QFT limit of TGD and space-time supersymmetry

The understanding of the QFT limit of TGD is now a twenty year old challenge. How to feed information about classical physics characterized by Kähler action has been the basic question. The conflict with Poincare invariance destroying all hopes about practical calculations looks unavoidable. Zero energy ontology and the addition of measurement interaction depending on momenta and color charges to modified Dirac action led to a resolution of this dilemma. The point is that the momenta act on the tip of causal diamond rather than space-time coordinates, which therefore appear as external parameters like the couplings in Hamiltonian. QFT in infinitely slowly varying background fields is the counterpart in ordinary QFT but in TGD there is no need to pose this restriction. One obtains for each space-time point its own QFT limit. A weighted integral over amplitudes corresponding to these limits is performed in analogy with what is done in the theory of spin glasses at the level of statistical physics. As a matter fact, TGD Universe is 4-D quantum spin glass.

This led also to the realization that space-time supersymmetry can be realized at the fundamental level as anticommutation relations of the fermionic oscillator operators associated with the modes of the induced spinor field. The next task was to construct the counterpart of SUSY QFT limit for TGD. Here the problem was that the value of N for the super-symmetry in question is large or even infinite so that the standard notions of chiral and vector superfields fail. N=∞ limit how forced to find the correct formalism. It is considerably simpler than the standard one since chiral condition is replaced with Grassman analyticity. Bosonic emergence is unavoidable in this framework relying strongly on zero energy ontology and on the identification of fermions (bosons) and their super-partners in terms of wormhole throats (contacts). The finiteness of the theory follows by extending the standard argument stating that fermion and sfermion loops cancel each other in SUSY. One prediction is a hierarchy of exotic particles with propagators behaving like 1/pⁿ. For boson exchanges with n=2m the corresponding interaction potentials behave like exp(-mr)r^2m-3. For massless case n=4 gives linear confining force possibly highly relevant for QCD. Also the information about space-time surface (corresponds to maximum of Kähler function) can be feeded to the theory by using modified gamma matrices defined by Kähler action without losing Poincare invariance.

I dare to regard the resulting formalism combining the ideas about the generalization of twistors and about bosonic emergence with other basic ideas of TGD as the final breakthrough. The resulting formalism makes possible concrete calculational recipes. During last months I have often experienced a deep and to me strange feeling of relief. After 32 years of work my great mission has been realized to a high extent! The practical part of me of course starts to worry whether this 59 old me can survive this kind of strange feelings of relief without total collapse;-)? Probably so! There is so much to do and one thing to do is to look how much of this formalism generalizes to TGD proper.

I attach below also the abstract of the new chapter Does the QFT Limit of TGD Have Space-time Super-Symmetry?, which can be found in the book "Towards M-Matrix".

Contrary to the original expectations, TGD seems to allow a generalization of the space-time super-symmetry. This became clear with the increased understanding of the modified Dirac action. The introduction of a measurement interaction term to the action allows to understand how stringy propagator results and provides profound insights about physics predicted by TGD.

The appearance of the momentum and color quantum numbers in the measurement interaction couples space-time degrees of freedom to quantum numbers and allows also to define SUSY algebra at fundamental level as anti-commutation relations of fermionic oscillator operators. Depending on the situation a finite-dimensional SUSY algebra or the fermionic part of super-conformal algebra with an infinite number of oscillator operators results. The addition of a fermion in particular mode would define particular super-symmetry. Zero energy ontology implies that fermions as wormhole throats correspond to chiral super-fields assignable to positive or negative energy SUSY algebra whereas bosons as wormhole contacts with two throats correspond to the direct sum of positive and negative energy algebra and fields which are chiral or antichiral with respect to both positive and negative energy theta parameters. This super-symmetry is badly broken due to the dynamics of the modified Dirac operator which also mixes M⁴ chiralities inducing massivation. Since righthanded neutrino has no electro-weak couplings the breaking of the corresponding super-symmetry should be weakest.

The question is whether this SUSY has a realization as a SUSY algebra at space-time level and whether the QFT limit of TGD could be formulated as a generalization of SUSY QFT. There are several problems involved.

1. In TGD framework super-symmetry means addition of fermion to the state and since the number of spinor modes is larger states with large spin and fermion numbers are obtained. This picture does not fit to the standard view about super-symmetry. In particular, the identification of theta parameters as Majorana spinors and super-charges as Hermitian operators is not possible.

2. The belief that Majorana spinors are somehow an intrinsic aspect of super-symmetry is however only a belief. Weyl spinors meaning complex theta parameters are also possible. Theta parameters can also carry fermion number meaning only the supercharges carry fermion number and are non-hermitian. The the general classification of super-symmetric theories indeed demonstrates that for D=8 Weyl spinors and complex and non-hermitian super-charges are possible. The original motivation for Majorana spinors might come from MSSM assuming that right handed neutrino does not exist. This belief might have also led to string theories in D=10 and D=11 as the only possible candidates for TOE after it turned out that chiral anomalies cancel.

3. The massivation of particles is basic problem of both SUSYs and twistor approach. The fact that particles which are massive in M⁴ sense can be interpreted as massless particles in M⁴×CP₂ suggests a manner to understand super-symmetry breaking and massivation in TGD framework. The octonionic realization of twistors is a very attractive possibility in this framework and quaternionicity condition guaranteing associativity leads to twistors which are almost equivalent with ordinary 4-D twistors.

4. The first approach is based on an approximation assuming only the super-multiplets generated by right-handed neutrino or both right-handed neutrino and its antineutrino. The assumption that right-handed neutrino has fermion number opposite to that of the fermion associated with the wormhole throat implies that bosons correspond to N=(1,1) SUSY and fermions to N=1 SUSY identifiable also as a short representation of N=(1,1) SUSY algebra trivial with respect to positive or negative energy algebra. This means a deviation from the standard view but the standard SUSY gauge theory formalism seems to apply in this case.

5. A more ambitious approach would put the modes of induced spinor fields up to some cutoff into super-multiplets. At the level next to the one described above the lowest modes of the induced spinor fields would be included. The very large value of N means that N > 32 SUSY cannot define the QFT limit of TGD for higher cutoffs. One must generalize SUSYs gauge theories to arbitrary value of N but there are reasons to expect that the formalism becomes rather complex. More ambitious approach working at TGD however suggest a more general manner to avoid this problem.
   1. One of the key predictions of TGD is that gauge bosons and Higgs can be regarded as bound states of fermion and antifermion located at opposite throats of a wormhole contact. This implies bosonic emergence meaning that it QFT limit can be defined in terms of Dirac action. The resulting theory was discussed in detail in and it was shown that bosonic propagators and vertices can be constructed as fermionic loops so that all coupling constant follow as predictions. One must however pose cutoffs in mass squared and hyperbolic angle assignable to the momenta of fermions appearing in the loops in order to obtain finite theory and to avoid massivation of bosons. The resulting coupling constant evolution is consistent with low energy phenomenology if the cutoffs in hyperbolic angle as a function of p-adic length scale is chosen suitably.

   2. The generalization of bosonic emergence that the TGD counterpart of SUSY is obtained by the replacement of Dirac action with action for chiral super-field coupled to vector field as the action defining the theory so that the propagators of bosons and all their super-counterparts would emerge as fermionic loops.

   3. The huge super-symmetries give excellent hopes about the cancelation of infinities so that this approach would work even without the cutoffs in mass squared and hyperbolic angle assignable to the momenta of fermions appearing in the loops. Cutoffs have a physical motivation in zero energy ontology but it could be an excellent approximation to take them to infinity. Alternatively, super-symmetric dynamics provides cutoffs dynamically.

6. The condition that N=∞ variants for chiral and vector superfields exist fixes completely the identification of these fields in zero energy ontology.
   1. In this framework chiral fields are generalizations of induced spinor fields and vector fields those of gauge potentials obtained by replacing them with their super-space counterparts. Chiral condition reduces to analyticity in theta parameters thanks to the different definition of hermitian conjugation in zero energy ontology (q is mapped to a derivative with respect to theta rather than to [`(q)]) and conjugated super-field acts on the product of all theta parameters.

   2. Chiral action is a straightforward generalization of the Dirac action coupled to gauge potentials. The counterpart of YM action can emerge only radiatively as an effective action so that the notion emergence is now unavoidable and indeed basic prediction of TGD.

   3. The propagators associated with the monomials of n theta parameters behave as 1/pⁿ so that only J=0,1/2,1 states propagate in normal manner and correspond to normal particles. The presence of monomials with number of thetas higher than 2 is necessary for the propagation of bosons since by the standard argument fermion and scalar loops cancel each other by super-symmetry. This picture conforms with the identification of graviton as a bound state of wormhole throats at opposite ends of string like object.

   4. This formulation allows also to use modified gamma matrices in the measurement interaction defining the counterpart of super variant of Dirac operator. Poincare invariance is not lost since momenta and color charges act on the tip of CD rather than the coordinates of the space-time sheet. Hence what is usually regarded as a quantum theory in the background defined by classical fields follows as exact theory. This feeds all data about space-time sheet associated with the maximum of Kähler function. In this approach WCW as a Kähler manifold is replaced by a cartesian power of CP₂, which is indeed quaternionic Kähler manifold. The replacement of light-like 3-surfaces with number theoretic braids when finite measurement resolution is introduced, leads to a similar replacement.

