# Physics/Essays/Fedosin/SPФ symmetry

SPФ symmetry is combined three-component symmetry of similarity of objects, phenomena and processes at different scale levels of matter. With its help in Theory of Infinite Hierarchical Nesting of Matter the similarity of matter levels is described and invariance of action of physical laws at these levels is proved. With the help of SPФ symmetry the meaning of scale dimension and scale relativity is clarified.
Theorem of SPФ symmetry was proved by Sergey Fedosin in 1999.
In combined SPФ transformation invariance of physical laws is revealed as 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 transformation of speeds S, transformation of sizes (scales) P and transformation of masses Ф. Values S, P and Ф are fixed by corresponding coefficients of similarity between the levels, where the transition is made. Examples of similarity coefficients are given in the articles: similarity of matter levels, quantization of parameters of cosmic systems, hydrogen system. Since objects of lower level of matter are part of object of higher scale level of matter, it allows us on the basis of physical laws and equations of matter state to deduce relations between coefficients of similarity S, P and Ф.
After substituting in Lagrangian, which determines the laws of motion of a physical system, new variables, taking into account SPФ transformations, the Lagrangian does not change its form. This means that physical laws are not changed during transitions between different levels of matter and corresponding phenomena occur in the similar way. In particular, at each level of matter, we can introduce its own Dirac constant as characteristic angular momentum ( spin) and quantum of action of typical objects and also write its own Heisenberg uncertainty principle. Another example is stellar constants corresponding to the level of stars.
If in system of physical units CGS we make similarity transformation for masses, sizes and speeds, it turns out that in Newton's law of gravitational attraction we need to transform not only masses and sizes, but also constant of gravitation. At the same time in system of physical units CGS electric constant is equal to 1 and transformation applies only to forces, charges and sizes. This means that in transition to atomic systems ordinary gravitation is replaced by strong gravitation and a new constant appears – strong gravitational constant. Strong gravitation is responsible for integrity of elementary particles, including nucleons, and in gravitational model of strong interaction it is an integral part of strong interaction. Transition to the atomic systems is accompanied by a significant increase not only of gravitation but also of electromagnetic fields acting near elementary particles. The value of electric constant does not change in CGS, or in any other system of physical units.
According to substantial neutron model and substantial proton model, equation of state of nucleon matter is similar to equation of state of neutron stars matter. Dependences of mass on radius are also similar. SPФ symmetry allows us to understand dependences, arising between mass and electric charge of the proton, to justify model of quark quasiparticles, to approach the essence of gravitational and electromagnetic forces in framework of Le Sage's theory of gravitation.
Based on postulate on equality of kinetic energy flux and fluxes of gravitational (in strong gravitation field) and electromagnetic energies in electron matter formulated by Sergey Fedosin, quantization of energy levels and angular momentum of electron during its rotation in atom is derived. Similar idea is used with respect to the Solar system, showing the probable cause of discrete planetary orbits. The law of redistribution of energy fluxes allows us to find stationary state of rotation of nucleon and neutron star similar to it, to connect many other phenomena in microworld and macroworld. In particular, it is assumed that equilibrium of nucleons in atomic nucleus is due to equality of forces and energies associated with attraction from strong gravitation and repulsion from gravitational torsion field (the given forces are main components of nuclear forces in gravitational model of strong interaction).
The combined three-component symmetry is also CPT symmetry connecting properties of particles and antiparticles with each other. There are works in which SPФ symmetry is confirmed.
As in SPФ symmetry, in scale relativity by Laurent Nottale 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, scale relativity of scale dimension is other example of relativity which extends special relativity to five dimensions of space-time.