decay b→ c+W_G,79 followed by W_G,79→ L+ν. The charge matrix of W_G,79 is not universal and CP breaking is involved. Hence one could have interference effects, which increase the branching fraction to τν or eν relative to μν depending on whether the state is long- or short-lived B meson.
   
   
2. The anomaly in decays producing charged lepton pairs in decayse of B⁺ does not involve
   CP breaking and would be due to the non-universality of Z_G,79 charge matrix.
   

TGD allows also to consider leptoquarks as pairs of leptons and quarks and there is some evidence for them too! I wrote a blog posting about this too (for an article see this). Also indications for M₈₉ and M_G,79 hadron physics with scaled up mass scales are accumulating and QCD is shifting to the verge of revolution (see this).

It seems that TGD is really there and nothing can prevent it showing up. I predict that next decades in physics will be a New Golden Age of both experimental and theoretical physics. I am eagerly and impatiently waiting that theoretical colleagues finally wake up from their 40 year long sleep and CERN will again be full of working physicists also during weekends (see this);-).

See the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis".

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

Indication for a scaled up variant of Z boson

Both Tommaso Dorigo and Lubos Motl tell about a spectacular 2.9 TeV di-electron event not observed in previous LHC runs. Single event of this kind is of course most probably just a fluctuation but human mind is such that it tries to see something deeper in it - even if practically all trials of this kind are chasing of mirages.

Since the decay is leptonic, the typical question is whether the dreamed for state could be an exotic Z boson. This is also the reaction in TGD framework. The first question to ask is whether weak bosons assignable to Mersenne prime M₈₉ have scaled up copies assignable to Gaussian Mersenne M₇₉. The scaling factor for mass would be 2^(89-89)/2= 32. When applied to Z mass equal to about .09 TeV one obtains 2.88 TeV, not far from 2.9 TeV. Eureka!? Looks like a direct scaled up version of Z!? W should have similar variant around 2.6 TeV.

TGD indeed predicts exotic weak bosons and also gluons. TGD based explanation of family replication phenomenon in terms of genus-generation correspondence forces to ask whether gauge bosons identifiable as pairs of fermion and antifermion at opposite throats of wormhole contact could have bosonic counterpart for family replication. Dynamical SU(3) assignable to three lowest fermion generations/genera labelled by the genus of partonic 2-surface (wormhole throat) means that fermions are combinatorially SU(3) triplets. Could 2.9 TeV state - if it would exist - correspond to this kind of state in the tensor product of triplet and antitriplet? The mass of the state should depend besides p-adic mass scale also on the structure of SU(3) state so that the mass would be different. This difference should be very small.

Dynamical SU(3) could be broken so that wormhole contacts with different genera for the throats would be more massive than those with the same genera. This would give SU(3) singlet and two neutral states, which are analogs of η′ and η and π⁰ in Gell-Mann's quark model. The masses of the analogs of η and π⁰ and the the analog of η′, which I have identified as standard weak boson would have different masses. But how large is the mass difference?

These 3 states are expected top have identical mass for the same p-adic mass scale, if the mass comes mostly from the analog of hadronic string tension assignable to magnetic flux tube. connecting the two wormhole contacts associates with any elementary particle in TGD framework (this is forced by the condition that the flux tube carrying monopole flux is closed and makes a very flattened square shaped structure with the long sides of the square at different space-time sheets). p-Adic thermodynamics would give a very small contribution genus dependent contribution to mass if p-adic temperature is T=1/2 as one must assume for gauge bosons (T=1 for fermions). Hence 2.95 TeV state could indeed correspond to this kind of state.

Can one imagine any pattern for the Mersennes and Gaussian Mersennes involved? Charged leptons correspond to electron (M₁₂₇), muon (M_G,113) and tau (M₁₀₇): Mersenne- Gaussian Mersenne-Mersenne. Does one have similar pattern for gauge bosons too: M₈₉- M_G,79 - M₆₁?