   5. Quantum TGD as a "complex square root" of thermodynamics approach suggests that one should take a superposition of the amplitudes defined by the points of a coherence region (identified in terms of the slicing associated with a given wormhole throat) by weighting the points with the Kähler action density. The situation would be highly analogous to a spin glass system since the modified gamma matrices defining the propagators would be analogous to the parameters of spin glass Hamiltonian allowed to have a spatial dependence. This would predict the proportionality of the coupling strengths to Kähler coupling strength and bring in the dependence on the size of CD coming as a power of 2 and give rise to p-adic coupling constant evolution. Since TGD Universe is analogous to 4-D spin glass, also a sum over different preferred extremals assignable to a given coherence regions and weighted by exp(K) is probably needed.

The latest discovery of Fermi telescope: electro-pions from lightnings?

Lubos Motl wrote a posting about the most recent discovery of Fermi space telescope.

It was discovered already years ago that lightnings are accompanied by gamma rays. For instance, the strong electric fields created by a positively charged region of cloud could accelerate electron from both downwards and upwards to this region. The problem is that atmosphere is not empty and dissipation would restrict the energies to be much lower than gamma ray energies which are in MeV range. Note that the temperatures in lightning are about 3× 10⁴ K and correspond to electron energy of 2.6 eV which is by a factor 10⁵ smaller than electron mass and gamma ray energy scale!

Situation changes if dissipation is absent so that electrons are accelerated without any energy losses. The alert reader of earlier postings can guess what I am going to say next;-)! Electrons reside in large hbar quantum phase at magnetic flux tubes so that dissipative losses are small and electrons can reach relativistic energies. This is the explanation that I provided years ago for the gamma rays associated with lightnings.

Fermi however observed also something completely new. There is also a peaking of gamma rays around energy .511 MeV. This requires a different mechanism. One such mechanism is a decay of some exotic particle to two gamma rays produced in a collision of electrons. This brings in exotic particles that I call lepto-hadrons. They represent one of the basic predictions of quantum TGD distinguishing it from standard model and its standard extensions (also string models). Basically color excited states of leptons are in question forming color bound states about which simplest examples are leptopions, in particular electro-pion whose mass is just twice the electron mass so that its decays wold produce gamma rays with energy .511 MeV. Leptohadron hypothesis is discussed extensively here, and the article predicting the particles was published already in 1990 (after this publishing became in practice impossible due to the censorship by string hegemony and blackmailing activities of finnish colleagues).

Amusingly, just year ago there was an intense debate going on about the evidence discovered by CDF for a new particle (see this and the subsequent posts). This particle could be identified as one of the exotic particles predicted by leptohadron hypothess. The interpretation was that CDF had found evidence for colored excitation of τ lepton and associated leptopion like particles. There was an intense debate and - quite predictably - the anomaly was forgotten after the explanation based on Nima Arkani Hamed's theory failed (Lubos already predicted Nobel prize for Nima!) and the only quantitative and working explanation had turned out to be the one based on TGD. This also led to oppressive actions in Finland: Helsinki University did not allow anymore to keep my homepage in University computer anymore and refused also to redirect visitors to the new address. Situation had got really dangerous and local powerholders had simply no other choice than the tactic of burned bridges applied to web links.

After this short sidetrack to the sociology of science (charming-isn't it?!) let us return to the leptopion associated with electron - electropion. It has mass slightly above 2m_e and decays to a pair of gamma rays with energy .511 MeV. The first evidence for leptopions was found surprisingly early- already in seventies in heavy ion collisions- just above the Coulomb wall. I constructed a model for these events around 1990. By general anomaly considerations it became clear that electropions are created when heavy nuclei collide near Coulomb wall. What is essential is the presence of mutually non-orthogonal electric and magnetic fields during the collision. The production amplitude is essentially the Fourier transform of the "instanton density" E·B. There are many other anomalies supporting this model- in particular, orthopositronium decay anomaly. There is also evidence for muo-pions and CDF provided it for tau-pions. All these anomalies have been forgotten- presumably for the simple reason that they do not fit to standard model and its standard extensions, which have become the prevailing ideology.

But experiment strikes back mercilessly! Now it seems that Fermi finds leptopions in lightning strikes! This must be a horrible nightmare for a theoretician firmly decided what can exist and what not! If these disgusting electro-pions are there, collisions of highly energetic particles lasting for time of about hbar/MeV are expected. The natural candidates for the colliding charged particles are electrons. The center of mass system -the system in which total momentum of colliding electron pair vanishes- should be in good approximation at rest with respect to Fermi space telescope. Otherwise the energy of gamma rays would be higher or lower than .511 MeV. The only possibility that I can imagine is that the second electron comes from below and second from above the positively charged region of the thunder cloud. Both arrive as dark electrons with a large value of hbar and are accelerated to relativistic energies since dissipation is very small. They could collide as dark electrons (the more probable option as will be found below) or suffer a phase transition transforming them to ordinary electrons before the collision. Electropion coherent state is created in the strong E·B created for a a period of time of order hbar₀/MeV. This state annihilates rapidly to pairs of gamma rays which are ordinary or transform to ordinary ones depending on whether electrons where dark or not.

What the phase transition of dark electrons to ordinary electrons means, needs some explaining. The generalized imbedding space is obtained by glueing almost copies of 8-D imbedding space M⁴×CP₂ along their common back to get a book like structure. Particles at different pages of the book are dark with respect to each other in the sense that they have no local interactions. This is enough to explain what is actually known about dark matter. Particles at different pages can however interact via classical fields and photon exchange (for instance). The phase transition of electron from dark to visible form preceding the collision of dark electrons would simply mean the leakage from large hbar page to the "visible" page with ordinary value of Planck constant.

Alert reader might be ready to ask the obvious question. Why not to test the hypothesis in laboratory? It should not be too difficult to allow two electrons to collide with a relativistic energy and find whether gamma pairs with energy .511 MeV are produced in rest system. Maybe gamma ray pairs have been missed for some reason? If not (the probable option), then colored electrons and leptopions are always dark. This would explain why the colored leptons do not contribute to the decay widths of weak gauge bosons which pose very strong constraints for the existence of light exotic particles.

For more details about leptohadron hypothesis see the chapter Recent Status of Leptohadron Hypothesis of "p-Adic Length Scale Hypothesis And Dark Matter Hierarchy".

An experimental breakthough in quantum understanding of telepathy?

Telepathy by quantum entanglement is one of the basic ideas of TGD inspired consciousness. This requires some new physics.

1. Macroscopic quantum coherence is needed in scales much longer than standard quantum mechanics allows. Hierarchy of Planck constants makes this certainly possible but one cannot exclude the possibility that mere magnetic flux tube like structures is enough: I do not believe in this option.

2. The idea that entangelment of selves gives rise to telepathy is plagued by a problem: in TGD framework entanglement means a loss of consciousness at the level of both selves since it is the fusion of selves which becomes the conscious entity! The subselves of self can however entangle if this entangelement is below the measurement resolution of selves and therefore does not lead to a loss of consciousness at the level of selves. Selves experience the fusion of subselves as a fusion of corresponding mental images to single shared mental image. Stereo consciousness is essentially in question. Stereo vision represents only one particular example of this. During sleep we ourselves could be the mental images fusing to a single gigantic stereo mental image of a higher level conscious entity. This mental image would represent "human condition".

3. Any quantal idea of TGD must have also geometrical space-time counterpart by quantum classical correspondence. The geometrical correlates for selves are space-time sheets. Subselves correspond to smaller space-time sheets topologically condensed at those of selves. The geometrical correlate for the entanglement are flux tubes connecting the space-time sheets associated with the selves. In the case of subselves these subselves are too "thin" to be visible in the resolution of selves.

Only fifteen years after the explicit formulation of the idea situation seems to be mature for the experimental verification as one learns from Hammock Physicist, a blog belonging to Scientific Bloggin. James Randi Educational Foundation might be forced to pay the one Megadollar prize that it has promised to anyone who can experimentally demonstrate some paranormal power.

The experimental arragement is simple. The two subject persons - not Alice and Bob at this time;-) but Cora and Reid - two postdocs in theoretical physics - color the 3×3 squares of a larger square. Reid follows the rule that each column contains an odd number of red squares (that is 1 or 3). Cora obeys the rule that each row contains an even number of red squares. Since the total number of red squares is odd in the first case and even in the second case, colorings satisfying both rules are not possible. It this were the case Cora and Reid could make an agreement about making only these optimal colorings in a fixed order for instance.

Each coloring process equals three steps and for a given step the row (column) to be colored is selected in random manner. Alice and Bob try to perform the coloring in such a manner that the intersection of the row of Cora and column of Reid has same color. The optimal coloring strategy would yield a success rate of 89 per cent on the average. In the preliminary test Alice and Bob involving 40 turns were however able to reach 100 per cent success rate! The probability of this using optimal strategy is 1 percent.

I must say that I am shocked. Only 15 years after I began to work systematically with TGD inspired theory of consciousness, one of its most spectacular predictions might be demonstratable by an extremely simple experiment having fantastic implications -not only for our views about consciousness and biology - but also for quantum theory itself.

The eight books about TGD inspired quantum theory of consciousness and biology can be found at my homepage.

Is the perturbation theory based on TGD inspired definitions of super fields UV finite?

In the case of infinite-dimensional super-space the definition of the super-fields is not quite straightforward since the super-space integrals of finite polynomials of theta parameters always vanish so that the construction of super-symmetric action as an integral over super-space would give a trivial result. For chiral fields the integrals are formally non-vanishing but in the case that the super-field reduces to a finite polynomial of theta at y^μ=0 the non-vanishing terms in real Lagrangian involve the action of an infinite number of operators D^cα_c (^c denotes overline for D and _c dot for Weyl spinor index) implying the proportionality to an infinite power of momentum which vanishes for massless states. It seems that one should be able to add in a natural manner terms which are obtained as theta derivatives of the product of all theta parameters and that the action should consist of the products of the terms associated with mononomials of theta and monomials of derivatives with respect to theta parameters acting on the infinite product of theta parameters, call it X.

