Octonions and quantum physics

Peter Woit reports in "This Week's Hype" string model hype about classical number fields, in particular the possible role of octonions. It would be nice to write a comment and tell how elegantly classical number fields appear in TGD framework and make dual descriptions in terms of 8-D Minkowski space (sub-space of complexified octonions) and M⁴× CP₂ unique. Unfortunately, Peter Woit wathces over his territory so jealously against invasion of anything which stinks like a good idea that it does not bother to take the risk of getting biten. Therefore John Baez - who as a Name is allowed to make intelligent comments- must continue to live in the illusion that no-one does anything to understand the role of octonions in physics.

The non-associativity of octonions is the basic problem if one attempts to build octonionic quantum mechanics. Nothing like this is tried in TGD. Instead, classical number fields appear at the level of classical physics (see this). Space-time surfaces as classical correlates of quantum physics are conjectured to decompose to associative (/quaternionic/Minkowskia)n and co-associative (/co-quaternionic/Euclidian) regions so that the weakness of octonionic quantum mechanics would turn into a strength making classical physics completely unique purely number theoretical. More precisely, the induced spinor structure for 8-D imbedding space has a special representation in terms of octonionic gamma matrices and the induced gamma matrices (not strictly speaking matrices anymore) are conjectured to span a quaternionic or co-quaternionic subspace of octonions over complex numbers at each point of the preferred extremal of Kähler action.

Addition: Also Motl has comments about octonions. The usual flood of insults and extremely arrogant super-stringy attitude towards anyone who does not regard superstrings as the laws of Moses for physics and dares to ask whether some aspects of super-strings might be part of a more successful physical theory. John Baez was the target of the aggression at this time. Maybe it is high time to Lubos to realize that the glamour of Harward does not last forever: we also remember that the exit of Lubos from Harward was not graceful. Some real output would be desperately needed if Lubos wants to keep his position as a blog authority and we have been waiting for years. My comment about the role of classical number fields in physics of course goes un-noticed: Lubos reads nothing which he has decided to represent crackpot theory. In any case, Lubos does a valuable work: he teaches us to tolerate people behaving like complete idiots. Learning this is after all the only manner to build a better world;-).

About GRT limit of TGD

TGD should have General Relativity type theory as an appropriate limit. Therefore it is interesting to see what one obtains when one applies TGD picture by replacing space-times as 4-surfaces with abstract geometries as in Einstein's theory and assumes holography in the sense that space-times satisfy besides Einstein-Maxwell equations also conditions guaranteeing Bohr orbit like property. The resulting picture could be also regarded as quantized GRT type limit of quantum TGD obtained by dropping the condition that space-times are surfaces. This limit could also provide totally new insights to the quantization of GRT.

Several pleasant surprises were in store.

1. Essentially the same formalism could apply to GRT limit of TGD as TGD itself meaning that Einstein-Maxwell system can be described as almost topological QFT with holography implying that action reduces to 3-D Chern-Simons action with a metric dependent constraint term expressing the weak form of electric-magnetic duality and quantizing electric charge.

2. The existence of this limit gives valuable information also about TGD itself. In particular, the interpretation of the weak form of electric-magnetic duality is sharpened. The space-time regions with Minkowskian signature would be those in which only electromagnetic and gravitational interactions make themselves visible and regions with Euclidian signature would be the interiors of generalized Feynman graphs in which electroweak and color interactions become manifest. In particular, Weinberg angle should vanish in the Minkowskian phase so that electromagnetic field reduces to induced Kähler field identifiable as Maxwell field of Einstein-Maxwell system. This conforms with the finding that Kähler coupling strength equals to fine structure constant within the very tight constraints available.

3. The limit also suggests how one could understand the extremely small value of cosmological constant characterizing the cosmology according to GRT in terms of CP₂ geometry providing idealization for the space-time region with Euclidian signature of metric representing generalized Feynman graphs also in GRT framework.

4. Non-Euclidian regions could correspond also to blackhole like regions in TGD framework, where only part of the interior of black hole is imbeddable. Black holes would naturally correspond to gigantic values of gravitational Planck constant implying that the Compton length of black-hole is of order of Schwartschild radius. Black hole would be elementary parton with very large fermion and antifermion numbers and large Planck constant and consist of dark matter in TGD sense. This picture is mathematically consistent since at event horizon the determinant of four-metric vanishes so that it is light-like just as it is at wormhole throats. Consistency with experimental factors is also achieved: about the interiors of blackholes we know nothing so that nothing prevents from assuming that it has Euclidian signature of metric: especially so if this explains the mysterious cosmological constant and standard model quantum numbers.

GRT is a more general theory than TGD in the sense that much more general space-times are allowed than in TGD - this leads also to difficulties - and one could also argue that the mathematical existence of WCW Kähler geometry actually forces the restriction of these geometries to those imbeddable in M⁴× CP₂ so that the quantization of GRT type theory would lead to TGD.

1. The conceptual framework of TGD

There are several reasons to expect that something analogous to thermodynamics results from quantum TGD. The following summarizes the basic picture, which will be applied to a proposal about how to quantize (or rather de-quantize!) Einstein-Maxwell system with quantum states identified as the modes of classical WCW spinor field with spinors identifiable in terms of Clifford algebra of WCW generated by second quantized induced spinor fields of H.

1. In TGD framework quantum theory can be regarded as a "complex square root" of thermodynamics in the sense that zero energy states can be described in terms of what I call M-matrices which are products of hermitian square roots of density matrices and unitary S-matrix so that the moduli squared gives rise to a density matrix. The mutually orthogonal Hermitian square roots of density matrices span a Lie algebra of a subgroup of the unitary group and the M-matrices define a Kac-Moody type algebra with generators proportional to powers of S assuming that they commute with S. Therefore this algebra acts as symmetries of the theory.

   What is nice that this algebra consists of generators multi-local with respect to partonic 2-surfaces and represents therefore a generalization of Yangian algebra. The algebra of M-matrices makes sense if causal diamonds (double light-cones) have sizes coming as integer multiples of CP₂ size. U-matrix has as its rows the M-matrices. One can look how much of this structure could make sense in GRT framework.

2. In TGD framework one is forced to geometrize WCW consisting of 3-surfaces to which one can assign a unique space-time surfaces as analogs of Bohr orbits and identified as preferred extremals of Kähler action (Maxwell action essentially). The 3-surfaces could be identified as the intersections space-time surface with the future and past light-like boundaries causal diamond (CDs analogous to Penrose diagrams). The preferred extremals associated with the preferred 3-surfaces allow to realize General Coordinate Invariance (GCI) and its natural to assign quantum states with these.

   GCI in strong sense implies even stronger form of holography. Space-time regions with Euclidian signature of metric are unavoidable in TGD framework and have interpretation as particle like structure and are identified as lines of generalized Feynman diagrams. The light-like 3-surfaces at which the signature of the induced metric changes define equally good candidates for 3-surfaces with which to assign quantum numbers. If one accepts both identifications then the intersections of the ends of space-time surfaces with these light-like surfaces should code for physics. In other words, partonic 2-surfaces plus their 4-D tangent space-data would be enough and holography would be more or less what the holography of ordinary visual perception is!

   In the sequel the 3-surfaces at the ends of space-time and and light-like 3-surfaces with degenerate 4-metric will be referred to as preferred 3-surfaces.

3. WCW spinor fields are proportional to a real exponent of Kähler function of WCW defined as Kähler action for a preferred extremal so that one has indeed square root of thermodynamics also in this sense with Kähler essential one half of Hamiltonian and Kähler coupling strength playing the role of dimensionless temperature in "vibrational" degrees of freedom. One should be able to identify the counterpart of Kähler function also in General Relativity and if one has Einstein-Maxwell system one could hope that the Kähler function is just the Maxwell action for a preferred extremal and therefore formally identical with the Kähler function in TGD framework.

   Fermionic degrees of freedom correspond to spinor degrees of freedom and are representable in terms of oscillator operators for second quantized induced spinor fields. This means geometrization of fermionic statistics. There is no quantization at WCW level and everything is classical so that one has "quantum without quantum" as far as quantum states are considered.