Recall that Lubos reported a dijet at 5.2 TeV: see the earlier posting. Dijet structure suggests some meson. One can imagine several candidates but no perfect fit if one assumes M₈₉ meson and one applies naive scaling. For instance, if kaon mass is scaled by factor 2¹⁰ rather than 512 - just like the mass of pion to get mass of the proposed M₈₉ pion candidate, one obtains 4.9 TeV. Naive scaling of 940 MeV mass of nucleon by 512 would predict that M₈₉ has mass of 4.8 TeV.

See the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis".

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

Evidence of ancient life discovered in mantle rocks deep below the seafloor

Physicalist who has learned his lessons sees life, evolution, generation of genetic code, etc.. as random thermal fluctuations. Empirical facts suggests that the situation is just the opposite. The emergence of life seems to be unavoidable but water seems to be a prerequisite for it. Now researchers have found evidence for ancient life in deep mantle rocks for about 125 million years ago. The emergence of life in mantle is believed to involve interaction of rocks with hydrothermal water originating from seawater and circulating in mantle (see the illustration).

A serious objection against the successful Urey-Miller experiments as a guideline to how prebiotic life emerged is that the atmosphere was not at that time reducing (reducing means that there are atoms able to donate electrons, oxygen does just the reverse).

This objection could serve as a motivation for assuming that prebiotic life evolved in mantle. For detailed vision about underground prebiology see the article More Precise TGD Based View about Quantum Biology and Prebiotic Evolution. This model predicts that Cambrian Explosion lasting for 20-25 million years was associated with a sudden expansion of Earth radius by a factor 2 about 542 million years ago.

Expanding Earth hypothesis would be reduced in TGD framework to the replacement of continuous cosmic expansion for astrophysical objects with a sequence of short expanding periods followed by long non-expanding periods in accordance with the finding that astrophysical objects do not participate in cosmic expansion (see this). This sudden expansion would have led to a burst of underground oceans to the surface of Earth and generated the oceans as we know them now. This prediction is consistent with the assumption that the hydrothermal water explaining the above described finding originated from seawater.

A killer prediction is that underground life would have developed photosynthesis, and the lifeforms would have been rather highly evolved as they burst on the surface of Earth. How this was possible is one of the questions for which answer is proposed in the article More Precise TGD Based View about Quantum Biology and Prebiotic Evolution. The new physics predicted by TGD - in particular hierarchy of Planck constants identified in terms of dark matter - is an essential element of the model.

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

Ontology-Epistemology duality?

Theorist suffering from a tendency to philosophize sooner or later encouters the strange self-referential question "Does my theory about Universe represent also itself as an aspect of the Universe?". For a dualist theory and reality are of course two different things. But are they? Could one make sense of the statement that theory is the reality, which it describes? Or more or less equivalently: epistemology is self-dual to ontology. This would be very nice, theory would not be something outside the reality. This must also relate closely to the question about observer in physics: in the recent quantum measurement theory observer is outsider affecting reality by quantum measuring it but is not described by the quantum theory.

TGD inspired theory of consciousness generalizes quantum measurement theory to a theory of consciousness and brings physicist part of the physical system. Indeed, the new view about state function reduction inspired by Zero Energy Ontology allows to identify "self" as a quantum physical entity and makes several testable killer predictions. In ZEO zero energy states are pairs of positive and negative energy states at the opposite light-like boundaries of CD. Self is identified as as a sequence of state function reductions at given boundary of CD - the members of state pairs at this passive boundary are not changed and the passive boundary itself remains unaffected: obviously this corresponds to Zeno effect.

What is new that the members of state pairs at opposite - active - boundary are changed and the active boundary receides from the passive boundary reduction by reduction so that the size of CD increases. This gives rise to the experienced arrow of geometric time identified as the proper time distance between the tips of CD. The first reduction to the opposite boundary is forced by Negentropy Maximization Principle to eventually occur, and means "death" of self and re-incarnation at the opposite boundary. Time reversal of the original self is generated and geometric time begins to flow in opposite direction.

