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Getting critical about twistor lift of TGD

It is sometimes very useful to become very critical about own ideas. Usually this leads to considerable progress. At this time I became very critical about the notion of twistor space in TGD.

Criticizing the notion of twistor space of M4

Twistor lift of TGD involves representation of space-time surfaces as 6-surfaces in twistor space of H having structure of S2 bundle over space-time surface resulting in dimensional reduction. These 6-surfaces would be holomorphic and thus minimal surfaces represented in terms of polynomials having same degree as the corresponding M8 octonionic polynomial by number theoretic universality.




I have assumed that what I call geometric twistor space of M4 is simply M4× S2. It however turned out that one can consider standard twistor space CP3 with metric signature (3,-3) as an alternative. This option reproduces the nice results of the earlier approach but the philosophy is different: there is no fundamental length scale but the hierarchy of causal d…

S-matrix and SUSY in TGD sense

The construction of S-matrix has been one of the eternity projects of TGD. There are many proposals such as the construction based on the quaternionic generalization of twistor Grassmannian approach for cognitive representations involving huge simplification due to the vanishing of loop diagrams but also this approach is indirect. SUSY in TGD sense finally suggests a quite concrete fundamental approach.




The construction would be based on the explicit solution of the super-symmetrized field equations. In principle everything reduces formally to classical partial differential equations for super-space-time surface and super-spinors. One solves preferred extremal as its super-variants which means solving the space-time evolution of multi-spinors defining super-coordinates and in this background one solves super-Dirac equation. This is highly non-trivial but in principle a well-defined procedure. If one gives initial values of various multi-spinor mods at the first light-like b…

What particles are in TGD Universe?

Savyasanchi Ghose asked the following question. I answer from TGD point of view differing in some respects from the standard view.



"What are the 'elementary particles'? We know that there are some methods to produce them like bombarding in a nuclear reactor, decay or ionization, but what really a 'particle' is? From Quantum field theory perspective, there aren't any particles, what we call as 'particles' are just the excitations in the respective fields, these excitations are tied up in a little bundles of energy which we call as particles, but this view doesn't explain how we perceive the material world as 'solid' matter rather than energy form'



I have also pondered this question many times. I started from a childish attempt to understand elementary particle masses about 45 years ago but gradually realized that I must understand many other things before answering this question!




Elementary particles in lab show their present quite conc…

Finiteness for the number of non-vanishing Wick contractions, quantum criticality, and coupling constant evolution

The consistency with number theoretic vision requires that the number of terms in the super-Taylor expansion of action is finite - otherwise one is led out from the extension: this applies both to the action determining space-time surfaces and to the corresponding modified Dirac action. There are several options that one can consider.




Normal ordering of the fermionic oscillator operators would be a straightforward manner to handle the situation. One would obtain finite number of terms since the number of quark oscillator operators is d=4+4=8. The maximal degree mmax of multiple partial derivative of action with respect to gradient of H-coordinate h would be mmax= d=8 and correspond to monomial with 4+4 quark oscillator operators. Note that the normal ordering of this term gives rise to c-number.

It however seems that the natural solution of the problem must involve cancellation of the Wick contractions when the degree m of the multiple partial derivative satisfies m>mmax. Som…

Evidence for 96 GeV pseudoscalar predicted by TGD

Lubos had a second posting mentioning new bump at around 96 GeV very near to the masses of weak bosons and tells that physicists seem to take it very seriously. Lubos of course wants to interpret it as a Higgs predicted by standard SUSY already excluded at the energies considered.

What about TGD interpretation?



TGD predicts besides weak gauge bosons, Higgs, and pseudoscalar: about the prediction of pseudoscalar I became aware only now. This follows taking tensor products for spin-isospin representations formed by quarks but for some reason I had not noticed this. The mass scale of pseudoscalar Higgs is most naturally the same as that of scalar Higgs or of weak bosons and p-adic mass calculations allow to estimate its mass. Higgs mass 125 GeV is very nearly the minimal mass for p-adic prime p≈ 2k, k=89. The minimal mass for k=90 defining also the p-adic mass scale of weak bosons would be 88 GeV so that the interpretation as pseudo-scalar with k=90 might make sense (…

Twistors in TGD Universe

This article was inspired by a longer paper "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors". I found it convenient to isolate the part of paper related to twistors. In twistor Grassmannian approach to N=4 SYM twistors are replaced with supertwistors and the extreme elegance of the description of various helicity states using twistor space wave functions suggests that super-twistors are realized at the level of M8 geometry. These supertwistors are realized at the level of momentum space.

In TGD framework M8-H duality allows to geometrize the notion of super-twistor in the sense that different components of super-field correspond to components of super-octonion each of which corresponds to a space-time surfaces satisfying minimal surface equations with string world sheets as singularities - this is geometric counterpart for masslessness.

In TGD particles are massless in 8-D sense and in general massive in 4-D sense…

SUSY in TGD Universe

What SUSY is in TGD framework is a longstanding question. In twistor Grassmannian approach to N=4 SYM twistors are replaced with supertwistors and the extreme elegance of the description of various helicity states using twistor space wave functions suggests that super-twistors are realizex at the level of M8 geometry. These supertwistors are realized at the level of momentum space.

In TGD framework M8-H duality allows to geometrize the notion of super-twistor in the sense that different components of super-field correspond to components of super-octonion each of which corresponds to a space-time surfaces satisfying minimal surface equations with string world sheets as singularities - this is geometric counterpart for masslessness.

