What could 4-fermion twistor amplitudes look like?

4-fermion twistor amplitudes are basic building bricks of twistor amplitudes in TGD framework. What can one conclude about them on basis of N=4 amplitudes? Instead of 3-vertices as in SYM, one has 4-fermion vertices as fundamental vertices and the challenge is to guess their general form. The basis idea is that N=4 SYM amplitudes could give as special case the n-fermion amplitudes and their supersymmetric generalizations

1. Attempt to understand the physical picture

One must try to identify the physical picture first.

1. Elementary particles consist of pairs of wormhole contacts connecting two space-time sheets. The throats are connected by magnetic fluxes running in opposite directions so that a closed monopole flux loop is in question. One can assign to the ordinary fermions open string world sheets whose boundary belong to the light-like 3-surfaces assignable to these two wormhole contacts. The question is whether one can restrict the consideration to single wormhole contact or should one describe the situation as dynamics of the open string world sheets so that basic unit would involve two wormhole contacts possibly both carrying fermion number at their throats.
   

   Elementary particles are bound states of massless fermions assignable to wormhole throats. Virtual fermions are massless on mass shell particles with unphysical helicity. Propagator for wormhole contact as bound state - or rather entire elementary particle would be from p-adic thermodynamics expressible in terms of Virasoro scaling generator as 1/L₀ in the case of boson. Super-symmetrization suggests that one should replace L₀ by G₀ in the wormhole contact but this leads to problems if G₀ carries fermion number. This might be a good enough motivation for the twistorial description of the dynamics reducing it to fermion propagator along the light-like orbit of wormhole throat. Super Virasoro algebra would emerged only for the bound states of massless fermions.
   
   

2. Suppose that the construction of four-fermion vertices reduces to the level of single wormhole contact. 4-fermion vertex involves wormhole contact giving rise to something analogous to a boson exchange along wormhole contact. This kind of exchange might allow interpretation in terms of Euclidian correlation function assigned to a deformation of CP₂ type vacuum extremal with Euclidian signature.
   

   A good guess for the interaction terms between fermions at opposite wormhole contacts is as current-current interaction j^α (x) j_α(y), where x and y parametrize points of opposite throats. The current is defined in terms of induced gamma matrices as ‾ΨΓ^αΨ and one functionally integrates over the deformations of the wormhole contact assumed to correspond in vacuum configuration to CP₂ type vacuum extremal metrically equivalent with CP₂ itself. One can expand the induced gamma matrix as a sum of CP₂ gamma matrix and contribution from M⁴ deformation Γ_α = Γ_α^CP2 + ∂_α m^kγ_k. The transversal part of M⁴ coordinates orthogonal to M²⊂ M⁴ defines the dynamical part of m^k so that one obtains strong analogy with string models and gauge theories.
   

The deformation Δ m^k can be expanded in terms of CP₂ complex coordinates so that the modes have well defined color hyper-charge and isospin. There are two options to be considered.

1. One could use CP₂ spherical harmonics defined as eigenstates of CP₂ scalar Laplacian D². The scale of eigenvalues would be 1/R², where R is CP₂ radius of order 10⁴ Planck lengths. The spherical harmonics are in general not holomorphic in CP₂ complex coordinates ξ_i, i=1,2. The use of CP₂ spherical harmonics is however not necessary since wormhole throats mean that wormhole contact involves only a part of CP₂ is involved.
   
   
2. Conformal invariance suggests the use of holomorphic functions ξ₁^mξ₂ⁿ as analogs of zⁿ in the expansion. This would also be the Euclidian analog for the appearance of massless spinors in internal lines. Holomorphic functions are annihilated by the ordinary scalar Laplacian. For conformal Laplacian they correspond to the same eigenvalue given by the constant curvature scalar R of CP₂. This might have interpretation as a spontaneous breaking of conformal invariance.
   

   The holomorphic basis zⁿ reduces to phase factors exp(inφ) at unit circle and can be orthogonalized. Holomorphic harmonics reduce to phase factors exp(imφ₁)exp(inφ₂) and torus defined by putting the moduli of ξ_i constant and can thus be orthogonalized. Inner product for the harmonics is however defined at partonic 2-surface. Since partonic 2-surfaces represent Kähler magnetic monopoles they have 2-dimensional CP₂ projection. The phases exp(imφ_i) could be functionally independent and a reduction of inner product to integral over circle and reduction of phase factors to powers exp(inφ) could take place and give rise to the analog of ordinary conformal invariance at partonic 2-surface. This does not mean that separate conservation of I₃ and Y is broken for propagator.
   
   

3. Holomorphic harmonics are very attractive but the problem is that they are annihilated by the ordinary Laplacian. Besides ordinary Laplacian one can however consider
   (Conformal Laplacian) defined as
   

   D_c²= -6D²+R
   

   and relating the curvatures of two conformally scaled metrics R denotes now curvature scalar). The overall scale factor and also its sign is just a convention. This Laplacian has the same eigenvalue for all conformal harmonics. The interpretation would be in terms of a breaking of conformal invariance due to CP₂ geometry: this could also relate closely to the necessity to assume tachyonic ground state in the p-adic mass calculations.
   

   The breaking of conformal invariance is necessary in order to avoid infrared divergences. The replacement of M⁴ massless propagators with massive CP₂ bosonic propagators in 4-fermion vertices brings in the needed breaking of conformal invariance. Conformal invariance is however retained at the level of M⁴ fermion propagators and external lines identified as bound states of massless states.
   

2. How to identify the bosonic correlation functions inside wormhole contacts?

The next challenge is to identify the correlation function for the deformation δ m^k inside wormhole contacts.

Conformal invariance suggests the identification of the analog of propagator as a correlation function fixed by conformal invariance for a system defined by the wormhole contact. The correlation function should depend on the differences ξ_i=ξ_i,1-ξ_i,2 of the complex CP₂ coordinates at the points ξ_i,1) and ξ_i,2 of the opposite throats and transforms in a simple manner under scalings of ξ_i. The simplest expectation is that the correlation function is power r^-n, where r²= [ξ₁|²+|ξ₂|² defines U(2) invariant coordinate distance squared. The correlation function can be expanded as products of conformal harmonics or ordinary harmonics of CP₂ assignable to ξ_i,1 and ξ_i,2 and one expects that the values of Y and I₃ vanish for the terms in the expansions: this just states that Y and I₃ are conserved in the propagation.

Second approach relies on the idea about propagator as the inverse of some kind of Laplacian. The approach is not in conflict with the general conformal approach since the Laplacian could occur in the action defining the conformal field theory. One should try to identify a Laplacian defining the propagator for δ m^k inside Euclidian regions.

1. The propagator defined by the ordinary Laplacian D² has infinite value for all conformal harmonics appearing in the correlation function. This cannot be the case.
   
   
2. If the propagator is defined by the conformal Laplacian D_c² of CP₂ multiplied by some numerical factor it gives fro a given model besides color quantum numbers conserving delta function a constant factor nR² playing the same role as weak coupling strength in the four-fermion theory of weak interactions. Propagator in CP₂ degrees of freedom would give a constant contribution if the total color quantum numbers for vanish for wormhole throat so that one would have four-fermion vertex.
   
   
3. One can consider also a third - perhaps artificial option - motivated for Dirac spinors by the need to generalize Dirac operator to contain only I₃ and Y. Holomorphic partial waves are also eigenstates of a modified Laplacian D²_C defined in terms of Cartan algebra as
   

   D²_C== [aY²+bI₃²]/R² ,
   

   where a and b suitable numerical constants and R denotes the CP₂ radius defined in terms of the length 2π R of CP₂ geodesic circle. The value of a/b is fixed from the condition Tr(Y²)=Tr(I₃²) and spectra of Y and I₃ given by (2/3,-1/3,-1/3) and (0,1/2,-1/2) for triplet representation. This gives a/b= 9/20 so that one has
   

   D²_C= ((9/20) Y²+ I₃²]× a/R² .
   

   In the fermionic case this kind of representation is well motivated since fermionic Dirac operator would be Y^k e^A_kγ_A+I₃^k e^A_kγ_A, where the vierbein projections Y^ke^A_k Y^ke^A_k and I₃^ke^A_k of Killing vectors represent the conserved quantities along geodesic circles and by semiclassical quantization argument should correspond to the quantized values of Y and I₃ as vectors in Lie algebra of SU(3) and thus tangent vectors in the tangent space of CP₂ at the point of geodesic circle along which these quantities are conserved. In the case of S² one would have Killing vector field L_z at equator.
   

Two general remarks are in order.

1. That a theory containing only fermions as fundamental elementary particles would have four-fermion vertex with dimensional coupling as a basic vertex at twistor level, would not be surprising. As a matter of fact, Heisenberg suggested for long time ago a unified theory based on use of only spinors and this kind of interaction vertex. A little book about this theory actually inspired me to consider seriously the fascinating challenge of unification.
   