This suggests that one could indeed see also theory as something not outside the physical world understood in sufficiently general sense.

What do I mean with theory? Can I imbed it to my tri-partistic ontology with three forms of existence: space-time surfaces as counterparts of classical states; quantum states as mathematical objects in ZEO ; quantum jumps as of building bricks of conscious existence giving rise to moments of consciousness and integrating to selves. This trinity is analogous to shape-matter-mind trinity. Let us call this holy trinity just A-B-C to reduce the amount of typing.

I want the equation Theory= Reality. There would be no separate reality behind theory. What would I mean with this statement?

The first attempt to give content to this equation is as equation Theory= quantum state as a mathematical object. Theory would be something restricted to the compartment B in A-B-C. Quantum state as quantum superposition of space-time surfaces ( implied by by holography implied General Coordinate Invariance) would be theory about reality, but there would be no distinct "physical reality" behind it. As far as conscious experiences are considered, this is enough since conscious experience is in the quantum jump between these mathematical objects.

One can however develop objections.

1. Quantum state in ZEO is counterpart of only one possible quantal time evolution. The theory is therefore very restricted and not enough in quantum Universe in which quantum jumps re-create this reality again and again. A real theory must be able to describe counterparts of all possible time evolutions: the collection of these evolutions should define kind of unified theory. The space of WCW spinor field would be the next trial for a theory and quantum jumps between different evolutions - points of WCW by holography - make it possible to gather conscious information about this landscape.
   
   
2. Theories involve also self-referentiality: statements about statements. Boolean algebra of set defining exponent set is the basic example and corresponds to binary valued from the set. Second quantization is what gives rise to a mathematical structure analogous to statements about statements. Many-fermion Fock states have the structure of quantum Boolean algebra.
   

   But this is not enough. Theorists make also statements about statements. In particular, very strong statetements about theories of other theorists. This can generate entire hierarchy of highly emotional statements about statements about... known as scientific debate. This suggests that one should allow iterated second quantization emerging from the notion of infinite primes obtained by a repeated second quantization of arithmetic quantum field theory with supersymmetry by starting from boson and fermion states labeled by finite primes.
   

   In a given quantization one obtains the analogs of both Fock states and even bound states purely number theoretically, and one can repeat this procedure again and again. This hierarchical process corresponds at the level of Boolean algebra formation of statements about statements about... It can be seen also as a hierarchy of logics with order labeled by non-negative integer n. Theories about theories about.... This hierarchy would have many-sheeted space-time as a space-time correlate with the hierarchy of quantizations assigned with the hierarchy of sheets.
   
   

3. But can "theory" really reside only inside compartment B? Theory should contain also the mental images of theoreticians and documentations about these. The documentations are represented in term of classical space-time as a huge generalization of written language - this forces to include compartment A. Also subselves defining mental images of theoreticians and thus entire self hierarchy must be there: therefore also compartment C is needed.
   

   Our equation would become Epistemelogy= Ontology in 3-partistic sense. Theory about what can be known would be equivalent to the theory about what can exist. This duality is self-duality rather than duality: the latter identification bothered me originally since the nex step would be to construct theory for theory and reader can guess the rest. Notice that this identification is not the physicalist's view saying that consciousness is an epiphenomenon since the ontology is monistic.
   
   

Consider now possible objections.

1. Theories are never complete: they have all kinds of failures. How can reality=theory be incomplete? How can it have failures?
   This is possible: the incompleteness is in conscious experience about theory, not theory. For some reason theorists have a strong tendency to erratically call it the theory. In tripartistic view about theory, incompleteness of the theory would be located at sector C. Conscious experience contains limited amount of information due to the presence of finite measurement resolution and cognitive resolution.
   

