**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.

The theorem of the SPФ symmetry was proved by Sergey
Fedosin in 1999. ^{[1]}

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. ^{[1]}

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. ^{[2]}
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.^{[3]} 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.^{[4]} There are works in which the SPФ symmetry
is confirmed.^{[5]} ^{[6]}

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.

1.
^{1.0} ^{1.1} Fedosin S.G. Fizika i filosofiia podobiia:
ot preonov do metagalaktik, Perm, (1999-06-09) 544 pp. ISBN
5-8131-0012-1.

2. Sergey Fedosin, The physical theories and infinite
hierarchical nesting of matter, Volume 1, LAP LAMBERT Academic Publishing, pages: 580,
ISBN-13: 978-3-659-57301-9.

3. 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).

4.
Griffiths, David J. (1987). Introduction to Elementary
Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.

5.
Recami E. Multi-verses, Micro-universes and
Elementary Particles (Hadrons). arXiv:physics/0505149v123,
May 2005.

6.
R. L. Oldershaw. Discrete Scale Relativity.
Astrophysics and Space Science, Vol. 311, No. 4, pgs. 431-433, October 2007.

- 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