Serveur d'exploration sur l'opéra

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

Superluminal neutrino phenomenon as a result of the equivalence principle violation

Identifieur interne : 000193 ( Istex/Corpus ); précédent : 000192; suivant : 000194

Superluminal neutrino phenomenon as a result of the equivalence principle violation

Auteurs : O F Batsevych ; R B Kapustiy

Source :

RBID : ISTEX:065AAAB89A3324EF85C29E2FD813C0B24F5A0332

Abstract

In this paper we show that the recently detected superluminal neutrino motion, which now is believed to be the result of a possible technical fault in the experiment, can alternatively be explained by the absence of the gravitational mass of the neutrino, and as a result, an absence of its interaction with a gravitational field. The neutrino velocity theoretically predicted in this paper is in full agreement with the experimental data obtained by the OPERA collaboration. The conducted calculations also predict a significant anisotropy of the neutrino velocity measurement depending on the direction of the Earths motion relative to the Galaxy, which allows for the validation of the obtained results.

Url:
DOI: 10.1088/0954-3899/39/8/085008

Links to Exploration step

ISTEX:065AAAB89A3324EF85C29E2FD813C0B24F5A0332

Le document en format XML

<record>
<TEI wicri:istexFullTextTei="biblStruct">
<teiHeader>
<fileDesc>
<titleStmt>
<title>Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
<author>
<name sortKey="Batsevych, O F" sort="Batsevych, O F" uniqKey="Batsevych O" first="O F" last="Batsevych">O F Batsevych</name>
<affiliation>
<mods:affiliation>89, Norway</mods:affiliation>
</affiliation>
<affiliation>
<mods:affiliation>E-mail: o-batsev@online.no</mods:affiliation>
</affiliation>
</author>
<author>
<name sortKey="Kapustiy, R B" sort="Kapustiy, R B" uniqKey="Kapustiy R" first="R B" last="Kapustiy">R B Kapustiy</name>
<affiliation>
<mods:affiliation>8, Lviv 79035, Ukraine</mods:affiliation>
</affiliation>
<affiliation>
<mods:affiliation>E-mail: r.kapustiy@gmail.com</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:065AAAB89A3324EF85C29E2FD813C0B24F5A0332</idno>
<date when="2012" year="2012">2012</date>
<idno type="doi">10.1088/0954-3899/39/8/085008</idno>
<idno type="url">https://api.istex.fr/document/065AAAB89A3324EF85C29E2FD813C0B24F5A0332/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000193</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title level="a">Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
<author>
<name sortKey="Batsevych, O F" sort="Batsevych, O F" uniqKey="Batsevych O" first="O F" last="Batsevych">O F Batsevych</name>
<affiliation>
<mods:affiliation>89, Norway</mods:affiliation>
</affiliation>
<affiliation>
<mods:affiliation>E-mail: o-batsev@online.no</mods:affiliation>
</affiliation>
</author>
<author>
<name sortKey="Kapustiy, R B" sort="Kapustiy, R B" uniqKey="Kapustiy R" first="R B" last="Kapustiy">R B Kapustiy</name>
<affiliation>
<mods:affiliation>8, Lviv 79035, Ukraine</mods:affiliation>
</affiliation>
<affiliation>
<mods:affiliation>E-mail: r.kapustiy@gmail.com</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series>
<title level="j">Journal of Physics G Nuclear and Particle Physics</title>
<idno type="ISSN">0954-3899</idno>
<idno type="eISSN">1361-6471</idno>
<imprint>
<publisher>IOP Publishing</publisher>
<date type="published" when="2012-08">2012-08</date>
<biblScope unit="volume">39</biblScope>
<biblScope unit="issue">8</biblScope>
</imprint>
<idno type="ISSN">0954-3899</idno>
</series>
<idno type="istex">065AAAB89A3324EF85C29E2FD813C0B24F5A0332</idno>
<idno type="DOI">10.1088/0954-3899/39/8/085008</idno>
<idno type="href">http://stacks.iop.org/JPhysG/39/085008</idno>
<idno type="ArticleID">jpg425190</idno>
</biblStruct>
</sourceDesc>
<seriesStmt>
<idno type="ISSN">0954-3899</idno>
</seriesStmt>
</fileDesc>
<profileDesc>
<textClass></textClass>
<langUsage>
<language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front>
<div type="abstract">In this paper we show that the recently detected superluminal neutrino motion, which now is believed to be the result of a possible technical fault in the experiment, can alternatively be explained by the absence of the gravitational mass of the neutrino, and as a result, an absence of its interaction with a gravitational field. The neutrino velocity theoretically predicted in this paper is in full agreement with the experimental data obtained by the OPERA collaboration. The conducted calculations also predict a significant anisotropy of the neutrino velocity measurement depending on the direction of the Earths motion relative to the Galaxy, which allows for the validation of the obtained results.</div>
</front>
</TEI>
<istex>
<corpusName>iop</corpusName>
<author>
<json:item>
<name>O F Batsevych</name>
<affiliations>
<json:string>Kongsberg Maritime AS, Bekkajordet St 8A, Horten 3189, Norway</json:string>
<json:string>E-mail: o-batsev@online.no</json:string>
</affiliations>
</json:item>
<json:item>
<name>R B Kapustiy</name>
<affiliations>
<json:string>UkrCell Ltd., Krymska St 28, Lviv 79035, Ukraine</json:string>
<json:string>E-mail: r.kapustiy@gmail.com</json:string>
</affiliations>
</json:item>
</author>
<subject>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>Particle Physics</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>04.20.Cv</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>13.15.g</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>98.35.a</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>superluminal neutrino</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>OPERA</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>galaxy</value>
</json:item>
<json:item>
<lang>
<json:string>eng</json:string>
</lang>
<value>equivalence principle</value>
</json:item>
</subject>
<language>
<json:string>eng</json:string>
</language>
<abstract>In this paper we show that the recently detected superluminal neutrino motion, which now is believed to be the result of a possible technical fault in the experiment, can alternatively be explained by the absence of the gravitational mass of the neutrino, and as a result, an absence of its interaction with a gravitational field. The neutrino velocity theoretically predicted in this paper is in full agreement with the experimental data obtained by the OPERA collaboration. The conducted calculations also predict a significant anisotropy of the neutrino velocity measurement depending on the direction of the Earths motion relative to the Galaxy, which allows for the validation of the obtained results.</abstract>
<qualityIndicators>
<score>5.743</score>
<pdfVersion>1.4</pdfVersion>
<pdfPageSize>595 x 842 pts (A4)</pdfPageSize>
<refBibsNative>true</refBibsNative>
<keywordCount>8</keywordCount>
<abstractCharCount>706</abstractCharCount>
<pdfWordCount>3923</pdfWordCount>
<pdfCharCount>20042</pdfCharCount>
<pdfPageCount>9</pdfPageCount>
<abstractWordCount>110</abstractWordCount>
</qualityIndicators>
<title>Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
<genre>
<json:string>research-article</json:string>
</genre>
<host>
<volume>39</volume>
<issn>
<json:string>0954-3899</json:string>
</issn>
<issue>8</issue>
<genre></genre>
<language>
<json:string>unknown</json:string>
</language>
<eissn>
<json:string>1361-6471</json:string>
</eissn>
<title>Journal of Physics G Nuclear and Particle Physics</title>
</host>
<publicationDate>2012</publicationDate>
<copyrightDate>2012</copyrightDate>
<doi>
<json:string>10.1088/0954-3899/39/8/085008</json:string>
</doi>
<id>065AAAB89A3324EF85C29E2FD813C0B24F5A0332</id>
<fulltext>
<json:item>
<original>true</original>
<mimetype>application/pdf</mimetype>
<extension>pdf</extension>
<uri>https://api.istex.fr/document/065AAAB89A3324EF85C29E2FD813C0B24F5A0332/fulltext/pdf</uri>
</json:item>
<json:item>
<original>false</original>
<mimetype>application/zip</mimetype>
<extension>zip</extension>
<uri>https://api.istex.fr/document/065AAAB89A3324EF85C29E2FD813C0B24F5A0332/fulltext/zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/document/065AAAB89A3324EF85C29E2FD813C0B24F5A0332/fulltext/tei">
<teiHeader>
<fileDesc>
<titleStmt>
<title level="a">Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
</titleStmt>
<publicationStmt>
<authority>ISTEX</authority>
<publisher>IOP Publishing</publisher>
<availability>
<p>IOP</p>
</availability>
<date>2012-06-27</date>
</publicationStmt>
<notesStmt>
<note>Retired from: Department of Theoretical Physics, Ivan Franko National University of Lviv, Drahomanov St. 12, Lviv 79005, Ukraine.</note>
</notesStmt>
<sourceDesc>
