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

*A.P. Yefremov*^{1}

(1) Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

### 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

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

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