   
2. A common problem of all these options seems to be that the 4-fermion coupling strength is of order R² - about 10⁸ times gravitational coupling strength and quite too weak if one wants to understand gauge interactions. It turns out however that color partial waves for the deformations of space-time surface propagating in loops can increase R² to the square L_p²= pR² of p-adic length scale. For D2_C assumed to serve as an propagator in an effective action of a conformal field theory one can argue that large renormalization effects from loops increase R² to something of order pR².
   

3. Do color quantum numbers propagate and are they conserved in vertices?

The basic questions are whether one can speak about conservation of color quantum numbers in vertices and their propagation along the internal lines and the closed magnetic flux loops assigned with the elementary particles having size given by p-adic length scale and having wormhole contacts at its ends. p-Adic mass calculations predict that in principle all color partial waves are possible in cm degreees of freedom: this is a description at the level of imbedding space and its natural counterpart at space-time level would be conformal harmonics for induced spinor fields and allowance of all of them in generalized Feynman diagrams.

1. The analog of massless propagation in Euclidian degrees of freedom would correspond naturally to the conservation of Y and I₃ along propagator line and conservation of Y and I₃ at vertices. The sum of fermionic and bosonic color quantum numbers assignable to the color partial waves woul be conserved. For external fermions the color quantum numbers are fixed but fermions in internal lines could move also in color excited states.
   
   
2. One can argue that the correlation function for the M⁴ coordinates for points at the ends of fermionic line do not correlate as functions of CP₂ coordinates since the distance between partonic 2-surface is much longer than CP₂ scale but do so as functions of the string world sheet coordinates as stringy description strongly suggests and that stringy correlation function satisfying conformal invariance gives this correlation. One can however couner argue that for hadrons the color correlations are different in hadronic length scale. This in turn suggests that the correlations are non-trivial for both the wormhole magnetic flux tubes assignable to elementary particles and perhaps also for the internal fermion lines.
   
   
3. I₃ and Y assignable to the exchanged boson should have interpretation as an exchange of quantum numbers between the fermions at upper and lower throat or change of color quantum numbers in the scattering of fermion. The problem is that induced spinors have constant anomalous Y and I₃ in given coordinate patch of CP₂ so that the exchange of these quantum numbers would vanish if upper and lower coordinate patches are identical. Should one expand also the induced spinor fields in Euclidian regions using the harmonics or their holomorphic variants as suggested by conformal invariance?
   

   The color of the induced spinor fields as analog of orbital angular momentum would realized as color of the holomorphic function basis in Euclidian regions. If the fermions in the internal lines cannot carry anomalous color, the sum over exchanges trivializes to include only a constant conformal harmonic. The allowance of color partial waves would conform with the idea that all color partial waves are allowed for quarks and leptons at imbedding space level but define very massive bound states of massless fermions.
   
   

4. The 4-fermion vertex would involve a sum over the exchanges defined by spherical harmonics or - more probably - by their holomorphic analogs. For both the spherical and conformal harmonic option the 4-fermion coupling strength would be of order R², where R is CP₂ length. The coupling would be extremely weak - about 10⁸ times the gravitational coupling strength G if the coupling is of order one. This is definitely a severe problem: one would want something like L_p², where p is p-adic prime assignable to the elementary particle involved.
   

   This problem provides a motivation for why a non-trivial color should propagate in internal lines. This could amplify the coupling strength of order R² to something of order L_p²=pR². In terms of Feynman diagrams the simplest color loops are associated with the closed magnetic flux tubes connecting two elementary wormhole contacts of elementary particle and having length scale given by p-adic length scale L_p. Recall that ν_L (ν_R)^c pair or its conjugate neutralizes the weak isospin of the elementary fermion. The loop diagrams representing exchange of neutrino and the fermion associated with the two wormhole contacts and thus consisting of two fermion lines assignable to "long" strings and two boson lines assignable to "short strings" at wormhole contacts represent the first radiative correction to 4-fermion diagram. They would give sum over color exchanges consistent with the conservation of color quantum numbers at vertices. This sum, which in 4-D QFT gives rise to divergence, could increase the value of four-fermion coupling to something of order L_p²= kpR² and induce a large scaling factor of $D^2_C$.
   
   

5. Why known elementary fermions correspond to color singlets and triplets? p-Adic mass calculations provide one explanation for this: colored excitations are simply too massive. There is however evidence that leptons possess color octet excitations giving rise to light mesonlike states. Could the explanation relate to the observation that color singlet and triplet partial waves are special in the sense that they are apart from the factor 1/(1+r²)^1/2 , r²=∑ |ξ_i|² for color triplet holomorphic functions?
   

4. Why twistorialization in CP₂ degrees of freedom?

A couple of comments about twistorialization in CP₂ degrees of freedom are in order.

1. Both M⁴ and CP₂ twistors could be present for the holomorphic option. M⁴ twistors would characterize fermionic momenta and CP₂ twistors to the quantum numbers assignable to deformations of CP₂ type vacuum extremals. CP₂ twistors would be discretized since I₃ and Y have discrete spectrum and it is not at all clear whether twistorialization is useful now. There is excellent motivation for the integration over the flag-manifold defining the choices of color quantization axes. The point is that the choice of conformal basis with well-defined Y and I₃ breaks overall color symmetry SU(3) to U(2) and an integration over all possible choices restores it.
   
   
2. Four-fermion vertex has a singularity corresponding to the situation in which p₁, p₂ and p₁+p₂ assignable to emitted virtual wormhole throat are collinear and thus all light-like. The amplitude must develop a pole as p₃+p₃= p₁+p₂ becomes massless. These wormhole contacts would behave like virtual boson consisting of almost collinear pair of fermion and anti-fermion at wormhole throats.
   

5. Reduction of scattering amplitudes to subset of N =4 scattering amplitudes

N=4 SUSY provides quantitative guidelines concerning the actual construction of the amplitudes.

1. For single wormhole contact carrying one fermion, one obtains two N=2 SUSY multiplets from fermions by adding to ordinary one-fermion state right-handed neutrino, its conjugate with opposite spin, or their pair. The net spin projections would be 0, 1/2 ,1 with degeneracies (1,2,1) for fermion helicity 1/2 and (0,-1/2, -1) with same degeneracies for fermion helicity -1/2. These N=2 multiplets can be imbedded to the N=4 multiplet containing 2⁴ states with spins (1,1/2,0,-1/2,-1) and degeneracies given by (1, 4, 6, 4, 1). The amplitudes in N=2 case could be special cases of N=4 amplitudes in the same manner as they amplitudes of gauge theories are special cases of those of super-gauge theories. The only difference would be that propagator factors 1/p² appearing in twistorial construction would be replaced by propagators in CP₂ degrees of freedom.
   
   
2. In twistor Grassmannian approach to planar SYM one obtains general formulas for n-particle scattering amplitudes with k positive (or negative helicities) in terms of residue integrals in Grassmann manifold G(n,k). 4-particle scattering amplitudes of TGD, that is 4-fermion scattering amplitudes and their super counterparts would be obtained by restricting to N=2 sub-multiplets of full N=4 SYM. The only non-vanishing amplitudes correspond for n=4 to k=2=n-2 so that they can be regarded as either holomorphic or anti-holomorphic in twistor variables, an apparent paradox understandable in terms of additional symmetry as explained and noticed by Witten. Four-particle scattering amplitude would be obtained by replacing in Feynman graph description the four-momentum in propagator with CP₂ momentum defined by I₃ and Y for the particle like entity exchanged between fermions at opposite wormhole throats. Analogous replacement should work for twistorial diagrams.
   
   
3. In fact, single fermion per wormhole throat implying 4-fermion amplitudes as building blocks of more general amplitudes is only a special case although it is expected to provide excellent approximation in the case of ordinary elementary particles. Twistorial approach could allow the treatment of also n>4-fermion case using subset of twistorial n-particle amplitudes with Euclidian propagator. One cannot assign right-handed neutrino to each fermion separately but only to the elementary particle 3-surface so that the degeneration of states due to SUSY is reduced dramatically. This means strong restrictions on allowed combinations of vertices.
   

Some words of critism is in order.

1. Should one use CP₂ twistors everywhere in the 3-vertices so that only fermionic propagators would remain as remnants of M⁴? This does not look plausible. Should one use include to 3-vertices both M⁴ and CP₂ type twistorial terms? Do CP₂ twistorial terms trivialize as a consequence of quantization of Y and I₃?
   
   
2. Nothing has been said about modified Dirac operator. The assumption has been that it disappears in the functional integration and the outcome is twistor formalism. The above argument however implies functional integration over the deformations of CP₂ type vacuum extremals.
   

For details see the new chapter Some fresh ideas about twistorialization of TGD or the article with the same title.