<biblStruct type="inbook">
<analytic>
<title level="a">Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
<author>
<persName>
<forename type="first">O F</forename>
<surname>Batsevych</surname>
</persName>
<email>o-batsev@online.no</email>
<affiliation>89, Norway</affiliation>
</author>
<author>
<persName>
<forename type="first">R B</forename>
<surname>Kapustiy</surname>
</persName>
<email>r.kapustiy@gmail.com</email>
<affiliation>8, Lviv 79035, Ukraine</affiliation>
</author>
</analytic>
<monogr>
<title level="j">Journal of Physics G Nuclear and Particle Physics</title>
<idno type="pISSN">0954-3899</idno>
<idno type="eISSN">1361-6471</idno>
<imprint>
<publisher>IOP Publishing</publisher>
<date type="published" when="2012-08"></date>
<biblScope unit="volume">39</biblScope>
<biblScope unit="issue">8</biblScope>
</imprint>
</monogr>
<idno type="istex">065AAAB89A3324EF85C29E2FD813C0B24F5A0332</idno>
<idno type="DOI">10.1088/0954-3899/39/8/085008</idno>
<idno type="href">http://stacks.iop.org/JPhysG/39/085008</idno>
<idno type="ArticleID">jpg425190</idno>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc>
<creation>
<date>2012-06-27</date>
</creation>
<langUsage>
<language ident="en">en</language>
</langUsage>
<abstract>
<p>In this paper we show that the recently detected superluminal neutrino motion, which now is believed to be the result of a possible technical fault in the experiment, can alternatively be explained by the absence of the gravitational mass of the neutrino, and as a result, an absence of its interaction with a gravitational field. The neutrino velocity theoretically predicted in this paper is in full agreement with the experimental data obtained by the OPERA collaboration. The conducted calculations also predict a significant anisotropy of the neutrino velocity measurement depending on the direction of the Earths motion relative to the Galaxy, which allows for the validation of the obtained results.</p>
</abstract>
<textClass>
<keywords scheme="keyword">
<list>
<head>article-type</head>
<item>
<term>Paper</term>
</item>
</list>
</keywords>
</textClass>
<textClass>
<keywords scheme="keyword">
<list>
<head>section</head>
<item>
<term>Particle Physics</term>
</item>
</list>
</keywords>
</textClass>
<textClass>
<keywords scheme="keyword">
<list>
<head>author-pacs</head>
<item>
<term>04.20.Cv</term>
</item>
<item>
<term>13.15.g</term>
</item>
<item>
<term>98.35.a</term>
</item>
</list>
</keywords>
</textClass>
<textClass>
<keywords scheme="keyword">
<list>
<head>Keywords</head>
<item>
<term>superluminal neutrino</term>
</item>
<item>
<term>OPERA</term>
</item>
<item>
<term>galaxy</term>
</item>
<item>
<term>equivalence principle</term>
</item>
</list>
</keywords>
</textClass>
</profileDesc>
<revisionDesc>
<change when="2012-06-27">Created</change>
<change when="2012-08">Published</change>
</revisionDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item>
<original>false</original>
<mimetype>text/plain</mimetype>
<extension>txt</extension>
<uri>https://api.istex.fr/document/065AAAB89A3324EF85C29E2FD813C0B24F5A0332/fulltext/txt</uri>
</json:item>
</fulltext>
<metadata>
<istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header">
<istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1" </istex:xmlDeclaration>
<istex:docType PUBLIC="-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" URI="http://ej.iop.org/dtd/nlm-3.0/journalpublishing3.dtd" name="istex:docType"></istex:docType>
<istex:document>
<article article-type="research-article">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">jpg</journal-id>
<journal-id journal-id-type="coden">JPGPED</journal-id>
<journal-title-group>
<journal-title>Journal of Physics G: Nuclear and Particle Physics</journal-title>
<abbrev-journal-title abbrev-type="IOP">JPhysG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="publisher">J. Phys. G: Nucl. Part. Phys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="ppub">0954-3899</issn>
<issn pub-type="epub">1361-6471</issn>
<publisher>
<publisher-name>IOP Publishing</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">jpg425190</article-id>
<article-id pub-id-type="doi">10.1088/0954-3899/39/8/085008</article-id>
<article-id pub-id-type="manuscript">425190</article-id>
<article-categories>
<subj-group subj-group-type="article-type">
<subject>Paper</subject>
</subj-group>
<subj-group subj-group-type="section">
<subject>Particle Physics</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Superluminal neutrino phenomenon as a result of the equivalence principle violation</article-title>
<alt-title alt-title-type="ascii">Superluminal neutrino phenomenon as a result of the equivalence principle violation</alt-title>
<alt-title alt-title-type="short">Superluminal neutrino phenomenon as a result of the equivalence principle violation</alt-title>
<alt-title alt-title-type="short-ascii">Superluminal neutrino phenomenon as a result of the equivalence principle violation</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Batsevych</surname>
<given-names>O F</given-names>
</name>
<xref ref-type="aff" rid="jpg425190af1">1</xref>
<xref ref-type="fn" rid="jpg425190afn1">3</xref>
<xref ref-type="aff" rid="jpg425190em1"></xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Kapustiy</surname>
<given-names>R B</given-names>
</name>
<xref ref-type="aff" rid="jpg425190af2">2</xref>
<xref ref-type="fn" rid="jpg425190afn1">3</xref>
<xref ref-type="aff" rid="jpg425190em2"></xref>
</contrib>
<aff id="jpg425190af1">
<label>1</label>
<institution>Kongsberg Maritime</institution>
’ AS, Bekkajordet St 8A, Horten 3189,
<country>Norway</country>
</aff>
<aff id="jpg425190af2">
<label>2</label>
<institution>UkrCell’ Ltd.</institution>
, Krymska St 28, Lviv 79035,
<country>Ukraine</country>
</aff>
<ext-link ext-link-type="email" id="jpg425190em1">o-batsev@online.no</ext-link>
<ext-link ext-link-type="email" id="jpg425190em2">r.kapustiy@gmail.com</ext-link>
<author-comment content-type="short-author-list">
<p>O F Batsevych and R B Kapustiy</p>
</author-comment>
</contrib-group>
<author-notes>
<fn id="jpg425190afn1">
<label>3</label>
<p>Retired from: Department of Theoretical Physics, Ivan Franko National University of Lviv, Drahomanov St. 12, Lviv 79005, Ukraine.</p>
</fn>
</author-notes>
<pub-date pub-type="ppub">
<month>8</month>
<year>2012</year>
</pub-date>
<pub-date pub-type="epub">
<day>27</day>
<month>6</month>
<year>2012</year>
</pub-date>
<volume>39</volume>
<issue>8</issue>
<elocation-id content-type="artnum">085008</elocation-id>
<history>
<date date-type="received">
<day>2</day>
<month>3</month>
<year>2012</year>
</date>
</history>
<permissions>
<copyright-statement>© 2012 IOP Publishing Ltd</copyright-statement>
<copyright-year>2012</copyright-year>
</permissions>
<self-uri xlink:href="http://stacks.iop.org/JPhysG/39/085008"></self-uri>
<abstract>
<title>Abstract</title>
<p>In this paper we show that the recently detected superluminal neutrino motion, which now is believed to be the result of a possible technical fault in the experiment, can alternatively be explained by the absence of the gravitational mass of the neutrino, and as a result, an absence of its interaction with a gravitational field. The neutrino velocity theoretically predicted in this paper is in full agreement with the experimental data obtained by the OPERA collaboration. The conducted calculations also predict a significant anisotropy of the neutrino velocity measurement depending on the direction of the Earth’s motion relative to the Galaxy, which allows for the validation of the obtained results.</p>
</abstract>
<kwd-group kwd-group-type="author-pacs">
<kwd>04.20.Cv</kwd>
<kwd>13.15.+g</kwd>
<kwd>98.35.−a</kwd>
</kwd-group>
<kwd-group kwd-group-type="author">
<kwd>superluminal neutrino</kwd>
<kwd>OPERA</kwd>
<kwd>galaxy</kwd>
<kwd>equivalence principle</kwd>
</kwd-group>
<counts>
<page-count count="9"></page-count>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>ccc</meta-name>
<meta-value>0954-3899/12/085008+09$33.00</meta-value>
</custom-meta>
<custom-meta>
<meta-name>printed</meta-name>
<meta-value>Printed in the UK & the USA</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec id="jpg425190s1">
<label>1.</label>
<title>Introduction</title>
<p>On 22 September 2011 the OPERA collaboration announced the registration of a muon neutrino exceeding the speed of light by 0.00248% [
<xref ref-type="bibr" rid="jpg425190bib01">1</xref>
