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On the physical interpretation and the mathematical structure of the combinatorial hierarchy

  • Ted Bastin
  • H. Pierre Noyes
  • John Amson
  • Clive W. Kilmister
Article

Abstract

The combinatorial hierarchy model for basic particle processes is based on elementary entities; any representation they may have is discrete and two-valued. We call themSchnurs to suggest their most fundamental aspect as concatenating strings. Consider a definite small number of them. Consider an elementary creation act as a result of which two different Schnurs generate a new Schnur which is again different. We speak of this process as a “discrimination.” By this process and by this process alone can the complexity of the universe be explored. By concatenations of this process we create more complex entities which are themselves Schnurs at a new level of complexity. Everything plays a dual role in which something comes in from the outside to interact, and also serves as a synopsis or concatenation of such a process. We thus incorporate the observation metaphysic at the start, rejecting Bohr's reduction to the haptic language of common sense and classical physics. Since discriminations occur sequentially, our model is consistent with a “fixed past-uncertain future” philosophy of physics. We demonstrate that this model generates four hierarchical levels of rapidly increasing complexity. Concrete interpretation of the four levels of the hierarchy (with cardinals 3,7,127,2127-1≈1038) associates the three levels which map up and down with the three absolute conservation laws (charge, baryon number, lepton number) and the spin dichotomy. The first level represents +, −, and ± unit charge. The second has the quantum numbers of a baryon-antibaryon pair and associated charged meson (e.g.,n¯n,p¯n,p¯p,n¯p,π + ,π0,π ). The third level associates this pair, now including four spin states as well as four charge states, with a neutral lepton-antilepton pair (e¯e orv¯v), each pair in four spin states (total, 64 states)—three charged spinless, three charged spin-1, and a neutral spin-1 mesons (15 states), and a neutral vector boson associated with the leptons; this gives 3+15+3×15=63 possible boson states, so a total correct count of 63+64=127 states. Something likeSU2×SU3 and other indications of quark quantum numbers can occur as substructures at the fourth (unstable) level. Breaking into the (Bose) hierarchy by structures with the quantum numbers of a fermion, if this is an electron, allows us to understand Parker-Rhodes' calculation ofm p /m e =1836.1515 in terms of our interpretation of the hierarchy. A slight extension gives us the usual static approximation to the binding energy of the hydrogen atom,α 2 m e c 2 . We also show that the cosmological implications of the theory are in accord with current experience. We conclude that we have made a promising beginning in the physical interpretation of a theory which could eventually encompass all branches of physics.

Keywords

Lepton Number Cosmological Implication Boson State Correct Count Neutral Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Ted Bastin
    • 1
  • H. Pierre Noyes
    • 2
  • John Amson
    • 3
  • Clive W. Kilmister
    • 4
  1. 1.GlastonburyEngland
  2. 2.Stanford Linear Accelerator CenterStanford UniversityStanford
  3. 3.The Mathematical InstituteThe University of St. AndrewsScotland
  4. 4.Department of Mathematics, King's CollegeUniversity of LondonEngland

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