måndag 29 oktober 2018

Why TGD?


The most frequently asked questions  about TGD   2014 .  The headlines:
  1. Why TGD? (pdf-article)
  2. How can TGD help to solve the problems of recent day theoretical physics?
  3. What are the basic principles of TGD?
  4. What are the basic guidelines in the construction of TGD?
The important is to catch the basic idea: technical details are not important, it is principles and concepts which really matter  + Problem solving. TGD itself and almost every new idea in the development of TGD has been inspired by a problem. Standard physics is plagued by problems deeply rooted in basic philosophical - even ideological - assumptions which boil down to -isms like reductionism, materialism, determinism - and locality.

Standard model summarize the recent understanding of physics. The attempts to extrapolate physics beyond standard model are often based on naive length scale reductionism and have produced Grand Unified Theories (GUTs), supersymmetric gauge theories (SUSYs). The attempts to include gravitation under the same theoretical umbrella with electroweak and strong interactions has led to superstring models and M-theory. These programs have not been successful, and the recent dead end culminating in the landscape problem (criticality lost?) of superstring theories and M-theory could have its origins in the basic ontological assumptions about the nature of space-time and quantum.

1. Why TGD?
 The question requires an overall view about the recent state of theoretical physics.
  • Thermodynamics, special relativity, and general relativity involve also postulates, which can be questioned, as in thermodynamics second law in its recent form, and the assumption about fixed arrow of thermodynamical time, since it is hard to understand biological evolution in this framework.
  • In general relativity the  symmetries of special relativity are in principle lost and with Noether's theorem this means also the loss of classical conservation laws, even the definitions of energy and momentum are in principle lost.
  • In quantum physics the basic problem is that the nondeterminism of quantum measurement theory   conflicts with the determinism of Schrödinger equation.

2. How can TGD help?  The view about space-time as 4-D surface in  fixed 8-D space-time is the starting point.
  • motivated by the energy problem of general relativity
  • fusion of the basic ideas of special and general relativities (a TOE).
This has led to other ideas:
  • dark matter as phases of ordinary matter characterized by non-standard value of Planck constant, this has a strong operative function
  • extension of physics in p-adic number fields  assumed to describe correlates of cognition and intentionality,
  • zero energy ontology (ZEO) - quantum states are identified as counterparts of physical events (two times required). 

    These new elements generalize considerably the view about space-time and quantum + give possibility to understand living systems and consciousness in  physics.

3. TGD as a mathematical theory, basic principles.
A generalization of Einstein's geometrization program from space-time level to the level of "world of classical Worlds" as space of 4-surfaces.

The infinite-dimensional geometry fixes it uniquely.
It is the modes of the classical imbedding space spinor fields - eigenstates of four-momentum and standard model quantum numbers - that define the ground states of the super-conformal representations. It is these modes that correspond to the 4-D spinor modes of QFT limit.

+TGD as a generalized number theory with three separate threads.
  • Number theoretical universality   from the need to fuse  p-adic physics and real physics to a coherent whole.
  • Classical number fields (reals, complex numbers, quaternions, and octonions) have dimensions which correspond to those appearing in TGD. Basic laws of both classical and quantum physics could reduce to the requirements of associativity and commutativity.
  • The  primes (and integer, rational, and algebraic number) can be generalized so infinite primes are possible.  Construction of infinite hierarchy of infinite primes using the primes of the previous level as building bricks to new level. This  is structurally identical with a repeated second quantization of supersymmetric arithmetic quantum field theory for which elementary bosons and fermions are labelled by primes.  Free many-particle states and also the analogs of bound states are obtained. The really hard part of quantum field theories - understanding of bound states - could have number theoretical solution.

  • It is not yet clear if both visions (geometrization and number theory) are needed. In any case their combination has provided a lot of insights about   quantum TGD.

    4. Guidelines in the construction of TGD.  The construction of physical theories is nowadays to a high degree guesses about the symmetries  and deduction of consequences. The very notion of symmetry has been generalized in this process. Super-conformal symmetries play even more powerful role in TGD than in superstring models and the gigantic symmetries of WCW  is a powerful 'proof'.

    In TGD context string like objects are not something emerging at Planck length scale but  in scales of elementary particle physics. The irony is that although TGD is not string theory, string like objects and genuine string world sheets emerge naturally from TGD in all length scales.

    Even TGD view about nuclear physics predicts string like objects.

    The most important guidelines:
    A kernel of WCW = a conjecture.
    M4× CP2 as choice for the imbedding space
    Number Theoretical Universality
    'Quantum classical correspondence'  where classical theory is no approximation but  an exact part of quantum theory.

    And  more technical guidelines:
    • Strong form of General Coordinate invariance (GCI) is a very strong assumption, that gives the assumption that Kähler function is Kähler action for a preferred extremal as a counterpart of Bohr orbit. Strict determinism not required.   Strong form of GCI requires that the light-like 3-surfaces represent partonic orbits and space-like 3-surfaces at the ends of causal diamonds are physically equivalents as effective 2-D states. The intersections of these two kinds of 3-surfaces and 4-D tangent space data at them   code for quantum states.
    • Quantum criticality means that Universe is analogous to a critical system with maximal structural richness.  Universe is at the boundary line between chaos and order. Quantum criticality fixes the basic coupling constant dictating quantum Dynamics.
    • Finite measurement resolution using  von Neumann algebras.  Usually the measurement problem is a messy, ugly duckling in theoretical physics.
    • Strong form of holography from strong form of GCI and TGD reduces to an almost topological QFT= a conjecture. Weak form of electric-magnetic duality is a TGD version of electric-magnetic duality discovered by Olive and Montonen.
    • Generalized Feynman diagrams. TGD leads to a realization of counterparts of Feynman diagrams at the level of space-time geometry and topology. The highly non-trivial challenge is to give them precise mathematical content. Twistor revolution has made possible a considerable progress in this respect and led to a vision about twistor Grassmannian description of stringy variants of Feynman diagrams.
    • The localization of spinor modes at string world sheets. There are three  reasons for the modes of the induced spinor fields to be localized to 2-D string world sheets and partonic 2-surfaces - or to the boundaries of string world sheets at them defining fermionic world lines.
      Thanks to holography fermions behave like pointlike particles, which are massless in 8-D sense. General relativity emerges as an approximation due to frustration.
      - gives em-charge as eigenstates. Spinor modes can have have well-defined electromagnetic charges - the induced classical W boson fields and perhaps also Z field vanish at string world sheets so that only em field and possibly Z field remain.
      - acts as spacetime 'genes'.
      - sign problems with partition, not necessary positive always. This is avoided in the 2D World sheet of TGD (many sheeted spacetime).

    This is a very compressed text about TGD. Go to the sources for better info.
    See the  article Why TGD? 2014.
    Why TGD and What TGD is? 2018 (with spinor part), 49 pp.
    A very short summary, a brief summary about TGD, 2018, 3 pp.

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