]. This news has been widely discussed in the mass media since this phenomenon went far beyond the limits of modern scientific concepts. The response of the scientific community to this uncanny neutrino behaviour was quite sceptical—a series of articles was released where attempts were made to identify possible errors in the experiment in order to discredit the result [
<xref ref-type="bibr" rid="jpg425190bib02">2</xref>
]. However, two months after the initial announcement, on 17 November a new publication was released by the OPERA collaboration in which the validity of the conducted experiment was confirmed once again [
<xref ref-type="bibr" rid="jpg425190bib03">3</xref>
].</p>
<p>In February 2012 OPERA informed [
<xref ref-type="bibr" rid="jpg425190bib04">4</xref>
] about two possible problems which may have affected the obtained results: the neutrino velocity may have been underestimated (the passage of time on the clocks between the arrival of the synchronizing signal has to be interpolated, which might not have been done correctly); the other one, in contrast, may have been an overestimation (due to a possible faulty link between the GPS signal and the OPERA master clock). In this connection one recalls that superluminal neutrinos were registered earlier as well, e.g. by the MINOS collaboration in 2007 [
<xref ref-type="bibr" rid="jpg425190bib05">5</xref>
]; there were no inaccuracies found in these experiments. Therefore, the existence of superluminal neutrinos seems quite plausible, and most probably will be confirmed by the forthcoming OPERA experiment this year.</p>
<p>Numerous attempts at the field-theory level have been made during the last few months to explain neutrino superluminality. Within this approach, the phenomenon is explained by the neutrino’s interaction with newly introduced auxiliary fields [
<xref ref-type="bibr" rid="jpg425190bib06">6</xref>
] emanated by the Earth, or even by such a construct as dark matter [
<xref ref-type="bibr" rid="jpg425190bib07">7</xref>
,
<xref ref-type="bibr" rid="jpg425190bib08">8</xref>
].</p>
<p>However, in this paper we show how the phenomenon of the superluminal neutrino can be explained within the general theory of relativity, without any additional fields and other far-fetched concepts. The only assumption which will be employed to that end is quite simple, however unobvious at first glance: we will assume a non-equivalence of the gravitational and inertial masses of the neutrino. More precisely, we assume that the gravitational mass of the neutrino is equal to zero. This means that the ubiquitous equivalence principle is violated by the neutrino, allowing us to obtain predictions which coincide perfectly with the experimental data.</p>
</sec>
<sec id="jpg425190s2">
<label>2.</label>
<title>Equation of free neutrino motion</title>
<p>The equation of free motion [
<xref ref-type="bibr" rid="jpg425190bib09">9</xref>
<xref ref-type="bibr" rid="jpg425190bib11">11</xref>
] of an ordinary mass particle having Cartesian coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn1.gif"></inline-graphic>
</inline-formula>
in a gravitational field is
<disp-formula id="jpg425190eqn01">
<label>1</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn01.gif"></graphic>
</disp-formula>
where the affine connection Γ
<sup>α</sup>
<sub>μν</sub>
is the source of the gravitational force acting on the particle.</p>
<p>Equation (
<xref ref-type="disp-formula" rid="jpg425190eqn01">1</xref>
) is written with the assumption that the gravitational
<italic>m
<sub>g</sub>
</italic>
and inertial
<italic>m
<sub>I</sub>
</italic>
masses of the object are the same, which is the essence of the equivalence principle. What should be written instead of equation (
<xref ref-type="disp-formula" rid="jpg425190eqn01">1</xref>
) if the two masses are not equal? The answer to this question is quite straightforward in the case of a weak field when a Newtonian approximation can be used to express the affine connection via the intensity of the field as
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn2.gif"></inline-graphic>
</inline-formula>
, where Φ is the gravitational potential. In this case equation (
<xref ref-type="disp-formula" rid="jpg425190eqn01">1</xref>
) becomes the well-known Newtonian law of gravitation
<disp-formula id="jpg425190ueq01">
<tex-math></tex-math>
<graphic xlink:href="jpg425190ueq01.gif"></graphic>
</disp-formula>
which follows from Newton’s second law
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn3.gif"></inline-graphic>
</inline-formula>
with the gravitational force
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn4.gif"></inline-graphic>
</inline-formula>
. If the ratio of the masses μ =
<italic>m
<sub>g</sub>
</italic>
/
<italic>m
<sub>I</sub>
</italic>
is not equal to 1, the gravitation reads
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn5.gif"></inline-graphic>
</inline-formula>
, and multiplier μ appears in front of Γ
<sup>α</sup>
<sub>μν</sub>
in equation (
<xref ref-type="disp-formula" rid="jpg425190eqn01">1</xref>
) as well.</p>
<p>Our main statement is that
<italic>the gravitational and the inertial masses of the neutrino are not equivalent, and the gravitational mass of the neutrino is equal to zero</italic>
. So below we will be interested in the special case of μ = 0. Hence, equation (
<xref ref-type="disp-formula" rid="jpg425190eqn01">1</xref>
) for the neutrino should be rewritten as
<disp-formula id="jpg425190eqn02">
<label>2</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn02.gif"></graphic>
</disp-formula>
</p>
<p>The solution of equation (
<xref ref-type="disp-formula" rid="jpg425190eqn02">2</xref>
) is a movement with the constant speed,
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn6.gif"></inline-graphic>
</inline-formula>
, or explicitly for the space component:
<disp-formula id="jpg425190eqn03">
<label>3</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn03.gif"></graphic>
</disp-formula>
</p>
<p>It is important to realize that equation (
<xref ref-type="disp-formula" rid="jpg425190eqn03">3</xref>
) holds not only in the space outside any local gravitational non-homogeneities, but also inside the gravitational field, even in one as strong as a black hole.</p>
<p>We remind the reader here that equation (
<xref ref-type="disp-formula" rid="jpg425190eqn02">2</xref>
) is written for a special case of Cartesian-like coordinates, for which the affine connection disappears in the absence of gravitation. Generally, the metric tensor
<italic>g
<sub>ij</sub>
</italic>
(
<bold>
<italic>x</italic>
</bold>
) and affine connection Γ
<sup>α</sup>
<sub>μν</sub>
(
<bold>
<italic>x</italic>
</bold>
) depend on coordinates
<bold>
<italic>x</italic>
</bold>
not only because of the presence of gravitational potential Φ, but also due to inherent properties of curvilinear coordinates. In such a general case, the equation of free motion for the gravitationally-neutral particle (neutrino) is
<disp-formula id="jpg425190eqn04">
<label>4</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn04.gif"></graphic>
</disp-formula>
where {
<sup>α</sup>
<sub>μν</sub>
}(
<bold>
<italic>x</italic>
</bold>
) = Γ
<sup>α</sup>
<sub>μν</sub>
(
<bold>
<italic>x</italic>
</bold>
)|
<sub>Φ=0</sub>
is the affine connection calculated for ‘switched off’ gravity and consequently in flat space-time.</p>
<p>Equation (
<xref ref-type="disp-formula" rid="jpg425190eqn04">4</xref>
) states that the neutrino ‘lives’ in Minkowski (
<italic>flat</italic>
) space-time equipped with the metric tensor η
<sub>
<italic>ij</italic>
</sub>
(
<bold>
<italic>x</italic>
</bold>
) =
<italic>g
<sub>ij</sub>
</italic>
(
<bold>
<italic>x</italic>
</bold>
)|
<sub>Φ=0</sub>
. The light trajectory lies on the null cone of the distorted space-time, d
<italic>s</italic>
=
<italic>g
<sub>ij</sub>
</italic>
d
<italic>x
<sup>i</sup>
</italic>
d
<italic>x
<sup>j</sup>
</italic>
= 0, while the neutrino’s trajectory lies on the Minkowski null cone, satisfying d
<italic>s</italic>
<sub>0</sub>
= η
<sub>
<italic>ij</italic>
</sub>
d
<italic>x
<sup>i</sup>
</italic>
d
<italic>x
<sup>j</sup>
</italic>
= 0 instead, yielding a space-like observable interval d
<italic>s</italic>
< 0 in the presence of gravitation.</p>
</sec>
<sec id="jpg425190s3">
<label>3.</label>
<title>Velocity of neutrino</title>
<p>An observer on the Earth’s surface is subject to the gravitational influence of many massive objects, the most important of which are summarized in table
<xref ref-type="table" rid="jpg425190t1">1</xref>
[
<xref ref-type="bibr" rid="jpg425190bib12">12</xref>
<xref ref-type="bibr" rid="jpg425190bib17">17</xref>
].</p>
<table-wrap id="jpg425190t1">
<label>Table 1.</label>
<caption id="jpg425190tc1">