The progress in understanding of M8-H duality throws also light to the problem whether SUSY is realized in TGD and what SUSY breaking does mean. It is now rather clear that sparticles are predicted and SUSY remains exact but that p-adic thermodynamics…

New Aspects of M8-H Duality

M8-H duality (H=M4× CP2) has become one of central elements of TGD. M8-H duality implies two descriptons for the states.




M8-H duality assumes that space-time surfaces in M8 have associative tangent- or normal space M4 and that these spaces share a common sub-space M2⊂ M4, which corresponds to complex subspace of octonions (also integrable distribution of M2(x) can be considered). This makes possible the mapping of space-time surfaces X4⊂ M8 to X4⊂ H=M4× CP2) giving rise to M8-H duality.



M8-H duality makes sense also at the level of 8-D momentum space in one-one correspondence with light-like octonions. In M8=M4× E4 picture light-like 8-momenta are projected to a fixed quaternionic M4T⊂ M8. The projections to M4T⊃ M2 momenta are in general massive. The group of symmetries is for E4 parts of momenta is Spin(SO(4))= SU(2)L× SU(2)R and identified as the symmetries of low energy hadron physics.

M4⊃ M2 can be also chosen so that the light-like 8-momentum is parallel to M4L⊂…

TGD view about McKay Correspondence, ADE Hierarchy, and Inclusions of Hyperfinite Factors

There are two mysterious looking correspondences involving ADE groups. McKay correspondence between McKay graphs characterizing tensor products for finite subgroups of SU(2) and Dynkin diagrams of affine ADE groups is the first one. The correspondence between principal diagrams characterizing inclusions of hyper-finite factors of type II1 (HFFs) with Dynkin diagrams for a subset of ADE groups and Dynkin diagrams for affine ADE groups is the second one.

I have considered the interpretation of McKay correspondence in TGD framework already earlier but the decision to look it again led to a discovery of a bundle of new ideas allowing to answer several key questions of TGD.




Asking questions about M8-H duality at the level of 8-D momentum space led to a realization that the notion of mass is relative as already the existence of alternative QFT descriptions in terms of massless and massive fields suggests (electric-magnetic duality). Depending on choice M4⊂ M8, one can describe…

Super-symmetry in TGD Universe

It is now clear that SUSY is realized in TGD Universe but that the realization is very different from that in super-symmetric quantum field theories. The question how to realize super-field formalism at the level of H=M4× CP2 led to a dramatic progress in the identification of elementary particles and SUSY dynamics.

This picture simplifies dramatically the view about particle spectrum and scattering amplitudes. The most surprising outcome was the possibility to interpret leptons and corresponding neutrinos as local 3-quark composites with quantum numbers of anti-proton and anti-neutron. Leptons belong to the same super-multiplet as quarks and are antiparticles of neutron and proton as far quantum numbers are consided. One implication is the understanding of matter-antimatter asymmetry.

Also bosons can be interpreted as local composites of quark and anti-quark. Hadrons and hadronic gluons would still correspond to the analog of monopole phase in QFTs. Homology charge would …

Copenhagen interpretation is dead: long live ZEO based quantum measurement theory!

I encountered a very interesting ScienceDaily article " Physicists can predict the jumps of Schrödinger's cat (and finally save it)" ). The experimental findings described in the article are extremely interesting from the point of view provide by TGD inspired quantum measurement theory relying on Zero Energy Ontology (ZEO) and provides a test for it.

In standard quantum measurement theory (Copenhagen interpretation) of Bohr quantum jump is random in the sense that it occurs with predictable probabilities to an eigenstate of the measured observables. Their occurrence cannot be predicted and even less prevented - except by monitoring - Zeno effect.

1. Findings

The findings of Minev et al are described in the article "To catch and reverse a quantum jump mid-flight". The outcome of quantum jump is indeed unpredictable but the time of occurrence is to high degree predictable: there is a detectable warning signal!

A curious feature is that the …

Gravitation as square of gauge interactions

I encountered in FB a link to an interesting popular article about theoretical physicist Henrik Johansson who has worked with supergravity in Wallenberg Academy. He has found strong mathematical evidence for a new duality. Various variants of super quantum gravity support the view that supersymmetric quantum theories of gravitation can be seen as a double copy of a gauge theory. One could say that spin 2 gravitons are gluons with color charge replaced with spin. Since the information about charges disappears, gluons can be understood very generally as gauge bosons for given gauge theory, not necessarily QCD.

The article of C. D. White entitled "The double copy: gravity from gluons explains in more detail the double copy duality and also shows that it relates in many cases also exact classical solutions of Einsteins equations and YM theories. One starts from L-loop scattering amplitude involving products of kinematical factors ni and color factors ci …

Three shorter articles related to "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors"

I decided to isolate from a rather long article TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors the following three shorter articles.

M8-H Duality and Consciousness.

This article is part of a longer paper "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors". I found it convenient to isolate the part of paper related to the possible implications for TGD inspired theory of consciousness. M8-H duality is one of the key ideas of TGD, and one can ask whether it has implications for TGD inspired theory of consciousness. Certain aspects of M8-H duality indeed challenge the recent view about consciousness based on ZEO (zero energy ontology).

The algebraic equations for space-time surfaces in M8 state the vanishing of either the real or imaginary part (defined in quaternionic sense) for octonion valued polynomial with real coefficients. Besides 4-D roots one obtains as universa…