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He is the author and inventor of the theory of <b>scale relativity</b>, which aims to unify <a href="/wiki/Quantum_Mechanics" class="mw-redirect" title="Quantum Mechanics">quantum physics</a> and <a href="/wiki/Theory_of_relativity" title="Theory of relativity">relativity theory</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Scientific_career">Scientific career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Laurent_Nottale&action=edit&section=1" title="Edit section: Scientific career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nottale began his professional work in the domain of <a href="/wiki/General_relativity" title="General relativity">general relativity</a>. He defended his PhD Thesis in June 1980, entitled "Perturbation of the Hubble relation by clusters of galaxies", in which he showed that clusters of galaxies as a whole may act as <a href="/wiki/Gravitational_lens" title="Gravitational lens">gravitational lenses</a> on distant sources.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Some of these results were reported in <a href="/wiki/Nature_(journal)" title="Nature (journal)"><i>Nature</i></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><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> </p><p>He also published a popular book <i>L'Univers et la Lumière</i>, Flammarion, Nouvelle Bibliothèque Scientifique 1994, Champs 1998) for which he received a prize in 1995 (Prix du livre d'Astronomie Haute-Maurienne-Vanoise). </p><p>According to Vincent Bontems and <a href="/w/index.php?title=Yves_Gingras&action=edit&redlink=1" class="new" title="Yves Gingras (page does not exist)">Yves Gingras</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Yves_Gingras" class="extiw" title="fr:Yves Gingras">fr</a>]</span> there are two distinct phases in Nottale's scientific career.<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> From 1975 to 1991 this included conventional topics, such as gravitational lenses, while from 1984 onwards he focused on developing his theory of scale relativity, a proposal for a theory of <a href="/wiki/Physics" title="Physics">physics</a> based on <a href="/wiki/Fractal" title="Fractal">fractal</a> <a href="/wiki/Space-time" class="mw-redirect" title="Space-time">space-time</a>. </p> <div class="mw-heading mw-heading2"><h2 id="The_theory_of_scale_relativity">The theory of scale relativity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Laurent_Nottale&action=edit&section=2" title="Edit section: The theory of scale relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The theory of scale relativity emerged out of a desire to establish a foundation for <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> based on first physical principles: the principle of <a href="/wiki/Principle_of_relativity" title="Principle of relativity">relativity</a>, the geometric interpretation of physical properties and the optimization principle interpreted as a <a href="/wiki/Geodesic" title="Geodesic">geodesic</a> principle.<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> In a similar way that <a href="/wiki/Gravity" title="Gravity">gravity</a> is the manifestation of the intrinsic curved geometry of <a href="/wiki/Spacetime" title="Spacetime">spacetime</a> in <a href="/wiki/General_relativity" title="General relativity">general relativity</a>, the quantum properties here are the manifestation of another property of spacetime at small scales, its intrinsic non-differentiability.<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> Besides proposing a better foundation for microphysical <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a>, it also proposes that many macroscopic classical systems with highly <a href="/wiki/Chaos_theory" title="Chaos theory">chaotic</a> behaviour can be considered as non-differentiable and thus described by macroscopic quantum-like laws.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Examples of such applications are: planetary formation in the <a href="/wiki/Protoplanetary_disk" title="Protoplanetary disk">protoplanetary disk</a> phase,<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> violent ejection processes such as the creation of <a href="/wiki/Planetary_nebulae" class="mw-redirect" title="Planetary nebulae">planetary nebulae</a><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> or <a href="/wiki/Turbulence" title="Turbulence">turbulence</a> in fluids.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The proposal has not attracted wide acceptance by the scientific community.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Selected_publications">Selected publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Laurent_Nottale&action=edit&section=3" title="Edit section: Selected publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Scale Relativity And Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics</i>. 2011 1st ed. World Scientific Publishing Company. (<style data-mw-deduplicate="TemplateStyles:r1238218222">.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.id-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.id-lock-limited a,.mw-parser-output .id-lock-registration.id-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.id-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}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.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}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1848166508" title="Special:BookSources/1848166508">1848166508</a>)</li> <li><i>Fractal Space-Time and Micro-physics</i>, Editions World Scientific, May 1993 (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9810208782" title="Special:BookSources/9810208782">9810208782</a>) (The reference book about Scale Relativity theory).