<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2002000200012</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Superluminal rates of separation and EPR photons]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Karles]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Perez Rojas]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Física ]]></institution>
<addr-line><![CDATA[Medellín Antioquia]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Instituto de Cibernética, Matemática y Física Grupo de Física Teórica ]]></institution>
<addr-line><![CDATA[La Habana ]]></addr-line>
<country>Cuba</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2002</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2002</year>
</pub-date>
<volume>48</volume>
<numero>2</numero>
<fpage>150</fpage>
<lpage>154</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2002000200012&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2002000200012&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2002000200012&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[We consider rates of separation between two particles greater than c (which is not in contradiction with special relativity) in understanding some conflict between special relativity and quantum mechanics found by moving observers of correlated EPR pairs of photons. The photon frequencies observed in the moving frame have opposite shifts than those found when the detectors are fixed in that frame. By observing from two different frames the arrival of a photon from an EPR pair to a given detector, it is illustrated how the measurement of the simultaneous arrival of the other photon of the EPR pair in one frame disturbs the measurement in the other frame.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Consideramos velocidades de separación entre dos partículas mayores que c (lo que no está en contradicción con la relatividad especial) en la búsqueda de la comprensión del conflicto entre la relatividad especial y la mecánica cuántica, encontrado por observadores móviles de pares correlacionados de fotones EPR en movimiento. Las frecuencias de los fotones observadas en el marco de referencia móvil tiene desplazamiento opuesto al que se encuentra cuando los detectores están fijos en tal marco. Mediante la observación, desde dos marcos diferentes, del arribo de uno de los fotones de un par EPR a un detector dado, se ilustra cómo la medición del arribo simultáneo del fotón contraparte en uno de los marcos, perturba la medición del arribo simultáneo de dicho fotón en cualquier otro marco.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Superluminal velocities]]></kwd>
<kwd lng="en"><![CDATA[correlated EPR photon pairs]]></kwd>
<kwd lng="es"><![CDATA[Velocidades superiores a la de la luz]]></kwd>
<kwd lng="es"><![CDATA[par de fotones correlacionados en EPR]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Ense&ntilde;anza</font></p>     <p align="justify">&nbsp;</p>  	    <p align="center"><font face="verdana" size="4"><b>Superluminal rates of separation and EPR photons</b></font></p> 	    <p align="center">&nbsp;</p>      <p align="center"><font face="verdana" size="2"><b>J. Karles<sup>1</sup>, H. Perez Rojas<sup>1,2,3</sup></b></font></p>     <p align="center">&nbsp;</p>      <p align="justify"><font face="verdana" size="2"><sup>1</sup> <i>Departamento de F&iacute;sica, Universidad Nacional, Sede Medell&iacute;n, Apartado Aereo 3840, Medell&iacute;n, Colombia.</i> email: <a href="mailto:jkarles@perseus.unalmed.edu.co">jkarles@perseus.unalmed.edu.co</a></font></p>  	    <p align="justify"><font face="verdana" size="2"><sup>2</sup> <i>Helsinki Institute</i> <i>of</i> <i>Physics, Siltavuorenpenger 20C, FIN&#45;00014, Helsinki, Finland.</i></font></p>  	    <p align="justify"><font face="verdana" size="2"><sup>3</sup> <i>Grupo de F&iacute;sica Te&oacute;rica, Instituto de Cibern&eacute;tica Matem&aacute;tica y F&iacute;sica, Calle E No. 309, Vedado, La Habana 4, Cuba.</i> email: <a href="mailto:hugo@cidet.icmf.inf.cu">hugo@cidet.icmf.inf.cu</a></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">Recibido el 9 de mayo de 2001.    <br> 	Aceptado el 9 de octubre de 2001.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>  	    <p align="justify"><font face="verdana" size="2">We consider rates of separation between two particles greater than <i>c</i> (which is not in contradiction with special relativity) in understanding some conflict between special relativity and quantum mechanics found by moving observers of correlated EPR pairs of photons. The photon frequencies observed in the moving frame have opposite shifts than those found when the detectors are fixed in that frame. By observing from two different frames the arrival of a photon from an EPR pair to a given detector, it is illustrated how the measurement of the simultaneous arrival of the other photon of the EPR pair in one frame disturbs the measurement in the other frame.</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Keywords:</b> Superluminal velocities; correlated EPR photon pairs.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>  	    <p align="justify"><font face="verdana" size="2">Consideramos velocidades de separaci&oacute;n entre dos part&iacute;culas mayores que c (lo que no est&aacute; en contradicci&oacute;n con la relatividad especial) en la b&uacute;squeda de la comprensi&oacute;n del conflicto entre la relatividad especial y la mec&aacute;nica cu&aacute;ntica, encontrado por observadores m&oacute;viles de pares correlacionados de fotones EPR en movimiento. Las frecuencias de los fotones observadas en el marco de referencia m&oacute;vil tiene desplazamiento opuesto al que se encuentra cuando los detectores est&aacute;n fijos en tal marco. Mediante la observaci&oacute;n, desde dos marcos diferentes, del arribo de uno de los fotones de un par EPR a un detector dado, se ilustra c&oacute;mo la medici&oacute;n del arribo simult&aacute;neo del fot&oacute;n contraparte en uno de los marcos, perturba la medici&oacute;n del arribo simult&aacute;neo de dicho fot&oacute;n en cualquier otro marco.</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Palabras clave:</b> Velocidades superiores a la de la luz; par de fotones correlacionados en EPR.</font></p>  	    ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">PACS: 03.65.Bz</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmf/v48n2/v48n2a12.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Acknowledgement</b></font></p>  	    <p align="justify"><font face="verdana" size="2">The authors thank H.H. Garc&iacute;a&#45;Compe&aacute;n, B. Mielnik, and R. Tarrach for discussion, criticism and comments. One of the authors (H.P.R) thank Prof. M. Chaichian and the University of Helsinki, as well as Universidad Nacional de Colombia, Medellin, for hospitality. The partial support from the Academy of Finland under project No. 163394 is also greately acknowledged by H. P. R.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">1. J.S. Bell, <i>Speakable and unspeakable in quantum mechanics</i> (Cambridge: University Press, 1987).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285344&pid=S0035-001X200200020001200001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    ]]></body>
