SPФ symmetry is combined three-component symmetry of similarity of objects, phenomena and processes at different scale levels of matter. With its help in the Theory of Infinite Hierarchical Nesting of Matter the similarity of matter levels is described and the invariance of action of the physical laws at these levels is proved. With the help of SPФ symmetry the meaning of the [scale dimension] and scale relativity is clarified.
In the combined SPФ transformation the invariance of physical laws is revealed as the result of transition from one scale level of matter to other levels of matter. To move from one level of matter to another using SPФ it is necessary simultaneously to make the transformation of the speeds S, the transformation of sizes (scales) P and the transformation of masses Ф. The values S, P and Ф are fixed by the corresponding coefficients of similarity between the levels, where the transition is made. The examples of similarity coefficients are given in the articles: similarity of matter levels, quantization of parameters of cosmic systems, hydrogen system. Since the objects of lower level of matter are part of the object of higher scale level of matter, it allows us on the basis of physical laws and equations of the matter state to deduce the relations between the coefficients of similarity S, P and Ф. 
After substituting in the Lagrangian, which determines the laws of motion of a physical system, the new variables, taking into account the SPФ transformations, the Lagrangian does not change its form. This means that the physical laws are not changed during transitions between different levels of matter and the corresponding phenomena occur in the similar way. In particular, at each level of matter, we can introduce its own Dirac constant as the characteristic angular momentum ( spin) and the quantum of action of typical objects and also write its own Heisenberg uncertainty principle. Another example is the stellar constants corresponding to the level of stars.
If in the system of physical units CGS we make similarity transformation for masses, sizes and speeds, it turns out that in the Newton's law of gravitational attraction we need to transform not only masses and sizes, but also the constant of gravitation. At the same time in the system of physical units CGS the electric constant is equal to 1 and transformation applies only to the forces, charges and sizes. This means that in the transition to the atomic systems the ordinary gravitation is replaced by the strong gravitation and a new constant appears – strong gravitational constant. The strong gravitation is responsible for the integrity of the elementary particles, including nucleons, and in the gravitational model of strong interaction it is an integral part of the strong interaction.  The transition to the atomic systems is accompanied by a significant increase not only of the gravitation but also of the electromagnetic fields acting near the elementary particles. The value of the electric constant does not change in the CGS, or in any other system of physical units.
According to the substantial neutron model and the substantial proton model, the equation of the state of the nucleon matter is similar to the equation of the state of neutron stars matter. The dependences of the mass on the radius are also similar. SPФ symmetry allows us to understand the dependences, arising between the mass and the electric charge of the proton, to justify the model of quark quasiparticles, to approach the essence of gravitational and electromagnetic forces in the framework of the Le Sage's theory of gravitation.
Based on the postulate on equality of the kinetic energy flux and the fluxes of gravitational (in the strong gravitation field) and electromagnetic energies in the electron matter formulated by Sergey Fedosin, quantization of the energy levels and the angular momentum of the electron during its rotation in the atom is derived. The similar idea is used with respect to the Solar system, showing the probable cause of the discrete planetary orbits. The law of redistribution of the energy fluxes formulated by Fedosin allows us to find the stationary state of rotation of the nucleon and the neutron star similar to it, to connect many other phenomena in the microworld and macroworld. In particular, it is assumed that the equilibrium of nucleons in the atomic nucleus is due to the equality of the forces and energies associated with the attraction from the strong gravitation and the repulsion from the gravitational torsion field (the given forces are the main components of the nuclear forces in the gravitational model of strong interaction).
The combined three-component symmetry is also the CPT symmetry connecting the properties of particles and antiparticles with each other. There are works in which the SPФ symmetry is confirmed. 
As in SPФ symmetry, in scale relativity by Laurent Nottale the fundamental laws of physics cannot involve scales themselves because their values are arbitrary choices. But this scale relativity is connected mostly with geometry of space-time in order explaining of physical properties of particles including their mass and charge. Such approach is close to attempts of general relativity to explain gravitational force with the help of metric tensor and space-time curvature. In contrast, the scale relativity of scale dimension is other example of relativity which extends the special relativity to five dimensions of space-time.
References[edit | edit source]
- Fedosin S.G. Fizika i filosofiia podobiia: ot preonov do metagalaktik, Perm, (1999-06-09) 544 pp. ISBN 5-8131-0012-1.
- Sergey Fedosin, The physical theories and infinite hierarchical nesting of matter, Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN 978-3-659-57301-9.
- Comments to the book: Fedosin S.G. Fizicheskie teorii i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages. ISBN 978-5-9901951-1-0. (in Russian).
- Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.
- Recami E. Multi-verses, Micro-universes and Elementary Particles (Hadrons). arXiv:physics/0505149v123, May 2005.
- R. L. Oldershaw. Discrete Scale Relativity. Astrophysics and Space Science, Vol. 311, No. 4, pgs. 431-433, October 2007.
See also[edit | edit source]
- Similarity of matter levels
- Quantization of parameters of cosmic systems
- Discreteness of stellar parameters
- Hydrogen system
- Stellar constants
- Stellar Dirac constant
- Stellar Planck constant
- Strong gravitation
- Gravitational model of strong interaction
- Model of quark quasiparticles
- Substantial electron model
- Substantial neutron model
- Substantial proton model