</li> <li><i>L'univers et la lumière, Cosmologie classique et mirages gravitationnels</i>, Éditions Flammarion, août 1993 (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/2082111830" title="Special:BookSources/2082111830">2082111830</a>)</li> <li><i>La Relativité dans tous ses états : du mouvements aux changements d'échelle</i>, Éditions Hachette, 1998 (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/201279002X" title="Special:BookSources/201279002X">201279002X</a>)</li> <li><i>Les arbres de l'évolution</i>, Laurent Nottale, <a href="/w/index.php?title=Jean_Chaline&action=edit&redlink=1" class="new" title="Jean Chaline (page does not exist)">Jean Chaline</a> et Pierre Grou, Éditions Hachette, mars 2000 (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/2012355528" title="Special:BookSources/2012355528">2012355528</a>)</li></ul> <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=Laurent_Nottale&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Fractal_cosmology" title="Fractal cosmology">Fractal cosmology</a></li></ul> <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=Laurent_Nottale&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">in French: "Les lentilles gravitationnelles par amas de galaxies"</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKarojiNottale1976" class="citation journal cs1">Karoji, H.; Nottale, L. (1976). "Possible implications of the Rubin-Ford effect". <i>Nature</i>. <b>259</b> (5538): 31–33. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1976Natur.259...31K">1976Natur.259...31K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F259031a0">10.1038/259031a0</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4287300">4287300</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Possible+implications+of+the+Rubin-Ford+effect&rft.volume=259&rft.issue=5538&rft.pages=31-33&rft.date=1976&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4287300%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F259031a0&rft_id=info%3Abibcode%2F1976Natur.259...31K&rft.aulast=Karoji&rft.aufirst=H.&rft.au=Nottale%2C+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottaleVigier1977" class="citation journal cs1">Nottale, L.; Vigier, J. P. (1977). "Continuous increase of Hubble modulus behind clusters of galaxies". <i>Nature</i>. <b>268</b> (5621): 608–610. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1977Natur.268..608N">1977Natur.268..608N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F268608a0">10.1038/268608a0</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4148388">4148388</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Continuous+increase+of+Hubble+modulus+behind+clusters+of+galaxies&rft.volume=268&rft.issue=5621&rft.pages=608-610&rft.date=1977&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4148388%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F268608a0&rft_id=info%3Abibcode%2F1977Natur.268..608N&rft.aulast=Nottale&rft.aufirst=L.&rft.au=Vigier%2C+J.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBontemsGingras2007" class="citation journal cs1">Bontems, Vincent; Gingras, Yves (2007). <a rel="nofollow" class="external text" href="http://www.archipel.uqam.ca/481/1/gingras_bontems_SSI.pdf">"De la science normale à la science marginale. Analyse d'une bifurcation de trajectoire scientifique: le cas de la Théorie de la Relativité d'Echelle"</a> <span class="cs1-format">(PDF)</span>. <i>Information Sur les Sciences Sociales</i>. <b>46</b> (4): 607–653. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0539018407082595">10.1177/0539018407082595</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144737764">144737764</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Information+Sur+les+Sciences+Sociales&rft.atitle=De+la+science+normale+%C3%A0+la+science+marginale.+Analyse+d%27une+bifurcation+de+trajectoire+scientifique%3A+le+cas+de+la+Th%C3%A9orie+de+la+Relativit%C3%A9+d%27Echelle&rft.volume=46&rft.issue=4&rft.pages=607-653&rft.date=2007&rft_id=info%3Adoi%2F10.1177%2F0539018407082595&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144737764%23id-name%3DS2CID&rft.aulast=Bontems&rft.aufirst=Vincent&rft.au=Gingras%2C+Yves&rft_id=http%3A%2F%2Fwww.archipel.uqam.ca%2F481%2F1%2Fgingras_bontems_SSI.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottale1993" class="citation book cs1">Nottale, L. (1993). <i>Fractal Space-Time and Microphysics</i>. World Scientific Publishing. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2F1579">10.1142/1579</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-02-0878-3" title="Special:BookSources/978-981-02-0878-3"><bdi>978-981-02-0878-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fractal+Space-Time+and+Microphysics&rft.pub=World+Scientific+Publishing&rft.date=1993&rft_id=info%3Adoi%2F10.1142%2F1579&rft.isbn=978-981-02-0878-3&rft.aulast=Nottale&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottale1989" class="citation journal cs1">Nottale, L. (1989). "Fractals and the Quantum Theory of Spacetime". <i>International Journal of Modern Physics A</i>. <b>04</b> (19): 5047–5117. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989IJMPA...4.5047N">1989IJMPA...4.5047N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2FS0217751X89002156">10.1142/S0217751X89002156</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Modern+Physics+A&rft.atitle=Fractals+and+the+Quantum+Theory+of+Spacetime&rft.volume=04&rft.issue=19&rft.pages=5047-5117&rft.date=1989&rft_id=info%3Adoi%2F10.1142%2FS0217751X89002156&rft_id=info%3Abibcode%2F1989IJMPA...4.5047N&rft.aulast=Nottale&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottale2011" class="citation book cs1">Nottale, L. (2011). <i>Scale Relativity and Fractal Space-time: A New Approach to Unifying Relativity and Quantum Mechanics</i>. World Scientific Publishing. