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 the invariance of action of the 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. [1]
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. [1]
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. [2] 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.[3] 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.[4] There are works in which SPФ symmetry is confirmed.[5] [6]
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.
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.