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class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikiversity</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div class="subpages">< <bdi dir="ltr"><a href="/wiki/Physics" title="Physics">Physics</a></bdi> | <bdi dir="ltr"><a href="/wiki/Physics/Essays" title="Physics/Essays">Essays</a></bdi> | <bdi dir="ltr"><a href="/wiki/Physics/Essays/Fedosin" title="Physics/Essays/Fedosin">Fedosin</a></bdi></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>SPФ symmetry</b> is combined three-component symmetry of similarity of objects, phenomena and processes at different scale levels of matter. With its help in the <a href="/wiki/Physics/Essays/Fedosin/Infinite_Hierarchical_Nesting_of_Matter" title="Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter">Theory of Infinite Hierarchical Nesting of Matter</a> the <a href="/wiki/Physics/Essays/Fedosin/Similarity_of_matter_levels" title="Physics/Essays/Fedosin/Similarity of matter levels">similarity of matter levels</a> is described and invariance of action of physical laws at these levels is proved. With the help of SPФ symmetry the meaning of <a href="/w/index.php?title=Scale_dimension&action=edit&redlink=1" class="new" title="Scale dimension (page does not exist)">scale dimension</a> and scale relativity is clarified. </p><p>The theorem of the SPФ symmetry was proved by <a href="/wiki/User:Fedosin" title="User:Fedosin"> Sergey Fedosin</a> in 1999. <sup id="cite_ref-Fed_1-0" class="reference"><a href="#cite_note-Fed-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>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: <a href="/wiki/Physics/Essays/Fedosin/Similarity_of_matter_levels" title="Physics/Essays/Fedosin/Similarity of matter levels">similarity of matter levels</a>, <a href="/w/index.php?title=Quantization_of_parameters_of_cosmic_systems&action=edit&redlink=1" class="new" title="Quantization of parameters of cosmic systems (page does not exist)">quantization of parameters of cosmic systems</a>, <a href="/w/index.php?title=Hydrogen_system&action=edit&redlink=1" class="new" title="Hydrogen system (page does not exist)">hydrogen system</a>. 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. <sup id="cite_ref-Fed_1-1" class="reference"><a href="#cite_note-Fed-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>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 <a href="https://en.wikipedia.org/wiki/Planck_constant" class="extiw" title="w:Planck constant">Dirac constant</a> as the characteristic <a href="https://en.wikipedia.org/wiki/angular_momentum" class="extiw" title="w:angular momentum"> angular momentum</a> (<a href="https://en.wikipedia.org/wiki/spin" class="extiw" title="w:spin"> spin</a>) and the quantum of action of typical objects and also write its own Heisenberg <a href="https://en.wikipedia.org/wiki/uncertainty_principle" class="extiw" title="w:uncertainty principle"> uncertainty principle</a>. Another example is the <a href="/w/index.php?title=Stellar_constants&action=edit&redlink=1" class="new" title="Stellar constants (page does not exist)">stellar constants</a> corresponding to the level of stars. </p><p>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 <a href="/wiki/Electric_constant" title="Electric constant">electric constant</a> 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 <a href="/wiki/Gravitation" title="Gravitation">gravitation</a> is replaced by the <a href="/w/index.php?title=Strong_gravitation&action=edit&redlink=1" class="new" title="Strong gravitation (page does not exist)">strong gravitation</a> and a new constant appears – <a href="/w/index.php?title=Strong_gravitational_constant&action=edit&redlink=1" class="new" title="Strong gravitational constant (page does not exist)">strong gravitational constant</a>. The strong gravitation is responsible for the integrity of the elementary particles, including nucleons, and in the <a href="/w/index.php?title=Gravitational_model_of_strong_interaction&action=edit&redlink=1" class="new" title="Gravitational model of strong interaction (page does not exist)">gravitational model of strong interaction</a> it is an integral part of the <a href="/wiki/Charges/Interactions/Strong" title="Charges/Interactions/Strong">strong interaction</a>. <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> 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. </p><p>According to the <a href="/wiki/Physics/Essays/Fedosin/Substantial_neutron_model" title="Physics/Essays/Fedosin/Substantial neutron model">substantial neutron model</a> and the <a href="/wiki/Physics/Essays/Fedosin/Substantial_proton_model" title="Physics/Essays/Fedosin/Substantial proton model">substantial proton model</a>, 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 <a href="/w/index.php?title=Model_of_quark_quasiparticles&action=edit&redlink=1" class="new" title="Model of quark quasiparticles (page does not exist)">model of quark quasiparticles</a>, to approach the essence of gravitational and electromagnetic forces in the framework of the <a href="https://en.wikipedia.org/wiki/Le_Sage%27s_theory_of_gravitation" class="extiw" title="w:Le Sage's theory of gravitation"> Le Sage's theory of gravitation</a>. </p><p>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.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> 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 <a href="/wiki/Gravitational_torsion_field" title="Gravitational torsion field">gravitational torsion field</a> (the given forces are the main components of the nuclear forces in the gravitational model of strong interaction). </p><p>The combined three-component symmetry is also the <a href="https://en.wikipedia.org/wiki/CPT_symmetry" class="extiw" title="w:CPT symmetry"> CPT symmetry</a> connecting the properties of particles and antiparticles with each other.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> There are works in which the SPФ symmetry is confirmed.