4. The dynamics of the theory must be consistent with holography. This means that the Kähler action for preferred extremal must reduce to an integral over 3-surface. Kähler action density decomposes to a sum of two terms. The first term is j^αA_α and second term a boundary term reducing to integral over light-like 3-surfaces and ends of the space-time surface. The first term must vanish and this is achieved if the Kähler current j^α is proportional to Abelian instanton current

   j^α ∝ *j^α=ε^{α β γ δ}A_βJ_{γ δ}

   since the contraction involves A_α twice. This is at least part of the definition of preferred extremal property but not quite enough. Note that in Einstein-Maxwell system without matter j^α vanishes identically so that the action reduces automatically to a surface term.

5. The action would reduce reduce to terms which should make sense at light-like 3-surfaces. This means that only Abelian Chern-Simons term is allowed. This is guaranteed if the weak form of electric-magnetic duality stating

   *F^nβ=kF^nβ

   at preferred at light-like throats with degenerate four-metric and at the ends of space-time surface. These conditions reduce the action to Chern-Simons action with a constraint term realizing what I call weak form of electric-magnetic duality. One obtains almost topological QFT since the constraint term depends on metric. This is of course what one wants.

   Here the constant k is integer multiple of basic value which is proportional to g_K² from the quantization of Kähler electric charge which corresponds to U(1) part of electromagnetic charge. Fractional charges for quarks require k=ng_K²/3. Physical particles correspond to several Kähler magnetically charged wormhole throats with vanishing net magnetic charge but with non-vanishing Kähler electric proportional to the sum ∑_i ε_i k_iQ_m,i, with ε_i=+/- 1 determined by the direction of the normal component of the magnetic flux for i:th throat.

   The first guess is that the length of magnetic flux tube associated with the particle is of order Compton length or perhaps corresponds to weak length scale as was the original proposal. The screening of weak isospin can be understood as magnetic confinement such that neutrino pair at the second end of magnetic flux tube screens the weak charged leaving only electromagnetic charge. Also color confinement could be understood in terms of flux tubes of length of order hadronic size scales. Compton length hypothesis is enough to understand color confinement and weak screening.

   Note that 1/g_K² factor in Kähler action is compensated by the proportionality of Chern-Simons action to g_K². This need not mean the absence of non-perturbative effects coming as powers of 1/g_K² since the constraint expressing electric magnetic duality depends on g_K² and might introduce non-analytic dependence on g_K².

6. In TGD the space-like regions replace black holes and a concrete model for them is as deformations of CP₂ type vacuum extremals which are just warped imbeddings of CP₂ to M⁴× CP₂ with random light-like random curve as M⁴ projection: the light-like randomness gives Virasoro conditions. This reflects as a special case the conformal symmetries of light-like 3-surfaces and those assignable to the light-like ends of the CDs.

One could hope that this picture more or less applies for the GRT limit of quantum TGD.

2. What one wants?

What one wants is at least following.

1. Euclidian regions of the space-time should reduce to metrically deformed pieces of CP₂. Since CP₂ spinor structure does not exist without the coupling of the spinors to Kähler gauge potential of CP₂ one must have Maxwell field. CP₂ is gravitational instanton and constant curvature space so that cosmological constant is non-vanishing unless one adds a constant term to the Maxwell action, which is non-vanishing only in Euclidian regions. It is matter of taste, whether one regards V₀ as term in Maxwell action or as cosmological constant term in gravitational part of the action. CP₂ radius is determined by the value of this term so that it would define a fundamental constant.

   This raises an interesting question. Could one say that one has a small value of cosmological constant defined as the average value of cosmological constant assignable to the Euclidian regions of space-time? The average value would be proportional to the fraction of 3-space populated by Euclidian regions (particles and possibly also macroscopic Euclidian regions). The value of cosmological constant would be positive as is the observed value. In TGD framework the proposed explanation for the apparent cosmological constant is different but one must remain open minded. In fact, I have proposed the description in terms of cosmological constant also as a proper description in the approximation to TGD provided by GRT like theory. The answer to the question is far from obvious since the cosmological constant is associated with Euclidian rather than Minkowskian regions: all depends on the boundary conditions at the wormhole throats where the signature of the metric changes.

2. One can also consider the addition of Higgs term to the action in the hope that this could allow to get rid of constant term which is non-vanishing only in Euclidian regions. It turns turns out that only free action for Higgs field is possible from the condition that the sum of Higgs action and curvature scalar reduces to a surface term and that one must also now add to the action the constant term in Euclidian regions. Conformal invariance requires that Higgs is massless.

   The conceptual problem is that the surface term from Higgs does not correspond to topological action since it is expressible as as flux of Φ∇ Φ. Hence the simplest possibility is that Kähler action contains a constant term in Euclidian regions just as in TGD, where curvature scalar is however absent. Einstein-Maxwell field equations however apply that it vanishes and is effectively absent also in GRT quantized like TGD.

3. Reissner-Nordström solutions are obtained as regions exterior to CP₂ type regions. In black hole horizon the metric becomes light-like and the solution can be glued to a deformed CP₂ type region with metric becoming degenerate at the 3-surface involved. This surface corresponds to wormhole throat in TGD framework. Blackhole is replaced with CP₂ type region. In TGD black hole solutions indeed fail to be imbeddable at certain radius so that deformed CP₂ type vacuum extremal is much more natural object than black hole. In the recent framework the finite size of CP₂ means that macroscopic size for the Euclidian regions requires large deformation of CP₂ type solution.

   Remark: In TGD framework large value of hbar and space-time as 4-surface property changes the situation. The generalization of Nottale's formula for gravitational Planck constant in the case of self gravitating system gives hbar_gr= GM²/v₀, where v₀/c<1 has interpretation as velocity type parameter perhaps identifiable as a rotation velocity of matter in black hole horizon. This gives for the Compton length associated with mass M the value L_C= hbar_gr/M= GM/v₀. For v₀=c/2 one obtains Scwartschild radius as Compton length. The interpretation would be that one has CP₂ type vacuum extremal in the interior up to some macroscopic value of Minkowski distance. One can whether even the large voids containing galaxies at their boundaries could correspond to Euclidian blackhole like regions of space-time surface at the level of dark matter.

4. The geometry of CP₂ allows to understand standard model symmetries when one considers space-times as surfaces. This is not necessarily the case for GRT limit.

   1. In the recent case one has different situation color quantum numbers make sense only inside the Euclidian regions and momentum quantum numbers in Minkowskian regions. This is in conflict with the assumption that quarks can carry both momentum and color. On the other, color confinement could be used to argue that this is not a problem.

   2. One could assume that spinors are actually 8-component M⁴× CP₂ spinors but this would be somewhat ad hoc assumption in general relativistic context. Also the existence of this kind of spinor structure is not obvious for general solutions of Einstein-Maxwell equations unless one just assumes it.

   3. It is far from clear whether the symplectic transformations of CP₂ could be interpreted as isometries of WCW in general relativity like theory. These symmetries certainly act in non-trivial manner on Euclidian regions but it is highly questionable whether this could give rise to a genuine symmetry. Same applies to Kac-Moody symmetries assigned to isometries of M⁴× CP₂ in TGD framework. These symmetries are absolutely essential for the existence of WCW Kähler geometry in infinite-D context as already the uniqueness of the loop space Kähler geometries demonstrates (maximal group of isometries is required by the existence of Riemann connection).

      Note that a generalization of Equivalence Principle follows in TGD framework from the assumption that coset representations of super-conformal symplectic algebra and super Kac-Moody algebra define conformally invariant physical states. The equality of gravitational and inertial masses follows from the condition that the actions of the super-generators of two algebras are identical. This also justifies the use p-adic thermodynamics for the scaling generator of either super-conformal algebra without a loss of conformal invariance.

5. One could argue that GRT limit does not make sense since in Minkowskian regions the theory knows nothing about the color and electroweak quantum numbers: there is only metric and Maxwell field. On the other hand, in TGD one has color confinement and weak screening by magnetic confinement. If the functional integral over Euclidian regions representing generalized Feynman diagrams is enough to construct scattering amplitudes, pure Einstein-Maxwell system in Minkowskian regions might be enough. All experimental data is expressible in terms of classical em and gravitational fields. If Weinberg angle vanishes in Minkowskian regions, electromagnetic field reduces to Kähler form and the interpretation of the Maxwell field as em field should make sense. The very tight empirical constraints on the value of Kähler coupling strength α_K indeed allow its identification as fine structure constant at electron length scale.