The fact that positive resp. negative energy vacuum is analogous to Dirac sea with negative resp. positive energy states filled suggests a remedy to the situation. This would mean that positive energy chiral field is just like its ordinary counterpart whereas negative energy chiral fields would be obtained by applying a polynomial of derivatives of theta to the product X=∏θ of all theta parameters. The theta integral of X is by definition equal to 1. In integral over theta parameters the monomials of theta associated with positive energy chiral field and negative energy chiral field would combine together and one would obtain desired action. In the following this approach is sketched. Devil lies in the details and detailed checks that everything works are not yet done.

This was what I wrote in the first version of this posting and I was right;-)! Devil indeed lies in the details! The calculations turned out to contain blunder (should I blame flu or market economy for the error or just admit that I have miserable calculational skills?;-)). It became clear that in TGD context the definition of super-covariant derivative reducing to ordinary partial derivative leads to much more elegant theory. In zero energy ontology super-symmetry reduces to analyticity with respect to theta parameters. In standard framework analyticity would not give kinetic terms to the chiral action but now the situation is different.

1. TGD variants of chiral super fields

Consider first the construction of chiral super-fields and of the super-counterpart of Dirac action.

1. Wormhole throats carry a collection of collinearly moving fermions with momentum appearing in the measurement interaction term identified as the total momentum. This suggests that kinetic terms behave positive powers of Dirac operator with one power for each theta parameter.

2. One must be careful with dimensions. The counterpart of Dirac operator is D = σ^k(p_k+Q_k)/M. The mass parameter M must be included for dimensional reasons and changes only the normalization of the theta parameters from that used earlier and changes the anti-commutation relations of the super-algebra in an obvious manner. The value of M is most naturally CP₂ mass defined as m(CP₂) = n× hbar₀/R, where R is the length of CP₂ geodesic and n is a numerical constant.

3. In the case of single wormhole throat one can speak about positive and negative energy chiral fields. Positive energy chiral fields are constructed as polynomials, and more generally, as Taylor series whereas negative energy chiral fields are obtained by mapping positive energy chiral fields to an operator in which each theta parameter θ is replaced with

   ∂_θD=∂_θσ^k(p_k+Q_k)/M .

   This operator acts in the product X of all theta parameters to give the negative energy counterpart of chiral field. The inclusion of sigma-matrices is necessary in order to obtain chiral symmetry at the level of H, in particular the counterpart of Dirac action. In the integral over all theta parameters defining the Lagrangian density the terms corresponding to mononomials M(θ,x) and their conjugates M(∂θ _cD^→,x) are paired and theta integrals can be carried out easily. Here → tells that the spatial derivatives appearing in D are applied to M.

4. There is an asymmetry between positive and negative energy states and the experience with the ordinary Dirac action Ψ^cD^→Ψ-Ψ^cD^←Ψ (^c denotes overline) suggests that one should add a term in which θ parameters are replaced with -Dθ so that space-time derivatives act on the positive energy chiral field and partial derivative ∂_θc appear as such. The most plausible interpretation is that the negative energy chiral field is obtained by replacing θs in the positive energy chiral field with ∂_θs and allowing to act on X. The addition of D would thus give rise to the generalization of the kinetic term.

5. Chiral condition can be posed and one can express positive energy chiral field in as an infinite powers series containing all finite powers of theta parameters whereas negative energy chiral field contains only infinite powers of θ. The interpretation is in terms of different Dirac vacuum. What one means which super-covariant derivatives is not quite clear.
   1. The usual definition of super covariant derivatives would be as

      D_iα=∂_iα+ i(θ_cD)_iα ,

      D^c_iαc=∂_iαc +i(Dθ)_iαc .

   2. A definition giving rise to the same anti-commutators would be as

   D_iα=∂_iα ,

   D^c_iαc=∂_iαc +2i(Dθ)_iαc

   In the recent case D^c does not appear at all in the chiral action since for negative energy chiral field conjugation does not correspond to θ→θ_c but to θ→ ∂_θ and 1→ X. Hence the simplest theory would result using D_α=∂_α.

   3. If one includes into the product of X of theta parameters only θs but not their conjugates, the two definitions are equivalent since the powers of θ_cDθ give nothing in theta integration. This definition of X is be possible using the definition of hermitian conjugation appropriate also for N=∞. This formalism of course works also for a finite value of N.

Consider now the resulting action obtained by performing the theta integrations. The interesting question is what form of the super-covariant derivatives one should use. The following considerations suggests that the two alternatives give almost identical -if not identical- results but that the simpler definitionD_α=∂_α is much more elegant.

1. For D_iα=∂_iα the propagators are just inverses of D^d where d is the number of theta parameters in the monomial defining the super-field component in question so that the Feynman rules for calculating bosonic propagators and vertices are very simple. Only the spinor and vector terms corresponding to degree d=1 and d=2 in theta parameters behave in the expected manner. This conforms with the collinearity. In particular, for spin 2 states the propagator would behave like p^-4 for large momenta. This conforms with the prediction that graviton cannot correspond to singlet wormhole throat but to a string like object consisting of a superposition of pairs of wormhole contacts and of wormhole throats. If this expansion makes sense, higher spin propagators would behave as increasingly higher inverse powers of momentum and would not contribute much to the high energy physics. At energies much smaller than mass scale they would give rise to contact terms proportional to a negative power of mass dictated by the number of thetas.

2. For D_iα=∂_iα+i(θ_cD) _iα the formulas become considerably more complex due to the infinite exponentials exp(i&theta_cDθ), and for N= ∞ one obtains infinite factors given essentially by N multiplying the propagators and vertices. These factors however cancel in the chiral loops defining bosonic vertices and propagators. Also a factor depending on momentum appears but cancel in these loops. The deviations from the first option are small but it seems that this option is so ugly that it can be safely forgotten.

2. TGD variant of vector super field

Chiral super-fields are certainly not all that is needed. Also interactions must be included, and this raises the question about the TGD counterpart of the vector super-field.

1. The counterpart of the chiral action would be a generalization of the Dirac action coupled to a gauge potential obtained by adding the super counterpart of the vector potential to the proposed super counterpart of Dirac action. The generalization of the vector potential would be the TGD counterpart of the vector super field. Vector particle include M⁴ scalars since Higgs behaves as CP₂ vector and H-scalars are excluded by chiral invariance.

2. Since bosons are bound states of positive and negative energy fermions at opposite wormhole throats it seems that vector super field must correspond to an operator slashed between positive and negative energy super-fields rather than ordinary vector super-field. The first guess is that vector super-field is an operator expressible as a Taylor series in which positive energy fermions correspond to the powers of θ and negative energy fermions correspond to the powers of derivatives ∂_θ. Naively, D in ∂_θD is replaced by D+V. Vector super-field must be hermitian (V=V⁺) with hermitian conjugation defined so that it maps theta parameters to the partial derivatives ∂_θ and performs complex conjugation. A better guess is that D appearing in the definition of the kinetic term is replaced with D+V where V is a hermitian super-field. This definition would be direct generalization of the minimal substitution rule.

3. It is difficult to imagine how a kinetic term for the vector super-field could be defined. This supports the idea that bosonic propagators and vertices emerge as one performs functional integral over components of the chiral fields.

4. There is also the question about gauge invariance. The super-field generalization of the non-Abelian gauge transformation formula looks more like the generalization of Dirac action to its super-counterpart: D→ D+V everywhere. Positive energy chiral field would transform as Φ₊→ exp(Λ)&Phi₊;, where Λ is a chiral field. The negative energy chiral field would transform as Φ_-→ exp(Λ⁺)&Phi_-; with hermitian conjugation (denotes by +) involving also the map of thetas to their derivatives. Each theta parameter would represent a fermion transforming under gauge symmetries in a manner dictated by its electro-weak quantum numbers (the inclusion of color quantum numbers is not quite trivial: probably they must be included as a label for quark modes). As in the case of Dirac action, the transformation formula for vector super-field would be dictated by the requirement that the derivatives of Λ coming from exp(Λ) are canceled by the derivative terms in the transformation formula for the vector super-field.

3. Is the perturbation theory UV finite?

Also for the proposed TGD inspired identifications of chiral super-fields and vector super-fields, the cancelation of UV divergences should be essentially algebraic and due to the cancelation of chiral contributions from the loops contributing to the vector super-field propagators and vertices. Also for the emerging bosonic effective action same mechanism should be at work.

The renormalization theorems state that the only renormalizations in SUSYs are wave function renormalizations. In the case of bosonic propagators loops therefore mean only the renormalization of the propagator. In the recent case only the chiral loops are included so that the situation is analogous to Abelian YM theory or N=4 super YM theory, where the beta functions for gauge couplings vanish. Hence one might hope that also now wave function renormalization is the only effect so that the radiatively generated contribution should be proportional to the standard form of the vector propagator. The worst that can occur is logarithmically diverging renormalization of the propagator which occur in many SUSYs. The challenge is to show that logarithmic divergences possibly coming from the θ^d, d=1,2, parts of the chiral super-field cancel. The condition for this cancelation is purely algebraic since the coupling to k=2 part is gradient coupling so that the leading divergences have same form. It could happen that the lowest contributions cancel but the contributions from field components with d>2 give a non-vanishing and certainly finite contribution.