<p>Gravitational influence of space objects on an Earth-located observer.</p>
</caption>
<table>
<colgroup>
<col align="left"></col>
<col align="left"></col>
<col align="left"></col>
<col align="left"></col>
<col align="left"></col>
<col align="left"></col>
</colgroup>
<thead>
<tr>
<th align="center">Space objects:</th>
<th align="center">Earth</th>
<th align="center">Sun</th>
<th align="center">Galaxy
<xref ref-type="fn" rid="jpg425190t1fn1">
<sup>a</sup>
</xref>
</th>
<th align="center">M31</th>
<th align="center">M33</th>
</tr>
</thead>
<tbody>
<tr>
<td>Gravitational mass (
<italic>M</italic>
, kg)</td>
<td>5.974 × 10
<sup>24</sup>
</td>
<td>1.9891 × 10
<sup>30</sup>
</td>
<td> 3.78 × 10
<sup>42</sup>
</td>
<td>2.45 × 10
<sup>42</sup>
</td>
<td>1.0 × 10
<sup>41</sup>
</td>
</tr>
<tr>
<td>Distance to the surface of the Earth (
<italic>R</italic>
, m)</td>
<td>6.371 × 10
<sup>6</sup>
</td>
<td>1.496 × 10
<sup>11</sup>
</td>
<td>2.59 × 10
<sup>20</sup>
(8.40 kpc)</td>
<td>2.43 × 10
<sup>22</sup>
(788 kpc)</td>
<td>2.62 × 10
<sup>22</sup>
(850 kpc)</td>
</tr>
<tr>
<td>Gravitational potential which creates mass
<italic>M</italic>
on the surface of the Earth (Φ, m
<sup>2</sup>
 s
<sup>−2</sup>
)</td>
<td>6.258 × 10
<sup>7</sup>
</td>
<td>8.874 × 10
<sup>8</sup>
</td>
<td>9.74 × 10
<sup>11</sup>
</td>
<td>6.73 × 10
<sup>9</sup>
</td>
<td>2.55 × 10
<sup>8</sup>
</td>
</tr>
<tr>
<td>The intensity of the gravitational field on the surface of the Earth (
<italic>g</italic>
= Φ/
<italic>R</italic>
, m s
<sup>−2</sup>
)</td>
<td>9.822</td>
<td>5.932 × 10
<sup>−3</sup>
</td>
<td>3.76 × 10
<sup>−9</sup>
</td>
<td>2.77 × 10
<sup>−13</sup>
</td>
<td>9.72 × 10
<sup>−15</sup>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="jpg425190t1fn1">
<label>a</label>
<p>The Galactic potential is defined with an assumption that the total mass of the Galaxy is localized at its centre.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>From table
<xref ref-type="table" rid="jpg425190t1">1</xref>
it follows that the strongest gravity field is that of our planet; however, the strongest gravitational potential is that of our Galaxy,
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn12.gif"></inline-graphic>
</inline-formula>
, by a few orders of magnitude. Therefore henceforth we will ignore all gravitational potentials, except Φ
<sub>Γ</sub>
. To describe the gravitational effects on the Earth’s observer, we will use the Schwarzschild metric, written in isotropic Cartesian coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn14.gif"></inline-graphic>
</inline-formula>
at rest relative to the Galactic centre (referred to henceforth as the Galactic-fixed coordinate system, GCS) as follows [
<xref ref-type="bibr" rid="jpg425190bib18">18</xref>
,
<xref ref-type="bibr" rid="jpg425190bib19">19</xref>
]
<disp-formula id="jpg425190eqn05">
<label>5</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn05.gif"></graphic>
</disp-formula>
</p>
<p>GCS is asymptotically plain, for significant distances
<italic>g</italic>
<sub>αβ</sub>
= η
<sub>αβ</sub>
. It is obvious that after ‘switching off’ gravity the equality
<italic>g</italic>
<sub>αβ</sub>
= η
<sub>αβ</sub>
will hold everywhere, and the free motion equation (
<xref ref-type="disp-formula" rid="jpg425190eqn02">2</xref>
) will give
<disp-formula id="jpg425190eqn06">
<label>6</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn06.gif"></graphic>
</disp-formula>
</p>
<p>Therefore an observer far from the centre of the Galaxy will measure the neutrino velocity
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn15.gif"></inline-graphic>
</inline-formula>
to be equal to
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn16.gif"></inline-graphic>
</inline-formula>
from equation (
<xref ref-type="disp-formula" rid="jpg425190eqn03">3</xref>
) for the neutrino emitted on the Earth. This is not the case for all other speed measurements, e.g. even light will be measured to have a speed
<italic>c
<sub>E</sub>
</italic>
of less than
<italic>c</italic>
.</p>
<p>The inertial Earth’s observer coordinate system (referred henceforth as iECS) is moving with speed
<disp-formula id="jpg425190eqn07">
<label>7</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn07.gif"></graphic>
</disp-formula>
relative to the GCS due to the measurements in iECS. Here
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn17.gif"></inline-graphic>
</inline-formula>
is the speed of the Sun’s orbital motion around the Galactic centre,
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn18.gif"></inline-graphic>
</inline-formula>
is the orbital speed of the Earth around the Sun, which has a period of change equal to one year.</p>
<p>To find the neutrino’s velocity
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn19.gif"></inline-graphic>
</inline-formula>
in iECS, we introduce first an inertial Galactic-fixed coordinate system (iGCS), which is located at the instantaneous Earth position, but at rest at the Galactic centre. Its coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn20.gif"></inline-graphic>
</inline-formula>
are related to the Galactic ones by the following
<italic>gravitational transformation</italic>
<italic>T</italic>
<sub>Γ</sub>
):
<disp-formula id="jpg425190eqn08">
<label>8</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn08.gif"></graphic>
</disp-formula>
Indeed, from equation (
<xref ref-type="disp-formula" rid="jpg425190eqn05">5</xref>
) it follows that coordinates (
<xref ref-type="disp-formula" rid="jpg425190eqn08">8</xref>
) yield a locally flat metric η
<sub>αβ</sub>
:
<disp-formula id="jpg425190eqn09">
<label>9</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn09.gif"></graphic>
</disp-formula>
hence they may be regarded as locally-inertial coordinates.</p>
<p>From equation (
<xref ref-type="disp-formula" rid="jpg425190eqn08">8</xref>
) it also follows that in the iGCS, an observer will measure the following neutrino velocity
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn22.gif"></inline-graphic>
</inline-formula>
:
<disp-formula id="jpg425190eqn10">
<label>10</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn10.gif"></graphic>
</disp-formula>
Neglecting terms of order
<italic>c</italic>
<sup>−4</sup>
and higher in equation (
<xref ref-type="disp-formula" rid="jpg425190eqn10">10</xref>
), we can write
<disp-formula id="jpg425190eqn11">
<label>11</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn11.gif"></graphic>
</disp-formula>
It is already obvious that the result of the gravitational transformation speed
<italic>V</italic>
′ will be greater than
<italic>v</italic>
 ′ by the factor
<disp-formula id="jpg425190eqn12">
<label>12</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn12.gif"></graphic>
</disp-formula>
This speed is measured in the iGCS, which is related to the Earth observer’s iECS coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn23.gif"></inline-graphic>
</inline-formula>
through the Lorentz boost
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn24.gif"></inline-graphic>
</inline-formula>
:
<disp-formula id="jpg425190eqn13">
<label>13</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn13.gif"></graphic>
</disp-formula>
where
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn25.gif"></inline-graphic>
</inline-formula>
.
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn26.gif"></inline-graphic>
</inline-formula>
, and
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn27.gif"></inline-graphic>
</inline-formula>
are the components of
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn28.gif"></inline-graphic>
</inline-formula>
, parallel and perpendicular, respectively, to
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn29.gif"></inline-graphic>
</inline-formula>
. From equation (
<xref ref-type="disp-formula" rid="jpg425190eqn13">13</xref>
) if follows that
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn30.gif"></inline-graphic>
</inline-formula>
and
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn31.gif"></inline-graphic>
</inline-formula>
are related via an ordinary relativistic speed addition formula
<disp-formula id="jpg425190eqn14">
<label>14</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn14.gif"></graphic>
</disp-formula>
</p>
<p>Taking into account equation (
<xref ref-type="disp-formula" rid="jpg425190eqn11">11</xref>
), we get an expression for the velocity of the neutrino
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn32.gif"></inline-graphic>
</inline-formula>
measured in the iECS through the velocity of the neutrino