6. One can worry about the almost total disappearance of the metric from the theory. This is not a problem in TGD framework since all elementary particles correspond to many-fermion states. For instance, gauge bosons are identified as pairs of fermion and antifermion associated with opposite throats of a wormhole connecting two space-time sheets with Minkowskian signature of the induced metric. Similar picture should make sense also now.

7. TGD possesses also approximate super-symmetries and one can argue that also these symmetries should be possessed by the GRT limit. All modes of induced spinor field generate a badly broken SUSY with rather large value of N (number of spinor modes) and right-handed neutrino and its antiparticle give rise to N=2 SUSY with R-parity breaking induced by the mixing of left- and right handed neutrinos induced by the modified Dirac equation. This picture is consistent with the existing data from LHC and there are characteristic signatures -such as the decay of super partner to partner and neutrino- allowing to test it. These super-symmetries might make sense if one replaces ordinary space-time spinors with 8-D spinors.

   Note that the possible inconsistency of Minkowskian and Euclidian 4-D spinor structures might force the use of 8-D Minkowskian spinor structure.

3. Preferred extremal property for Einstein-Maxwell system

Consider now the preferred extremal property defined to be such that the action reduces to Chern-Simons action at space-like 3-surfaces at the ends of space-time surface and at light-like wormhole throats.

1. In Maxwell-Einstein system the field equations imply

   j^α=0 .

   so that the Maxwell action for extremals reduces automatically to a surface term assignable to the preferred 3-surfaces. Note that Higgs field could in principle serve as a source of Kähler field but its presence does not look like a good idea since it is not present in the field equations of TGD and because the resulting boundary term is not topological.

2. The condition

   J=k× *J

   at preferred 3-surfaces guarantees that the surface term from Kähler action reduces to Abelian Chern-Simons term and one has hopes about almost topological QFT.

   Since CP₂ type regions carry magnetic monopole charge and since the weak form of electric-magnetic duality implies that electric charge is proportional to the magnetic charge, one has electric charge without electric charge as Wheeler would express it. The identification of elementary building blocks as magnetic monopoles leads in TGD context to the picture about particle as Kähler magnetic flux tubes having opposite magnetic charges at their ends. It is not quite clear what the length of the tubes is. One possibility is Compton length and second possibility is weak length scale and the color confinement length scale. Note that in TGD the physical charges reside at the wormhole throats and correspond to massless fermions.

3. CP₂ is constant curvature space and satisfies Einstein equations with cosmological constant. The simplest manner to realize this is to add to the action constant volume term which is non-vanishing only in Euclidian regions. This term could be also interpreted as part of Maxwell action so that it is somewhat a matter of taste whether one speaks about cosmological constant or not. In any case, this would mean that the action contains a constant potential term

   V= V₀× (1+sign(g))/2 ,

   where sign(g)=-1 holds true in Minkowskian regions and sign(g)=1 holds true in Euclidian regions.

   Note that for a piece of CP₂ V₀ term can be expressed is proportional to Maxwell action and by self-duality this is proportional to instanton action reducible to a Chern-Simons term so that V₀ is indeed harmless from the point of view of holography.

4. For Einstein-Maxwell system with similar constant potential in Euclidian regions curvature scalar vanishes automatically as a trace of energy momentum tensor so that no interior or surface term results and the only surface term corresponds to a pure Chern-Simons term for Maxwell field. This is exactly the situation also in quantum TGD. The constraint term guaranteeing the weak form of electric-magnetic duality implies that the metric couples to the dynamics and the theory does not reduce to a purely topological QFT.

5. In TGD framework a non-trivial theory is obtained only if one assumes that Kähler function corresponds apart from sign to either the Kähler action in the Euclidian regions or its negative in Minkowskian regions. This is required also by number theoretic vision. This implies a beautiful duality between field descriptions and particle descriptions.

   This also guarantees that the Kähler function reducing to Chern-Simons term is negative definite: this is essential for the existence of the functional integral and unitarity of the theory. This is due to the fact that Kähler action density as a sum of magnetic and electric energy densities is positive definite in Euclidian regions. This duality would be very much analogous to that implied by the possibility to perform Wick rotation in QFTs. Therefore it seems natural to postulate similar duality also in the proposed variant of quantized General Relativity.

6. The Kähler function of the WCW would be given by Chern-Simons term with a constraint expressing the weak form of electric-magnetic duality both in TGD and General Relativity. One should be able regard also in GRT framework WCW as a union of symmetric spaces with Kähler structure possessing therefore a maximal group of isometries. This is an absolutely essential prerequisite for the existence of WCW Kähler geometry. The symmetric spaces in the union are labelled by zero modes which do not contribute to the line element and would represent classical degrees of freedom essential for quantum measurement theory. In TGD the induced CP₂ Kähler form would represents such degrees of freedom and the quantum fluctuating degrees of freedom would correspond to symplectic group of δ M⁴_+/-× CP₂.

   The difference between TGD and GRT would be that light-like 3-surfaces for all possible space-times containing Euclidian and Minkowskian regions would be considered for GRT type theory. In TGD these space-times are representable as surfaces of M⁴× CP₂. In TGD framework the imbeddability assumption is crucial for the mathematical existence of the theory since it eliminates space-times with non-physical characteristics. The problem posed by arbitrarily large values of cosmological constants is one of the basic problems solved by this assumption. Also mass density is sub-critical for cosmologies with infinite duration and critical cosmologies are unique apart from their duration and quantum critical cosmologies replace inflationary cosmologies.

7. Note that one could consider assigning the gravitational analog of Chern-Simons term with the preferred 3-surfaces: this kind of term is discussed by Witten in this classic work about Jones polynomial. This term is a non-abelian version of Chern-Simons term and one must replace curvature tensor with its contraction with sigma matrices so that 4-D spinor structure is necessarily involved. The objection is that this term contains second derivatives. In TGD spinor structure is induced from that of M⁴× CP₂ and this kind of term need not make sense as such since gamma matrices are expressed in terms of imbedding space gamma matrices: among other things this resolves the problems caused by the non-existence of spinor structure for generic 4-geometries. The coupling to the metric however results from the constraint term expressing weak form of electric-magnetic duality.

   The difference between TGD and GRT would be basically due to the factor of scattering amplitudes coming from the duality expressing electric-magnetic duality and due to the fact that induced metric in terms of H-coordinates and Maxwell potential is expressible in terms of CP₂ coordinates. The latter implies topological field quantization and many-sheeted space-time crucial for the interpretation of quantum TGD.

4. Could ZEO and the notion of CD make sense in GRT framework?

The notion of CD is crucial in ZEO and one can ask whether the notion generalizes to GRT context. In the previous arguments related to EG the notion of ZEO plays a fundamental role since it allows to replace S-matrix with M-matrix defining "complex square root" of density matrix.

1. In TGD framework CDs are Cartesian products of Minkowskian causal diamonds of M⁴ with CP₂. The existence of double light-cones in curved space-time would be required and its is not clear whether this makes sense generally. TGD suggest that the scales of these diamonds defined in terms of the proper time distance between the tips are integer multiples of CP₂ scale defined in terms of the fundamental constant V₀ (the more restrictive assumption allowing only 2ⁿ multiples would explain p-adic length scale hypothesis but would not allow the generalization of Kac-Moody algebra spanned by M-matrices). The difference between boundaries of GRT CDs and wormhole throats would be that four-metric would not be degenerate at CDs.

2. The conformal symmetries of light-cone boundary and light-like wormhole throats generalize also now since they are due to the metric 2-dimensionality of light-like 3-surfaces. It is however far from clear whether one can have anything something analogous to conformal variants of symplectic algebra of δ M⁴_+/-× CP₂ and isometry algebra of M⁴× CP₂.

