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Русская версия

**Zoran Majkic**

International Society for Research in Science and Technology

PO Box 2464 Tallahassee, FL 32316 - 2464 USA

We consider the 3-dimensional (3-D) model of the massive particles, represented as the rest-mass energy-density wave-packets, which is analog to the common physical objects which we experiment in our every-day life, if we consider a physical object with a mass $m$ for example, as a matter/energy-density contained in this 3-D form, such that the integration of this energy-density contained in this 3-D volume is equal to the energy E = mc^2. This is a complete revision and improvement of previous work [10] or the analysis of particle's internal dynamic during particle's accelerations and hence we use the three conservation laws for the compressive fluids: energy/matter conservation, momentum conservation and internal energy conservation laws. Consequently, we show the new method for computation of the hydrostatic equilibrium of a massive elementary particle during inertial propagation in a vacuum with a stable spherically symmetric rest-mass energy density distribution, such that with this stationary distribution the internal self-gravitational force is constant and equal in each point inside the particle. Then we show how the self-gravitational forces generated by the rest-mass energy-density of massive particles in 3-D provide the auto-stability process during the small perturbations, which cause particle's accelerations, and their return to the inertial propagation in the vacuum.

- namics
- Non point-like particles
- Particle internal dy-
- Quantum Physics

- D. Lehmkul, Why Einstein did not believe that general relativity geometrizes gravity. Studies in History and Philosophy of Modern Physics 46, pages 316-326, 2014
- G. Perelman. The entropy formula for the Ricci flow and its geometric applications. arXiv:math. DG/0211159, 2002
- G. Perelman. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. arXiv:math. DG/0307245, 2003
- G. Perelman. Ricci flow with surgery on three-manifolds. arXiv:math. DG/0303109, 2003
- R. Hamilton. Three-manifolds with positive Ricci curvature. Journal of Differential Geometry, vol. 17, n. 2, pages 255-306, 1982
- R. T. Gressman and R. M. Strain. Global classical solutions of the Boltzmann equation with long range interactions. arXiv:1002. 3639[math. AP], 2010
- Z. Majkic. Partial differential equations for wave packets in the Minkowski 4-dimensional spaces. E-Journal Differential Equations and Control Processes, N. 1 February 2011, Publisher: Mathematics and Mechanics Faculty of Saint-Petersburg State University, Russia, http://www.math.spbu.ru/diffjournal/pdf/madjkic.pdf , 2011
- Z. Majkic. Schrodinger equation and wave packets for elementary particles in the Minkowski spaces. E-Journal Differential Equations and Control Processes, N. 3 July 2011, Publisher: Mathematics and Mechanics Faculty of Saint-Petersburg State University, Russia, http://www.math.spbu.ru/diffjournal/pdf/madjkic2.pdf , 2011
- Z. Majkic. Differential equations for elementary particles: Beyond duality. LAP LAMBERT Academic Publishing, Saarbrucken, Germany, 2013
- Z. Majkic. Completion and Unification of Quantum Mechanics with Einstein's GR Ideas, Part I. Nova Science Publishers, New York, ISBN:978-1-53611-946-6, July, 2017
- Z. Majkic. Completion and Unification of Quantum Mechanics with Einstein's GR Ideas, Part II. Nova Science Publishers, New York, ISBN:978-1-53611-947-3, September, 2017