It could happen that the d<1 contributions cancel exactly as they do in SUSYs but the contributions from field components with d> 2, give a non-vanishing and certainly finite contribution. If this were the case then the exotic chiral field components with propagators behaving like 1/p^d, d> 2, would make possible the propagation for the components of the vector super-fíeld.

For the proposed SUSY limit of TGD see the new chapter Does the QFT Limit of TGD Have Space-time Super-Symmetry? of the book "Towards M-Matrix".

Why SUSY would not allow fields with spin higher than two?

The recent progress in understanding QFT limit of TGD led to a question, which I would be happy to find an answer. The standard wisdom says that N=8 is absolute upper bound for the super-symmetry (spins larger than 2 are not regarded as physical). In TGD N=8 emerges naturally for space-time surfaces due to the dimension D=8 of imbedding space and the fact that imbedding space spinors with given H-chirality (quarks and leptons which color appearing as partial waves in CP₂ have 8 complex components. One obtains N=8 if one considers only the super-algebra defined by the oscillator operators associated with the lowest modes of these spinor fields at light-like 3-surfaces obtained as a solutions of the modified Dirac equation with measurement interaction term.

It is also possible to consider the supersymmetry generated by all modes of the induced spinor fields and thus with a quite large (even infinite for string like objects) number N of super generators. This supersymmetry is broken as all supersymmetries in TGD framework. This means that rather high spins are present in the analogs of scalar and vector multiplets and the Kähler potential (expected to be closely related to the Kähler function of the world of the classical worlds (WCW)) describing interaction of chiral multiplet with a vector multiplet can be constructed also for any value of N - at least formally. If one believes on the generalization of the bosonic emergence, one expects that bosonic part of the action is generated radiatively as one functionally integrates over the fields appearing in the chiral multiplet.

I tried to find material from web about possibly existing proposals for N>8 SUSY theories or D>12 SUSY theories containg higher spin fields. I found proposals for higher spin theories with N=1 for instance, but nothing else. Superstring thinking has really made its way through: D=12 (F-theory) and N=8 are the absolute upper bounds! It seems that my colleagues enjoying a monthly salary are maximally rational career builders.

The standard wisdom says that is is not possible to construct interactions for higher spin fields. Is this really true? Why wouldn't the analogs of scalar (chiral/hyper) and vector multiplets make sense for higher values of N? Why would it be impossible to define an spin 1/2 chiral super-field associated with the vector-multiplet and therefore the supersymmetric analog of YM action using standard formulas? Why the standard coupling to chiral multiplet would not make sense? Could some-one better-informed tell me the answer?

One objection against higher spins is of course the lack of the geometric interpretation. Spin 1 and Spin 2 fields allow it. Can one then imagine any geometric interpretation for higher spin components of super-fields? John Baez and others are busily developing non-Abelian generalizations of group theory, categories and geometry and speak about things that they call n-groups, n-categories, and n-geometries. Could the generalization of ordinary geometry to n-geometry in which parallel translations are performed for higher dimensional objects rather than points provide a natural interpretation for gauge fields assigned to higher spins? One would have natural hierarchy. Parallel translations of points would give rise curves, parallel translations of curves would give rise to surfaces, and so on. As as a special case the entire hierarchy of these parallel translations would be induced by ordinary parallel translation as I suggested in this blog for years ago.

Addition: At this moment one can make only guesses concerning the super-fields describing wormhole throats and contacts as particles.

1. The physical picture suggested by the notion of emergence is that kinetic terms behave negative powers of Dirac operator since wormhole throats carry a collection of collinearly moving fermions with momentum appearing in the measurement interaction term identified as the total momentum.

2. This suggests a construction of a super-field from any finite polynomial P(θ,x) of theta parameters by assigning to each monomial appearing in it the monomial P(∂_θc σ_c ^k ∂_k →,x) and applying it to the conjugate of X. Here → tells that the derivative is applied to P itself. All theta parameters can be included and _c denotes conjugation denoted by overline usually. By restricting the degree of the monomial to one half of the maximal the construction works also for a finite value of N.

3. In the analog of the chiral action monomials and their conjugates would combine to form a term involving a power of Dirac operator equal to the degree of the monomial of thetas so that kinetic terms would come as powers of σ^k∂_k.

4. Only the spinor and vector terms would behave in the expected manner and scalar term would vanish. In particular, for spin 2 - the propagator would behave like p^-4 for large momenta. This conforms with the view that graviton must correspond to a string like object consisting of a superposition of pairs of wormhole contacts and of wormhole throats rather than single wormhole throat. If this expansion makes sense, higher spin propagators would behave as increasingly higher inverse powers of momentum and would not contribute much to the high energy physics. At energies much smaller than mass scale they would give rise to contact terms proportional to a negative power of mass dictated by the number of thetas.

5. This is certainly not all that is needed since interactions must be included too. Here one might consider a generalization of Dirac action as a trilinear interaction term formed from similar "chiral field" assignable to bosons described as wormhole contacts with negative and positive energy thetas and from positive and negative energy fermionic super fields. Generalization of bosonic emergence would give purely bosonic part of action as radiative corrections. More conventional approach would add the bosonic kinetic term also the action.

For the proposed SUSY limit of TGD see the new chapter Does the QFT Limit of TGD Have Space-time Super-Symmetry? of the book "Towards M-Matrix".

Space-Time Super-Symmetry and TGD

Contrary to the original expectations, TGD seems to allow a generalization of the space-time super-symmetry. This became clear with the increased understanding of the modified Dirac action. The introduction of a measurement interaction term to the action allows to understand how stringy propagator results and provides profound insights about physics predicted by TGD (see the new chapter Does the Modified Dirac Equation Define the Fundamental Action Principle of "TGD: Physics as Infinite-Dimensional Geometry").

The appearance of the momentum and color quantum numbers in the measurement interaction couples space-time degrees of freedom to quantum numbers and allows also to define SUSY algebra at fundamental level as anti-commutation relations of fermionic oscillator operators. Depending on the situation a finite-dimensional SUSY algebra or the fermionic part of super-conformal algebra with an infinite number of oscillator operators results. The addition of a fermion in particular mode would define particular super-symmetry. Zero energy ontology implies that fermions as wormhole throats correspond to chiral super-fields assignable to positive or negative energy SUSY algebra whereas bosons as wormhole contacts with two throats correspond to the direct sum of positive and negative energy algebra and fields which are chiral or antichiral with respect to both positive and negative energy theta parameters. This super-symmetry is badly broken due to the dynamics of the modified Dirac operator which also mixes M⁴ chiralities inducing massivation. Since righthanded neutrino has no electro-weak couplings the breaking of the corresponding super-symmetry should be weakest.

The question is whether this SUSY has a realization as a SUSY algebra at space-time level and whether the QFT limit of TGD could be formulated as a generalization of SUSY QFT. There are several problems involved.

1. In TGD framework super-symmetry means addition of fermion to the state and since the number of spinor modes is larger states with large spin and fermion numbers are obtained. This picture does not fit to the standard view about super-symmetry. In particular, the identification of theta parameters as Majorana spinors and super-charges as Hermitian operators is not possible.

2. The belief that Majorana spinors are somehow an intrinsic aspect of super-symmetry is however only a belief. Weyl spinors meaning complex theta parameters are also possible. Theta parameters can also carry fermion number meaning only the supercharges carry fermion number and are non-hermitian. The the general classification of super-symmetric theories indeed demonstrates that for D=8 Weyl spinors and complex and non-hermitian super-charges are possible. The original motivation for Majorana spinors might come from MSSM assuming that right handed neutrino does not exist. This belief might have also led to string theories in D=10 and D=11 as the only possible candidates for TOE after it turned out that chiral anomalies cancel.

3. The massivation of particles is basic problem of both SUSYs and twistor approach. The fact that particles which are massive in M⁴ sense can be interpreted as massless particles in M⁴×CP₂ suggests a manner to understand super-symmetry breaking and massivation in TGD framework. The octonionic realization of twistors is a very attractive possibility in this framework and quaternionicity condition guaranteing associativity leads to twistors which are almost equivalent with ordinary 4-D twistors.

4. The first approach is based on an approximation assuming only the super-multiplets generated by right-handed neutrino or both right-handed neutrino and its antineutrino. The assumption that right-handed neutrino has fermion number opposite to that of the fermion associated with the wormhole throat implies that bosons correspond to N=(1,1) SUSY and fermions to N=1 SUSY identifiable also as a short representation of N=(1,1) SUSY algebra trivial with respect to positive or negative energy algebra. This means a deviation from the standard view but the standard SUSY gauge theory formalism seems to apply in this case.

5. A more ambitious approach would put the modes of induced spinor fields up to some cutoff into super-multiplets. At the level next to the one described above the lowest modes of the induced spinor fields would be included. The very large value of N means that N > 32 SUSY cannot define the QFT limit of TGD for higher cutoffs. One must generalize SUSYs gauge theories to arbitrary value of N but there are reasons to expect that the formalism becomes rather complex. More ambitious approach working at TGD however suggest a more general manner to avoid this problem.
   1. One of the key predictions of TGD is that gauge bosons and Higgs can be regarded as bound states of fermion and antifermion located at opposite throats of a wormhole contact. This implies bosonic emergence meaning that it QFT limit can be defined in terms of Dirac action. The resulting theory was discussed in detail in and it was shown that bosonic propagators and vertices can be constructed as fermionic loops so that all coupling constant follow as predictions. One must however pose cutoffs in mass squared and hyperbolic angle assignable to the momenta of fermions appearing in the loops in order to obtain finite theory and to avoid massivation of bosons. The resulting coupling constant evolution is consistent with low energy phenomenology if the cutoffs in hyperbolic angle as a function of p-adic length scale is chosen suitably.