   Finite resolution is necessary in order to avoid drowning into a sea of irrelevant information. Finite resolution leads to an ordering of bits (more generally pinary digits) by 2-adic (p-adic) norm. The realization of the finite measurement resolution is in terms of quantum criticality involving hierarchy of Planck constants and hierarchy of inclusions of hyper-finite factors to which one can assign a hierarchy of dynamical symmetry groups represented physically. Therefore finite measurement resolution is actually something very useful - many beautiful things follow just by being sloppy (but only with the non-significant bits!).
   

   What Ontology=Epistemology implies that quantum states themselves provide a representation for the finite measurement resolution. It is not something characterizing only the measurement but also the target of measurement. This is very radical change of view point. This is realized quite concretely in the representation of quantum states in terms of partonic two-surfaces and strings connecting them. The large the number of partonic 2-surfaces and the number of strings connecting them, the better the measurement resolution.
   
   

2. There is also an objection relating to self-referentiality. Quantum states provide a representation/theory about itself, are their own mirror images. Doesn't this lead to a kind of self-referential loop and infinite regression? If self is conscious about being conscious about something, one ends up to a similar infinite regression.
   

   The resolution of the problem is that one self becomes conscious about contents consciousness for previous moment of consciousness. The infinite regress is replaced with endless evolution. Zero energy states become more and more complex as the information about previous moments of consciousness is represented quantum mechanically and classically. By NMP the universe is generating negentropic entanglement giving rise to kind of Akashic records and negentropy resources are increasing. Biological evolution and evolution of sciences are not just random thermodynamical fluctuations but coded to the basic laws of quantum physics and consciousness.
   
   

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

Sharpening of Hawking's argument

I already told about the latest argument of Hawking to solve information paradox associated with black holes (see this and this).

There is now a popular article explaining the intuitive picture behind Hawking's proposal. The blackhole horizon would involve tangential flow of light and particles of the infalling matter would induce supertranslations on the pattern of this light thus coding information about their properties to this light. After that this light would be radiated away as analog of Hawking radiation and carry out this information.

The objection would be that in GRT horizon is no way special - it is just a coordinate singularity. Curvature tensor does not diverge either and Einstein tensor and Ricci scalar vanish. This argument has been used in the firewall debates to claim that nothing special should occur as horizon is traversed. Why light would rotate around it? No reason for this!

The answer in TGD would be obvious: horizon is replaced for TGD analog of blackhole with a light-like 3-surface at which the induced metric becomes Euclidian. Horizon becomes analogous to light front carrying not only photons but all kinds of elementary particles. Particles do not fall inside this surface but remain at it!

The objection now is that photons of light front should propagate in direction normal to it, not parallel. The point is however that this light-like 3-surface is the surface at which induced 4-metric becomes degenerate: hence massless particles can live on it.

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

TGD view about black holes and Hawking radiation: part II

In the second part of posting I discuss TGD view about blackholes and Hawking radiation. There are several new elements involved but concerning black holes the most relevant new element is the assignment of Euclidian space-time regions as lines of generalized Feynman diagrams implying that also blackhole interiors correspond to this kind of regions. Negentropy Maximization Principle is also an important element and predicts that number theoretically defined black hole negentropy can only increase. The real surprise was that the temperature of the variant of Hawking radiation at the flux tubes of proton Sun system is room temperature! Could TGD variant of Hawking radiation be a key player in quantum biology?

The basic ideas of TGD relevant for blackhole concept

My own basic strategy is to not assume anything not necessitated by experiment or not implied by general theoretical assumptions - these of course represent the subjective element. The basic assumptions/predictions of TGD relevant for the recent discussion are following.

1. Space-times are 4-surfaces in H=M⁴× CP₂ and ordinary space-time is replaced with many-sheeted space-time. This solves what I call energy problem of GRT by lifting gravitationally broken Poincare invariance to an exact symmetry at the level of imbedding space H.
   

   GRT type description is an approximation obtained by lumping together the space-time sheets to single region of M⁴, with various fields as sums of induced fields at space-time surface geometrized in terms of geometry of H.
   

