Wednesday, May 25, 2005

Superstring Revolution or TGD Liberation?

Lubos Motl wrote a nice posting about next super string revolution making a list of questions. What made me astonished and happy was the openness to new ideas giving hopes of getting out from the recent dead end. I would perhaps express my dream differently and speak about TGD liberation rather than super string revolution. M-theorists have developed enormous know how about advanced mathematics and since M-theory has produced practically no experimental predictions, I see no deep reason why one should stick to the M-theory context. Standard model symmetries are of course something totally different. In order to proceed all of us should do just what Lubos proposes and I did for almost 27 years ago, and ask what is possibly wrong in the recent approach, which has developed from GUT type unifications to M-theory sharing with it the basic interpretation of quantum number spectrum. There are three kinds of key questions I can imagine of making. a) What are the deep questions which might be asked even by non-professionals and which are not properly answered in the recent conceptual framework of physics? b) What we can really conclude about basic symmetries using experimental facts from particle physics and cosmology? c) Is the recent form of quantum field/string theory based on the poorly defined path integral concept final? Could one imagine generalizations of the basic quantum theory?

A. Philosophical questions

  • Do we really understand the notions of inertial and gravitational energy? The notions of energy and momentum are well defined in Special Relativity but become poorly defined in General Relativity. Poincare momenta are conserved but gravitational momenta are not conserved in cosmological length scales. Should one weaken Equivalence Principle somehow? Could one unify special and general relativities? Space-time as a 4-surface in M4×S does this. Poincare invariance at the level of imbedding spaces. Classical gravitational field identified as induced metric. This means also a generalization of string models by replacing string with a 3-surface. One basic prediction is that Poincare energy can have both signs. The proposal is that gravitational energy corresponds to the absolute value of inertial energy and is thus non-conserved and in general non-vanishing for inertial vacua. Robertson-Walker cosmologies are predicted to be inertial vacua: in other words, inertial mass density should vanish in cosmological length scales. The possibility of negative energies and signals propagating backwords in geometric time as deep implications both for the understanding of living matter and energy/communication technology. Phase conjugate photons could be perhaps interpreted as negative energy photons. Questions: Is the identification of the space-time as a 4-surface in 8-D space M4×CP2consistent with experimental facts? Is d=8 too low a dimension for classical gravitations. Many-sheetedness allows extreme flexibility and cosmological predictions (mass density cannot be over-critical) provide strong supprt for the proposal.
  • Should one generalize the geometrization of physics program to infinite-dimensional context? Configuration space of 3-surfaces, the world of classical worlds, as a basic object to be endowed with Kähler geometry and spinor structure. Quantum states of the Universe as modes of classical spinor fields in CH.
    • General coordinate invariance for space-time surfaces much more general concept. The definition of configuration space Kähler metric assigns a unique space-time surface to given 3-surface. Space-time as a Bohr orbit of 3-surface.
    • Is the infinite dimensional Kähler geometric existence unique? Loop space Kähler geometries are unique and in higher-dimensional context the constraints from existence of Riemann connection are even stronger. Loop space has an infinite Ricci scalar, which signals that something must go wrong with string models. The world fo classical worlds as a union of symmetric spaces for which all points are metrically equivalent: gives hopes of calculability. Parameters labelling the spaces in the union are non-quantum fluctuation zero modes identifiable as classical observables of quantum measurement theory. The requirement of finite curvature scalar means its vanishing and Einstein tensor must vanish. Hyper Kähler structure is expected. Imbedding space not dynamical but "God given" so that landscape misery disappears.