   2. The generalization of bosonic emergence is natural in the sense that the TGD counterpart of SUSY is obtained by the replacement of Dirac action with action for chiral super-field coupled to vector field as the action defining the theory so that the propagators of bosons and all their super-counterparts would emerge as fermionic loops.

   3. The huge super-symmetries give excellent hopes about the cancelation of infinities so that this approach would work even without the cutoffs in mass squared and hyperbolic angle assignable to the momenta of fermions appearing in the loops. Cutoffs have a physical motivation in zero energy ontology but it could be an excellent approximation to take them to infinity. Alternatively, super-symmetric dynamics provides cutoffs dynamically.

6. The intriguing formal analogy of the Kähler potential and super-potential with the Kähler function defining the Kähler metric of WCW and determined up to a real part of analytic function of the complex coordinates of WCW. This analogy suggests that the action defining the SUSY-Kähler potential- is identifiable as the Kähler function defining WCW Kähler metric at its maximum. Super-potential in turn would correspond to a holomorphic function defining the modification of Kähler function due and the space-time sheet due to measurement interaction. This beautiful correspondence would make WCW geometry directly visible in the properties of QFT limit of TGD.

To sum up, the new chapter fuses three ideas developed during this year. The generalization of the twistor formalism via the induced octonionic twistor structure and masslessness in 8-D sense as a prerequisite for twistorialization and higher N super-symmetry, bosonic emergence, and the possibility to realize space-time super-symmetry algebra via the introduction of the measurement interaction term in the modified Dirac action. It seems that all basic prerequisite for developing quantum TGD to a calculable theory exist but a collective effort is of course needed to achieve this.

For the details see the new chapter Does the QFT Limit of TGD Have Space-time Super-Symmetry? of the book "Towards M-Matrix".

New evidence for macroscopic quantum coherence in living matter

The idea that living systems might be quantum systems emerged around 1980 in Esalem conference. David Finkelstein - the chief editor of International Journal of Theoretical Physics, in which I was able to publish my works at that time - was the primus motor. Around 1995 an intense period of discussions in email groups began. Hameroff-Penrose model was one of the models discussed. The books of Penrose had a great impact on the gradual transformation of quantum consciousness to a respectable scientific topic (not everywhere: there are some distant corners of the globe such as my home country where quantum consciousness is still regarded as a pseudoscience). At that that I began serious and almost whole-daily work in TGD inspired theory of consciousness and quantum biology. The wisdom gained in this process in turn led to a progress in the mathematical formulation of quantum TGD proper made possible by a radically new vision about fundamentals.

The attitude towards the quantum vision about living systems depend on the basic prejudices of the scientist. Average hard wired guy willing to appear as an authority relies on text book wisdom and of course immediately tells that quantum effects cannot be significant in length and time scales involved and that there is absolutely no evidence for them. We should not however trust text book wisdom and -as I have learned- even less to average physicists;-)! After all, living systems look very quantal and we experience directly what could be called free will. We should rely on what we directly experience and ability to think rationally rather than authorities and be ready to question also the existing view about quantum physics.

What could biology and neuroscience give to the quantum physics? This should be the question. If the standard quantum physics does not allow the needed macroscopic quantum phases, we must modify the quantum physics. Even quantum consciousness theorists have usually adopted the view that wave mechanics is enough for understanding of living matter. Penrose has been an exception since he proposes that quantum gravity could be important. Perhaps it is not a mere co-incidence that persons who most passionately believe that the old theory is enough, have also the most limited skills as theorists.

During years I have learned that there is a lot of indirect experimental evidence for the quantum view (the strange findings about the functioning of cell membrane, the effects of ELF em fields on vertebrate brain,...), and have used these bits of experimental data to develop TGD based view about quantum physics. This involves the identification of dark energy and dark matter in terms of macroscopic quantum phases with non-standard large value of Planck constant, the new view about space-time and about the relationship between experienced time and time of physicists, new view about quantum states based on zero energy ontology, etc.. Also p-adic physics is essential in the proposed view about correlates of cognition and intention. Of course, this all this is very speculative and my frustrating realization has been that the good theory necessarily comes long before the experiments directly testing it.

During years the experimentation to test the presence of quantum effects in living matter has begun. And the positive evidence is accumulating. In Discover magazine there is an article titled Is Quantum Mechanics Controlling Your Thoughts? telling among other things about the latest direct evidence of quantum effects provided by experiments related to photosynthesis and odor perception.

Quantum coherence and photosynthesis

The article summarizes in popular terms the contents of the paper Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems by Fleming and collaborators reporting evidence for quantum coherence in photosynthesis. The absorption of photon induces electron current from the point of capture- chlorosome- to the reaction centers. The semiclassical theory predicts the dissipation of the electronic energy to be about 20 per cent whereas the observed dissipation is only about 5 per cent. This suggests quantum coherence. The following abstract of the original article summarizes the essentials.

Photosynthetic complexes are exquisitely tuned to capture solar light efficiently, and then transmit the excitation energy to reaction centres, where long term energy storage is initiated. The energy transfer mechanism is often described by semiclassical models that invoke 'hopping' of excited-state populations along discrete energy levels. Two-dimensional Fourier transform electronic spectroscopy has mapped6 these energy levels and their coupling in the Fenna–Matthews–Olson (FMO) bacteriochlorophyll complex, which is found in green sulphur bacteria and acts as an energy 'wire' connecting a large peripheral light-harvesting antenna, the chlorosome, to the reaction centre. The spectroscopic data clearly document the dependence of the dominant energy transport pathways on the spatial properties of the excited-state wavefunctions of the whole bacteriochlorophyll complex. But the intricate dynamics of quantum coherence, which has no classical analogue, was largely neglected in the analyses—even though electronic energy transfer involving oscillatory populations of donors and acceptors was first discussed more than 70 years ago11, and electronic quantum beats arising from quantum coherence in photosynthetic complexes have been predicted and indirectly observed. Here we extend previous two-dimensional electronic spectroscopy investigations of the FMO bacteriochlorophyll complex, and obtain direct evidence for remarkably long-lived electronic quantum coherence playing an important part in energy transfer processes within this system. The quantum coherence manifests itself in characteristic, directly observable quantum beating signals among the excitons within the Chlorobium tepidum FMO complex at 77 K. This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path.

The popular article translates the article to the following piece of text.

To unearth the bacteria’s inner workings, the researchers zapped the connective proteins with multiple ultra-fast laser pulses. Over a span of femto­seconds, they followed the light energy through the scaffolding to the cellular reaction centers where energy conversion takes place. Then came the revelation: Instead of haphazardly moving from one connective channel to the next, as might be seen in classical physics, energy traveled in several directions at the same time. The researchers theorized that only when the energy had reached the end of the series of connections could an efficient pathway retroactively be found. At that point, the quantum process collapsed, and the electrons’ energy followed that single, most effective path.

My own interpretation would be following.

1. Remarkably long lived electronic quantum coherence is claimed to be present. Authors propose that quantum computation like process - quantum random walk -could be in question. If I have understood correctly, the proposed process can halt only by a state function reduction localizing the electron at the reaction center. Completely standard Schrödinger evolution in the network would be otherwise in question. The good news is that the average time to find from the entrance to exit in this kind of process is exponentially shorter than in the classical random walk. One can say that exit plus all other points are always reached after some minimum time and it is enough to perform the state function reduction localizing the electron to the exit.

2. Somewhat confusingly, the popularizers claim that the authors argue (I do not have access to the original article) that the quantum random walk selects the shortest path from the chlorosome to the reaction center is in question. Quantum collapse is a non-deterministic process and if it selects the path in this particular case it can select any path with some probability, not always the shortest one. The selection of the shortest path is not necessarily needed since the quantum random walk with fixed entrance and exit is by its inherent nature exponentially faster than its classical counterpart. The proposed interpretation makes sense only if the state function reduction takes place immediately after the electron's state function at the exit becomes non-vanishing. Does it? I cannot say.

If one accepts this view, the sole problem is to understand how macroscopic quantum coherence is possible in the length scales considered. There are good arguments supporting the view that this is not the case for the ordinary quantum mechanics. In TGD framework the hierarchy of Planck constants suggests that both macroscopic quantum coherence and very low dissipation rate are due to the large value of hbar for electrons. For instance, for hbar=5×hbar₀ the naive estimate is that dissipation rate should reduce by a factor 1/5 and coherence times and lengths should increase by a factor 5. I have proposed much larger values of hbar in the model of living system. In particular, the model for high temperature super-conductivity assigns to these systems basic biological length scales from p-adic length scale hypothesis (5 nm thickness of lipid layer of cell membrane corresponds to L(149), 10 nm thickness of lipid layer to L(151) and the length scale 2.5 μm of cell nucleus to L(167)). The electron Compton length is scaled up by a factor 2¹¹ to so that it corresponds to the p-adic length scale L(149)=5 nm. This would scale up the fundamental bio-time scale of .1 seconds predicted by TGD to be the time scale assignable to causal diamond of electron by factor 2²² to about 4 × 10⁵ seconds.

For TGD based ideas about photosynthesis see this.

Odor perception and quantum coherence

The article discusses also the work of the biophysicist Luca Turin related to odor perception as additional support for quantum brain. Before going to the article it is good to summarize the basic ideas about sensory qualia (colors, odors, ...) in TGD inspired theory of consciousness.