   Space-time surface has both Minkowskian and Euclidian regions. Euclidian regions are identified in terms of what I call generalized Feynman/twistor diagrams. The 3-D boundaries between Euclidian and Minkowskina regions have degenerate induced 4-metric and I call them light-like orbits of partonic 2-surfaces or light-like wormhole throats analogous to blackhole horizons and actually replacing them. The interiors of blackholes are replaced with the Euclidian regions and every physical system is characterized by this kind of region.
   

   Euclidian regions are identified as slightly deformed pieces of CP₂ connecting two Minkowskian space-time regions. Partonic 2-surfaces defining their boundaries are connected to each other by magnetic flux tubes carrying monopole flux.
   

   Wormhole contacts connect two Minkowskian space-time sheets already at elementary particle level, and appear in pairs by the conservation of the monopole flux. Flux tube can be visualized as a highly flattened square traversing along and between the space-time sheets involved. Flux tubes are accompanied by fermionic strings carrying fermion number. Fermionic strings give rise to string world sheets carrying vanishing induced em charged weak fields (otherwise em charge would not be well-defined for spinor modes). String theory in space-time surface becomes part of TGD. Fermions at the ends of strings can get entangled and entanglement can carry information.
   
   

2. Strong form of General Coordinate Invariance (GCI) states that light-like orbits of partonic 2-surfaces on one hand and space-like 3-surfaces at the ends of causal diamonds on the other hand provide equivalent descriptions of physics. The outcome is that partonic 2-surfaces and string world sheets at the ends of CD can be regarded as basic dynamical objects.
   

   Strong form of holography states the correspondence between quantum description based on these 2-surfaces and 4-D classical space-time description, and generalizes AdS/CFT correspondence. Conformal invariance is extended to the huge super-symplectic symmetry algebra acting as isometries of WCW and having conformal structure. This explains why 10-D space-time can be replaced with ordinary space-time and 4-D Minkowski space can be replaced with partonic 2-surfaces and string world sheets. This holography looks very much like the one we are accustomed with!
   
   

3. Quantum criticality of TGD Universe fixing the value(s) of the only coupling strength of TGD (Kähler coupling strength) as analog of critical temperature. Quantum criticality is realized in terms of infinite hierarchy of sub-algebras of super-symplectic algebra actings as isometries of WCW, the "world of classical worlds" consisting of 3-surfaces or by holography preferred extremals associated with them.
   

   Given sub-algebra is isomorphic to the entire algebra and its conformal weights are n≥ 1-multiples of those for the entire algebra. This algebra acts as conformal gauge transformations whereas the generators with conformal weights m<n act as dynamical symmetries defining an infinite hierarchy of simply laced Lie groups with rank n-1 acting as dynamical symmetry groups defined by Mac-Kay correspondence so that the number of degrees of freedom becomes finite. This relates very closely to the inclusions of hyper-finite factors - WCW spinors provide a canonical representation for them.
   

   This hierarchy corresponds to a hierarchy of effective Planck constants h_eff=n× h defining an infinite number of phases identified as dark matter. For these phases Compton length and time are scale up by n so that they give rise to macroscopic quantum phases. Super-conductivity is one example of this kind of phase - charge carriers could be dark variants of ordinary electrons. Dark matter appears at quantum criticality and this serves as an experimental manner to produce dark matter. In living matter dark matter identified in this manner would play a central role. Magnetic bodies carrying dark matter at their flux tubes would control ordinary matter and carry information.
   
   

4. I started the work with the hierarchy of Planck constants from the proposal of Nottale stating that it makes sense to talk about gravitational Planck constant h_gr=GMm/v₀, v₀/c≤ 1 (the interpretation of symbols should be obvious). Nottale found that the orbits of inner and outer planets could be modelled reasonably well by applying Bohr quantization to planetary orbits with tge value of velocity parameter differing by a factor 1/5. In TGD framework h_gr would be associated with magnetic flux tubes mediating gravitational interaction between Sun with mass M and planet or any object, say elementary particle, with mass m. The matter at the flux tubes would be dark as also gravitons involved. The Compton length of particle would be given by GM/v₀ and would not depend on the mass of particle at all.
   