   Could one perhaps identify four-momenta as parameters associated with the representations of the conformal algebras involved? This hope might be unrealistic in TGD framework: the basic idea behind TGD indeed is that Poincare invariance lost in GRT is retained if space-times are surfaces in H=M⁴× CP₂. The reason is that that super-Kac-Moody symmetries correspond to localized isometries of H whereas the super-conformal algebra associated with the symplectic group is assignable to the light-like boundaries δ M⁴_+/-× CP₂ of CD of H rather than space-time surface.

3. One could of course argue that some physical conditions on GRT -most naturally just the highly non-trivial mathematical existence of WCW Kähler geometry and spinor structure- could force the representability of physically acceptable 4-geometries as surfaces M⁴× CP₂. If so, then also CDs would the same CDs as in TGD and quantization of GRT would lead to TGD and all the huge symmetries would emerge from quantum GRT alone.

   The first objection is that the induced spinor structure in TGD is not consistent with that natural in GRT. Second objection is that in TGD framework Einstein-Maxwell equations are not true in general and Einstein's equations can be assumed only in long length scales for the vacuum extremals of Kähler action. The Einstein tensor would characterize the energy momentum tensor assignable to the topologically condensed matter around these vacuum extremals and neither geometrically nor topologically visible in the resolution defined by very long length scale. If Maxwell field corresponds to em field in Minkowskian regions, the vacuum extremal property would make sense in scales where matter is electromagnetic neutral and em radiation is absent.

5. What can one conclude?

The previous considerations suggest that a surprisingly large piece of TGD can be applied also in GRT framework and raise the possibility about quantization of Einstein-Maxwell system in terms of Kähler geometry of WCW consisting of 3-geometries instead of 3-surfaces. One can even consider a new manner to understand TGD as resulting from the quantization of GRT in terms of WCW Kähler geometry in the space of 3-metrics realizing holography and making classical theory an exact part of quantum theory. Since the space-times allowed by TGD define a subset of those allowed by GRT one can ask whether the quantization of GRT leads to TGD or at least sub-theory of TGD. The arguments represented above however suggest that this is not the case.

The generalization of S-matrix to a complex of U-matrix, S-matrix and algebra of M-matrices forced by ZEO gives a natural justification for the modification of EG allowing gravitons and giving up the rather nebulous idea about emergent space-time. Whether ZEO crucial for EG makes sense in GRT picture is not clear. A promising signal is that the generalization of EG to all interactions in TGD framework leads to a concrete interpretation of gravitational entropy and temperature, to a more precise view about how the arrow of geometric time emerges, to a more concrete realization of the old idea that matter antimatter asymmetry could be due to different arrows of geometric time for matter and antimatter, and to the idea that the small value of cosmological constant could correspond to the small fraction of non-Euclidian regions of space-time with cosmological constant characterized by CP₂ size scale.

The above considerations were inspired by the attempt to understand what is good and what is bad in the entropic gravity scenario of Verlinde in TGD framework with the basic idea being that quantum TGD as a square root of thermodynamics must predict something analogous to thermalization of the lines of generalize Feynman graphs. The above interpretation for the lines of Feynman graphs as analogs of blackholes indeed allows to understand blackhole temperature and entropy as a manifestation of this underlying thermodynamics. The generalization of blackhole thermodynamics implies that both virtual gravitons and gauge bosons are thermalized. For details see the article TGD inspired vision about entropic gravity.

D0 reports a new 3 sigma bump with mass around 325 GeV

It seems that experimentalists have gone totally crazy. Maybe new physics is indeed emerging from LHC and they want to publish every data bit in the hope of getting paid visit to Stockholm. CDF and ATLAS have told about bumps and now Lubos tells about a new 3 sigma bump reported by D0 collaboration at mass 325 GeV producing muon in its decay producing W boson plus jets. The proposed identification of bump is in terms of decay of t' quark producing W boson.

Lubos mentions also second mysterious bump at 324.8 GeV or 325.0 GeV reported by CDF collaboration and discussed by Tommaso Dorigo towards the end of the last year. The decays of these particles produce 4 muons through the decays of two Z bosons to two muons. What is peculiar is that two mass values differing by .2 GeV are reported. The proposed explanation is in terms of Higgs decaying to two Z bosons. TGD based view about new physics suggests strongly that the three of four particles forming a multiplet is in question.

One can consider several explanations in TGD framework without forgetting that these bumps very probably disappear. Consider first the D0 anomaly alone.

1. TGD predicts also higher generations but there is a nice argument based on conformal invariance and saying that higher particle families are heavy. What "heavy" means is not clear. It could of mean heavier that intermediate gauge boson mass scale. This explanation does not look convincing to me.
2. Another interpretation would be in terms of scaled up variant of top quark. The mass of top is around 170 GeV and p-adic length scale hypothesis would predict that the mass should equal to a multiple of half octave of top quark mass. Single octave would give mass of 340 GeV. The deviation from predicted mass would be 5 per cent. This quark could correspond to t quark of scaled up hadron physics predicted by TGD and discussed in previous postings (see this, this, abd this).

The prediction of the scaled up hadron physics allows to ask whether a common explanation for all these particles as decay products of kaons of M₈₉ hadron physics could exist. Could charged kaon produceneutral pion and single W boson and therefore muon just as the 300 GeV charged pion would produce W boson plus neutral pion decaying to two jets. This explanation excludes the the interpretation of ATLAS bump as neutral pion and CDF bump as charged kaon but CDF and D0 bumps could live peacefully together.

If there indeed are two slightly different masses one can can ask whether the two different masses could be due to CP breaking. The mass difference between short-lived and long-lived ordinary kaon is however extremely small- 3.5×10^-12 MeV- and scaling by a factor 512 would give quite too small mass difference. That CP (or even CPT) breaking should be so large for the scaled up version of hadron physics looks odd. As a matter fact, the splitting is of the same order as electromagnetic splitting between mesons with different charges obtained by scaling with factor 512 from the mass splitting of order 1 MeV for ordinary mesons.

Addition: The newest rumor is that ATLAS rumor about too photo-philic Higgs with exactly the same mass of 115 GeV as the hegemony wanted it to have was not more than a rumor. Sorry Lubos;-).

For me the newest rumor is a relief since it makes it more easier to find room for the remaining rumors in zoomed up hadron physics. The CDF rumor about 145 GeV bump would be interpreted in terms of charged pion. The latest D0 rumor weighting 325 GeV and producing W bosons, and the earlier CDF rumor having two slightly different masses around 325 GeV and producing two Z bosons would in turn be interpreted in terms of scaled up charged and neutral kaons.

However, if a strict scaling would hold true for the meson masses, one could conclude that either 145 GeV or 325 rumour is only a humor since the mass scale ratio 325/145 ≈ 2.24 is smaller than the mass scale ratio for ordinary kaon and pion about 490/140≈ 3.5. This would leave only one or two rumors to be killed. Probably they suffer a natural death within week or two in any case. I have not taken main stream theorists seriously for decades but believed that experimentalists are somehow more rooted in reality. Has the hype disease infected also experimentalists? This would be sad. Addition: The latest rumor about Atlas by Peter Woit tells that New Science has received inner information that ATLAS bump has not been found in other experiments. Tommaso in turn claims that this cannot be true! From which some reader concludes between lines that ATLAS has observed photo-philic Higgs after all!! When physics blogs came, I thought that they would provide forums for a genuine discussion about new ideas and could also serve some kind of educational function: for instance, about statistical methods of particle physics. I was wrong: they are forums for a chat about what names have said, for boosting the ego of the blogger, for the endlessly boring n sigma talk, and speculations around rumors and counter rumors. Does the situation in the web of so called respected blogs reflect the situation also in experimental particle physics? I sincerely hope that this is not the case.

Objection against zero energy ontology and quantum classical correspondence

The motivation for requiring geometry and topology of space-time as correlates for quantum states is the belief that quantum measurement theory requires the representability of the outcome of quantum measurement in terms of classical physics -and if one believes in geometrization- one ends up with generalization of Einstein's vision.

There is however a counter argument against this view and second one against zero energy ontology in which one assigns eigenstates of four-momentum with causal diamonds (CDs).

1. One can argue that momentum eigenstates for which particle regarded as a topological inhomogenuity of space-time surface, which is non-localized cannot allow a space-time correlate.