1. In TGD framework the identification of qualia follows from the identification of quantum jump as a moment of consciousness. Just as quantum numbers characterize the physical state, the increments of quantum numbers characterize the quantum jump between two states. This leads to a capacitor model of the sensory receptor in which the sensory perception corresponds to a generalized di-electric breakdown in which various particles carrying some quantum numbers flow between electrodes and the change of the quantum numbers at second electrodes gives rise to the sensory quale in question.

2. It is important that sensory qualia are assigned to the sensory receptors rather than to the neural circuitry of brain as in standard neuroscience. This leads to objections (phantom leg for instance) which are circumvented in TGD based vision about 4-D brain. For instance, phantom leg would correspond to sensory memory resulting by sharing the mental image about pain residing in the geometric past when the leg still existed. A massive back-projection generating virtual sensory input from brain (or from the magnetic body via brain) is needed to build the actual perception as a kind of art-work by filtrating from the actual sensory input a lot of unessential stuff and amplifying the essential features.
3. The discovery of Callahan that odor perception of insects seems to be based on IR light inspired my own the proposal that photons at IR frequencies could be involved with the odor perception so that odor perception would be at molecular level seeing by IR light. Even hearing could involve similar "seeing" in appropriate frequency range. Massless extremals (topological light rays) would serve as kind of wave guides parallel to axons along which light would propagate as kind of laser beams between receptor and brain. This would also explain why the mediation of auditory input takes so rapidly.

4. I have also proposed frequency coding for the sensory qualia. The first proposal which I dubbed as "Spectroscopy of Consciousness" stated that cyclotron frequencies assignable to various biologically important ions -much below IR range- associated with as such correspond to sensory qualia. Later I gave up this idea and proposed that frequencies code provide only a symbolic representations- define their names- as one might say. The information about qualia and more general sensory data would be represented in terms of cyclotron frequencies inducing dynamical patterns of the cyclotron Bose-Einstein condensates of biologically important ions residing at the magnetic body receiving the sensory information.

I attach a small piece of the article here to give a popular summary about the work of Luca Turin.

Quantum physics may explain the mysterious biological process of smell, too, says biophysicist Luca Turin, who first published his controversial hypothesis in 1996 while teaching at University College London. Then, as now, the prevailing notion was that the sensation of different smells is triggered when molecules called odorants fit into receptors in our nostrils like three-dimensional puzzle pieces snapping into place. The glitch here, for Turin, was that molecules with similar shapes do not necessarily smell anything like one another. Pinanethiol [C10H18S] has a strong grapefruit odor, for instance, while its near-twin pinanol [C10H18O] smells of pine needles. Smell must be triggered, he concluded, by some criteria other than an odorant’s shape alone.

What is really happening, Turin posited, is that the approximately 350 types of human smell receptors perform an act of quantum tunneling when a new odorant enters the nostril and reaches the olfactory nerve. After the odorant attaches to one of the nerve’s receptors, electrons from that receptor tunnel through the odorant, jiggling it back and forth. In this view, the odorant’s unique pattern of vibration is what makes a rose smell rosy and a wet dog smell wet-doggy.

The article A spectroscopic mechanism for primary olfactory perception by Turin explains in detail his theory and various experimental tests. Here are the core ideas in more quantitative terms.

1. The theory originates from the proposal of Dyson (not that Dyson;-)!) proposed already 1938 that odor perception might rely on the vibrational spectrum of the odorant rather than its shape alone. The spectrum would be in the wave length range 2.5-10 μm corresponding to photon energies in the range .5 eV - .125 eV. This vibrational spectrum would be excited by the current of electrons tunneling from the receptor to the odorant molecule.

2. The proposal is that odor receptor can be regarded as a pair formed by a source and sink of electrons. If there is nothing between source and sink, tunneling can occur if there is electronic energy state with same energy in both source and sink. If there is an odorant molecule between source and sink with vibrational energy E, tunneling can occur indirectly: the electron can excite a vibrational state with this energy and tunneling can occur only if the difference of electron energies in source and sink is E. Therefore the presence of odor molecule would be detected from the occurrence of the tunneling and vibrational energy spectrum would characterize the odor molecule.

One can compare the model of Turin with TGD based ideas.

1. The theory of Turin conforms at the general level with the receptor model. The "electrodes" of the sensory capacitor would correspond to the source and sink of electrons and the presence of the odorant molecule between the "electrodes" would induce the current. The current of electrons from the source to the sink should induce the change of total quantum numbers defining the odor quale.

2. The first thing to notice is that the upper bound .5 eV for IR energies corresponds to the nominal value of the metabolic energy quantum identified as the energy liberated as proton drops from the atomic space-time sheet with k=137 to a very large space-time sheet or the same process for electron Cooper at k=149 space-time sheet. If Cooper pairs are involved, the latter process would occur in the length scale defined by the thickness of the lipid layer of the cell membrane (5 nm). The lower bound corresponds to a metabolic energy quantum assignable to k= 139 for protons and k=151 transition for electrons (thickness of cell membrane).

3. Second point to notice is that TGD predicts a fractal hierarchy of spectra of metabolic energy quanta coming as E(Δk,n)= 2^-ΔkE₀(1-2^-n), n=1,2,..., converging to E(Δk,∞)= 2^-ΔkE₀ for given p-adic length scale characterized by the difference Δk=k-k₀ . E₀ denotes the zero point kinetic energy of particle at space-time sheet with p-adic length scale k=k₀ and is inversely proportional to the mass of the particle. The transfer of electrons and/or protons between different space-time sheets with any perception for purely metabolic reasons. The simplest option is that since the electrons at the side of the source receive their energy in this manner, their energy spectrum is given by E(Δk,n) (there is of course some resolution meaning a cutoff in n). The specificity of the receptor would require preference of some specific metabolic energy quanta E(Δk,n). If this spectrum characterizes the receptor independently of its chemistry, then not only metabolic energy quanta but also the mechanism of sensory perception is universal. This proposal fails if the receptor has always same spectrum of E(Δk,n) since all receptors would detect all odors.

It is interesting to relate the theory of Turin with the hypothesis of Callahan that the odor perception of insects uses IR light.

1. Callahan's work (Callahan, P. S. (1977). Moth and Candle: the Candle Flame as a Sexual Mimic of the Coded Infrared Wavelengths from a Moth Sex Scent. Applied Optics. 16(12) 3089-3097) suggests that the IR photons emitted by the odorant in the transitions between the vibrational states and received by the odor receptor are basically responsible for the odor perception. Turin in turn proposes that the pattern of vibrational excitations in the odor molecule characterizes the perception. These views are consistent if the pattern of vibrational excitations is in 1-1 correspondence with the flow pattern of electrons between different space-time sheets at the receptors if a kind of self-organization pattern results: this is expected to take place in presence of a metabolic energy feed.

2. In Callahan's model for the odor perception of insects the simplest odor receptor would "see" the IR light emitted by the odor molecules. Also Turin explains -with different assumptions- that the situation is analogous to that prevailing in retina in that there are receptors sensitive to characteristic energy ranges of photons. One would expect that the odor perception of insects is something very simple. The so called vomeronasal organ is known to be responsible for the perception of socially important odors not generating conscious experience at our level of self hierarchy but having important effect on behavior (perfume industry has long ago realized this!). Vomeronasal organ could utilize this kind of primitive odor receptors.

3. The rate for the spontaneous transitions emitting IR light could be rather low. A more advanced receptor would induce more transitions by using tunneling electrons to excite vibrational energy levels in the odorant. This would be like using lamp to see better! The analogy with the transistor is also suggestive: the small base current induced by IR radiation generated by the odor molecule would be amplified in the process. Since the source contains electrons in excited states (at smaller space-time sheets), odor molecules could send negative energy photons dropping electrons to the large space-time sheet along which tunneling is possible. Induced emission would cause a domino like flow of electrons and excitations of the vibrational states of the odor molecule as the counterpart of di-electric breakdown would take place.

4. What could then the physical correlates for the primary odor qualia? The increments of some quantum numbers assignable to electrons at the source should be in question. Could the energies E(k,n) characterizing the receptor define the primary odors? Odors and tastes are indeed very intimately related to metabolic activities;-). A natural consequence would be that besides the radiation generated by the transfer of electrons between space-time sheets would induce odor and perhaps also taste sensation. Organisms serve as food for other organisms so that an optimal detection of nutrients would be the outcome.

Could one assume that also other receptors use metabolic energy quanta as basic excitation energies?

1. The first objection is that similar "metabolic qualia" would result in all receptors. This is not a problem if these qualia are qualia not conscious to us but conscious to neuronal selves. For instance, in the TGD based model for visual colors the increments of color quantum numbers (in QCD sense!) define the basic colors, which means that colored particles must be in question (TGD variant of quark color implies the existence of scaled variants of QCD like physics and predicts that also electrons have colored excitations for which there is indeed a growing experimental evidence).

2. Second objection is that it does not seem possible to identify E(k,n) as excitation energies in the case of vision. The relevant range of photon energies is [1.65,3.3] eV. By scaling the metabolic energy quantum by a power of 2, the nominal values of relevant maximal metabolic energy quanta E(k,n=∞) are 2 eV and 4 eV. The series of energies approaching 2 eV below 2 eV is 1, 1.5, 1.75, ..., 2 eV so that the range below 2 eV representing red light would be covered. Above 2 eV the series is 2, 3, 3.50,...,4 eV so that the region above 2 eV (orange, yellow, green, blue, indigo, violet) would contain only single line at 3 eV (violet). If the incoming photon can kick the electron to an excited state with energy E₀ at the smaller space-time sheet the spectrum contains also the energies E(k,n)+E₀. For E₀=1.3 eV these excitation energies would come as 2.3, 2.8, 3.05,... 3.3 eV and cover this range.