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn33.gif"></inline-graphic>
</inline-formula>
measured in the GCS as follows
<disp-formula id="jpg425190eqn15">
<label>15</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn15.gif"></graphic>
</disp-formula>
</p>
<p>Due to the relative movement of these reference systems, the numerator of equation (
<xref ref-type="disp-formula" rid="jpg425190eqn15">15</xref>
) has a drift term
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn34.gif"></inline-graphic>
</inline-formula>
. To avoid it, we must express
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn35.gif"></inline-graphic>
</inline-formula>
via the velocity of the neutrino
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn36.gif"></inline-graphic>
</inline-formula>
measured in
<italic>(flat)</italic>
the Earth-fixed coordinate system (ECS) which follows the Earth at all times. The ECS is related to the GCS via the Lorentz boost
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn37.gif"></inline-graphic>
</inline-formula>
where, due to the gravitational transformation,
<disp-formula id="jpg425190eqn16">
<label>16</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn16.gif"></graphic>
</disp-formula>
is the Earth’s speed measured in the GCS. Therefore
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn38.gif"></inline-graphic>
</inline-formula>
can be expressed through neutrino velocity
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn39.gif"></inline-graphic>
</inline-formula>
, measured in the ECS, similarly to equation (
<xref ref-type="disp-formula" rid="jpg425190eqn14">14</xref>
)
<disp-formula id="jpg425190eqn17">
<label>17</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn17.gif"></graphic>
</disp-formula>
where
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn40.gif"></inline-graphic>
</inline-formula>
.</p>
<p>Substituting equation (
<xref ref-type="disp-formula" rid="jpg425190eqn17">17</xref>
) into equation (
<xref ref-type="disp-formula" rid="jpg425190eqn15">15</xref>
), we finally get
<disp-formula id="jpg425190eqn18">
<label>18</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn18.gif"></graphic>
</disp-formula>
</p>
<p>This formula contains no drift terms, as it relates the speeds of the neutrino in two Earth-fixed reference systems, namely, flat (ECS) and inertial (iECS).</p>
<p>Formula (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
) is the one we have been looking for, as it relates the Earth-measured velocity of neutrino
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn41.gif"></inline-graphic>
</inline-formula>
to the ‘flat’ velocity of the neutrino
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn42.gif"></inline-graphic>
</inline-formula>
, which is ordinary velocity and can, for example, be expressed through the experimentally measured neutrino energy
<italic>E</italic>
as
<disp-formula id="jpg425190eqn19">
<label>19</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn19.gif"></graphic>
</disp-formula>
</p>
<p>An interesting peculiarity of formula (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
), which may be a basis for the future experimental validation of our model, is the dependence of the measured velocity on the direction at which the neutrino was emitted relative to the Earth’s velocity.</p>
</sec>
<sec id="jpg425190s4">
<label>4.</label>
<title>Alternative derivation</title>
<p>A derivation of formula (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
) was based on the sequence of the transitions between the coordinate systems ECS → GCS → iGCS → iECS. In terms of the Lorentz boosts Λ( · ) and
<italic>gravitational transformation</italic>
<italic>T</italic>
<sub>Γ</sub>
) defined by equation (
<xref ref-type="disp-formula" rid="jpg425190eqn08">8</xref>
), this may be summarized by
<disp-formula id="jpg425190eqn20">
<label>20</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn20.gif"></graphic>
</disp-formula>
where all calculation complexities arise due to the fact that
<italic>T</italic>
<sub>Γ</sub>
) and Λ( · ) are not commuting with each other.</p>
<p>The impossibility of making a gravitational transformation on the spot is due to the fact that the Schwarzschild metric is given in the GCS, which is at rest relative to the Galactic centre, while an observer on the Earth is moving. Let us now rewrite the Schwarzschild interval (
<xref ref-type="disp-formula" rid="jpg425190eqn05">5</xref>
) in terms of the ECS coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn45.gif"></inline-graphic>
</inline-formula>
related to the GCS coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn46.gif"></inline-graphic>
</inline-formula>
by the Lorentz boost
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn47.gif"></inline-graphic>
</inline-formula>
:
<disp-formula id="jpg425190eqn21">
<label>21</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn21.gif"></graphic>
</disp-formula>
Substituting these expressions in equation (
<xref ref-type="disp-formula" rid="jpg425190eqn05">5</xref>
) we get with an accuracy of
<italic>O</italic>
<sub>Γ</sub>
/
<italic>c</italic>
<sup>2</sup>
) the following:
<disp-formula id="jpg425190eqn22">
<label>22</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn22.gif"></graphic>
</disp-formula>
where
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn49.gif"></inline-graphic>
</inline-formula>
.</p>
<p>Expression (
<xref ref-type="disp-formula" rid="jpg425190eqn22">22</xref>
) defines the space-time distortion created by a point of mass moving with speed
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn50.gif"></inline-graphic>
</inline-formula>
about the origin, therefore it may be interpreted as a Galactic potential acting on the Earth’s observer. Formula (
<xref ref-type="disp-formula" rid="jpg425190eqn22">22</xref>
) was in purpose written in a form with an explicitly extracted squared factor near
<italic>c</italic>
<sup>2</sup>
, which immediately allows us to perform the transition to the inertial coordinate system iECS with the coordinates
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn51.gif"></inline-graphic>
</inline-formula>
as follows:
<disp-formula id="jpg425190eqn23">
<label>23</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn23.gif"></graphic>
</disp-formula>
</p>
<p>And for neutrino velocity
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn52.gif"></inline-graphic>
</inline-formula>
we obtain
<disp-formula id="jpg425190eqn24">
<label>24</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn24.gif"></graphic>
</disp-formula>
</p>
<p>This formula is equivalent to equation (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
) with an accuracy of
<italic>O</italic>
(
<italic>c</italic>
<sup>−5</sup>
), as during the simplification of the expression for the interval (
<xref ref-type="disp-formula" rid="jpg425190eqn22">22</xref>
) we freely neglected the terms of order
<italic>O</italic>
<sup>2</sup>
<sub>Γ</sub>
/
<italic>c</italic>
<sup>4</sup>
) and higher.</p>
</sec>
<sec id="jpg425190s5">
<label>5.</label>
<title>Comparison with the experimental data</title>
<p>Since the experiments of the OPERA collaboration in which their scientists measured
<italic>V</italic>
>
<italic>c</italic>
referring to the muon neutrino, then in this paper we will discuss exactly this type of neutrino [
<xref ref-type="bibr" rid="jpg425190bib03">3</xref>
]. However, it is most likely that all of the conclusions of the article will also be fully compatible for the other types of neutrino.</p>
<p>In the experiments, light covered the distance of
<italic>S</italic>
= 731 278.0 m in
<italic>t
<sub>c</sub>
</italic>
= 2 439 280.9 ns, while the neutrino was ahead of light by
<disp-formula id="jpg425190eqn25">
<label>25</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn25.gif"></graphic>
</disp-formula>
The relative deviation of the neutrino’s velocity from the velocity of light, defined as
<disp-formula id="jpg425190eqn26">
<label>26</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn26.gif"></graphic>
</disp-formula>
is
<disp-formula id="jpg425190eqn27">
<label>27</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn27.gif"></graphic>
</disp-formula>
Experimental measurements were split on two datasets with the neutrino energies of
<italic>E</italic>
<sub>1</sub>
= 13.9 GeV and
<italic>E</italic>
<sub>2</sub>
= 42.9 GeV. Experiments detected no dependence of the muon neutrino’s velocity on its energy, which indicates that the (inertial) mass of the neutrino is very small.</p>
<p>There are many estimates of the upper limit of the muon neutrino’s mass at rest; we will use the maximal one [