Addition: Unfortunately, the blog page is not avaible at this moment: the owners of the webhotel lost their interest to hotel business and many people lost their money, homepage, and their data when the website ceased to exist. I lost even more: my lifework disappeared from web since the owners decided to do a really dirty trick: just for fun these psychopaths refuse to give a formal permission to have a homepage in a new physical location with the same domain name (, which of course is my property!). I find it incredible that this kind of situation can even develop. Net ethics does not yet exist.

Addition: The homepage is temporarily at new address obtained from the earlier one by replacing "com" by "fi".

About the SUSY generated by covariantly constant right-handed neutrinos

The interpretation of covariantly constant right-handed neutrinos (briefly ν_R in what follows) in M⁴× CP₂ has been a continual head-ache. Should they be included to the spectrum or not. If not, then one has no fear/hope about space-time SUSY of any kind and has only conformal SUSY. First some general observations.

1. In TGD framework right-handed neutrinos differ from other electroweak charge states of fermions in that the solutions of the modified Dirac equation for them are delocalized at entire 4-D space-time sheets whereas for other electroweak charge states the spinors are localized at string world sheets (see this).
   
   
2. Since right-handed neutrinos are in question so that right-handed neutrino are in 1-1 correspondence with complex 2-component Weyl spinors, which are eigenstates of γ₅ with eigenvalue say +1 (I never remember whether +1 corresponds to right or left handed spinors in standard conventions).
   
   
3. The basic question is whether the fermion number associated with covariantly constant right-handed neutrinos is conserved or conserved only modulo 2. The fact that the right-handed neutrino spinors and their conjugates belong to unitarily equivalent pseudoreal representations of SO(1,3) (by definition unitarily equivalent with its complex conjugate) suggests that generalized Majorana property is true in the sense that the fermion number is conserved only modulo 2. Since ν_R decouples from other fermion states, it seems that lepton number is conserved.
   
   
4. The conservation of the number of right-handed neutrinos in vertices could cause some rather obvious mathematical troubles if the right-handed neutrino oscillator algebras assignable to different incoming fermions are identified at the vertex. This is also suggested by the fact that right-handed neutrinos are delocalized.
   
   
5. Since the ν_R:s are covariantly constant complex conjugation should not affect physics. Therefore the corresponding oscillator operators would not be only hermitian conjugates but hermitian apart from unitary transformation (pseudo-reality). This would imply generalized Majorana property.
   
   
6. A further problem would be to understand how these SUSY candidates are broken. Different p-adic mass scale for particles and super-partners is the obvious and rather elegant solution to the problem but why the addition of right-handed neutrino should increase the p-adic mass scale beyond TeV range?
   

If the ν_R:s are included, the pseudoreal analog of N=1 SUSY assumed in the minimal extensions of standard model or the analog of N=2 or even N=4 SUSY is expected so that SUSY type theory might describe the situation. The following is an attempt to understand what might happen. For an earlier attempt see this.

1. Covariantly constant right-handed neutrinos as limiting cases of massless modes

For the first option covariantly constant right-handed neutrinos are obtained as limiting case for the solutions of massless Dirac equation. One obtains 2 complex spinors satisfying Dirac equation n^kγ_ku=0 for some momentum direction n^k defining quantization axis for spin. Second helicity is unphysical: one has therefore one helicity for neutrino and one for antineutrino.

1. If the oscillator operators for ν_R and its conjugate are hermitian conjugates, which anticommute to zero (limit of anticommutations for massless modes) one obtains the analog of N=2 SUSY.
   

2. If the oscillator operators are hermitian or pseudohermitian, one has pseudoreal analog of N=1 SUSY. Since ν_R decouples from other fermion states, lepton number and baryon number are conserved.
   

Note that in TGD based twistor approach four-fermion vertex is the fundamental vertex and fermions propagate as massless fermions with non-physical helicity in internal lines. This would suggest that if right-handed neutrinos are zero momentum limits, they propagate but give in the residue integral over energy twistor line contribution proportional to p^kγ_k, which is non-vanishing for non-physical helicity in general but vanishes at the limit p^k→ 0. Covariantly constant right-handed neutrinos would therefore decouple from the dynamics (natural in continuum approach since they would represent just single point in momentum space). This option is not too attractive.

2. Covariantly constant right-handed neutrinos as limiting cases of massless modes

For the second option covariantly constant neutrinos have vanishing four-momentum and both helicities are allowed so that the number of helicities is 2 for both neutrino and antineutrino.

1. The analog of N=4 SUSY is obtained if oscillator operators are not hermitian apart from unitary transformation (pseudo reality) since there are 2+2 oscillator operators.
   
   
2. If hermiticity is assumed as pseudoreality suggests, N=2 SUSY with right-handed neutrino conserved only modulo two in vertices obtained.
   
   
3. In this case covariantly constant right-handed neutrinos would not propagate and would naturally generate SUSY multiplets.
   

3. Could twistor approach provide additional insights?

Concerning the quantization of ν_R:s, it seems that the situation reduces to the oscillator algebra for complex M⁴ spinors since CP₂ part of the H-spinor is spinor is fixed. Could twistor approach provide additional insights?

As discussed, M⁴ and CP₂ parts of H-twistors can be treated separately and only M⁴ part is now interesting. Usually one assigns to massless four-momentum a twistor pair (λ^a, ξ^a') such that one has p^aa'= λ^aξ^a' ( ξ denotes for "\hat(\lambda)" which html does not allow to express). Dirac equation gives λ^a= +/- (ξ^a')^*, where +/- corresponds to positive and negative frequency spinors.

1. The first - presumably non-physical - option would correspond to limiting case and the twistors λ and ξ would both approach zero at the p^k→ 0 limit, which again would suggest that covariantly constant right-handed neutrinos decouple completely from dynamics.
   
   
2. For the second option one can assume that either λ or ξ^a' vanishes. In this manner one obtains 2 spinors λ_i, i=1,2 and their complex conjugates ξ^a'_i as representatives for the super-generators and could assign the oscillator algebra to these. Obviously twistors would give something genuinely new in this case. The maximal option would give 4 anti-commuting creation operators and their hermitian conjugates and the non-vanishing anti-commutators would be proportional to δ_a,bλ^a_i(λ^b)_j^* and δ_a,bξ^a'_i(ξ^a'_j)^*.
   If the oscillator operators are hermitian conjugates of each other and (pseudo-)hermitian, the anticommutators vanish.
   

An interesting challenge is to deduce the generalization of conformally invariant part of four-fermion vertices in terms of twistors associated with the four-fermions and also the SUSY extension of this vertex.

For details see the new chapter Some fresh ideas about twistorialization of TGD of "Towards M-matrix" or the article with the same title. The homepage is off just now as I told in previous posting but I hope that the situation changes within week or two.

Sorry: problems with homepage again

My homepage was closed suddenly: before this it became impossible to transfer material to it. I am sorry for inconvenience. I cannot get any contact with the service provider : the emails are returned as trash with appropriate warnings. Neither are the questions send to service provider from web page for clients are not answered. I am getting help but it takes some time. This is not the first problematic situation with this particular service provider and I should have changed the service provider for long time ago.

These strange unexpected closure of the webpage is not the first one. Last time this occurred two years ago. Strangely enough that service is still available although I was told for almost two years ago that it will be closed. During these four years I have been forced to change homepage address twice meaning that TGD has disappeared totally from web: Helsinki University was responsible for the first cold shower. This would be the third time unless I manage to get contact with the service provider. If this is possible (and it should be if the service provider follows finnish law) then the contents of the homepage can be transferred to the new service provider without any changes in URLs. Otherwise TGD disappears from web again. I can only hope that plain sense wins and a contact with the service provider becomes possible.

In any case, all this looks very strange to me. As a long time scientific out-of-law in Finland I cannot avoid asking whether these strange events are really co-incidences.

Addition: I have now a new temporary domain name tgdtheory.fi. To get accdess to the file in URL http://www.tgdtheory.com/... it is enough to change "com" to "fi": this leads to temporary homepage tgdtheory.fi.

TGD books and articles are also in viXra.org eprint archive: one can get a partial list about articles and books by giving my name in search. I found however that it is not possible to see all the articles. The technology does not work perfectly.

Articles about TGD are also in the journals of Huping Hu and also in Journal of Nonlocality edited by Lian Sidorov.

Addition: What makes me however happy that even string theorists are finally admitting that string approach has failed: something that I have been patiently telling for more than 30 years in vain and also provided the alternative. Leonard Susskind expressed his changed views quite recently. It is ironic that at the moment of victory I am doomed to disappear web.

Some fresh ideas about twistorialization of TGD

I found from web an article by Tim Adamo titled "Twistor actions for gauge theory and gravity". The work considers the formulation of N=4 SUSY gauge theory directly in twistor space instead of Minkowski space. The author is able to deduce MHV formalism, tree level amplitudes, and planar loop amplitudes from action in twistor space. Also local operators and null polygonal Wilson loops can be expressed twistorially. This approach is applied also to general relativity: one of the challenges is to deduce MHV amplitudes for Einstein gravity. The reading of the article inspired a fresh look on twistors and a possible answer to several questions (I have written two chapters about twistors and TGD giving a view about development of ideas).