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011srfs.book.....N">2011srfs.book.....N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2Fp752">10.1142/p752</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84816-650-9" title="Special:BookSources/978-1-84816-650-9"><bdi>978-1-84816-650-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scale+Relativity+and+Fractal+Space-time%3A+A+New+Approach+to+Unifying+Relativity+and+Quantum+Mechanics&rft.pub=World+Scientific+Publishing&rft.date=2011&rft_id=info%3Adoi%2F10.1142%2Fp752&rft_id=info%3Abibcode%2F2011srfs.book.....N&rft.isbn=978-1-84816-650-9&rft.aulast=Nottale&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottale1996" class="citation journal cs1">Nottale, L. (1996). "Scale relativity and quantization of extra-solar planetary systems". <i>Astronomy and Astrophysics</i>. <b>315</b>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996A&A...315L...9N">1996A&A...315L...9N</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Scale+relativity+and+quantization+of+extra-solar+planetary+systems&rft.volume=315&rft.date=1996&rft_id=info%3Abibcode%2F1996A%26A...315L...9N&rft.aulast=Nottale&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottale1997" class="citation journal cs1">Nottale, L. (1997). "Scale relativity and quantization of the solar system". <i>Astronomy and Astrophysics</i>. <b>322</b>: 1018. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997A&A...322.1018N">1997A&A...322.1018N</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Scale+relativity+and+quantization+of+the+solar+system&rft.volume=322&rft.pages=1018&rft.date=1997&rft_id=info%3Abibcode%2F1997A%26A...322.1018N&rft.aulast=Nottale&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottale2000" class="citation journal cs1">Nottale, L. (2000). "Scale relativity and quantization of exoplanet orbital semi-major axes". <i>Astronomy and Astrophysics</i>. <b>361</b>: 379. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000A&A...361..379N">2000A&A...361..379N</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Scale+relativity+and+quantization+of+exoplanet+orbital+semi-major+axes&rft.volume=361&rft.pages=379&rft.date=2000&rft_id=info%3Abibcode%2F2000A%26A...361..379N&rft.aulast=Nottale&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFda_RochaNottale2003" class="citation arxiv cs1">da Rocha, D.; Nottale, L. (2003). "On the morphogenesis of stellar flows: application to planetary nebulae". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0310031">astro-ph/0310031</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=On+the+morphogenesis+of+stellar+flows%3A+application+to+planetary+nebulae&rft.date=2003&rft_id=info%3Aarxiv%2Fastro-ph%2F0310031&rft.aulast=da+Rocha&rft.aufirst=D.&rft.au=Nottale%2C+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottaleLehner2019" class="citation journal cs1">Nottale, L.; Lehner, T. (2019). "Turbulence and scale relativity". <i>Phys. Fluids</i>. <b>31</b> (10). <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1807.11902">1807.11902</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019PhFl...31j5109N">2019PhFl...31j5109N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.5108631">10.1063/1.5108631</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119204997">119204997</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Fluids&rft.atitle=Turbulence+and+scale+relativity&rft.volume=31&rft.issue=10&rft.date=2019&rft_id=info%3Aarxiv%2F1807.11902&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A119204997%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1063%2F1.5108631&rft_id=info%3Abibcode%2F2019PhFl...31j5109N&rft.aulast=Nottale&rft.aufirst=L.&rft.au=Lehner%2C+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNottaleLehner2023" class="citation journal cs1">Nottale, L.; Lehner, T. (2023). <a rel="nofollow" class="external text" href="https://hal.science/hal-04272392v1/document">"The turbulent jet in the scale relativity framework"</a>. <i>HAL Open Science</i>. <b>36</b> (4): 045118. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2024PhFl...36d5118N">2024PhFl...36d5118N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F5.0187140">10.1063/5.0187140</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=HAL+Open+Science&rft.atitle=The+turbulent+jet+in+the+scale+relativity+framework&rft.volume=36&rft.issue=4&rft.pages=045118&rft.date=2023&rft_id=info%3Adoi%2F10.1063%2F5.0187140&rft_id=info%3Abibcode%2F2024PhFl...36d5118N&rft.aulast=Nottale&rft.aufirst=L.&rft.au=Lehner%2C+T.&rft_id=https%3A%2F%2Fhal.science%2Fhal-04272392v1%2Fdocument&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeter2013" class="citation journal cs1">Peter, Patrick (2013). <a rel="nofollow" class="external text" href="https://hal.archives-ouvertes.fr/hal-03645526/file/Peter2013.pdf">"Laurent Nottale: Scale relativity and fractal space-time"</a> <span class="cs1-format">(PDF)</span>. <i>General Relativity and Gravitation</i>. <b>45</b> (7): 1459–61. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013GReGr..45.1459P">2013GReGr..45.1459P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10714-013-1535-8">10.1007/s10714-013-1535-8</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:118685362">118685362</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=General+Relativity+and+Gravitation&rft.atitle=Laurent+Nottale%3A+Scale+relativity+and+fractal+space-time&rft.volume=45&rft.issue=7&rft.pages=1459-61&rft.date=2013&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118685362%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs10714-013-1535-8&rft_id=info%3Abibcode%2F2013GReGr..45.1459P&rft.aulast=Peter&rft.aufirst=Patrick&rft_id=https%3A%2F%2Fhal.archives-ouvertes.fr%2Fhal-03645526%2Ffile%2FPeter2013.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALaurent+Nottale" class="Z3988"></span></span> </li> </ol></div> <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=Laurent_Nottale&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://scale.relativity.free.fr">Laurent Nottale's personal page</a></li> <li>265 articles on line (1975-2021) : <a rel="nofollow" class="external text" href="https://scholar.google.com.au/citations?hl=en&user=xX9J7ggAAAAJ&view_op=list_works&sortby=pubdate">Google Scholar</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output 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