<xref ref-type="bibr" rid="jpg425190bib20">20</xref>
]
<italic>m
<sub>I</sub>
</italic>
<sub>μ</sub>
)
<italic>c</italic>
<sup>2</sup>
=
<italic>E</italic>
<sub>0</sub>
= 2.2 MeV. For the experimentally detected neutrino energies, the deviation of the neutrino velocity
<italic>v</italic>
(in the flat coordinate system ECS), from the speed of light given by
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn54.gif"></inline-graphic>
</inline-formula>
, will be
<disp-formula id="jpg425190eqn28">
<label>28</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn28.gif"></graphic>
</disp-formula>
These numbers are far lower than the amount (
<xref ref-type="disp-formula" rid="jpg425190eqn27">27</xref>
) by which the light speed is exceeded, and we will neglect the difference of the neutrino velocity in the ECS from
<italic>c</italic>
without any loss of precision. So, henceforth we put
<disp-formula id="jpg425190eqn29">
<label>29</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn29.gif"></graphic>
</disp-formula>
The above experimental studies were not the first to indicate that the neutrino velocity can exceed the speed of light. In particular, similar results were obtained back in 2007 by a group of scientists from the MINOS collaboration [
<xref ref-type="bibr" rid="jpg425190bib05">5</xref>
]. However, in all of the previous studies, the accuracy of the obtained results was much smaller; therefore, one could not definitely state the fact that the speed of light was exceeded by a neutrino.</p>
<p>Taking into account equation (
<xref ref-type="disp-formula" rid="jpg425190eqn29">29</xref>
), we can expand the neutrino velocity (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
) into a series, and neglecting the terms of the order
<italic>O</italic>
(
<italic>c</italic>
<sup>−3</sup>
) and higher, we get
<disp-formula id="jpg425190eqn30">
<label>30</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn30.gif"></graphic>
</disp-formula>
</p>
<p>Consequently,
<disp-formula id="jpg425190eqn31">
<label>31</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn31.gif"></graphic>
</disp-formula>
</p>
<p>Putting in formula (
<xref ref-type="disp-formula" rid="jpg425190eqn30">30</xref>
) the most recent estimates for the numerical values
<italic>V
<sub>E</sub>
</italic>
= 2.55 × 10
<sup>5</sup>
 m s
<sup>−1</sup>
and Φ
<sub>Γ</sub>
= 9.74 × 10
<sup>11</sup>
 m
<sup>2</sup>
 s
<sup>−2</sup>
, we obtain the following expression for the absolute value of the neutrino velocity
<disp-formula id="jpg425190eqn32">
<label>32</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn32.gif"></graphic>
</disp-formula>
</p>
<p>So, the experimentally measured value of δ
<italic>V</italic>
must belong to the interval
<disp-formula id="jpg425190eqn33">
<label>33</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn33.gif"></graphic>
</disp-formula>
where the second term is the purely anisotropic part; maximal or minimal values of δ
<italic>V</italic>
are reached when the neutrino is emitted strictly collinear forward or backward, respectively, to the Earth’s speed relative to the Galaxy.</p>
<p>An amazing coincidence of our estimate (
<xref ref-type="disp-formula" rid="jpg425190eqn33">33</xref>
) with the experimental value (
<xref ref-type="disp-formula" rid="jpg425190eqn27">27</xref>
) is the strong confirmation of our hypothesis. Another possible way to verify the given hypothesis would be an experimental approval of the neutrino velocity anisotropy, but this certainly would demand an increase of the accuracy of the measurements by two orders of magnitude.</p>
<p>There are other factors which can make δ
<italic>V</italic>
variable. One of them is the seasonal movement of the Earth
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn56.gif"></inline-graphic>
</inline-formula>
, equation (
<xref ref-type="disp-formula" rid="jpg425190eqn07">7</xref>
). Taking, for simplicity, that the orbit of the Earth around the Sun is circular and the angle between the Earth’s orbital plane and the vector
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn57.gif"></inline-graphic>
</inline-formula>
is θ = 60° [
<xref ref-type="bibr" rid="jpg425190bib17">17</xref>
], it is easy to find that the absolute value of
<inline-formula>
<tex-math></tex-math>
<inline-graphic xlink:href="jpg425190ieqn58.gif"></inline-graphic>
</inline-formula>
is given by
<disp-formula id="jpg425190eqn34">
<label>34</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn34.gif"></graphic>
</disp-formula>
where ω ∈ [0, 2π] is the angle of the annual motion of the Earth around the Sun,
<italic>V
<sub>S</sub>
</italic>
= 2.54 × 10
<sup>5</sup>
 m s
<sup>−1</sup>
[
<xref ref-type="bibr" rid="jpg425190bib16">16</xref>
], and the average
<italic>V</italic>
<sub>
<italic>E</italic>
/
<italic>S</italic>
</sub>
= 2.978 × 10
<sup>4</sup>
 m s
<sup>−1</sup>
[
<xref ref-type="bibr" rid="jpg425190bib17">17</xref>
]. The maximal and minimal values of
<italic>V
<sub>E</sub>
</italic>
then will be
<disp-formula id="jpg425190eqn35">
<label>35</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn35.gif"></graphic>
</disp-formula>
<disp-formula id="jpg425190eqn36">
<label>36</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn36.gif"></graphic>
</disp-formula>
</p>
<p>Performing numerical calculations of δ
<italic>V</italic>
for
<italic>V</italic>
<sub>
<italic>E</italic>
, min/max</sub>
, we obtain the correction to δ
<italic>V</italic>
<disp-formula id="jpg425190eqn37">
<label>37</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn37.gif"></graphic>
</disp-formula>
</p>
<p>The final expression which incorporates all corrections may be presented as
<disp-formula id="jpg425190eqn38">
<label>38</label>
<tex-math></tex-math>
<graphic xlink:href="jpg425190eqn38.gif"></graphic>
</disp-formula>
</p>
</sec>
<sec id="jpg425190s6">
<label>6.</label>
<title>Conclusion and discussion</title>
<p>Our attempt to explain superluminal neutrino velocity measured in the OPERA experiment was made by assuming that the gravitational neutrino mass is equal to zero, which makes neutrino movement insensitive to gravitational space-time distortion. Formulas (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
) and (
<xref ref-type="disp-formula" rid="jpg425190eqn24">24</xref>
) were obtained, relating neutrino velocity
<italic>V</italic>
( >
<italic>c</italic>
) measured by an observer on the Earth (laboratory) with neutrino velocity
<italic>v</italic>
( ⩽
<italic>c</italic>
) which is what it would have if it were an ordinary particle. Taking into account that the neutrino’s velocity for experimentally measured energies is very close to the speed of light in the
<italic>flat</italic>
coordinate system, we set
<italic>v</italic>
<italic>c</italic>
, giving a possible error no higher than 10
<sup>−8</sup>
. The theoretical estimate of the relative neutrino velocity deviation from the speed of light δ
<italic>V</italic>
gives a positive value (
<xref ref-type="disp-formula" rid="jpg425190eqn38">38</xref>
), which coincides perfectly with the OPERA result (
<xref ref-type="disp-formula" rid="jpg425190eqn27">27</xref>
).</p>
<p>This coincidence is even more remarkable if we take into account that the gravitational potential of the Galaxy and other variables which are involved in formula (
<xref ref-type="disp-formula" rid="jpg425190eqn18">18</xref>
) are known with substantial inaccuracy, as well as other simplifying assumptions, such as neglecting the gravitational influence of all objects on the Earth with the exception of the Galaxy, or the approximation of the metric tensor if it were generated by the point mass located in the centre of the Galaxy etc.</p>
<p>Another confirmation of the correctness of our model is an astronomical registration of the neutrino and light emission from the supernova outburst SN 1987A [
<xref ref-type="bibr" rid="jpg425190bib21">21</xref>
,
<xref ref-type="bibr" rid="jpg425190bib22">22</xref>
] in the Large Magellanic Cloud, which showed a 4-h neutrino outrun. If a neutrino were travelling with a constant speed constantly measured by OPERA, the outrun would be 4 years. In our model, the neutrino is not an ordinary tachyon, which is always faster than light, so the smaller the neutrino’s energy, the smaller its velocity. It is well known that the energy of the detected neutrino from SN 1987A was three orders of magnitude smaller than in the OPERA experiments. Thus, in intergalactic space where the metric is flatter, the neutrino travels with a velocity not greater than the speed of light. Therefore, the registered light delay was only 4 h rather than 4 years.</p>