Both M⁴ and CP₂ are highly unique in that they allow twistor structure and in TGD one can overcome the fundamental "googly" problem of the standard twistor program preventing twistorialization in general space-time metric by lifting twistorialization to the level of the imbedding space containg M⁴ as a Cartesian factor. Also CP₂ allows twistor space identifiable as flag manifold SU(3)/U(1)× U(1) as the self-duality of Weyl tensor indeed suggests. This provides an additional "must" in favor of sub-manifold gravity in M⁴× CP₂. Both octonionic interpretation of M⁸ and triality possible in dimension 8 play a crucial role in the proposed twistorialization of H=M⁴× CP₂. It also turns out that M⁴× CP₂ allows a natural twistorialization respecting Cartesian product: this is far from obvious since it means that one considers space-like geodesics of H with light-like M⁴ projection as basic objects. p-Adic mass calculations however require tachyonic ground states and in generalized Feynman diagrams fermions propagate as massless particles in M⁴ sense. Furthermore, light-like H-geodesics lead to non-compact candidates for the twistor space of H. Hence the twistor space would be 12-dimensional manifold CP₃× SU(3)/U(1)× U(1).

Generalisation of 2-D conformal invariance extending to infinite-D variant of Yangian symmetry; light-like 3-surfaces as basic objects of TGD Universe and as generalised light-like geodesics; light-likeness condition for momentum generalized to the infinite-dimensional context via super-conformal algebras. These are the facts inspiring the question whether also the "world of classical worlds" (WCW) could allow twistorialization. It turns out that center of mass degrees of freedom (imbedding space) allow natural twistorialization: twistor space for M⁴× CP₂ serves as moduli space for choice of quantization axes in Super Virasoro conditions. Contrary to the original optimistic expectations it turns out that although the analog of incidence relations holds true for Kac-Moody algebra, twistorialization in vibrational degrees of freedom does not look like a good idea since incidence relations force an effective reduction of vibrational degrees of freedom to four. The Grassmannian formalism for scattering amplitudes generalizes practically as such for generalized Feynman diagrams.

For background and details see the new chapter Some fresh ideas about twistorialization of TGD or the article with the same title.

Preconscious mechanism of hypnotically altered colors

I learned recently about very interesting work on hypnosis by finnish researchers Mika Koivisto, Svetlana Kirjanen, Antti Revonsuo and Sakari Kallio. The article "A Preconscious Neural Mechanism of Hypnotically Altered Colors: A Double Case Study" is published in journal Plos ONE and is available here.

Here is the abstract of the article:

Hypnotic suggestions may change the perceived color of objects. Given that chromatic stimulus information is processed rapidly and automatically by the visual system, how can hypnotic suggestions affect perceived colors in a seemingly immediate fashion? We studied the mechanisms of such color alterations by measuring electroencephalography in two highly suggestible participants as they perceived briefly presented visual shapes under posthypnotic color alternation suggestions such as “all the squares are blue”. One participant consistently reported seeing the suggested colors. Her reports correlated with enhanced evoked upper beta-band activity (22 Hz) 70–120 ms after stimulus in response to the shapes mentioned in the suggestion. This effect was not observed in a control condition where the participants merely tried to simulate the effects of the suggestion on behavior. The second participant neither reported color alterations nor showed the evoked beta activity, although her subjective experience and event-related potentials were changed by the suggestions. The results indicate a preconscious mechanism that first compares early visual input with a memory representation of the suggestion and consequently triggers the color alteration process in response to the objects specified by the suggestion. Conscious color experience is not purely the result of bottom-up processing but it can be modulated, at least in some individuals, by top-down factors such as hypnotic suggestions.

According to the announcement of finnish academy, the results challenge the existing theories of hypnosis. I developed for some time ago a model of hypnosis as one particular instance of remote mental interactions on basis of TGD inspired quantum theory of consciousness. Quantum entanglement between parts of separate brains, the notion of magnetic body, and TGD based view about sensory organs play key roles in the model. In TGD framework the primary qualia are at the level of sensory organs and sensory representations involve a feedback from magnetic body via brain to sensory organs in terms of dark photons so that the sensory percepts consist of standardized mental images - being more like an artworks emphasizing important features rather than a faithful representation of reality.

TGD based view about hypnosis

I attach below the abstract of the chapter appearing also as an article.

In TGD framework one can argue that hypnosis represents an example about the fact that brain is not "private property": hypnotist uses the biological body and brain of the subject as instrument. Therefore remote mental interaction is in question. This idea generalizes: if one accepts self hierarchy, one can assign to any kind of higher level structure - family, organization, species, .... - a higher level self and magnetic body carrying dark matter, and these magnetic bodies can use lower level magnetic bodies as their instruments to realize their intentions. Biological bodies would be an important level in the hierarchy, which would continue down to cellular, molecular, and perhaps to even lower levels.

This view challenges the prevailing views about brain as a sole seat of consciousness and the assumption that conscious entities assigned with brains are completely isolated. Given magnetic body can use several biological bodies although one can assign to it the one providing the sensory input - at least during wake-up state. Note however that it is easy to produce illusion that some foreign object is part of biological body.

For more than decade ago I proposed a model for so called bi-camerality based on the notion of semitrance. In semitrance the brain of subject becomes partially entangled with a higher level self - in this case the self of family or more general social group uses the biological body of member for its purposes. Higher level self gives its commands and advice interpreted by the bicameral as "God's voice". The consciousness of schizophrenic might be basically bicameral. Also hypnotic state and dream consciousness are candidates for bicameral consciousness.

In this article I develop essentially this idea but using as input the recent understanding of about TGD inspired theory of consciousness and quantum biology and end up with a proposal for a detailed mechanism for how the magnetic body hijacks some parts of the brain of the subject: prefrontal cortex and anterior cingulate cortex are argued to be the most plausible targets of hijacking. Also a mechanism explaining how the sensory hallucinations and motor actions are induced by hypnotist by inhibiting a halting mechanism preventing imagined motor actions to become real and sensory imagination to become "qualiafied".

TGD based interpretation of the findings

The findings of about hypnosis can be used also to test TGD based view about hypnosis. As the abstract concludes, color experience in not purely the result of bottom-up processing but can be modulated by top-down factors. In TGD framework this reflects the basic difference between standard neuroscience and TGD deriving from two assumptions.

• Sensory organs are carriers of primary qualia - the phenomenal experience.
  
• Brain is manufacturer of sensory and memory representations decomposing perceptive field to standardized mental images representing objects and naming them. Virtual sensory input is used to achieve this.
  

In the experiments the form-color correlation created by hypnotic suggestion could be in conflict with the real visual input. The other subject person sensitive to hypnosis managed to transform the real color percept to a percept consistent with the suggestion. The other subject person also sensitive to hypnotic suggestions reported that his/her eyes and brain "saw" different colors.

In TGD Universe the interpretation would be that magnetic body and brain below it in the self hierarchy imagined the correlation consistent with the suggested one in both case. The imagined color was produced by a virtual sensory input realized as dark photons propagating down from magnetic body to cortex and to the lower levels of brain. This applies to imagination in general. For the sensory imagination the propagation halts before reaching sensory organ - now retina. For hallucinations this halting does not happen. Hypnotic suggestion can prevent this halting so that imagined color transforms to a hallucinated color. This happened for the first subject in the experiments. The second subject experienced both the real color and possibly conflicting imagined color associated with the virtual sensory input halting to some higher level in brain between visual cortex and retina. Note that this serves as evidence for the notion of self hierarchy, which is a basic prediction of TGD inspired theory of consciousness.

Also a comment about time scales involved is in order. The peak in the EEG of the person, who experienced the suggested color-shape correlation appeared after an average time of T= .1 seconds from the visual input. T corresponds to 10 Hz fundamental bio-rhythm and the cronon of sensory experience. In TGD framework T characterizes the scale of causal diamond (CD) defining the spotlight of consciousness assignable also to sensory percepts. That T is also the secondary p-adic length scale assigned with electron in TGD conforms with the proposal that electron Cooper pairs play a central role in sensory perception. Primary and secondary p-adic length and time scales (the latter are macroscopic) characterizing elementary particles represents new physics predicted by TGD. R=.05 seconds corresponds to distance R= cT= 15 Mm, which is more than twice the radius of Earth equal to 6.4 Mm. Hence a signal propagating with velocity of light could travel to a layer of magnetic body with this size and back during time .1 seconds.