    • Geometrization of the fermionic oscillator operators and conformal super generators via the identification as configuration space gamma matrices. The new element is that gammas carry fermion number and half odd integer spin. Majorana condition must be given up already by the separate conservation of quark and lepton numbers, which correspond to different chiralities of M4×CP2spinors. Number theoretically favoured D=8 for imbedding space becomes thus possible.
    • Clifford algebra of CH (for which tangent space is separable Hilber space) is a hyper-finite factor of type II1. Quantum groups, conformal theories, ...are an automatic outcome. Jones inclusions as subsystem-system inclusions. The value of hbar characterizes inclusion. Dynamical hbar highly suggestive.
    • Generalization of 2-D conformal invariance requires D=4 for space-time. Lightlike 3-D CDs metrically 2-dimensional and allow generalization of 2-D conformal invariance. Stringy conformal invariance generalizes and fixes space-time dimension to be D=4. Effective 2-dimensionality is means that 2-dimensional partonic surface code for physical states. The dependence of states on normal derivatives at boundary components means that there is actually 3-dimensionality. There is a hydrodynamical analogue for this: the fluxes of various conserved quantities over 2-D surfaces surrounding sub-systems code for the evolution of the state of the system in practise.
  • Quantum measurement theory Quantum measurement theory is plagued by paradoxes.
    • What differentiates between experienced time and geometric time? There are many paradoxes resulting from the identification of these two times in quantum measurement theory and thermodynamics. The generalization of the notion of quantum jump so that deterministic quantum evolution identifiable as quantum superposition of classical evolutions is replaced with a new one would resolve these logical paradoxes. Experience time would correspond to the sequence of quantum jumps and correspond to geometric time only under special conditions. Some implications: space-time surface as a living system; four-dimensional brain and quantum model of memory.
    • Configuration space (the world of classical worlds) zero modes as genuine classical variables characterizing the shape and other non-quantum fluctuating aspects of space-time surface?
    • Quantum and consciousness: should one make conscious observer part of the system studied? Matter and theory of matter as part of physical a system in generalized sense. von Neumann inclusions could realize the hierarchy of matter, theory about matter, theory about theory of matter,... Zero energy states entangled by a crossing symmetric S-matrix have interpretation as Connes tensor product. S-matrix would realize laws of quantum physics in the structure of the zero energy state. Cognitive representation would be in question. Infinite hierarchy of Jones inclusions would correspond to a hierarchy of levels of reflective consciousness.
    • Quantum classical correspondence. Also quantum jump sequences should have space-time correlates. Forces the breaking of strict classical non-determinism. Maxwell action for the projection of CP2 Kähler form to space-time surface is a unique choice guaranteing this. Pure gauge solutions give rise to infinite vacuum degeneracy implying non-determinism for non-vacua and make universe quantum spin glass.
  • Should one give up the reductionistic dogma? Is the reduction to Planck scale an illusion: can we really understand living matter from M-theory? Is Planck scale the fundamental scale or does it follow as a prediction? Many-sheeted space-time breaks reductionistic view.