2. Even worse, CDs have finite size so that strict four-momentum eigenstates strictly are not possible.

On the other hand, the paradoxical fact is that we are able to perceive momentum eigenstates and they look localized to us. This cannot be understood in the framework of standard Poincare symmetry.

The resolution of the objections and of the apparent paradox could rely on conformal symmetry assignable to light-like 3-surfaces implying a generalization of Poincare symmetry and other symmetries with their Kac-Moody variants for which symmetry transformations become local.

1. Poincare group is replaced by its Kac-Moody variant so that all non-constant translations act as gauge symmetries. Translations which are constant in the interior of CD and trivial at the boundaries of CDs are physically equivalent with constant translations. Hence the latter objection can be circumvented.

2. The same argument allows also a localization of momentum eigenstates at the boundaries of CD. In the interior the state is non-local. Classically the momentum eigenstate assigned with the partonic 2-surface is characterized by its 4-D tangent space data coding for momentum classically. The modified Dirac equation and Kähhler action indeed contain and additional term representing coupling to four-momenta of particles. Formally this corresponds only to a gauge transform linear in momentum but Kahler gauge potential has U(1) gauge symmetry only as a spin glass like degenary, not as a gauge symmetry so that space-time surface depends on momenta.

3. Conscious observer corresponds in TGD inspired theory of consciousness to CD and the sensory data of the observer come from partonic 2-surfaces at the boundaries of CD and its sub-CDs. This implies classicality of sensory experience and momentum eigenstates look classical for conscious perceiver.

The usual argument resolving the paradox is based on the notion of wave packet and also this notion could be involved. The notion of finite measurement resolution is key notion of TGD and it is quite possible that one can require the localization of momentum eigenstates at the boundaries of CDs only modulo finite measurement resolution for the position of the partonic 2-surfaces.

For background see the chapter Construction of Quantum Theory: M-matrix of "Towards M-matrix".

How arrow of geometric time is selected at quantum level?

I have discussed in the chapter About the Nature of Time of "Matter, Mind, Quantum" how the arrow of geometric time as a correlate for the experienced arrow of geometric time might be selected in TGD Universe. The discussion does not touch the question what arrow of time means at the level of quantum states. Therefore the notion of negative energy signal propagating backwards in geometric time crucial for TGD inspired quantum biology remains somewhat fuzzy.

The recent progress in the understanding of the basic properties of zero energy states makes it possible to understand what arrow of geometric time and the notion of negative energy state and signals propagating to the direction of geomeric past mean at the level of zero energy states. This understanding has surprisingly non-trivial philosophical implications. In the following I shall briefly the quantum view about arrow of time.

Arrow of time as an inherent property of zero energy states?

The basic idea can be expressed in very conscise form. In positive energy ontology arrow of time characterizes dynamics. In zero energy ontology arrow of time characterizes quantum states.

1. The breaking of time reversal invariance (see this) means that zero energy states can be localized with respect to particle number and other quantum numbers only for future or past light-like boundary of CD but not both. M-matrix generalizing S-matrix provides the time-like entanglement coefficients expressing the state at the second boundary as quantum superposition of states with well-defined particle numbers and other quantum numbers. But only at the second end of CD since one cannot choose freely the states at both boundaries: if this were the case the counterpart of Schrödinger equation would be completely non-deterministic. This is what the breaking of time reversal symmetry means. It occurs spontaneously and assigns to the arrow of subjective time geometric arrow of time.

   This picture gives a precise meaning to the arrow of geometric time and therefore also for the otherwise fuzzy notion of negative energy signals propagating backwards in space-time playing key role in TGD based models of memory, metabolism, and intentional action (see this).

2. Quantum jump begins with the unitary U-process between zero energy states generating a superposition of zero energy states. After that follows state function reduction cascade proceeding from the level of CD to the level of sub-CDs forming a fractal hierarchy. The reductions cannot take independently at both light-like boundaries of CD as is also clear from the fact that scattering state leads from a prepared state to a quantum superposition of prepared states.

   The first guess is that the cascade takes place for the second boundary of CD only so that the arrow of geometric time would be same in all scales. This need not be the case always: the geometric arrow of time seems to change in some situations: phase conjugate laser light and spontaneous self-assembly of bio-molecules are good examples about this (see this and this). In fact, one of the defining properties of living matter could be just the possibility that the arrow of geometric time is not same in all scales (size scales of CDs) so that memory, metabolism, and intentional action become possible. In any case, the second end remains a superposition of quantum states.

   The lack of quantum measurements at the second end of space-times could explain why the conscious percepts are sharply localized in time at the second end of CD. This could also allow to understand memories as reductions occurring at the second, non-standard, end of sub-CDs in the geometric past.

3. The correspondence between the reduced state and the quantum superposition of states at the opposite boundary of CD allows an interpretation in terms of logical implication arrow with all statements present in the superposition implying the statement represented by the reduced state. Only implication arrow rather than equivalence is possible unless the M-matrix is diagonal meaning that there are no interactions. If it is possible to diagonalize M-matrix then in diagonal basis one has equivalences. It must be however emphasized that the physically preferred state basis fixed as in terms of eigenstates of density matrix does not allow diagonal M-matrix. Number theoretic conditions required that the density matrix corresponds to fixed algebraic extension of rationals can also make possible the diagonalization without leaving the extension and this condition might be highly relevant in the TGD inspired view about cognition relying on p-adic number fields and their algebraic extensions (see this).

4. In classical logic implication corresponds to the inclusion of subset by subset. In quantum case it corresponds to the inclusion for sub-space of state space. The inclusions of hyper-finite factors (WCW spinors define HFF of type II₁) realize the notion of finite measurement resolution, which would suggest that inclusion arrow has also interpretation in terms of finite measurement resolution.

   All quantum states equivalent with a given state in the resolution used imply it. Finite measurement resolution would mean that there would infinite number of instances always in the quantum superposition representing the rule A → B. Ironically, both finite measurement resolution and dissipation implying the arrow of geometric time and usually regarded as something negative from the point of view of information processing would be absolutely essential element of logical thinking in this framework.

5. Conscious theorem proving would has as correlate to building of sequences zero energy states representing A → B, B→ C, C → D with basic building bricks representing simple basic rules. These sequences would represent more complex truths.

Does state function-state preparation sequence correspond to alternating arrow of geometric time?

The state function reduction at light-like boundary of CD implies delocalization at the opposite boundary. This inspires so fascinating questions.

1. Could the state function reduction process take place alternately at the two boundaries of CD so that a kind of flip-flop in which the arrow of geometric time changes back and forth would result, and have interpretation as an alternating sequence of state function reductions and state preparations in the framework of positive energy ontology?

2. State function reductions are needed for sensory percepts. Could the sleep-wake-up period correspond to this kind of process so that during what we call sleep the past boundary of our personal CD would be in wake-up state? Could dreams and memories represent sharing of mental images of this kind of consciousness? Could it be that in the time scale of entire life cycle death is accompanied by birth at the second boundary of personal CD? Could this quantum physics representation for endless sequence of deaths and rebirths? Could the fact that old people often spend they last years in childhood have interpretation in this framework?

3. State preparation-reduction cycle might characterize only living matter whereas for inanimate matter second choice for the arrow of time would be dominant between two U-processes. TGD based reformulation of entropic gravity idea of Verlinde in terms of ZEO does not assume the absence of gravitons and the emergence of space-time (see this). The formulation leads to the proposal that thermodynamical stability selects the arrow of the geometric time and that it could be different for matter and antimatter implying that matter and antimatter reside at different space-time sheets. This would explain the apparent absence of antimatter and also support the view that the arrow alternates only in living matter.

The arrow of geometric time and the arrow of logical implication

If physics is mathematics in the sense that there is nothing behind quantum states regarded as purely mathematical objects, Boolean logic must have a direct manifestation in the structure of physical states. Physical states should represent quantal Boolean statements which get their meaning via quantum jumps. In TGD framework WCW ("world of classical worlds") spinor fields represent quantum states of the Universe and WCW spinors correspond to fermionic Fock states for second quantized induced spinor fields at space-time surface. Fock state basis has interpretation in terms of Boolean algebra. In positive energy ontology the problem is that fermion number as a super-selection rule would allow very limited number of Boolean statements to be represented. In ZEO the situation changes.