   The identification h_gr=h_eff is an additional hypothesis motivated by quantum biology, in particular the identification of biophotons as decay products of dark photons satisfying this condition. As a matter fact, one can talk also about h_em assignable to electromagnetic interactions: its values are much lower. The hypothesis is that when the perturbative expansion for two particle system does not converge anymore, a phase transition increasing the value of the Planck constant occurs and guarantees that coupling strength proportional to 1/h_eff increases. This is one possible interpretation for quantum criticality. TGD provides a detailed geometric interpretation for the space-time correlates of quantum criticality.
   

   Macroscopic gravitational bound states not possible in TGD without the assumption that effective string tension associated with fermionic strings and dictated by strong form of holography is proportional to 1/h_eff². The bound states would have size scale of order Planck length since for longer systems string energy would be huge. h_eff=h_gr makes astroscopic quantum coherence unavoidable. Ordinary matter is condensed around dark matter. The counterparts of black holes would be systems consisting of only dark matter.
   
   

5. Zero energy ontology (ZEO) is central element of TGD. There are many motivations for it. For instance, Poincare invariance in standard sense cannot make sense since in standard cosmology energy is not conserved. The interpretation is that various conserved quantum numbers are length scale dependent notions.
   

   Physical states are zero energy states with positive and negative energy parts assigned to ends of space-time surfaces at the light-like boundaries of causal diamonds (CDs). CD is defined as Cartesian products of CP₂ with the intersection of future and past directed lightcones of M⁴. CDs form a fractal length scale hierarchy. CD defines the region about which single conscious entity can have conscious information, kind of 4-D perceptive field. There is a hierarchy of WCWs associated with CDs. Consciously experienced physics is always in the scale of given CD.
   

   Zero energy states identified as formally purely classical WCW spinor fields replace positive energy states and are analogous to pairs of initial and final, states and the crossing symmetry of quantum field theories gives the mathematical motivation for their introduction.
   
   

6. Quantum measurement theory can be seen as a theory of consciousness in ZEO. Conscious observer or self as a conscious entity becomes part of physics. ZEO gives up the assumption about unique universe of classical physics and restricts it to the perceptive field defined by CD.
   

   In each quantum jump a re-creation of Universe occurs. Subjective experience time corresponds to state function reductions at fixed, passive bounary of CD leaving it invariant as well as state at it. The state at the opposite, active boundary changes and also its position changes so that CD increases state function by state function reduction doing nothing to the passive boundary. This gives rise to the experienced flow of geometric time since the distance between the tips of CD increases and the size of space-time surfaces in the quantum superposition increases. This sequence of state function reductions is counterpart for the unitary time evolution in ordinary quantum theory.
   

   Self "dies" as the first state function reduction to the opposite boundary of CD meaning re-incarnation of self at it and a reversal of the arrow of geometric time occurs: CD size increases now in opposite time direction as the opposite boundary of CD recedes to the geometric past reduction by reduction.
   

   Negentropy Maximization Principle (NMP) defines the variational principle of state function reduction. Density matrix of the subsystem is the universal observable and the state function reduction leads to its eigenspaces. Eigenspaces, not only eigenstates as usually.
   

   Number theoretic entropy makes sense for the algebraic extensions of rationals and can be negative unlike ordinary entanglement entropy. NMP can therefore lead to a generation of NE if the entanglement correspond to a unitary entanglement matrix so that the density matrix of the final state is higher-D unit matrix. Another possibility is that entanglement matrix is algebraic but that its diagonalization in the algebraic extension of rationals used is not possible. This is expected to reduce the rate for the reduction since a phase transition increasing the size of extension is needed.
   