    B. Questions inspired by particle physics and cosmology

    • Standard model symmetries something more fundamental than thought?
      • Does standard model gauge group have much deeper meaning than thought? CP2 codes for standard model gauge group and M4×CP2 predicts conserved B and L. Proton would not decay. There are also other differences. Color corresponds to CP2 partial waves. CP2 codes for quaternionic planes of octonionic space containing fixed complex plane. Standard model symmetries from number theory?
      • Are space-time supersymmetries really there? There is no evidence for the super partners yet. Majorana spinors forced by space-time supersymmetry lead to M-theory. In TGD conformal super-symmetries correspond to non-Hermitian super-generators generators carrying quark and lepton numbers. It seems clear that space-time supersymmetries are absent. Both Particle Data Table, the construction of the geometry of the world of classical worlds, and the number theoretic approach favour space-time dimension 4 and imbedding space dimension 8.
      • Are Higgs particles/scalars really there? Could p-adic thermodynamics give the dominant part of fermionic mass? Ew gauge couplings favour Higgs but it is not yet clear do they force its existence. Could the couplings of possibly existing Higgs to fermions define only a small shift of fermion masses? Small couplings to fermions would explain why Higgs has not been observed.
      • Family replication phenomenon: topological explanation from effective 2-dimensionality. Fermion generations correspond to 2-dimensional orientable topologies labelled by genus (sphere, torus, etc.). One could perhaps understand why g≥ 3 topologies are different, presumably heavy and short lived, on basis of hyper-ellipticity which means the existence of a global conformal Z2 symmetry. g≤ 2 surfaces are always hyper-elliptic but not those with g≥3. The ground states in conformal moduli should be maximally symmetric and concentrate strongly around 2-surfaces with Z2 conformal symmetry. One the other hand, elementary particle vacuum functionals vanish for hyper-elliptic surfaces for g&ge 3 so that they must correspond to "higher partial waves" and could be heavy for this reason.
    • The problem of mass scales Elementary particles are characterized by widely different mass scales. This forces to ask whether Planck length really the only fundamental length scales and where the mystery number 1038 comes from?
      • When I got interested on p-adic numbers in the beginning of nineties I soon found that leptons, hadrons, and intermediate gauge bosons seem to correspond naturally to Mersenne primes M127, M107, M89 if their mass scales are proportional to √p as implied by the simple attempts to calculate particle masses. This finding generalized to the p-adic length scale hypothesis stating that p-adic primes near integer powers of 2 are especially interesting physically. Number theory would thus explain the fundamental mass scales.
      • Super-conformal invariance and p-adic thermodynamics for Virasoro generator L0 lead to successful predictions for elementary particle and hadron mass spectrum and a lot of new predictions follow. The totally different mass scales of fermion generations can be also understood on basis of p-adic length scale hypothesis.
      • A given p-adic topology would serve as an effective topology of real space-time sheet in an appropriate length scale range. The inherent non-determinism of p-adic differential equations for some value of p would resemble the nondeterminism for Kähler action. p-Adic non determinism would also characterize different quantum non-determisnisms and the basic prediction would be long range correlations to which local chaos would be superposed.
    • Cosmological questions
      • Why mass density is not over-critical? Robertson Walker cosmologies imbeddable to M4×CP2 are necessary sub-critical or critical. RW metric during the critical period is unique apart from the parameter characterizing the duration of this period.
      • Inflation or quantum criticality? Inflationary scenario troubled by scalar fields for which no experimental evidence exists. Quantum criticality does not require them and predicts also flat 3-space since it requires vanishing of constants with dimensions of length so that 3-D curvature scalar for RW cosmology must vanish. Critical period corresponds to a phase transition from cosmic string dominated phase to an ordinary space-time. Similar phase transitions occur as scaled up versions with cosmic strings replaced by magnetic flux tubes.
      • How to explain the smallness of cosmological constant and accelerated cosmic expansion? Many-sheeted space-time with a spectrum of Hubble constants depending on size of the space-time sheet explains the small value of Hubble constant observed for photons from very distant objects. The acceleration of the expansion can be understood as an apparent effect.
      • The problem of initial values: are all physically acceptable universes creatable from vacuum? Inertial energy density vanishes in cosmological scales whereas gravitational energy density does not. If the states of the universe are creatable from vacuum (vanishing total conserved quantum numbers), the problem about what are the values of net conserved quantum numbers of the Universe disappears. Also the problem of initial values disappears. Fine tuning of various parameters can be understood as a result of self-organization by quantum jumps replacing entire 4-D cosmology (also initial values) with a new one.
    • Questions related to quantum gravitation
      • What are dark matter and dark energy? Does dark matter reside at larger space-time sheets? Does dark energy correspond to magnetic energy of magnetic flux tubes so that cosmological constant would characterize the density of energy assignal to magnetic flux tubes. Λ depends on the p-adic length scale of space-time sheet and its recent smallness can be understood.
      • Should one start quantizing gravitation from bound states just as Bohr did in case of atomic physics. Length of order Schwartschild radius is a natural counterpart of Bohr radius in the quantization of gravitational bound states? hbargr would have a gigantic value. Ordinary matter would corresponds to very large values of principal quantum number n and small hbar. Could dark matter correspond to small values of n and astrophysical quantum phase?
      • Is there really need for assuming a dynamical imbedding space? In M-theories it leads to landscape misery. All depends on whether many-sheeted space-time is capable of explaining what is known about gravitation plus making new successful predictions.
      • What black holes are? Can one identify black hole like objects as highly tangled strings in Hagedorn temperature? Do their scaled up variants with effective gravitational constant defined by p-adic length scale instead of Planck length exist. RHIC observations suggest that this is the case in case of hdaronic case. 3-D color magnetic flux tubes in Hagedorn temperature containing gluon condensate would explain the observations. Could black holes be the ultimate quantum computing structures in macroscopic quantum phase with large value of hbar?