After having received the announcement of Finnish academy and before seeing the abstract of the article, my own guess was that the high-frequency EEG refers to 40 Hz thalamo-cortical resonance studied by Antti Revonsuo - one of the authors of the recent work. I was wrong. What Revonsuo found was that 40 Hz resonance does not serve as a correlate of mental image as conjectured by Crick and Koch but for the emergence of a new mental image. What was studied was a situation in which the subject person experienced the emergence of 3-D geometric pattern from a chaotic set of dots and lines. 40 Hz activity accompanied only the eureka period: a possible TGD inspired interpretation is that the direct eureka experience was transformed to a memory, which did not generate 40 Hz activity. The 20 Hz activity involved with the change of the perceived color to the suggested color would also correspond to similar re-organization of the perceptive field induced by virtual sensory input masking the real one. What is interesting is that 10,20,40, 80 Hz frequencies appear as resonances in EEG and that they are octaves of 10 Hz. TGD indeed strongly suggests that preferred CD scales come as octaves. Primary p-adic length scales in turn would come as half octaves.

For details see the new chapter Hypnosis as remote mental interaction of "TGD based view about living matter and remote mental interactions" or the article with the same title.

About naturality, fine tuning, and the recent ego catastrophe in theoretical physics

There has been a considerable amount of discussion in blogs about the recent situation in fundamental physics. Do the results from LHC mean end of theoretical physics as a predictive discipline? Should we accept multiverse? Should we give up the notion of naturalness and accept fine tuning? These are the questions.

Phil Gibbs answered affirmatively to these questions in his blog post, Lubos wrote in more skeptic tone about these topics, and Peter Woit touched these questions in his comments about talks held in "Prospects in Theoretical Physics" - a program for graduate students and postdocs in Princeton. I wrote a couple of comments about the situation to the blog of Phil Gibbs and combine them below to a more polished commentary.

To my opinion the situation in fundamental physics should be looked from a wider perspective than that given by last forty - not very successful - years of theoretical high energy physics. Physics is definitely in crisis. Multiverse scenario and the view about necessity of fine tuning are conclusions from sticking to certain basic dogmas and refusal to admit that some of them might be badly wrong. I do not believe in all these dogmas and therefore do not share these pessimistic conclusions. I tend to see the recent situation as an ego catastrophe (we failed to find the theory so that there can be is no theory) which is outcome of accepting quite too many ad hoc assumptions as final truths. The situation can be also seen as the final collapse of reductionistic view about physics.

Alternative for multiverse

I believe that standard model symmetries have fundamental meaning being selected by their very special mathematical and physical character. GUT approach denied this possibility and led theoreticians on wrong track leading to standard SUSY and eventually to M-theory landscape. Also the fact that that the observed space-time is 4-dimensional very probably contains a very important message. But also the idea about 4-dimensional space-time became old-fashioned as super string revolutions revolutions followed each other. Sociological factors played a key role in the process. The attitude that thousands of brilliant theoreticians cannot be wrong allowed the situation to develop to a catastrophe made manifest by the findings at LHC. Even in this situation we are told that we should continue to follow the leaders and now give up even the belief that theoretical physics can explain and predict - the very motivation of super string theory originally. And this only because few generations of theoretical particle physicists became victims of mass psychosis. I will not eat this cake!

Standard model symmetries and also space-time dimension would be forced by the existence of geometry for infinite-dimensional space - "world of classical worlds" (WCW) consisting of 3-surfaces defining the analog of Wheeler's superspace. WCW geometry would realize a generalization of Einstein's geometrization program to a geometrization of the entire quantum physics rather than of only the classical physics. In the case of much simpler loop spaces the mere existence of this Käahler geometry fixes it uniquely for given group G defining the loop group (the existence of Riemann connection requires infinite-dimensional Kac-Moody group as isometries as shown by Freed). Standard model symmetries fix WCW (equivalently, the imbedding space H =M⁴×CP₂ containing space-times as 4-surfaces) and the conjecture is that the mathematical existence of WCW Kahler geometry implies the same WCW. In accordance with the vision about physics as generalized number theory, standard model symmetries would have also number theoretical interpretation in terms of classical number fields. For instance, color group would correspond to isometries of CP₂ and subgroup of automorphisms of octonions.

Concerning the fine tuning of coupling parameters: I believe that fine tuning of dynamical parameters is a basic aspect of quantum evolution leading to life as we identify it, but that standard model symmetries and space-time dimension are mathematical necessities rather than outcomes of evolution in some region of multiverse. p-Adic length scale hypothesis and selection of preferred p-adic primes provides a realization of the evolution selecting preferred mass scales for elementary particles. One should therefore accept the obvious: superstring model describes physics of 2-D space-time but - as has become clear - the attempts to deduce real physics from it are doomed to fail. Nature does not love tricks. Super-conformal symmetry remains the genuine contribution of string models to physics and the natural next step is to finally generalize this symmetry to four dimensions.

Reductionism as the basic cause of the catastrophe

I have spent much time during last decades in trying to understand why we have gradually ended up with this dead end and why the professionals are not able to see that there is no way out except radical rethinking of fundamentals. The history of physics is history of bold and often wrong generalizations. The naive length scale reductionism is one of the most influental of these wrong assumptions. It has been raised to a level of dogma and together with materialistic world view more or less defines nowadays what it is to be scientific. Fractality is very natural candidate for replacing the reductionism and quantum theory strongly encourages to give up materialism but still taken as givens by particle physicists. Reductionism is indeed responsible for many far reaching and probably wrong dogmas in recent day physics.

Reductionism forces us to believe that the strange findings at RHIC and LHC about heavy ion collisions and proton heavy ion collisions are consistent with QCD although here we would have the new physics that we are so desperately searching for. This relates also to naturalness. To my opinion, the attempt to understand mass ratios of various fermion generations group theoretically is doomed to fail. If one accepts the notion of length scale hierarchy implied by fractality there is no need to extend standard model symmetries. The fact that separate B and L conservation is consistent with experimental facts provides an additional strong constraint.

Length scale reductionism also forces us to believe that biology and brain science are just complexity, consciousness is just an epiphenomenon, and free will is an illusion. Theoretical physicists lose a huge treasure trove of anomalies which could help to achieve the sought for unification. As a consequence of this isolation from experiental reality, theoretical physicists have divided into half-religious sects such as super-stringers and loop gravitists. Feynman has talked about general relativists gathering to their yearly meetings and discussing again and again the same old dead ideas. Sadly, Feynman's characterization seems to apply quite well also to Strings 2013 and Loops 2013.

Length scale reductionism guides us to search dark matter from elementary particle length scales. This direction might be completely wrong: TGD suggests generalization of quantum theory by introducing the hierarchy of effective Planck constants and in this framework dark matter as quantum coherent phases would emerge in long length scales. Ironically, already Tesla made observations, which one might be interpret as indications for the existence of something behaving much like dark matter in TGD sense. Tesla spoke of "cold electricity" not seen in ampere-meter but as a child of his time assigned with it what he called aether particles. Did Tesla discover the dark matter for more than century ago? One cannot exclude this possibility since his experiments typically used high voltages, low frequencies, and using sudden pulses resulting in switching on of electrical circuits and in this manner testing the boundaries of Maxwell's theory in long rather than short scales (as particle physics does). In this context one must mention also the strange quantum like effects of ELF radiation on vertebrate brain and the fact that cell membrane resting potential corresponds to an electric field above the dielectric breakdown in air. Tesla's vision about future technology was also surprisingly far reaching and he also saw a possible connection with the energy technology and biology: his ideas are still revolutionary. To me the example of Tesla demonstrates that the history of science is not steady linear evolution but a continual fight between mediocrits and visionaries and mediocrits quite too often win in the short run.

About the art of rediscovery

Lubos has been talking about recent progress related to firewall paradox of blackhole physics (see this and this). Lubos has been especially happy about Maldacena-Susskind proposal for wormhole connections as a correlate of entanglement. I believe that this idea as such is wrong and represents the last attempts to save the general relativity based view about space-time: to make real progress in quantum gravity one must leave the general relativity based view about geometry and replace it with sub-manifold geometry as done in TGD.

The idea about about geometric correlates of entanglement is however deep. The braiding of magnetic flux tubes connecting entangled systems would serve as a geometric and topological space-time correlate of entanglement. It also happens to be ten year old basic ideas of TGD. I have been talking a lot about it also in this blog - and probably also in Lubos blog and viXra log where Lubos has also often visited- and it is nice that my blog is read. Lubos however refused from any public blog communications because he believes that I suffer some fatal infective disease - maybe academic equivalent of leprosy;-).

As a matter of fact, I have been patiently waiting that some name would finally realize the depth of the idea about geometric correlates of entanglement and decide to rediscover it. Now my patience has been repaid. This correspondence has even got a name: ER-EPR correspondence. Maldacena and Susskind apply this idea to solve firewall paradox. This is very nice but to my opinion the idea is applied to solve a wrong problem. The idea of this caliber would deserve something much better.

I see the firewall paradox as a pseudo-problem due to wrong belief about what blackhole interior is (see this and this). In TGD framework blackhole interior is generalized and becomes Euclidian region of space-time surface. Firewall paradox disappears. The Minkowskian-Euclidian horizon is of course something very real: the outer surface of a line of generalised Feynman diagrams thickened to four-surface. If TGD view is correct, the applications are much more wider to every day physics, especially so in biophysics and a detailed vision about quantum biophysics is developing. Here is a something really juicy for a namy-enough rediscoverer!