   The weak form of NMP does not demand that the negentropy gain is maximum: this allow the conscious entity responsible for reduction to decide whether to increase maximally NE resources of the Universe or not. It can also allow larger NE increase than otherwise. This freedom brings the quantum correlates of ethics, moral, and good and evil. p-Adic length scale hypothesis and the existence of preferred p-adic primes follow from weak form of NMP and one ends up naturally to adelic physics.
   
   

The analogs of blackholes in TGD

Could blackholes have any analog in TGD? What about Hawking radiation? The following speculations are inspired by the above general vision.

1. Ordinary blackhole solutions are not appropriate in TGD. Interior space-time sheet of any physical object is replaced with an Euclidian space-time region. Also that of blackhole by perturbation argument based on the observation that if one requires that the radial component of blackhole metric is finite, the horizon becomes light-like 3-surface analogous to the light-like orbit of partonic 2-surface and the metric in the interior becomes Euclidian.
   
   
2. The analog of blackhole can be seen as a limiting case for ordinary astrophysical object, which already has blackhole like properties due to the presence of h_eff=n× h dark matter particles, which cannot appear in the same vertices with visible manner. Ideal analog of blackhole consist of dark matter only, and is assumed to satisfy the h_gr=h_eff already discussed. It corresponds to region with a radius equal to Compton length for arbitrary particle R=GM/v₀=r_S/2v₀, where r_S is Schwartschild radius. Macroscopic quantum phase is in question since the Compton radius of particle does not depend on its mass. Blackhole limit would correspond to v₀/c→ 1 and dark matter dominance. This would give R=r_S/2. Naive expectation would be R=r_S (maybe factor of two is missing somewhere: blame me!).
   
   
3. NMP implies that information cannot be lost in the formation of blackhole like state but tends to increase. Matter becomes totally dark and the NE with the partonic surfaces of external world is preserved or increases. The ingoing matter does not fall to a mass point but resides at the partonic 2-surface which can have arbitrarily large surface. It can have also wormholes connecting different regions of a spherical surface and in this manner increase its genus. NMP, negentropy , negentropic entanglement between h_eff=n× h dark matter systems would become the basic notions instead of second law and entropy.
   
   
   
4. There is now a popular article explaining the intuitive picture behind Hawking's proposal. The blackhole horizon would involve tangential flow of light and particles of the infalling matter would induce supertranslations on the pattern of this light thus coding information about their properties to this light. After that this light would be radiated away as analog of Hawking radiation and carry out this information.
   

   The objection would be that in GRT horizon is no way special - it is just a coordinate singularity. Curvature tensor
   does not diverge either and Einstein tensor and Ricci scalar vanish. This argument has been used in the firewall debates to claim that nothing special should occur as horizon is traversed. So: why light would rotate around it? No reason for this! The answer in TGD would be obvious: horizon is replaced for TGD analog of blackhole with a light-like 3-surface at which the induced metric becomes Euclidian. Horizon becomes analogous to light front carrying not only photons but all kinds of elementary particles. Particles do not fall inside this surface but remain at it!
   
   

5. The replacement of second law with NMP leads to ask whether a generalization of blackhole thermodynamics does make sense in TGD Universe. Since blackhole thermodynamics characterizes Hawking radiation, the generalization could make sense at least if there exist analog for the Hawking radiation. Note that also geometric variant of second law makes sense.
   

   Could the analog of Hawking radiation be generated in the first state function reduction to the opposite boundary, and be perhaps be assigned with the sudden increase of radius of the partonic 2-surface defining the horizon? Could this burst of energy release the energy compensating the generation of gravitational binding energy? This burst would however have totally different interpretation: even gamma ray bursts from quasars could be considered as candidates for it and temperature would be totally different from the extremely low general relativistic Hawking temperature of order
   

   T_GR=[hbar/8π GM ] ,
   

   which corresponds to an energy assignable to wavelength equal to 4π times Schwartschild radius. For Sun with Schwartschild radius r_S=2GM=3 km one has T_GR= 3.2× 10^-11 eV.
   