For TGD based view about qualia see the chapter Quantum Model for Qualia of the book "Bio-systems as Conscious Holograms".

Malevolent backwards causation as source of problems at LHC and other non-conventional ideas

The recent paper by Holger Nielsen and Masao Ninomiya - discussing the quite unconventional idea that signals from future making detection of Higgs impossible are responsible for the diffifulties of LHC and for why the construction of SSC (Superconducting Super Collider) was stopped by Congress - has received a lot of attention. After Dennies Overbye wrote about it in New York Times, bloggers have expressed their views one after another. Sean Carroll wrote quite a balanced and humorous comments trying to convince that everything in theoretical physisc is not lost althogh this paper has appeared in archive. Lubos - the militant of theoretical physics- wrote about the subject with the characteristic highly emotional tone (negative as usual). Also Kea has written about the topic -even twice- and I got an opportunity to tell my remembrances about discussions with Holger, one of the most friendly persons in the known Universe and also one of the very few intelligent life-forms who have shown keen and genuine interest in TGD.

Very few have taken the paper as a joke allowing to concretize in a humorous manner delicate and difficult and yet unresolved questions related to the notion of time. People with strong beliefs firmly based on text book wisdom about physics as it was in their youth are aggressively attacking ideas that the joke meant to concretize. Typical blog behavior of course.

There are three unconventional ideas involved which tend to be seen as sources of all the evil.

1. The action defining quantum field theory could have imaginary part suppressing some histories (in this case those allowing a successful production of Higgs in laboratory).

2. Action could possess space-time locality unlike actions of quantum field theories usually have.

3. The idea of backward causation meaning that signals can propagate backward in time: here one should however specify what one exactly means with time and causation.

Since these unconventional ideas relate very closely to the basic distinctions between quantum TGD and standard approach, I will try to demonstrate that they are not a threat for the civilization.

Should we tolerate imaginary part and space-time non-locality of action?

The idea about imaginary part of action supressing some histories need not be crackpottish if properly formulated. There is also a good motivation for something like this: the basic difficulty of both quantum field theories and string model is that path integral is not well-defined mathematically.

1. One could try to overcome the problem by adding an imaginary part to the action so that phase factor is replaced with a complex exponent and some histories are indeed supressed and one obtains a well-defined integral around minimum of the real part of the imaginary exponent of action (usually the extremal with a stationary phase defines the perturbationt theory). The loss of unitarity is the obvious objection.
2. Unfortunately this is not enough. Space-time locality of quantum field theory implies infinities in n-point functions of the theory. So that there is order also for non-locality. The problem with non-locality is how to realize it in a non-ad-hoc manner.

It seems that a solution of problem generates new problems. These new problems are avoided in quantum TGD.

1. Light-like 3-surfaces (or equivalently space-like 3-surfaces are taken as fundamental objects and the fundamental variational principle assigns to them unique 4-D space-time surface. This is nothing but quantum holography. Don't be afraid. This is a good thing;-).

2. Path integral is replaced with a functional integral over 3-surfaces with the exponent of Kähler action for a preferred extremal (space-time surface) defining the analog of Gaussian. The infinite-dimensional integral over 3-surfaces is well defined since exponential suppression occurs and local divergences are absent since the counterpart of action depends in a non-local manner on 3-surface. This represent 20 years old layer of TGD.

3. The loss of unitarity is not a catastrophe in zero energy ontology where S-matrix is replaced with M-matrix defined as a "complex square root" of the density matrix having S-matrix as a "multiplicative phase factor" so that quantum theory becomes "complex square root" of thermodynamics. Quantum field theory at non-zero temperature is a respected branch of theoretical physics and its TGD counterpart emerges at the level of fundamental formulation. This layer of TGD is about half decade old.

Should we tolerate backward causation?

I see nothing crackpottish even in the notion of backward causation. What is crackpottish or probably just a joke is to propose that this would explain why Higgs has not been discovered yet. As far as plausibility is considered this proposal brings to my mind the brane constructions meant to reproduce standard model symmetries (certainly not intended to be jokes)!

1. In zero energy ontology physical states are replaced with zero energy states formed by entangled pairs of positive and negative energy states at opposite light-like boundaries of causal diamonds (CDs) defined as intersections of future and past directed light-cones. Zero energy ontology allows positive energy signals propagating to geometry future as well as negative energy signals propagating to geometric past. Negative energy signals justify the notion of backwards causation and it forms the corner stone of TGD inspired quantum biology and consciousness theory. It also resolves fundamental philosophical problems of theoretical physics posed by some innocent looking questions (What are the total conserved quantum numbers of the Universe and why are there values what they are?).

2. When the time scale of observations is larger than the size of CD involved with the phenomenon studied, standard thermodynamics applies. If not, the signals propagating in both time directions are significant somewhat like in standard Feynman diagrammatics. The recent formulation of quantum TGD indeed supports the view that antimatter is in negative energy states near the opposite light-like boundary of CDs. This would conform completely with Feynman's view and explain the generation of matter antimatter asymmetry.

3. The hierarchy of Planck constants - motivated by the mysteries of dark matter and dark energy plus intriguing observations suggesting quantum effects in both biology and astrophysics- leads to a generalization of 8-D imbedding space to a book like structure with pages partially characterized by the values of Planck constant. This hierarchy makes possible quantum coherence in arbitrary long scales so that there exist always sheets of the many-sheeted space-time at which second law cannot be applied at all or applies in both directions of geometric time. Biology would represent a basic example of this kind of situation.

4. Quantum biology is one of the basic applications of quantum TGD and the basic mechanisms of intentional action, metabolism, and memory rely on backwards causation. One must of course make a clear distinction between geometric time and subjective time (identified as a sequence of quantum jumps) in order to avoid paradoxes. The precise articulation of this distinction in TGD framework has turned out to be extremely useful exercise and could be also seen as one of the motivations for TGD inspired theory of consciousness besides the challenge of making observer a genuine part of the physical system by introducing the notion of self.

5. Most importantly, backwards causation has experimental support. Libet's paradoxical finding that neural activity precedes conscious decision finds in this framework a nice explanation without giving up free will. Phase conjugate laser beams provide the direct experimental evidence at the level of physics: for instance, they obey second law in reversed direction of geometric time: this has even technological application.

Since the generally accepted conceptual framework is lacking, theoretical physicists follow Wittgenstein's advice and prefer to be silent about the fascinating phenomena related to backwards causation. And about many other things too: it seems that the recent day theoretical physics is filled with taboos;-)).

Multiverse as space of quaternionic sub-algebras of local octonionic Clifford algebra?

Multiverses as quantum superpositions of geometric objects are unavoidable in any theory of quantum gravitation starting from a geometric description of gravitation.

The notion of multiverse in M-theory context is however extremely poorly defined. Should one introduce probability amplitudes in all possible 11-D space-times and try to geometrize this space and show that Calabi-Yau times circle times M⁴:s appears as preferred ones? Should one also introduce probability amplitudes for all possible configurations of all possible branes inside particular 11-D manifold? Should one introduce at classical level decomposition of 11-D space-time to regions in good approximation of the desired form?

To me this is a hopeless mess both mathematically and physically. Like thermodynamics before Boltzman whose work colleagues stubbornly refused to recognize with tragic consequences (it seems that the situation is equally difficult with the "complex square root" of thermodynamics;-)).

My own modest proposal is following. Let us start by asking whether the higher-D space-time could be selected uniquely, say by starting from the idea that associativity fixes physics completely.

1. 8-D space-times with Minkowski signature allow octonionic representation of gamma matrices as products of octonions and Pauli's sigma matrices. Consider local Clifford algebra in M⁸, which is the simplest possible choice.

2. Ask what are the local associative sub-algebras of this algebra (one could and must also consider co-associative sub-algebras). Associativity corresponds to a restriction of local Clifford algebra elements to 4-D (hyper-)quaternionic surface Quaternionicity means that one can assign quaternionic plane, not necessarily tangent plane, to each of its points by some rule. If the 4-D quaternionic planes form an integrable distribution in some sense, we have got 4-D space-time.

3. Do these quaternionic local Clifford sub-algebras allow commutative local sub-algebras? They do. This leads to a slicing of given hyper-quaternionic space-time surface by 2-D stringy surfaces (they are commutative) with slices parametrized by what I call partonic 2-surfaces (Euclidian string world sheets). In finite measurement implying discretization you get a collection of strings. Could M⁸ should allow slicings by quaternionic local Clifford sug-algebras with slicings parametrized by coquaternionic sub-algebras? This proposal is not a new one but appears naturally in this context.

4. These properties imply M⁸-M⁴×CP₂ duality that is mapping of these surfaces in M⁸ to M⁴×CP₂ giving standard model symmetries and TGD in its basic form.

5. The meaning of (hyper-)quaternionicity depends on the criteria assigning to given point of space-time surface quaternionic plane. Classical variational principle provides this criterion. For volume as action (non-physical choice) one obtains standard induced gamma matrices spanning tangent space. For Kahler action one obtains modified gammas and quaternionic sub-algebra does not span tangent space. This option is physical and besides producing standard model gauge field dynamics it provides the richests structure (quantum criticality, inclusion hierarchy of super-conformal algebras corresponding to that for HFFS of type II_1, etc..).