Susskind already earlier discovered the p-adic number fields and applied them to solve some problem of some hopeless cosmological scenario inspired by string theory - much more intelligent applications are waiting for rediscovery - just visit my hope page and choose your favourite idea! Earlier Susskind rediscovered holography: in TGD framework it follows as a 4-D version from general coordinate invariance (see this). Few years ago TGD version of the holographic principle was replaced with a stronger form in which 2-D surfaces and their 4-D tangent space data carry the data characterising quantum state: effective 2-dimensionality.

Holography represents the oldest layer of quantum TGD born around 1990 when the vision about the geometry of WCW as space of 3-surfaces whose Kähler metric is determined by Kähler function defined by a preferred extremal of Kä:hler action - a 4-surface uniquely associated with a given 3-surface as analog of Bohr orbit: this is just a statement of holographic principle tying together quantum classical correspondence, general coordinate invariance, and making classical physics exact part of quantum physics. This became four years before Susskind's "The world as a hologram". Most importantly, TGD holography is holography in 4-D context and replaces the unphysical 10-D space with 4-D real space-time and - as it became clear much later - also leads to stringy description of elementary particles. I am eagerly waiting that the strong form of holography would be discovered by some name.

Also Tom Banks - the teacher of Lubos - has been busily re-discovering TGD related visions: his CV already contains hyper finite factors of type II₁ and causal diamonds. I am really happy that big names understand the value of great ideas and are ready to take trouble of rediscovering them. It is of course a pity that they forget to mention the real father of the idea! But I of course understand that big names have much more important things to do than worrying about minor details like this!

About Concrete Realization of Remote Metabolism

The idea of remote metabolism - or quantum credit card as I have also called it - emerged for more than decade ago and zero energy ontology (ZEO) provides justification for it. The idea is that the system needing energy sends negative energy to a system able to receive the negative energy and make a transition to a lower energy state. This kind of mechanism would be ideal for biology, where rapid reactions to a changing environment are essential for survival and there is no time for sending a request for energy.

The model of remote metabolism is applied to biology. It is shown that the basic notions of the theory of Ling about cell metabolism inspired by various anomalies have natural counterparts in TGD based model relying on the notion of magnetic body. Remote metabolism can be considered as a completely general mechanism of metabolism with magnetic body of ATP or system containing it carrying the metabolic energy and sucked from it by the user. In particular, the role of ATP is discussed in Ling's theory and from the point of view of TGD inspired theory of consciousness.

It is easy to imagine new technologies relying on negative energy signals propagating to the geometric past and ZEO justifies these speculations. Remote metabolism could make possible a new kind of energy technology making it un-necessary to carry fuel. The discoveries of Tesla made more than century ago plus various free energy anomalies provide excellent material for developing these ideas, and one ends up with a concrete proposal for how dark photons and dark matter could be produced in capacitor like systems analogous to cell membranes and acting as Josephson junctions and how energy could be sucked from "large" magnetic bodies.

The model identifies Josephson frequency with the subharmonic of the frequency characterizing the periodicity of a periodic voltage perturbation assumed to correspond to cyclotron frequency in biological applications. Together with quantization conditions for charge and effective Planck constant leads to precise quantitative predictions for capacitor like systems acting as dark capacitors. Also a relationship between the magnetic field at magnetic body of the system and the voltage of the capacitor like Josephson junction emerges.

The predictions allow new quantitative insights about biological evolution as emergence of Josephson junctions realized as capacitor like systems both at the level of cell, DNA and proteins, and brain. h_eff can be related to Josephson frequency and cyclotron frequency and thus to measurable parameters. h_eff serves as a kind of intelligence quotient and its maximization requires the maximization of both the voltage and area of the membrane like capacitor system involved. This is what has happened during evolution. Indeed, the internal cell membranes, cortical layers and of DNA double strand in chromosomes are strongly folded, and the value of membrane electric field is roughly twice the value of the electric field for which di-electric breakdown occurs in air. Even 40 Hz thalamocortical resonance frequency can be understood in the framework of model.

See the new chapter About Concrete Realization of Remote Metabolism of "Biosystems as conscious holograms" for details.

Evidence for M89 pion at LHC?

Lubos reported interesting news from LHC. The title of the post of Lubos was "Evidence for second Higgs boson at 136.5 GeV". The title is misleading and reflects the dream of Lubos that standard SUSY predicting 5 Higgs like particles could be found at LHC despite all the evidence against standard SUSY. What has been actually found is some evidence for the existence of a particle decaying to two gammas: this of course does not imply that second Higgs is in question. This is not the first time when Lubos is quite too hasty in his conclusions.

The article by CMS where the evidence is discuss is titled "Properties of the observed Higgs-like resonance decaying into two photons". A search for possible other resonance decaying to a gamma pair was made, and the results are given by figure 3 of the paper, which can be found also in the posting of Lubos. The figure demonstrates excess around 136.5 GeV. The local signficance is reported to be 2.73 sigma, which is far from the discovery value of 5 sigma. It must be emphasized that ATLAS does not see the bump: Matt Strassler draws from this the conclusion that there is nothing there. Also this logic is wrong: either ATLAS or CMS is wrong and we cannot a priori know which of them.

The basic LHC prediction of TGD is a scaled up copy of ordinary hadron physics. I have used to call this physics M₈₉ hadron physics since it corresponds to Mersenne prime M₈₉ whereas ordinary hadron physics corresponds to M₁₀₇. The strange findings made already at RHIC and repeated at LHC for both heavy ion collisions and proto-heavy ion collisions in conflict with the expectations from perturbative QCD expectations could be explainable in terms of string like objects of M₈₉ hadrons physics decaying to ordinary hadrons. If one takes seriously the observations of Fermi satellite suggesting the existence of particle with mass about 135 GeV and identifies it as the pion of M₈₉ hadron physics, one can wonder whether also LHC has detected M₈₉ pion from its decays to gamma pairs. Note that the standard interpretation of Fermi particle as a dark matter particle assignable to SUSY has been excluded. This would be encouraging but the experiences during few years have however taught that these bumps come and go and must be taken as entertainment in the dull life of theoretician.

Hypnosis as remote mental interaction

In TGD framework one can argue that hypnosis represents an example about the fact that brain is not "private property": hypnotist uses the biological body and brain of the subject as instrument. Therefore remote mental interaction is in question. This idea generalizes: if one accepts self hierarchy, one can assign to any kind of higher level structure - family, organization, species, .... - a higher level self and magnetic body carrying dark matter, and these magnetic bodies can use lower level magnetic bodies as their instruments to realize their intentions. Biological bodies would be an important level in the hierarchy, which would continue down to cellular, molecular, and perhaps to even lower levels.

This view challenges the prevailing views about brain as a sole seat of consciousness and the assumption that conscious entities assigned with brains are completely isolated. Given magnetic body can use several biological bodies although one can assign to it the one providing the sensory input - at least during wake-up state. Note however that it is easy to produce illusion that some foreign object is part of biological body.

For more than decade ago I proposed a model for so called bicamerality based on the notion of semitrance. In semitrance the brain of subject becomes partially entangled with a higher level self - in this case the self of family or more general social group uses the biological body of member for its purposes. Higher level self gives its commands and advice interpreted by the bicameral as "God's voice". The consciousness of schizophrenic might be basically bicameral. Also hypnotic state and dream consciousness are candidates for bicameral consciousness.

Hypnosis as hijacking of brain?

In TGD framework hypnotist and subject would partially share the biological body of the subject, and hypnotist could realize motor actions using the biological body of the subject and also induce sensory experiences by sending suggestions generating virtual sensory input to the sense organs of the subject (this if one accepts TGD view about the role of sensory organs).

One could see hypnosis as a kind of hijacking of some parts of the subject's brain. Could one identify these parts? The general finding is that there is no universal neural or EEG signature of hypnotic state and possible changes in neural activity can be interpreted as neural correlates of imagination. Only in the case of persons highly susceptible to hypnotic induction one can identify a change of neural activity pattern identifiable as a correlete of hypnotic state.

"Hijacking" can be of course criticized for its negative tone. A more positive manner to express the idea is to say that the subject is voluntarily provides part of her brain to the use of the hypnotist's magnetic body. This conforms with the acronym "TEAM" symbolizing the subject's orientation to hypnosis in terms of "trust", "expectation", "attitude", and "motivation".

The neurophysiological findings conform with the view that the really interesting phenomena take at the level of magnetic bodies. The changes - when they occur - take place in prefrontal cortex (PFC) and anterior cingulate cortex (ACC): this together what is known about methods of hypnotic induction provides hints about what might occur in the hijacking process. The almost-prediction would be a correlation between EEGs of the hypnotist and subject person reflecting the sharing of parts of the subject's brain. It would be therefore highly interesting to study the correlations of the EEGs of subject and hypnotist.