One can of course have fun with formulas to see whether the generalizaton of blackhole thermodynamics assuming the replacement h→ h_gr could make sense physically. Also the replacement r_S→ R, where R is the real radius of the star will be made.

1. Blackhole temperature can be formally identified as surface gravity
   

   T=(h_gr/hbar) × [GM/2π R²] = [h_gr/h] × [r_S²/R²]× T_GR = 1/[4π v₀] [r_S²/R²] .
   

   For Sun with radius R= 6.96× 10⁵ km one has T/m= 3.2× 10^-11 giving T= 3× 10^-2 eV for proton. This is by 9 orders higher than ordinary Hawking temperature. Amazingly, this temperature equals to room temperature! Is this a mere accident? If one takes seriously TGD inspired quantum biology in which quantum gravity plays a key role (see this) this does not seem to be the case. Note that for electron the temperature would correspond to energy 3/2× 10^-5 eV which corresponds to 4.5 GHz frequency for ordinary Planck constant.
   

   It must be however made clear that the value of v₀ for dark matter could differ from that deduced assuming that entire gravitational mass is dark. For M→ M_D= kM and v₀→ k^1/2v₀ the orbital radii remain unchanged but the velocity of dark matter object at the orbit scales to k^1/2v₀. This kind of scaling is suggested by the fact that the value of h_gr seems to be too large as compared by the identification of biophotons as decay results of dark photons with h_eff=h_gr (some arguments suggest the value k≈ 2× 10^-4).
   

   Note that for the radius R=[r_S/2v₀π] the thermal energy exceeds the rest mass of the particle. For neutron stars this limit might be achieved.
   
   
   

2. Blackhole entropy
   

   S_GR= [A/4 hbar G]= 4π GM²/hbar=4π [M²/M_Pl²]
   

   would be replaced with the negentropy for dark matter making sense also for systems containing both dark and ordinary matter. The negentropy N(m) associated with a flux tube of given type would be a fraction h/h_gr from the total area of the horizon using Planck area as a unit:
   

   N(m)=[h/h_gr] × [A/4hbar G]= [h/h_gr] × [R²/r_S²] ×S_GR = v₀×[M/m]× [R²/r_S²] .
   

   The dependence on m makes sense since a given flux tube type characterized by mass m determining the corresponding value of h_gr has its own negentropy and the total negentropy is the sum over the particle species. The negentropy of Sun is numerically much smaller that corresponding blackhole entropy.
   
   

3. Horizon area is proportional to (GM/v₀)²∝ h_eff² and should increase in discrete jumps by scalings of integer and be proportional to n².
   
   

How does the analog of blackhole evolve in time? The evolution consists of sequences of repeated state function reductions at the passive boundary of CD followed by the first reduction to the opposite boundary of CD followed by a similar sequence. These sequences are analogs of unitary time evolutions. This defines the analog of blackhole state as a repeatedly re-incarnating conscious entity and having CD, whose size increases gradually. During given sequence of state function reductions the passive boundary has constant size. About active boundary one cannot say this since it corresponds to a superposition of quantum states.

The reduction sequences consist of life cycles at fixed boundary and the size of blackhole like state as of any state is expected to increase in discrete steps if it participates to cosmic expansion in average sense. This requires that the mass of blackhole like object gradually increases. The interpretation is that ordinary matter gradually transforms to dark matter and increases dark mass M= R/G.

Cosmic expansion is not observed for the sizes of individual astrophysical objects, which only co-move. The solution of the paradox is that they suddenly increase their size in state function reductions. This hypothesis allows to realize Expanding Earth hypothesis in TGD framework (see this). Number theoretically preferred scalings of blackhole radius come as powers of 2 and this would be the scaling associated with Expanding Earth hypothesis.

See the chapter Criticality and dark matter" or the article TGD view about black holes and Hawking radiation.

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