The fermionic parts of positive and negative energy parts can be seen as quantum superpositions of Boolean statements with fermion number in given mode (equal to 0 or 1) representing yes/no or true/false. Also various spin like quantum numbers associated with oscillator operators have same interpretation. Zero energy state could be seen as quantum superposition of pairs of elements of Boolean algebras associated with positive and negative energy parts of the zero energy state.

The first - and incorrect - interpretation is that zero energy state represents a quantum superposition of equivalent statements a↔ b and thus abstraction A<---> B involving several instances of A and B. The breaking of time reversal invariance allowing localization to definite fermionic quantum numbers at single end of CD only however implies that quantum states can only represent abstraction of logical implication to A→ B rather than equivalence. p-Adic physics for various primes p (see this) would represent correlates for cognition and intentionality.

For background see the chapter About the Nature of Time of "Matter, Mind, Quantum".

Water memory made visible

Water memory is one of those phenomena crucially important for understanding living matter whose existence is stubbornly forbidden by skeptics who say that water is just H₂O and nothing else since this is what they learned in the elementary school.

The latest demonstrations of water memory is by the research group of HIV Nobelist Montagnier giving also strong support for a completely new realization of genetic realized somehow by water (see this) but finnish skeptics concluded that Montagnier and his group are either swindlers or that the group knows nothing about basics of experimental biology. Only a complete idiot can have the self-confidence and ignorance possessed by the most pathological finnish skeptics.

In our neighboring country Sweden skeptics have totally different attitude towards truth. For instance, two swedish physics professors admitted that the recent demonstrations of cold fusion by Italian researchers (see this) suggest strongly that new kind of nuclear reactions taking place at low temperatures are involved. The other professor leads swedish skeptics society (see this).

TGD based view about dark matter leads to a model of dark nucleon with size of order DNA triplet in which nucleon states consisting of three quarks are in one-one correspondence with DNA,RNA,tRNA, and aminoacids and vertebrate genetic code has a simple and beatiful realization (see this). This supports the view that genetic code is realized at the nuclear physics level for dark matter in water, and that the chemical realization emerged much later. This would have profound implications for the understanding of evolution and also for what happens in the cellular water of living organisms also now.

Fischer Gabor sent me Youtube video making water memory directly visible. For instance, water droplets remember the person who prepared them or the flower dropped to the water by the structure of the droplets made visible by the method used by the researchers. Essentially holographic memory is in question. Maybe this video might open some eyes to see the fascinating reality in all its beauty. Enjoy!

TGD based view about entropic gravity

I discussed entropic gravity of Verlinde for some time ago in rather critical spirit but made also clear that quantum TGD in the framework of zero energy ontology could be called square root of thermodynamics so that thermodynamics- or its square root- should emerge at the level of the lines of generalized Feynman diagrams. The intolerable-to-me features of entropic gravity idea are the claimed absence of gravitons and the nonsense talk about the emergence of dimensions assuming at the same time basic formulas of general relativity.

I returned to the topic later again with a boost given by one of the few people in the finnish academic establishment who have regarded me as a life form with some indications about genuine intelligence. What demonstrates the power of a good idea is that just posing some naturally occurring questions led rapidly to a TGD inspired phenomenology of EG allowing to see what is good and what is bad in EG hypothesis and also to see possible far reaching connections with apparently completely unrelated basic problems of recent day physics.

Consider first the phenomenology of EG in TGD framework.

1. Gravitating bodies can be seen as sources of virtual and real gravitons propagating along flux tubes. The gravitons at flux tubes are thermalized and thus characterized by temperature and entorpy when the wavelength is much shorter than the distance between the source and receiver. One can say that massive object serves as a heat source. One could also say that the pair of bodies connected by flux tubes serves as a heat source for the flux tubes with temperature determined by reduced mass so that their is a complete symmetry between the two bodies.

2. The expression for the gravitonic entropy of the flux tube is naturally proportional to the length of flux tube at a given "holographic screen" - and for the gravitonic temperature-naturally proportional to the inverse of distance squared in absence of other heat sources from standard Laplace equation- are consistent with their forms at the non-relativistic limit discussed by Sabine Hossenfelder in very transparent manner. In general case, the stringy slicing for the preferred extremals of Kähler action provide the preferred coordinates in which gravitational potential and the counterpart of the radial coordinate can be identified.

3. EG generalizes to all interactions but negative temperatures mean a severe problem. This in turn suggests a direct connection with matter-antimatter asymmetry. Could thermally stable matter and antimatter correspond in zero energy ontology to different arrows of geometric time and appear therefore in different space-time regions? I have made this question also earlier but with a motivation coming directly from the formalism of quantum TGD.

This approach leads to the question whether the mathematical formalism of quantum TGD could make sense also in General Relativity when appropriately modified. In particular, do the notions of zero energy ontology and causal diamond and the identification of generalized Feynman diagrams as space-time regions of Euclidian signature of the metric make sense? Does the Kähler geometry for world of classical worlds realizing holography in strong sense lead to a formulation of GRT as almost topological QFT characterized by Chern-Simons action with a constraint depending on metric?

1. Einstein-Maxwell theory generalizes Kähler action and the conditions guaranteing reduction of action to 3-D "boundary term" are realized automatically by Einstein-Maxwell equations and the weak form of electric-magnetic duality leads to Chern-Simons action.

2. One distinction beween GRT and TGD is the possibility of space-time regions of Euclidian signature of the induced metric in TGD representing the lines of generalized Feynman diagrams. The deformations of CP₂ type vacuum extremals with Euclidian signature of the induced metric represent these lines replace black holes in TGD Universe. Black hole horizons are big particles and are suggested to possess gigantic effective value of Planck constant for which Schwartshild radius is essentially the Compton length for gravitational Planck constant so that black hole becomes indeed a particle in quantum sense. Blackholes represent dark matter in TGD sense.

3. CP₂ type vacuum extremals are solutions of Einstein's equations with a unique value of cosmological constant fixing CP₂ radius and this constant can be non-vanishing only in regions of Euclidian signature. The average value of the cosmological constant would be proportional to the ratio of the three-volume of Euclidian regions to the whole volue of 3-space and therefore very small. Could this be equivalent with the smallness of the actual cosmological constant? To answer the question one should understand the interaction between Euclidian and Minkowskian regions. I have proposed alternative manners to understand apparent cosmological constant in TGD Universe. Negative pressure could be understood in terms of the magnetic energy of magnetic flux tubes. On the other hand, quantum critical cosmology replacing inflation in TGD framework characterized by single parameter - its duration- corresponds to "negative pressure". These explanations need not be mutually exclusive.

At the formal level the formalism for WCW Kähler geometry generalizes as such to almost topological quantum field theory but the conditions of mathematical existence are extremely powerful and the conjecture is that this requires sub-manifold property.

1. The number of physically allowed space-times is much larger in GRT than in TGD framework and this leads to space-time with over-critical and arbitrarily large mass density and other problems plaguing GRT. M-theory exponentiates the problem and leads to landscape misery. The natural conjecture is that one cannot do without assuming that physically acceptable metrics are representable as surfaces in M⁴× CP₂.

2. CP₂ type regions give rise to electroweak quantum numbers and Minkowskian regions to four-momentum and spin. This almost gives standard model quantum numbers just from Einstei-Maxwell system! It is however far from clear whether one obtains both of them at the wormhole throats between the Minkowskian and Euclidian regions (perhaps from the representations of super-conformal algebras associated with light-like 3-surfaces by their geometric 2-dimensionality). Since both are needed it seems that one must replace geometry with sub-manifold geometry. Also electroweak spin is obtained naturally only if spinors are induced spinors of the 8-D imbedding space rather than 4-D spinors for which also the existence of spinor structure poses problems in the general case.

For more details see the article TGD inspired vision about entropic gravitation.