    C. Should quantum theory be modified and/or generalized?

    • The Clifford algebra for the tangent space of the world of classical worlds is basic example of a hyper-finite factors of type II1. Inclusions of hyper-finite factors relate very closely to quantum groups, conformal field theories, quantum spaces, knot invariants, 3-manifold invariants, braidings, etc. There is a unique inherent unitary time evolution operator defining a propagator for 3-surface (or 2-D partonic surface) as automorphism of algebra: for the imbedding of factor M to N this corresponds to a unitary rotation. von Neuman algebra M becomes an extended particle moving inside algebra N! One obtains generalized Feynmann rules. Hierarchy of S-matrices results corresponding to a hierarchy of inclusions results. At the lowest level is the S-matrix for matter. The states entangled by S-matrix have necessarily vanishing total quantum numbers and would have interpretation as cognitive states representing quantum dynamics (S-matrix) in their own structure. Crossing symmetric S-matrix defines a cognitive entanglement consistent with Connes tensor product. Feynman rules for cognition would result and reduce to the Feynman rules of matter apart from the different single particle time evolution!
    • Is hbar dynamical and quantized? Can one express the quantization in terms of Beraha numbers closely related to the square of quantum dimension as von Neumann inclusions suggest? Variation of the fine structure constant would be a prediction and there is indeed a variation by about 10-6 depending on determination. Does hbar characterize Jones inclusion for hyperfinite type II1 factors? Can one identify dark matter as a conformally confined macroscopically quantum coherent phase (conformal weights for particles are in the most general case complex and expressible in terms of non-trivial zeros of zeta and net conformal weight for the many particle state must be real). Could dark matter be staring directly to our face? Dark matter as a quantum coherent matter with a large value of hbar? Living matter and dark matter? Dark matter and grey matter?
    • Should one give up the poorly defined path integral approach? Are generalized Feynman diagrams always equivalent with tree diagrams or diagrams with single N-vertex? This would conform with the classical picture in which only generalized Bohr orbits appear instead of all extremals. The reduction implies strong constraints on vertices allowing algebraic formulation. Unitary is implied by the conditions. Couplings constants fixed points of ordinary coupling constant evolution. There is infinite number of fixed points labelled by p-adic primes and p-adic coupling constant evolution replaces ordinary coupling constant evolution.
    • Physics as a generalized number theory?
      • p-Adic number fields and fusion of p-adic number fields and their extensions and reals to a larger structure? Does physics in various number fields resilt by an algebraic continuation from rational number based physics? p-Adic physics as physics of intentionality and imagination since p-adic non-determinism allows mimicry. Classical non-determinism in real context resembles p-adic non-determinism for some p in some length scale range always. Does the transformation of intention to action correspond to a quantum jump replacing p-adic space-time sheet representing intention with a real space-time sheet representing action.
      • Quaternions and octonions and space-time dimensions. Effective 2-dimensionality and dimensions of space-time and imbeddings space relate to the dimensions of classical division algebras. Hyper-octonions/-quaternions are forced by the requirement that number-theoretic norm defines metric with Minkowski signature (hyper octonions/quaternions correspond to a sub-space of complexified octonions/quaternions obtained by multiplying non-commuting imaginary units by a commuting √(-1)). The dynamics of the Kähler action defining generalized Bohr orbits could correspond to a purely number theoretic dynamics: space-time surfaces as hyper-quaternionic or co-hyperquaternionic sub-manifolds of the hyper-octonionic imbedding spaces. This approach suggests several number theoretic dualities. In particular, there is a generalization of wave-particle duality relating descriptions based on the identification of space-time surface as a surface in M8 defined by the conserved classical currents associated with M4 translations and SU(3) isometries in the complement of U(2) as functions of space-time point on hand, and as a surface of M4×CP2. The values of these densities depend on the choise of time coordinate but general coordinate invariance is achieved by using the lightcone proper time as a preferred time coordinate.
      • Infinite primes. Construction isomorphic to a repeated second quantization of an algebraic quantum field theory. Infinite primes correspond to Fock states for a supersymmetric arithmetic quantum field theory. Hierarchy of infinite primes could correspond to the hierarchy of space-time sheets and infinite primes/integers/... would have representation as four-surfaces somewhat like ordinary primes/integers/... have representation as points of real axis.
    Matti Pitkänen P.S. You are wellcome to my re-constructed home page.


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