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>As in SPФ symmetry, in <a href="https://en.wikipedia.org/wiki/scale_relativity" class="extiw" title="w:scale relativity">scale relativity</a> 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 <a href="/w/index.php?title=Scale_dimension&action=edit&redlink=1" class="new" title="Scale dimension (page does not exist)">scale dimension</a> is other example of relativity which extends the special relativity to five dimensions of space-time. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Physics/Essays/Fedosin/SP%D0%A4_symmetry&veaction=edit&section=1" title="Edit section: References" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Physics/Essays/Fedosin/SP%D0%A4_symmetry&action=edit&section=1" title="Edit section's source code: References"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r2661605">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Fed-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Fed_1-0">1.0</a></sup> <sup><a href="#cite_ref-Fed_1-1">1.1</a></sup></span> <span class="reference-text"> Fedosin S.G. <a rel="nofollow" class="external text" href="http://lccn.loc.gov/2009457349">Fizika i filosofiia podobiia: ot preonov do metagalaktik,</a> Perm, (1999-06-09) 544 pp. <style data-mw-deduplicate="TemplateStyles:r2527938">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/5-8131-0012-1" title="Special:BookSources/5-8131-0012-1">5-8131-0012-1</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"> <a href="/wiki/User:Fedosin" title="User:Fedosin"> Sergey Fedosin</a>, <a rel="nofollow" class="external text" href="https://www.lap-publishing.com/catalog/details//store/gb/book/978-3-659-57301-9/the-physical-theories-and-infinite-hierarchical-nesting-of-matter-volume-1">The physical theories and infinite hierarchical nesting of matter</a>, Volume 1, LAP LAMBERT Academic Publishing, pages: 580, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2527938"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-659-57301-9" title="Special:BookSources/978-3-659-57301-9">978-3-659-57301-9</a>. </span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"> <a rel="nofollow" class="external text" href="http://sergf.ru/com.htm">Comments to the book:</a> Fedosin S.G. Fizicheskie teorii i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2527938"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-5-9901951-1-0" title="Special:BookSources/978-5-9901951-1-0">978-5-9901951-1-0</a>. (in Russian).</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2527938"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-60386-4" title="Special:BookSources/0-471-60386-4">0-471-60386-4</a>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Recami E. <a rel="nofollow" class="external text" href="http://arxiv.org/abs/physics/0505149">Multi-verses, Micro-universes and Elementary Particles (Hadrons).</a> arXiv:physics/0505149v123, May 2005. </span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"> R. L. Oldershaw. <a rel="nofollow" class="external text" href="http://arxiv.org/abs/physics/0701132v3">Discrete Scale Relativity.</a> Astrophysics and Space Science, Vol. 311, No. 4, pgs. 431-433, October 2007. </span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Physics/Essays/Fedosin/SP%D0%A4_symmetry&veaction=edit&section=2" title="Edit section: See also" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Physics/Essays/Fedosin/SP%D0%A4_symmetry&action=edit&section=2" title="Edit section's source code: See also"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Physics/Essays/Fedosin/Similarity_of_matter_levels" title="Physics/Essays/Fedosin/Similarity of matter levels">Similarity of matter levels</a></li> <li><a href="/w/index.php?title=Quantization_of_parameters_of_cosmic_systems&action=edit&redlink=1" class="new" title="Quantization of parameters of cosmic systems (page does not exist)">Quantization of parameters of cosmic systems</a></li> <li><a href="/w/index.php?title=Discreteness_of_stellar_parameters&action=edit&redlink=1" class="new" title="Discreteness of stellar parameters (page does not exist)">Discreteness of stellar parameters</a></li> <li><a href="/w/index.php?title=Hydrogen_system&action=edit&redlink=1" class="new" title="Hydrogen system (page does not exist)">Hydrogen system</a></li> <li><a href="/w/index.php?title=Stellar_constants&action=edit&redlink=1" class="new" title="Stellar constants (page does not exist)">Stellar constants</a></li> <li><a href="/wiki/Physics/Essays/Fedosin/Stellar_Dirac_constant" title="Physics/Essays/Fedosin/Stellar Dirac constant">Stellar Dirac constant</a></li> <li><a href="/wiki/Physics/Essays/Fedosin/Stellar_Planck_constant" title="Physics/Essays/Fedosin/Stellar Planck constant">Stellar Planck constant</a></li> <li><a href="/w/index.php?title=Strong_gravitation&action=edit&redlink=1" class="new" title="Strong gravitation (page does not exist)">Strong gravitation</a></li> <li><a href="/w/index.php?title=Gravitational_model_of_strong_interaction&action=edit&redlink=1" class="new" title="Gravitational model of strong interaction (page does not exist)">Gravitational model of strong interaction</a></li> <li><a href="/w/index.php?title=Model_of_quark_quasiparticles&action=edit&redlink=1" class="new" title="Model of quark quasiparticles (page does not exist)">Model of quark quasiparticles</a></li> <li><a href="/wiki/Physics/Essays/Fedosin/Substantial_electron_model" title="Physics/Essays/Fedosin/Substantial electron model">Substantial electron model</a></li> <li><a href="/wiki/Physics/Essays/Fedosin/Substantial_neutron_model" title="Physics/Essays/Fedosin/Substantial neutron model">Substantial neutron model</a></li> <li><a href="/wiki/Physics/Essays/Fedosin/Substantial_proton_model" title="Physics/Essays/Fedosin/Substantial proton model">Substantial proton model</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Physics/Essays/Fedosin/SP%D0%A4_symmetry&veaction=edit&section=3" title="Edit section: External links" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Physics/Essays/Fedosin/SP%D0%A4_symmetry&action=edit&section=3" title="Edit section's source code: External links"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.wikiznanie.ru/ru-wz/index.php/SP%D0%A4-%D1%81%D0%B8%D0%BC%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F">SPФ symmetry in Russian</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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