New 150 GeV boson stimulates emotions and bad rhetorics

This bump at 150 GeV manages to generate strong emotional responses. Very understandable. All predictions of the hegemony which has dominated particle physics the last thirty years seem to fail and anomalies suggesting unexpected new physics are emerging. It is intolerable that the theory of this TGD guy who has tried to talk sense for thirty years and been ruthlessly silenced and ridiculed can explain the 150 GeV anomaly elegantly using 15 years old predictions of his theory.

The latest example about highly emotional response is from Lubos. I glue below my two comments to the posting of Lubos, the response of Lubos and my response to it: I do not know whether Lubos allows it to appear in the blog. Note that Lubos carefully avoids of saying anything about the contents of my comments since he simply cannot make any reasonable counter argument. Lubos also argues against completely nonsensical statements that he has put to my mouth: another telltale signature of the rhetoric of a poor loser. Draw your own conclusions.

My first comment

TGD suggests two explanations for the possible new particle. Exotic octet of weak bosons is the first guess: it fails because there is no preference to decays to quarks.

Second explanation is in terms of a decay of charged pion of scaled up variant of ordinary hadron physics: scaling factor is 512 for the mass scale from the ratio for the Mersenne primes M_107 and M_89 labeling corresponding p-adic mass scales. According to the recent view not identical with the original one, pions would be produced abundantly and ρ meson or the first p-adic octave of charged pion would decay to W and neutral pion in turn producing quark jets. One signature of the new hadron physics would be monochromatic photon pairs with photon energy in the range 60-80 GeV. The naive scaling argument from ordinary pion mass would give mass of 71.4 GeV. p-Adic scaling with 2 is possible and produces mass 143.4 GeV to be compared with 145 GeV mentioned by Lubos.

Maybe the most dramatic prediction of TGD will be verified within next years! For details see my blog posting .

My second comment

Internal consistency arguments force to conclude that new physics is in TeV scale and the people in CDF are high rank professionals. Therefore I would be cautious in making skeptic or even cynical comments about their skills and even motivations unless I were a similar top professional myself.

Those who predict take this kind of potential discoveries quite seriously for understandable reasons. Both the forward-backward asymmetry in ttbar production and the new particle candidate can be understood in terms of scaled up variant of hadron physics predicted by TGD as I explain in detail at my blog.

Personally I cannot take seriously any model postulating ad hoc particle with hoc couplings to explain single anomaly. Principle is needed. I though for decades ago that after the advent of superstrings theorists would start to predict entire new branches of physics instead of single particle with couplings tinkered to explain single experimental anomaly.

In any case, LHC will certainly tell within few years what is the truth. We can only wait.

Lubos

Don't be silly, Matti. Most of similar 3-sigma bumps supporting "previously unexpected physics" that have ever been promoted by similar teams turned have been showed to be flukes or mistakes. I have surely done similar things at the top global level so if you ask me whether I consider myself competent to judge the likelihood that this is just hogwash resulting from some rather silly errors, the answer is a resounding Yes. Your encouragement to irrationally worship people who are at least as fallible as I am and who have done lots of very problematic and complex manipulations doesn't belong to science. Science just doesn't operate and cannot operate in this way, by intimidating researchers by the "expertise" of other experts. Science can only get settled if the arguments are being verified and multiplied, not by mindless agreement with some people who are promoted to infallible holy fathers (and, in this case, also mothers).

Your TGD crackpot junk will be left without comments.

Also, it's nonsense that the LHC will need "years" to decide about similar effects. First of all, the D0 Collaboration - the second team at the Fermilab - will publicize its own verdict within weeks. And the LHC could already have the answer in their collected data, too. If it doesn't, it will have the answer this year. The more likely answer is that the effect is bunk. But if it is not bunk, it is not because of infallibility of the CDF folks who have contributed to this paper.

My response

Dear Lubos,

I am just saying that those people who have theories able to predict something (not very many of them!) are quite interested in these bumps, at I have a high respect to the work of the people doing the hard work with experiments and analyzing their results, and that I do not see why this respect could be somehow crackpottish. Certainly this respect does not mean a blind belief to the correctness of their analysis. We are all human beings and most of us are doing their best.

The person who takes the scientific discussion as a battle rather than exchange and comparison of ideas must fight against the temptation to use as the last weapon the crackpot claim. I can understand that for a fanatic string model aficionado the failure of the cherished theory is extremely traumatic experience. But still: I am disappointed that you could not resist this temptation. You are one of the *very* few blog physicists whom I can take seriously and I would respect you much more if you would make at least a single argument about the explanation provided by TGD. Why it is wrong? Why it is nonsensical? No emotional bursts: just answers to these questions in the spirit of normal scientific argumentation. Just arguments about content instead of crackpot rhetorics.

Lubos

Dear Matti, apologies but your comment that followed my comment above was so atrocious that I had to use it to ban you.

My comment

Dear Lubos,

it is amusing that you are telling someone that his posting is too atrocius;-)! It was not. I just told that your put my mouth something I never said as anyone can directly check. I also asked you tell tell why my proposal is wrong instead of labeling me as a crackpot. This is just ordinary scientific discussion.

I added to my blog the comments including the comment that you deleted so that anyone can see what is involved: see http://matpitka.blogspot.com/2011/04/new-150-gev-boson-stimulates-emotions.html .

I added also a simple estimate of the decay width of the pion of M₈₉ hadron physics (dominating contribution comes from the box diagram with 3 gluons and one quark decaying to W at edges). The order of magnitude for the decay rate is around 20 GeV as required if one assumes flavor octet explaining also top quark asymmetry.

If you respect the rules of normal scientific debate you should tell what is wrong with the proposed mechanism for associated production of W boson and quark pair from pions produced abundantly. You could also tell what is wrong with the estimate for the decay width: what makes standard calculation crackpottish? The estimate can be found at

http://matpitka.blogspot.com/2011/04/is-decay-width-of-new-150-gev-particle.html .

You can of course delete also this posting but I will add it to my blog so that everyone can see what is involved.

With Best Regards.

Matti Pitkanen

I could not get this comment through. The blog program told that it has more than 3000 characters. It had about 1000. Perhaps this is the manner to realize the ban. I am really surprised. The briliant Lubos Motl who has been talking about intellectual honesty is afraid of a real scientific debate and uses this kind of tricks to avoid it?! Why so? If the opponent is just a miserable crackpot it should be extremely easy to demonstrate that his arguments are wrong!

New particle at mass about 150 GeV?

Tommaso tells about the newest result from CDF. The eprint of CDF collaboration (the first name in the long list of names is T. Aaltonen who comes from Finland) reports evidence for a new resonance like state, presumably a boson with mass around 150 GeV. The interpretation as Higgs is definitely excluded. Nature seems to be mercilessly humiliating the arrogant theoreticians;-). Tommaso promised to represent further comments already today and we are eagerly waiting! Also this posting is expected to develop in steps.

This posting has been updated a couple of times and reflects the evolution of my confused picture about what is involved. As I said: Nature seems to mercilessly humiliate arrogant theorists, me included. I shall confess below all my silly mistakes: enjoy!

First impressions

For the inhabitant of the TGD Universe the most obvious identification of the new particle would be as an exotic weak boson. The TGD based explanation of family replication phenomenon predicts that gauge bosons come in singlets and octets of a dynamical SU(3) symmetry associated with three fermion generations (fermion families correspond to topologies of partonic wormhole throats characterized by the number of handles attached to sphere). Exotic Z or W boson could be in question.

If the symmetry breaking between octet and singlet is due to different value of p-adic prime alone then the mass would come as an multiple of half-octave of the mass of Z or W. For W boson one would obtain 160 GeV consistent with 150 GeV. Z would give 180 GeV mass which is perhaps too high. The Weinberg angle could be however different for the singlet and octet so that the naive p-adic scaling need not hold true exactly.

Note that the strange forward backward asymmetry in the production of top quark pairs might be understood in terms of exotic gluon octet whose existence means neutral flavor changing currents.

One day later

Bloggers have reacted intensively to the possibility of a new particle. Tommaso has now a nice detailed analysis about the intricacies of the analysis of the data leading to the identification of the bump. Also Lubos and Resonaances have commented the new particle. Its existence have been actually known for months in physics circles. The flow of eprints to arXiv explaining the new particle has begun.

