Structured relativistic particle, helix-type Minkowski diagram, and "more general" relativity

A.P. Yefremov1

Abstract

A model of a 3D classical particle built up of micro-scale spinor fragments, hence structured, is proved sufficient (demands no additional postulates) to generate a theory of relativistic motion, provided the velocity of light in vacuum is the speed limit. In this case, the particle's structure endows a mechanical action with a clear geometric sense and allows for derivation of a Lagrangian function of the same form as in special relativity. But the graphic image of motion becomes a 3D helix instead of a 4D space-time world line. A forced distortion of the helix line (curved and compressed) results in emerging of variable metric components thus leading to an equation of particle motion under the influence of a geometric potential, an equation identical to that of 4D geodesic. The logical line of the theory is traced in detail.

References

  1. A. P. Yefremov, Pregeometric structure of quantum and classical particles in terms of quaternion spinors, Grav. Cosmol. 19(2), 71 (2013).
  2. D. Bohm, A suggested interpretation of the quantum theory in terms of 'hidden' variables. I, Phys. Rev. 85, 166 (1952).
  3. A. P. Yefremov, Quaternion Spaces, Frames of Reference and Fields (PFUR Publ., Moscow, 2005).
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