The world of classical worlds (WCW) is the multiverse of TGD and can be identified as the space of these quaternionic sub-algebras of the octonionic local Clifford and entire quantum TGD follows from mere algebra. Quantum states are spinor fields in WCW formed by quaternionic local Clifford sub-algebras. No landscape is obtained in this multiverse. Standard model symmetries are always the fundamental symmetries having purely number theoretical meaning. This picture is mathematically precisely defined with well-developed connections with existing physics. Mathematicians could immediately start to apply their methodology and intuition to develop TGD as a purely mathematical discipline.

But first something should be done. Maybe Nobel committee should follow their strategy when it gave peace price for Kissinger: Nobels to the leading string gurus! String wars would cease, landscape nightmare -the Vietnam of physics- would be soon forgotten, and theoreticians would be eagerly studying physics again;-).

What shook up Saturn's rings in 1984?

Solar system provides a continual supply of surprises. Now New Scientist reports that something shook up Saturn's rings in 1984. No convincing explanation has been found hitherto.

Something warped the inner D rings and also outer C rings into a ridged spiral like pattern like the grooves in a vinyl record. The amplitudes of grooves are about 1 km for D rings with width of about 8.000 km and about 100 m for the C rings with width of about 17.000 km. Recall that Saturn's ring span an annulus with width of order 60.000 km and with distance from planet of the same order of magnitude. Their thickness is only about 20 m so that a warping for a very thin sheet of paper is an excellent analogy. Warping in a precise mathematical sense means bending of plane without tearing it (so that the Riemann geometry of the sheet remains flat) and occurs almost spontaneously as the experimentation with a sheet of paper shows. Locally the process would look like an ideal warping of plane along parallel lines but in long scales -thanks to the gravitational pull of Saturn- these lines could become curved and form spirals.

The guess of Matthew Hedman of Cornell University was that some perturbation - perhaps a comet or asteroid- should have caused this warping by tilting the rings with respect to the plane of Saturn's equator so that the gravitation of Saturn (Saturn is not a perfect sphere) would have caused tidal forces putting the rings into a wobbling motion and created the spiral grooving pattern. By running equations of motion backwards in time Hedman and colleagues showed that the event should have occurred around 1984. The pattern is however so widespread that the explanation in terms of a comet or asteroid must be given up.

TGD inspired model for the sheets would be as condensations of visible matter around dark matter forming similar structures. Could it be that a quantum counterpart of Earth quake but at the level of dark matter rings with large Planck constant and therefore in large length scales took place? Could this explain why the event was missed by telescopes and space-crafts?

A new cosmological finding challenging General Relativity

I learned this morning about highly interesting new results challenging general relativity based cosmology. Sean Carroll and Lubos Motl commented the article A weak lensing detection of a deviation from General Relativity on cosmic scales by Rachel Bean. The article Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges by Chung-Pei Ma and Edmund Bertschinger allows to understand the mathematics related to the cosmological perturbation theory necessary for a deeper understanding of the article of Bean.

The message of the article is that under reasonable assumptions General Relativity leads to a wrong prediction for cosmic density perturbations in the scenario involving cold dark matter and cosmological constant to explain accelerated expansion. The following represents my first impressions after reading the article of Rachel Bean and the paper about cosmological perturation theory.

1. Assumptions

"Reasonable" means at least following assumptions about the perturbation of the metric and of energy momentum tensor.

1. The perturbations to the Robertson-Walker metric contain only two local scalings parameterized as dτ²→ (1+2Ψ)dτ² and dxⁱdx_i→ (1-2Φ)dxⁱdx_i. Vector perturbations and tensor perturbations (gravitational radiation classically) are neglected.

2. The traceless part (in 3-D sense) of the perturbation of energy momentum tensor vanishes. Geometrically this means that the perturbation does not contain a term for which the contribution to 3-curvature would vanish. In hydrodynamical picture the vanishing of this term would mean that the mass current for the perturbation contains only a term representing incompressible flow. During the period when matter and radiation were coupled this assumption makes sense. The non-vanishing of this term would mean the presence of a flow component - say radiation of some kind- which couples only very weakly to the background matter. Neutrinos would represent one particular example of this kind of contribution.

3. The model of cosmology used is so called ΛCDM (cosmological constant and cold dark matter).

These assumptions boil down to a simple equation

η= Φ/Ψ=1.

2. The results

The prediction can be tested and Rachel Bean indeed did it.

1. Ψ makes itself visible in the motion of massive objects such as galaxies since they couple to Newton's potential. This motion in turn makes itself visible as detected modifications of the microwave background from ideal. The so called Integrated Sachs-Wolfe effect is due to the redshift of microwave photons between last surface of scattering and Earth and caused by the gravitational fields of massive objects. Ordinary matter does not contribute to this effect but dark energy does.

2. Φ makes itself visible in the motion of light. The so called Weak lensing effect distorts the images of the distant objects: apparent size is larger than the real one and there is also distortion of the shape of the object.

From these two data sources Rachel Bean deduces that η differs significantly from the GRT value and concentrates around η=1/3 meaning that the scaling of the time component of the metric perturbation is roughly 3 times larger than for spatial scaling.

3. What could be the interpretation of the discrepancy?

What η=1/3 could mean physically and mathematically?

1. From Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges one learns that for neutrinos causing shear stress one has Φ= (1+2R_ν/5)Ψ, where R_ν is mass fraction of neutrinos: hence η should increase rather than decrease! If this formula generalizes, a negative mass fraction R= -5/3 would be present! Something goes badly wrong if one tries to interpret the result in terms of the perturbations of the density of matter - irrespective of whether it is visible or dark!

2. What about the perturbations of the density of dark energy? Geometrically η=1/3 would mean that the trace of the metric tensor defined in terms of the background metric is not affected. This means conservation of the metric determinant for the deformations so that small four-volumes are not affected. As a consequence, the interaction term T^αβ δg_αβ receives a contribution from G^αβ but not from the cosmological term Λg^αβ. This would suggest that the perturbation is not that of matter but of the vacuum energy density for which one would have

   Λg^αβ δ g_αβ=0 .

The result would not challenge General Relativity (if one accepts the notion of dark energy) but only the assumption about the character of the density perturbation. Instead of matter it would be the density of dark energy which is perturbed.

4. TGD point of view

What TGD could say about this.

1. In TGD framework one has many-sheeted space-time, dark matter hierarchy represented by the book like structure of the generalized imbedding space, and dark energy is replaced with dark matter at pages of the book with gigantic Planck constant so that the Compton lengths of ordinary particles are gigantic and the density of matter is constant in long scales so that one can speak about cosmological constant in General Relativity framework. The periods with vanishing 3-curvature are replaced by phase transitions changing the value of Planck constant at some space-time sheets and inducing lengthening of quantum scales: the cosmology during this kind of periods is fixed apart from the parameter telling the maximal duration of the period. Also early inflationary period would correspond to his kind of phase transition. Obviously, many new elements are involved so that it is difficult to say anything quantitative.

2. Quantum criticality means the existence of deformations of space-time surface for which the second variation of Kähler action vanishes. The first guess would be that cosmic perturbations correspond to this kind of deformations. In principle this would allow a quantitative modeling in TGD framework. Robertson-Walker metrics correspond to vacuum extremals of Kähler action with infinite spectrum of this kind of deformations (this is expected to hold true quite generally although deformations disappear as one deforms more and more the vacuum extremal).

3. Why the four-volumes defined by the Robertson-Walker metric should remain invariant under these perturbations as η=1/3 would suggest? Are the critical perturbations of the energy momentum tensor indeed those for the dominating part of dark matter with gigantic values of Planck constant and having an effective representation in terms of cosmological constant in GRT so that the above mentioned equations implying conservation of four-volume result as a consequence?

4. The most natural interpretation for the space-time sheets mediating gravitation is as magnetic flux tubes connecting gravitationally interacting objects and thus string like objects of astrophysical size. For this kind of objects the effectively 2-dimensional energy momentum tensor is proportional to the induced metric. Could this mean -as I proposed many years ago when I still took seriously the notion of the cosmological constant as something fundamental in TGD framework- that in the GRT description based on the replacement string like objects with energy momentum tensor the resulting energy momentum tensor is proportional to the induced metric? String tension would explain the negative pressure preventing the identification of dark energy in terms of ordinary particles.

For a background see the chapters TGD and Cosmology and Cosmic Strings of the book "Physics in Many-Sheeted Space-time".

Does TGD allow the counterpart of space-time super-symmetry?

The question whether TGD allows space-time super-symmetry or something akin to it has been a longstanding problem. A considerable progress in the respect became possible with the better understanding of the modified Dirac equation. At the same time I learned from Tommaso Dorigo's blog about almost 15 year old striking eeγγ+missing transversal energy event detected by CDF collaboration for which an explanation in terms super-symmetry has been proposed.

p-Adic length scale hypothesis assuming that the mass formulas for particles and sparticles are same but p-adic length scale is possibly different, combined with kinematical constraints fixes the masses of TGD counterparts of selectron, higgsino, and Z^0-gluino to be 131 GeV (just at the upper bound allowed kinematically), 45.6 GeV, and 91.2 GeV (Z^0 mass) respectively. The masses are consistent with the bounds predicted by the MSSM inspired model.

Instead of typing 6 pages of text in html format I just give a link to the pdf file Does TGD allow the counterpart of space-time supersymmetry?

For a background see the chapter p-Adic Mass Calculations: New Physics of the book "p-Adic Length Scale Hypothesis And Dark Matter Hierarchy".