People are already now talking about an entirely new interaction. I have done this for more than decade! Actually I have talked about entire hierarchy of scaled up variants of hadron physics (Aaaarrrrgggghhh!; do not get scared: it was an expression of extreme irritation by some colleague who believes that physics proceeds by infinitesimal steps) associated with Mersenne primes and strongly suggested by p-adic length scale hypothesis!

Why an exotic weak boson a la TGD cannot be in question

From the additional data bits leaking via the blogs I can conclude that the new particle cannot be exotic weak boson but more plausibly the basic signature for what I call M₈₉ hadron physics and for which the proton mass is by a factor 512 higher than for the ordinary hadron physics. Pions are abundantly produced in any hadron physics and the signature of any hadron physics are the weak and electromagnetic decays of pions.

The extremely important data bit that I did not have yesterday is that the decays to two jets favor quark pairs over lepton pairs. A model assuming exotic Z -called Z^'- produced together with W and decaying preferentially to quark pairs has been proposed as an explanation. Neither ordinary nor the exotic weak gauge bosons of TGD Universe have this kind of preference to decay to quark pairs so that my first guess was wrong.

The resonance appears to be produced in association with W boson. Now comes the confession! This led on my side to an extremely stupid misunderstanding lasting for weeks. I thought that it is the 150 GeV bump which decays to W boson and dijet and forgot to check this when more data came. Stupid me! Ironically, it turned out that later evidence for the production of Wjj state in a decay of resonance with mass slightly below 150 GeV emerged so that the stupid error might have contained a seed of truth.

Remark: It has turned out that bump does not disappear and the most recent analysis assigns 4.1 sigma signicance to it. The mass of the bump would be at 147+/- 5 GeV. Also some evidence that the entire Wjj system results in the decay of a resonance with mass slightly below 300 GeV has emerged.

Is a scaled up copy of hadron physics in question?

The natural explanation for preference of quark pairs would be that strong interactions are somehow involved. This suggests a state analogous to a charged pion decaying to W boson and two gluons annihilating to the quark pair (box diagram). This kind of proposal is indeed made in Technicolor at the Tevatron and has as its analog second fundamental prediction of TGD that p-adically scaled up variants of hadron physics should exist and one of them is waiting to be discovered in TeV region. This prediction emerged already for about 15 years ago as I carried out p-adic mass calculations and discovered that Mersenne primes define fundamental mass scales (see this).

Sidestep: Also colored excitations of leptons and therefore leptohadron physics are predicted (see this). What is amusing that CDF discovered towards the end of 2008 what became known as CDF anomaly giving support for tau-pions. The evidence for electro-pions and mu-pions had emerged already earlier (for details see the link above). All these facts have been buried underground because they simply do not fit to the standard model wisdom. TGD based view about dark matter is indeed needed to circumvent the fact that the lifetimes of weak bosons do not allow new light particles. There is a long series of postings in my blog about CDF anomaly: see for instance this. At that time I did of course my best to inform colleagues about the predicted scaled up version of hadron physics. The only visible outcome of my efforts was that I lost my right to use the computer of Helsinki University since finnish colleagues got really angry! In any case, it would be nice if CDF would have discovered two new hadron physics without even knowing it!

Back to the topic: TGD indeed predicts p-adically scaled up copy of hadron physics in TeV region and the lightest hadron of this physics is a pion like state produced abundantly in the hadronic reactions. Ordinary hadron physics corresponds to Mersenne prime M₁₀₇=2¹⁰⁷-1 whereas the scaled up copy would correspond to M₈₉. The mass scale would be 512 times the mass scale 1 GeV of ordinary hadron physics so that the mass of M₈₉ proton should be about 512 GeV. The mass of the M₈₉ pion would be by a naive scaling 71.7 GeV and about two times smaller than the observed mass in the range 120-160 GeV and with the most probable value around 145 GeV as Lubos reports. 2*71.7 GeV = 143.4 GeV would be the guess of the believer in the p-adic scaling hypothesis and the assumption that pion mass is solely due to quarks. It is important to notice that this scaling works precisely only if CKM mixing matrix is same for the scaled up quarks and if charged pion consisting of u-d quark pair is in question. The well-known current algebra hypothesis that pion is massless in the first approximation would mean that pion mass is solely due to the quark masses whereas proton mass is dominated by other contributions if one assumes that also valence quarks are current quarks with rather small masses. The alternative which also works is that valence quarks are constituent quarks with much higher mass scale.

The killer prediction for the scaled up hadron physics hypothesis are gamma pairs with gamma energy in the range 60-80 GeV. The naivest assumption would give gamma energy of 71.7 GeV. My guess based on deep ignorance about the experimental side is that this signature should be easily testable: one should scan the energy range 60-80 GeV for mono-chromatic gamma pairs.

The simplest identification of the 150 GeV resonance

The picture about CDF resonance has become clearer during the last weeks (see the postings Theorists vs. the CDF bump and More details about the CDF bump. One of the results is that leptophobic Z' can explain only 60 per cent of the production rate.

Situation is coming also clearer for me. A really cold shower came as I found an incredibly silly misunderstanding in my earlier model which assumed that Wjj results from 150 GeV resonance that I identified as charged pion of M₈₉ hadron physics. It is of course jj which results from 150 GeV bump. This is unforgivable sloppiness. Ironically, there is now however evidence that my erratic assumption was correct in the sense that the entire Wjj might results from a resonance with mass slightly below 300 GeV. This suggests that its mass is in good accuracy two times the mass of 150 GeV bump for which best estimate is 147+/-5 GeV.

This brings in mind the explanation for the two and half year old CDF anomaly in which tau-pions with masses coming as octaves of basic tau-pion played a key role (masses were in good approximation 2^k× m(&pi_τ), m(&pi_τ)≈ 2m_&tau:, k=1,2. The same mechanism would explain the discrepancy between the DAMA and Xenon100 experiments. Could this mechanism be at work also now so that 300 GeV bump would correspond to the first octave M₈₉ pion which would have mass 150 GeV. This would mean that the one first octave of charged M₈₉ pion decaying to W and neutral M₈₉ pion with mass slightly below 150 GeV in turn decaying to two jets. Parity conservation would force the decay via emission of W boson. Parity conservation would prevent the decays to two pions. The nasty question is why the octaves of pion are realized as resonances in ordinary hadron physics. One could indeed imagine the mother particle to be ρ meson of M₈₉ hadron physics: in this case derivative coupling would make the decay rate small near the threshold. One can also ask whether the lightest state of M₈₉ pion could be actually around 73 GeV as the naivest possible scaling of pion mass predicts. If so then the situation would be very similar to that in the case of tau-pion.

Connection with the top pair backward-forward asymmetry?

The predicted exotic octet of gluons proposed as an explanation of the anomalous backward-forward asymmetry in top pair production could actually correspond to the gluons of the scaled up variant of hadron physics. M₁₀₇ hadron physics would correspond to ordinary gluons only and M₈₉ only to the exotic octet of gluons only so that a strict scaled up copy would not be in question. Could it be that given Mersenne prime tolerates only single hadron physics or leptohadron physics?

In any case, this would give a connection with the TGD based explanation of the backward-forward asymmetry in the production of top pairs. In the collision incoming quark of proton and antiquark of antiproton would topologically condense at M₈₉ hadronic space-time sheet and scatter by the exchange of exotic octet of gluons: the exchange between quark and antiquark would not destroy the information about directions of incoming and outgoing beams as s-channgel annihilation would do and one would obtain the large asymmetry.

Yesterday I generated irritation in learned colleagues by writing: "It would be nice if LHC would add to the Particle Data Tables both gluonic and electroweak octets and TGD to the text books;-)". Remaining in super-optimistic mood I would like to induce even more irritation by writing: "It would be nice if LHC would add to the Particle Data Tables not only exotic gluonic and electroweak octets but entire new hadron physics - and as a side product TGD to the text books;-;.). Good physics is fun! Enjoy!

For more about new physics predicted by TGD see the chapter p-Adic mass calculations: New Physics of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy". For reader's convenience I have added a short pdf article Is the new boson reported by CDF pion of M₈₉ hadron physics? at my homepage.