Strongly focused attention to hypnotic suggestion is mentioned as a basic aspect of hypnosis and distinguishes it sharply from sleep. This feature brings in mind various altered states of consciousness reached in meditation and it has been suggested that meditation is one form of self-hypnosis. In TGD framework personal magnetic body has layered onyon-like structure with layers characterized by p-adic length and time scales and the value of hbar_eff. Thefore meditative state could be seen as a resharing of biological body and brain by these layers and even by foreign magnetic bodies.

Do social interactions share something with hypnosis?

More generally, one can also ask whether the phenomena of collaboration and synergy on one hand, and influence, "power" and fight for power on the other hand, could be modelled in terms of the partial ownership of the biological bodies by magnetic bodies identified as intentional agents.

Social structures and organizations are complex networks in which the arrows characterizing relationships between individuals in the simplest situations are uni-directional and static. The person at either end of the arrow is in command. In more complex situtations members are connected by several arrows of this kind, their directions can vary, and need not be static.

Should one therefore give up what physicist would call "single-particle" view and replace it with "many-particle" view by bringing in the notion of magnetic body attaching to several biological bodies and organizing them to loosely bound states of individuals? Under what conditions this kind of partial fusion of conscious entities can take place? Does it occur only only when there is complete trust in either direction or can fear about consequences be enough? It would not be surprising if immune systems against hijacking of the biological body would have evolved: this would allow to understand why the reality of remote mental interactions is so difficult to demonstrate. They could however take place on daily basis in social interactions if the proposed picture makes sense.

The dynamical sharing of biological bodies can be seen also positively: this sharing would make possible collaboration and synergy at much deeper level than we have been used to think. This kind of shared use of biological bodies perhaps defines the direction to which human kind should proceed. Also the possibility to directly experience what it is to be "the other one" - something not allowed by the standard view about consciousness confined inside individual brain - is implicated.

The new view about influence and power might allow to understand better the often highly irrational looking behaviors of organizations and their members - in particular blind obediance of orders and fight for power. The hierarchy of magnetic bodies could serve as a physical correlate for the hierarchy of biological and social structures. In particular, the fight for power could be seen as fight between magnetic bodies for the ownership of biological bodies or lower level magnetic bodies. The dark matter realized as a hierarchy of phases with non-standard value of effective Planck constant would represent a new physics necessary for understanding the physical correlates of these phenomena.

In the new chapter devoted to hypnosis as remote mental interaction I will introduce some basic notions, ideas and theories about hypnosis: the Wikipedia article gives a good overall view about the subject. The techniques of hypnotic induction provide valuable clues if one wants to imagine what hypnosis is. I will also describe the classical test for hypnotic susceptibility using Chevreul pendulum (to me it was quite a stunning experience to find that I am highly susceptible to hypnotic induction!), and propose an explanation in terms of hijacking of PFC and ACC by the magnetic body of hypnotist. The model makes an assumption about the logic of brain functions. Imagined motor action "Don't (really) do this" is realized as "Do this" followed by "Don't" stopping the imagined motor action proceeding otherwise from the magnetic body to PFC to motor regions of cortex via ACC to a real motor action.

In TGD framework sensory perception and motor action are related by time reversal and therefore an analogous mechanism applies to imagination realized as a genuine hallucination unless "Don't" is realized. Hypnotist should therefore hijack the brain regions realizing "Don't" by catching their attention so that they cannot perform their function. ACC is a good candidate for the region in which "Don't" is realized under normal circumstances. This logic makes possible to induce motor actions and sensory hallucinations analogous to dreams. Dreams would be realized in terms of virtual sensory input to sensory organs (REM) rather than only to higher levels in hierarchy of sensory representations at cortex, which do not carry visual qualia conscious-to-us.

For details see the new chapter Hypnosis as remote mental interaction of "TGD based view about living matter and remote mental interactions" or the article with the same title.

Great Unconformity as a new piece of support for Expanding Earth model

I wrote for some years ago to "Genes and Memes" a chapter entitled Expanding Earth model and Precambrian evolution of continents, climate and life . Single hypothesis - a sudden phase transition increasing the radius of Earth by a factor 2 natural in the many-sheeted space-time of TGD - explains Cambrian explosion in biology (a sudden emergence of huge number of life forms after very slow Precambrian evolution, and also provides a model for Precambrian evolution of continents, climate and life.

Already Darwin realized that the absence of fossils from Precambrian era is a deep problem for his theory and assumed that this is an artefact due to the incomplete fossil record. Fossils of Precambrian origin have been indeed found after Darwin's time but they are simple and very rare, and the conclusion is that Cambrian explosion meaning huge diversification was real. Two mysteries therefore remain. Why the development of life was so slow during Precambrian era? Why the diversification was so incredibly fast during Cambrian explosion? Various explanations have been proposed. Did the oxygen content of the atmosphere reach a critical value and lead to the diversification? Or did predation pose the evolutionary pressure making the pace of evolution dramatically faster?

In New Scientist geologists Robert Gaines and Shanan Peters describe a geological finding perhaps related to the Cambrian Explosion: the mysterious "Great Unconformity", which is a juxtaposition of two different types of rock of very different geological ages along a prominent surface of erosion. This surface represents a very long span of "missing" time. More than 1 billion years of geological record is missing in many places! From the figure of the Wikipedia article about Great Unconformity visible in Grand Canyon the thickness of the missing layer can be estimated to be about 12.6 km. Somehow before the Cambrian the uppermost rocks of the continents were stripped away exposing the underlying crystalline basement rocks. The cause of this gap remains a complete mystery so that we have three mysteries! Plus the mysteries related to the evolution of climate (problems of Snowball Earth model).

The authors suggest that the formation of Great Unconformity relates to the Cambrian explosion. Large scale erosion and chemical weathering of the the exposed crystalline rock caused mineralization of the sea water. The hypothesis is that this led to bio-mineralization: animal groups possessing mineral skeletons - such as silica shells and calcium carbonate shells - emerged. This hypothesis looks rather plausible but does not solve the three great mysteries.

The authors indeed leave open the question about the origin of Great Unconformity and of Cambrian explosion. The TGD based explanation of Cambrian explosion comes from the model realizing the old idea about Expanding Earth in terms of TGD inspired new physics. Already Wegener observed that continents can be fit together nicely and this led to the recent view about plate tectonics. Wegener's model however fits only "half" of the continent boundaries together. One could however do much better: the observation is that the continents would fit nicely to cover the entire surface of Earth if the radius of Earth were 1/2 of its recent value! Expanding Earth model postulates that the radius of Earth grows slowly. Geologists have not taken Expanding Earth model seriously: one good reason is that there is no physics allowing it.

TGD predicts this physics.

1. At given sheet of the many-sheeted space-time cosmic expansion is predicted to take place as sudden phase transitions in which the size of some space-time sheet suddenly increases. By p-adic length scale hypothesis the preferred scaling factors are powers of 2 and the most favored scaling factor is just two. The proposal is that during the Precambrian era life resided in underground seas being thus shielded from meteor bombardment and cosmic rays. This explains the scarcity of the fossil records and the simplicity of the fossils found. The sudden phase transition was a very violent process increasing the area of the Earth's surface by a factor of 4. The area of continents is 29.1 per cent from the recent area of the Earth's surface - not too far from the naively predicted fraction 1/4.
   
   
2. It is easy to imagine that the uppermost rocks of the continent covering the entire Earth were stripped away and correspond nowadays to 100 km thick continental tectonic plates consisting of mainly silicon and aluminium). This expansion created split first the topmost layer as continental plates and regions between them giving rise to oceans. The magma which was uncovered by the process cooled down and solidifed and the continued expansion gave rise to ocean plates with different composition (mainly silicon and magnesium).
   
   
3. The expansion phase corresponds to criticality so that fractality of the expansion is expected. At least for continental plates this process could have been fractal occurring in various length scales characterizing the thickness and the area of the sub-plates generated in the process. p-Adic length scale hypothesis suggests that the scales involved should appear as powers of 2^1/2 or 2. Generation of Great Unconformity as a process in which the underlying crystalline basement rocks were uncovered could correspond to a splitting of a layer of the continental plates to pieces. The length scale characterizing the thickness is 12.6 km from the above estimate and with 1 per cent accuracy by a factor 1/8 shorter than 100 km length scale for tectonic plates. This conforms with p-adic fractality. If the process of expansion involved a cascade of scalings by factor 2, one can wonder whether it proceeded from long to short length scales or vice versa. In other words: did continental and oceanic tectonic plates form first and after than the smaller structures such as the Great Unconformity or vice versa?
   