<p>The justification of the neutrino’s superluminal velocity made in this paper has far-reaching consequences, as superluminality itself had. It may be a hint to the validation of alternative theories of gravitation, such as for example, Rosen’s bi-metric theory [
<xref ref-type="bibr" rid="jpg425190bib23">23</xref>
,
<xref ref-type="bibr" rid="jpg425190bib24">24</xref>
]. ‘Legalization’ of the superluminal neutrino means a revision of quantum field theory principles as well. Indeed, the superluminality of a neutrino implies a violation of causal relationships, which was an allowance only previously made for virtual particles.</p>
<p>Despite the aforementioned explanations of the existing experimental facts provided by our model, one can finally confirm its correctness only by experimentally detecting the anisotropy of neutrino velocity. This will certainly demand an increase of the measurement accuracy by two orders of magnitude. The detection of seasonal velocity fluctuations, also predicted by our model, will need an even higher precision.</p>
</sec>
</body>
<back>
<ref-list content-type="numerical">
<title>References</title>
<ref id="jpg425190bib01">
<label>1</label>
<element-citation publication-type="preprint">
<person-group person-group-type="author">
<name>
<surname>Adam</surname>
<given-names>T</given-names>
</name>
<etal></etal>
</person-group>
<year>2011</year>
<article-title>Measurement of the neutrino velocity with the OPERA detector in the CNGS beam</article-title>
<comment>arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/hep-ex/1109.4897v1">1109.4897v1</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib02">
<label>2</label>
<element-citation publication-type="preprint">
<person-group person-group-type="author">
<name>
<surname>van Elburg</surname>
<given-names>R</given-names>
</name>
</person-group>
<year>2011</year>
<article-title>Measuring time of flight using satellite-based clocks</article-title>
<comment>arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/physics.gen-ph/1110.2685v4">1110.2685v4</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib03">
<label>3</label>
<element-citation publication-type="preprint">
<person-group person-group-type="author">
<name>
<surname>Adam</surname>
<given-names>T</given-names>
</name>
<etal></etal>
</person-group>
<year>2011</year>
<article-title>Measurement of the neutrino velocity with the OPERA detector in the CNGS beam</article-title>
<comment>arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/hep-ex/1109.4897v2">1109.4897v2</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib04">
<label>4</label>
<element-citation publication-type="communication">
<person-group person-group-type="author">
<name>
<surname>Reich</surname>
<given-names>E S</given-names>
</name>
</person-group>
<year>2012</year>
<article-title>Flaws found in faster-than-light neutrino measurement</article-title>
<comment>doi:
<ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1038/nature.2012.10099">10.1038/nature.2012.10099</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib05">
<label>5</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Adamson</surname>
<given-names>P</given-names>
</name>
<etal></etal>
</person-group>
<year>2007</year>
<source>Phys. Rev.
<named-content content-type="jnl-part">D</named-content>
</source>
<volume>76</volume>
<elocation-id content-type="artnum">072005</elocation-id>
<comment>(arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/hep-ex/0706.0437v3">0706.0437v3</ext-link>
)</comment>
<pub-id pub-id-type="doi">10.1103/PhysRevD.76.072005</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib06">
<label>6</label>
<element-citation publication-type="preprint">
<person-group person-group-type="author">
<name>
<surname>Dvali</surname>
<given-names>G</given-names>
</name>
<name>
<surname>Vikman</surname>
<given-names>A</given-names>
</name>
</person-group>
<year>2011</year>
<article-title>Price for environmental neutrino-superluminality</article-title>
<comment>arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/hep-ph/1109.5685v1">1109.5685v1</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib07">
<label>7</label>
<element-citation publication-type="preprint">
<person-group person-group-type="author">
<name>
<surname>Schechter</surname>
<given-names>J</given-names>
</name>
<name>
<surname>Shahid</surname>
<given-names>M N</given-names>
</name>
</person-group>
<year>2012</year>
<article-title>Neutrinos with velocities greater than
<italic>c</italic>
?</article-title>
<comment>arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/1201.4374v1">1201.4374v1</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib08">
<label>8</label>
<element-citation publication-type="preprint">
<person-group person-group-type="author">
<name>
<surname>Ciuffoli</surname>
<given-names>E</given-names>
</name>
<name>
<surname>Evslin</surname>
<given-names>J</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Jie</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Xinmin</given-names>
</name>
</person-group>
<year>2011</year>
<article-title>OPERA and a neutrino dark energy model</article-title>
<comment>arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/1109.6641v2">1109.6641v2</ext-link>
</comment>
</element-citation>
</ref>
<ref id="jpg425190bib09">
<label>9</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Weinberg</surname>
<given-names>S</given-names>
</name>
</person-group>
<year>1972</year>
<source>Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity</source>
<publisher-loc>New York</publisher-loc>
<publisher-name>Wiley</publisher-name>
<fpage>p 657</fpage>
</element-citation>
</ref>
<ref id="jpg425190bib10">
<label>10</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Landau</surname>
<given-names>L D</given-names>
</name>
<name>
<surname>Lifshitz</surname>
<given-names>E M</given-names>
</name>
</person-group>
<year>1988</year>
<source>The Classical Theory of Fields</source>
<series>Course of Theoretical Physics</series>
<volume>vol 2</volume>
<publisher-loc>Moscow</publisher-loc>
<publisher-name>Nauka</publisher-name>
<fpage>p 512</fpage>
</element-citation>
</ref>
<ref id="jpg425190bib11">
<label>11</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Stephani</surname>
<given-names>H</given-names>
</name>
<name>
<surname>Kramer</surname>
<given-names>D</given-names>
</name>
<name>
<surname>MacCallum</surname>
<given-names>M</given-names>
</name>
<name>
<surname>Hoenselaers</surname>
<given-names>C</given-names>
</name>
<name>
<surname>Herlt</surname>
<given-names>E</given-names>
</name>
</person-group>
<year>2003</year>
<source>Exact Solution of the Einstein’s Field Equations</source>
<publisher-loc>Cambridge</publisher-loc>
<publisher-name>Cambridge University Press</publisher-name>
<fpage>p 732</fpage>
<pub-id pub-id-type="doi">10.1017/CBO9780511535185</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib12">
<label>12</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>McMillan</surname>
<given-names>P J</given-names>
</name>
</person-group>
<year>2011</year>
<source>Mon. Not. R. Astron. Soc.</source>
<volume>414</volume>
<fpage>2446</fpage>
<lpage>2457</lpage>
<page-range>2446–57</page-range>
<pub-id pub-id-type="doi">10.1111/j.1365-2966.2011.18564.x</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib13">
<label>13</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Karachentsev</surname>
<given-names>I D</given-names>
</name>
<name>
<surname>Kashibadze</surname>
<given-names>O G</given-names>
</name>
</person-group>
<year>2006</year>
<source>Astrophysics</source>
<volume>49</volume>
<fpage>3</fpage>
<lpage>18</lpage>
<page-range>3–18</page-range>
<pub-id pub-id-type="doi">10.1007/s10511-006-0002-6</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib14">
<label>14</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Corbelli</surname>
<given-names>E</given-names>
</name>
</person-group>
<year>2003</year>
<source>Mon. Not. R. Astron. Soc.</source>
<volume>342</volume>
<fpage>199</fpage>
<lpage>197</lpage>
<page-range>199–7</page-range>
<pub-id pub-id-type="doi">10.1046/j.1365-8711.2003.06531.x</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib15">
<label>15</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Evans</surname>
<given-names>N W</given-names>
</name>
<name>
<surname>Wilkinson</surname>
<given-names>M I</given-names>
</name>
</person-group>
<year>2000</year>
<source>Mon. Not. R. Astron. Soc.</source>
<volume>316</volume>
<fpage>929</fpage>
<lpage>942</lpage>
