Wednesday, June 26, 2019

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!

  1. Elementary particles in lab show their present quite concretely as particle like entities. Say as tracks in magnetic field. In QFT theory description many particle states have purely algebraic description as Fock states created by creation operators labelled by momenta. There is no apparent connection with the concrete geometric picture. The scattering rates are deduced from QFT by rather highly counter-intuitive procedure. Particles correspond to poles for momentum space Fourier transforms of correlation functions for fields representing particles. In path integral approach one studies essentially correlations of classical fields in an analog of thermodynamical partition function defined by the exponent of action. Classical physics results in stationary phase approximation, which need not be good.

  2. The connection with particles become more concrete when one replaces momentum eigenstates with localized modes which however do not remain such in time development. Gaussian wave packets replace momentum replace momentum eigenstates and one has reasonable localization in ordinary space. The observed particles would correspond to these wave packets. Particles in QFT have no geometric size: they are point-like and the ony size is quantum size defined by the support of the wave function.

    For solitonic states appearing in integrable theories- typically 2-D - solitons represent objects having also geometric size and can be de-localized in center of mass degrees of freedom.

TGD view is different in the sense that particle have also geometric size. This is essential for understanding particle massivation not really understood in QFT approach.
  1. Particles correspond to 3-surfaces and their orbits as 4-D regions of space-time surfaces. Particles have geometric size instead of being point-like. The 4-D orbit of particle is a region carrying induced classical fields determined by the imbedding to 8-D H=M4×CP2 in terms of its geometry and spinor structure. Standard model fields and gravitational field are geometrized so that Einstein's dream is realised.

    What is important is that field-particle duality is realised also classically. Induced fields propagate inside the "wave cavity" defined by the orbit of the particle as 3-surface.

  2. The connection with oscillator operator description of QFT comes from the presence of second quantized induced spinor fields creating quarks and possibly also leptons as opposite chiralities of M^4xCP_2 spinor fields. The situation was clarified dramatically quite recently when I finally understood what SUSY is in TGD framework. The conservation of quark number and the behavior of propagators consistent with statistics fixes the TGD view about SUSY.

    1. Super-coordinates of H make sense and have super-part expressible as local hermitian monomials of quark oscillator operators with vanishing quark number. They create point like particles such as weak bosons and graviton. One has creation and annihilation operators rather than anticommuting theta parameters: this is the big difference with respect to the ordinary SUSY and forced by the fact that Majorana spinors are not possible.

    2. Super-Dirac field is odd monomial of quark creation operators and the action depends on the super-coordinates of H. One obtains directly second quantize theory with quarks as fundamental fermions. Anti-leptons correspond to local 3 quark states so that electron as spartner of an antiquark would have been discovered already 1897! Matter antimatter asymmetry finds a nice solution too. Here I had to give up the earlier assumption that also leptons appear as fundamental fermions.

One finally has a concrete view about S-matrix at fundamental level. There are of course many proposals already such as the construction based on quaternionic generalization of twistor Grassmannian approach but the difference is that now one has really fundamental approach.

  1. All reduces formally to classical partial differential equations for super-space-time surface and super-spinors. One solves preferred extremal and its super-variant which means solving the space-time evolution of multi-spinors defining super-coordinates and in this background super-Dirac equation is solve. This is highly non-trivial but in principle precisely defined procedure. If one gives initial values of spinor modes at the first light-like boundary of causal diamond (CD), one can deduce super-spinor field at opposite boundary of CD and express it as a superposition of its basic modes with well-defined quark number and other quantum numbers. This gives S-matrix.

  2. Vertices at partonic 2-surfaces are super-symmetric but in TGD sense and reduce to points at which quark lines meet: one can say that local multi-quark-antiquark states split to local multi-quark-antiquark states. Vertices are determined as vacuum expectations of the bosonic action and super-Dirac action and analogous to those defined by theta integral in SUSY.

  3. No further quantization is needed since super-symmetrization corresponds to second quantization. This is part of the realization of the dream about geometrizing also quantum theory. This should have been realized long time ago also by colleagues since SUSY algebra is Clifford algebra like also oscillator operator algebra.

  4. Situation simplifies dramatically for discrete cognitive representation replacing space-time surface with the set of points having imbedding space coordinates in extension of rationals defining the adele.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

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