<body><![CDATA[<!-- ref --><p align="justify"><font face="verdana" size="2">2. R. Chiao, <i>Phys. Rev.</i> A 48 (1993) R34.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285346&pid=S0035-001X200200020001200002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">3. J.I. Latorre, P. Pascual, R. Tarrach, <i>Nuc. Phys.</i> B437 (1995) 60.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285348&pid=S0035-001X200200020001200003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">4. A. Einstein, <i>Ann. der Physik</i> 17 (1905) 871.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285350&pid=S0035-001X200200020001200004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">5. R.P. Feynman, R.S. Leighton and M. Sands M, <i>The Feynman's Lectures on Physics I,</i> (Massachusetts: Addison Wesley 1963) 15.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285352&pid=S0035-001X200200020001200005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">6. V.A. Fock, <i>The Theory of Space Time and Gravitation</i> (London: Pergamon Press, 1964) 45</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285354&pid=S0035-001X200200020001200006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">7. A.D. Linde, <i>Inflation and Quantum Cosmology</i> (Boston: Academic Press, 1991).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285355&pid=S0035-001X200200020001200007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">8. J. Karles, <i>Rev. Mex. Fis.</i> 38 (1992) 951.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285357&pid=S0035-001X200200020001200008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">9. J. von Neumann, <i>Mathematical Foundations</i> <i>of</i> <i>Quantum Mechanics</i> ( Princeton: Princeton University Press, 1955).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285359&pid=S0035-001X200200020001200009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">10. R. Penrose, <i>The Emperor's New Mind,</i> (New York:Penguin Books, 1991)</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285361&pid=S0035-001X200200020001200010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">11. Y. Aharonov, D.Z. Albert <i>Phys. Rev.</i> D 24 (1981) 359.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8285362&pid=S0035-001X200200020001200011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>      ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bell]]></surname>
<given-names><![CDATA[J.S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Speakable and unspeakable in quantum mechanics]]></source>
<year>1987</year>
<publisher-loc><![CDATA[Cambridge ]]></publisher-loc>
<publisher-name><![CDATA[University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chiao]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. A]]></source>
<year>1993</year>
<volume>48</volume>
<page-range>R34</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Latorre]]></surname>
<given-names><![CDATA[J.I.]]></given-names>
</name>
<name>
<surname><![CDATA[Pascual]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Tarrach]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nuc. Phys.]]></source>
<year>1995</year>
<volume>B437</volume>
<page-range>60</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Einstein]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ann. der Physik]]></source>
<year>1905</year>
<volume>17</volume>
<page-range>871</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Feynman]]></surname>
<given-names><![CDATA[R.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Leighton]]></surname>
<given-names><![CDATA[R.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Sands M]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Feynman's Lectures on Physics I]]></source>
<year>1963</year>
<page-range>15</page-range><publisher-loc><![CDATA[^eMassachusetts Massachusetts]]></publisher-loc>
<publisher-name><![CDATA[Addison Wesley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fock]]></surname>
<given-names><![CDATA[V.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Theory of Space Time and Gravitation]]></source>
<year>1964</year>
<page-range>45</page-range><publisher-loc><![CDATA[London ]]></publisher-loc>
<publisher-name><![CDATA[Pergamon Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Linde]]></surname>
<given-names><![CDATA[A.D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Inflation and Quantum Cosmology]]></source>
<year>1991</year>
<publisher-loc><![CDATA[Boston ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Karles]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Rev. Mex. Fis.]]></source>
<year>1992</year>
<volume>38</volume>
<page-range>951</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[von Neumann]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Foundations of Quantum Mechanics]]></source>
<year>1955</year>
<publisher-loc><![CDATA[Princeton ]]></publisher-loc>
<publisher-name><![CDATA[Princeton University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Penrose]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Emperor's New Mind]]></source>
<year>1991</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Penguin Books]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aharonov]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Albert]]></surname>
<given-names><![CDATA[D.Z.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. D]]></source>
<year>1981</year>
<volume>24</volume>
<page-range>359</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