<page-range>929–42</page-range>
<comment>(arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/astro-ph/0004187">astro-ph/0004187</ext-link>
)</comment>
<pub-id pub-id-type="doi">10.1046/j.1365-8711.2000.03645.x</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib16">
<label>16</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Reid</surname>
<given-names>M J</given-names>
</name>
<etal></etal>
</person-group>
<year>2009</year>
<source>Astrophys. J.</source>
<volume>700</volume>
<fpage>137</fpage>
<lpage>148</lpage>
<page-range>137–48</page-range>
<comment>(arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/0902.3913v2">0902.3913v2</ext-link>
)</comment>
<pub-id pub-id-type="doi">10.1088/0004-637X/700/1/137</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib17">
<label>17</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Bakulin</surname>
<given-names>P I</given-names>
</name>
<name>
<surname>Kononovich</surname>
<given-names>E V</given-names>
</name>
<name>
<surname>Moroz</surname>
<given-names>V I</given-names>
</name>
</person-group>
<year>1977</year>
<source>General Course of Astronomy</source>
<publisher-loc>Moscow</publisher-loc>
<publisher-name>Nauka</publisher-name>
<fpage>p 544</fpage>
</element-citation>
</ref>
<ref id="jpg425190bib18">
<label>18</label>
<element-citation publication-type="book">
<person-group person-group-type="author">
<name>
<surname>Eddington</surname>
<given-names>A S</given-names>
</name>
</person-group>
<year>1924</year>
<source>The Mathematical Theory of Relativity</source>
<publisher-loc>Cambridge</publisher-loc>
<publisher-name>Cambridge University Press</publisher-name>
<fpage>p 284</fpage>
</element-citation>
</ref>
<ref id="jpg425190bib19">
<label>19</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Buchdahl</surname>
<given-names>H A</given-names>
</name>
</person-group>
<year>1985</year>
<source>Int. J. Theor. Phys.</source>
<volume>24</volume>
<fpage>731</fpage>
<lpage>739</lpage>
<page-range>731–9</page-range>
<pub-id pub-id-type="doi">10.1007/BF00670880</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib20">
<label>20</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Angelov</surname>
<given-names>N</given-names>
</name>
<etal></etal>
</person-group>
<year>2006</year>
<source>Nucl. Phys.
<named-content content-type="jnl-part">A</named-content>
</source>
<volume>780</volume>
<fpage>78</fpage>
<lpage>89</lpage>
<page-range>78–89</page-range>
<comment>(arXiv:
<ext-link ext-link-type="arxiv" xlink:href="http://arxiv.org/abs/nucl-ex/0605002">nucl-ex/0605002</ext-link>
)</comment>
<pub-id pub-id-type="doi">10.1016/j.nuclphysa.2006.09.011</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib21">
<label>21</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Arnett</surname>
<given-names>W D</given-names>
</name>
<etal></etal>
</person-group>
<year>1989</year>
<source>Annu. Rev. Astron. Astrophys.</source>
<volume>27</volume>
<fpage>629</fpage>
<lpage>700</lpage>
<page-range>629–700</page-range>
<pub-id pub-id-type="doi">10.1146/annurev.aa.27.090189.003213</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib22">
<label>22</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Imshennik</surname>
<given-names>V S</given-names>
</name>
</person-group>
<year>2010</year>
<source>Usp. Fiz. Nauk</source>
<volume>180</volume>
<fpage>N11</fpage>
<pub-id pub-id-type="doi">10.3367/UFNr.0180.201011a.1121</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib23">
<label>23</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Rosen</surname>
<given-names>N</given-names>
</name>
</person-group>
<year>1940</year>
<source>Phys. Rev.</source>
<volume>57</volume>
<fpage>147</fpage>
<lpage>150</lpage>
<page-range>147–50</page-range>
<pub-id pub-id-type="doi">10.1103/PhysRev.57.147</pub-id>
</element-citation>
</ref>
<ref id="jpg425190bib24">
<label>24</label>
<element-citation publication-type="journal">
<person-group person-group-type="author">
<name>
<surname>Rosen</surname>
<given-names>N</given-names>
</name>
</person-group>
<year>1973</year>
<source>Gen. Rel. Grav.</source>
<volume>4</volume>
<fpage>435</fpage>
<lpage>447</lpage>
<page-range>435–47</page-range>
<pub-id pub-id-type="doi">10.1007/BF01215403</pub-id>
</element-citation>
</ref>
</ref-list>
</back>
</article>
</istex:document>
</istex:metadataXml>
<mods version="3.6">
<titleInfo>
<title>Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
</titleInfo>
<titleInfo type="alternative" contentType="CDATA">
<title>Superluminal neutrino phenomenon as a result of the equivalence principle violation</title>
</titleInfo>
<name type="personal">
<namePart type="given">O F</namePart>
<namePart type="family">Batsevych</namePart>
<affiliation>89, Norway</affiliation>
<affiliation>E-mail: o-batsev@online.no</affiliation>
<role>
<roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">R B</namePart>
<namePart type="family">Kapustiy</namePart>
<affiliation>8, Lviv 79035, Ukraine</affiliation>
<affiliation>E-mail: r.kapustiy@gmail.com</affiliation>
<role>
<roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="research-article" displayLabel="research-article"></genre>
<subject>
<genre>article-type</genre>
<topic>Paper</topic>
</subject>
<subject>
<genre>section</genre>
<topic>Particle Physics</topic>
</subject>
<originInfo>
<publisher>IOP Publishing</publisher>
<dateIssued encoding="w3cdtf">2012-08</dateIssued>
<dateCreated encoding="w3cdtf">2012-06-27</dateCreated>
<copyrightDate encoding="w3cdtf">2012</copyrightDate>
</originInfo>
<language>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
<languageTerm type="code" authority="rfc3066">en</languageTerm>
</language>
<physicalDescription>
<internetMediaType>text/html</internetMediaType>
</physicalDescription>
<abstract>In this paper we show that the recently detected superluminal neutrino motion, which now is believed to be the result of a possible technical fault in the experiment, can alternatively be explained by the absence of the gravitational mass of the neutrino, and as a result, an absence of its interaction with a gravitational field. The neutrino velocity theoretically predicted in this paper is in full agreement with the experimental data obtained by the OPERA collaboration. The conducted calculations also predict a significant anisotropy of the neutrino velocity measurement depending on the direction of the Earths motion relative to the Galaxy, which allows for the validation of the obtained results.</abstract>
<note type="footnotes">Retired from: Department of Theoretical Physics, Ivan Franko National University of Lviv, Drahomanov St. 12, Lviv 79005, Ukraine.</note>
<subject>
<genre>author-pacs</genre>
<topic>04.20.Cv</topic>
<topic>13.15.g</topic>
<topic>98.35.a</topic>
</subject>
<subject>
<genre>Keywords</genre>
<topic>superluminal neutrino</topic>
<topic>OPERA</topic>
<topic>galaxy</topic>
<topic>equivalence principle</topic>
</subject>
<relatedItem type="host">
<titleInfo>
<title>Journal of Physics G Nuclear and Particle Physics</title>
</titleInfo>
<genre type="Journal">journal</genre>
<identifier type="ISSN">0954-3899</identifier>
<identifier type="eISSN">1361-6471</identifier>
<identifier type="PublisherID">jpg</identifier>
<part>
<date>2012</date>
<detail type="volume">
<caption>vol.</caption>
<number>39</number>
</detail>
<detail type="issue">
<caption>no.</caption>
<number>8</number>
</detail>
<extent unit="pages">
<total>9</total>
</extent>
</part>
</relatedItem>
<identifier type="istex">065AAAB89A3324EF85C29E2FD813C0B24F5A0332</identifier>
<identifier type="DOI">10.1088/0954-3899/39/8/085008</identifier>
<identifier type="href">http://stacks.iop.org/JPhysG/39/085008</identifier>
<identifier type="ArticleID">jpg425190</identifier>
<accessCondition type="use and reproduction" contentType="copyright">2012 IOP Publishing Ltd</accessCondition>
<recordInfo>
<recordContentSource>IOP</recordContentSource>
</recordInfo>
</mods>
</metadata>
<serie></serie>
</istex>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Musique/explor/OperaV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000193 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000193 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Musique
   |area=    OperaV1
   |flux=    Istex
   |étape=   Corpus
   |type=    RBID
   |clé=     ISTEX:065AAAB89A3324EF85C29E2FD813C0B24F5A0332
   |texte=   Superluminal neutrino phenomenon as a result of the equivalence principle violation
}}

Wicri

This area was generated with Dilib version V0.6.21.
Data generation: Thu Apr 14 14:59:05 2016. Site generation: Thu Oct 8 06:48:41 2020