   
4. Note that the p-adic length scale L(237) corresponding p∼ 2²³⁷ is 88 km - ten per cent smaller than 100 km. Maybe thermal expansion could account the discrepancy if the original thickness was L(237). There is a nice fractal analogy with cell membrane. The p-adic length scale L(239) defined by the Gaussian Mersenne M_k,G=(1+i)^k-1 , k=239- the first one after the Gaussian Mersenne M_167,G defining the size of cell nucleus - equals 2× L(237). Remarkably, also M_241,G is Gaussian Mersenne. What it interesting that the scale L(127)=88 km would be in the same relation to L(239) associated with M_k=239,G as the thickness L(149) of the lipid layer of cell membrane to the cell membrane thickness L(151) characterized by Gaussian Mersenne M_151,G. The two kind tectonic plates (continental and oceanic) would be analogous to the lipid layers of cell membrane. Note that 88 km is rather precisely the thickness of the atmosphere above which begins ionosphere. The thickness of Kennelly–Heaviside layer inside which radiowaves used in terrestrial radio communications propagate, has thickness about 150 km which roughly corresponds to L(239). Also the fact Continental litosphere has typical thickness of 200 km (L(239)) whereas oceanic litosphere is 100 km thick (L(237)) fits nicely with the proposed formation mechanism of continental tectonic plates.
   
   
   
5. The rapid expansion process could have also brought in daylight the underground seas and the highly developed life in them so that Cambrian diversification would have been only apparent. Skeptic can of course ask whether it is necessary to assume that life resided in underground seas during Precambrian era. Could just the violent geological process be enough to induce extremely fast diversification? This might of course be true.
   
   
6. There is one further argument in favor of the Expanding Earth model. The fact that the solar constant was during proto Earth period only 73 per cent from its recent value, is a problem for the models of the very early evolution of life. If the radius of Earth was 1/2 of its recent value the duration of day and night was from conservation of angular momentum only 1/4:th of the recent value and thus 3 hours. This could have made the environment much more favorable for the evolution of life even at the surface of the Earth since the range for the temperature variation would have been much narrower.
   

This model relates also to the Snowball Earth model of Precambrian climate in an interesting manner. The reader interested in details should read the chapter Expanding Earth model and Precambrian evolution of continents, climate and life of "Genes and Memes".

Biophysics of activated water and the mechanism of water memory

Applied Biophysics of Activated Water by Vysotskii et al gives a nice summary about the experiments carried out by using what they call activated water. One can say that the experiments provide a strong support for the notion of water memory. In the following I present a short summary about the contents of the book with associations to TGD inspired view about water memory and homeopathy. What comes as a surprise is the extreme simplicity of the basic mechanism of water memory and also the profound implications of this mechanism for the evolution.

For background and details see the chapter Homeopathy in Many-Sheeted Space-time or the article "Applied biophysics of activated water" and the basic mechanism of water memory in TGD framework".

Consciousness as a phenomenon in the operational architectonics of brain organization: Criticality and self-organization considerations

I received an interesting article by brothers Fingelkurts (Andrew and Alexander) and Carlos Neves to be published in Chaos, Solitons \& Fractals (to appear here). The title of the article is Consciousness as a phenomenon in the operational architectonics of brain organization: Criticality and self-organization considerations.

Already on basis of the title it is clear that article is interesting also from the point of view of Topological Geometrodynamics (TGD) (for overview see Topological Geometrodynamics: an Overview, especially the part II), where quantum criticality replaces thermodynamical criticality as a basic characteristic of the Universe dictating uniquely the dynamics fixing the geometry of the "world of classical worlds" (WCW) consisting of 3- surfaces in certain 8-dimensional space-time. Quantum criticality is also central in TGD inspired theory of consciousness and the basic picture is roughly the same as in OA model. The chapter Comparison of TGD Inspired Theory of Consciousness with Some Other Theories of Consciousness might help to get an overview about TGD inspired theory of consciousness.

Quantum self-organization is second key element of TGD inspired theory of consciousness and corresponds to a cascade of quantum jumps proceeding from level of given causal diamond (CD) defined as intersection of future and past directed light-cones of 4-D Minkowski space to shorter scales (sub-CDs, their sub-CDs, etc..). Quantum jump corresponds to a state function reduction at either boundary of CD and have interpretation as sensory perception and motor action (time reversed sensory perception). CD is identified as geometric correlate for "spotlight of consciousness".

In this article and also in the chapter "Quantum Model of EEG" of "TGD and EEG" I summarize the basic concepts and ideas of the article and compare them with TGD approach to consciousness. There is also a section devoted to quantum criticality in TGD Universe. The approach is certainly TGD centred and I can only apologize this.

What is the basic mechanism of homeopathic healing?

After a work of more than decade after the realisation that homeopathy might be understood in TGD Universe, I still find that I have not given an absolutely convincing answer to the question "What is the exact mechanism of homeopathy?". The basic rules is that "like cures alike". Why should this be the case? Let us go our arguments through once again.

1. Certainly the imprinting of water using molecules causing the illness - call these molecules just I for brevity - must be an essential part of the healing mechanism. The imprinting means imprinting of water with some frequencies in the low frequency spectrum of I. The TGD inspired idea is that the magnetic body of appropriate water cluster or even dark nucleon sequence representing DNA sequence, call this entity I^*, is able to mimic I in the sense that its cyclotron frequency spectrum is same.
   
   
2. This in turn strongly suggests that the molecules in the organism to be healed - call them P - have a long range interaction with molecules I induced by dark photons with cyclotron frequencies but having energies above thermal threshold. The interaction involves a formation of a magnetic flux tube accompanied by a parallel topological light ray/ "massless extremal" (ME) along which dark photons at specific resonance frequencies propagate and induce resonant interaction between P and I. Thus both the formation of flux tube bridge and the resonant interaction made possible by it, would be essential for the homeopathic healing to take place. In fact, in TGD inspired theory of consciousness, the formation of resonating flux tube connections makes possible the quantum coherence for the combined system I+P and serves as a correlate for attention between I and P.
   
   
3. The presence of the entities I^* able to mimic the cyclotron frequency spectrum of I and forming resonant flux tube bonds with molecules H is however not enough to explain the healing effect (I have already considered some answers but they do not convince me). To understand this, one must be able to understand how I causes the illness. The answer of the standard medicine is that the mechanism is chemical and thus requires contact interaction between I and P. It is easy to believe this. Standard medicine also tells that in order to prevent the chemical interaction between I and P , one must use some medicine molecules M, preventing this chemical interaction. It is easy to believe also this.
   
   In TGD Universe there is indeed a very natural mechanism preventing the chemical interaction between I and P. The reduction of the value of the effective Planck constant associated with the flux tubes connecting I and P leads to a contraction of the flux tube length (proportional to hbar_eff). This indeed makes possible a chemical contact interaction between both I and P causing the illness. In fact, I have proposed this mechanism as a completely general mechanism of catalyst action allowing biomolecules to find each other in the the dense bio-molecular soup. But this holds true also for I^* and P! Using terms of "molecular psychology" , the entities I^* mimicking I steal the attention of molecules P so that molecules I cannot cause the illness anymore!
   

This indeed looks extremely simple and natural and thus also convincing. What is important is that the proposed mechanism is not in conflict with standard medicine: it only makes possible the miracles of bio-chemistry and provides a completely new mechanism of healing. It is easy to imagine that a new kind of medicine using only water imprinted by the cyclotron frequency spectra of molecules responsible for the illness. This medicine would be completely free of the negative -basically chemical - side effects of the ordinary drugs. This mechanism would also use all the knowledge gained by ordinary biochemistry based medicine: if the relevant molecule I is known, it can be used to imprint water to get I^*.

Also the effect of vaccines could rely on the "like cures alike" mechanism albeit in different form. Now the molecules or organisms - call them just B - causing the disease would be injected directly into the body rather than water. Water memory could give rise to a mimicry of B:s and give rise to primitive immunity. A more refined mechanism proposed earlier would involve dark DNA mimicking B:s and translating to ordinary DNA sequences coding for proteins able to catch B:s by the same flux tube mechanism.

The proposed mechanism of homeopathic healing leaves open the exact mechanism behind the cyclotron mimicry. The entities I^* could be water clusters with magnetic bodies mimicking those of I, they could be water clusters which have stolen the magnetic bodies of I, or they could be even dark DNA accompanying water molecules and able to mimic I. Of course, the least science fictive option is that the possibly existing dark DNA couples only with ordinary DNA by the flux tube mechanism.

The interpretation of biophotons as decay products of dark photons in energy conserving phase transition hbar_eff→ hbar suggests that the dark photons involved with the communications have rather large value of hbar_eff given by hbar_eff=f_h/f_l. The simplest working hypothesis is that dark photons have same energy spectrum as biophotons. The prediction would be that biophoton spectrum from a homeopathic remedy - in particular its fluctuations - should correlate with the spectrum of the cyclotron frequencies. A weaker hypothesis is that the energies of dark photons are above thermal energy at physiological temperature.

For background see the chapter Homeopathy in Many-Sheeted Space-time of "Biosystems as Conscious Holograms".