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Isotropic line
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<h2 id="relativity">Relativity</h2> <p>Isotropic lines have been used in cosmological writing to carry light. For example, in a mathematical encyclopedia, light consists of <a href="/facts/Photon/mFNhAEzA">photons</a>: "The <a href="/facts/Worldline/rluamMcf">worldline</a> of a zero rest mass (such as a non-quantum model of a photon and other elementary particles of mass zero) is an isotropic line."<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> For isotropic lines through the origin, a particular point is a <a href="/facts/Null_vector/sjkdQtdS">null vector</a>, and the collection of all such isotropic lines forms the <a href="/facts/Light_cone/GwJ0Yhjf">light cone</a> at the origin. </p><p><a href="/facts/%C3%89lie_Cartan/Uvhkp66S">Élie Cartan</a> expanded the concept of isotropic lines to <a href="/facts/Multivector/brM3rUny">multivectors</a> in his book on <a href="/facts/Spinors_in_three_dimensions/f9or1bg5">spinors in three dimensions</a>.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> </p> <ul><li>Pete L. Clark, <a href="http://www.math.miami.edu/~armstrong/685fa12/pete_clark.pdf">Quadratic forms chapter I: Witts theory</a> from <a href="/facts/University_of_Miami/2rPFYefT">University of Miami</a> in <a href="/facts/Coral_Gables,_Florida/CcMbTzfg">Coral Gables, Florida</a>.</li> <li><a href="/facts/O._Timothy_O%27Meara/4ST6KEXf">O. Timothy O'Meara</a> (1963, 2000) <i>Introduction to Quadratic Forms</i>, page 94</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Edmond Laguerre (1870) "Sur l’emploi des imaginaires en la géométrie", Oeuvres de Laguerre 2: 89 <a href="/wiki/Edmond_Laguerre" target="_blank">/wiki/Edmond_Laguerre</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Edmond Laguerre (1870) "Sur l’emploi des imaginaires en la géométrie", Oeuvres de Laguerre 2: 89 <a href="/wiki/Edmond_Laguerre" target="_blank">/wiki/Edmond_Laguerre</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>C. E. Springer (1964) Geometry and Analysis of Projective Spaces, page 141, W. H. Freeman and Company <a href="/wiki/W._H._Freeman_and_Company" target="_blank">/wiki/W._H._Freeman_and_Company</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Emil Artin (1957) Geometric Algebra, page 119 via Internet Archive <a href="/wiki/Emil_Artin" target="_blank">/wiki/Emil_Artin</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Encyclopedia of Mathematics World line <a href="/wiki/Encyclopedia_of_Mathematics" target="_blank">/wiki/Encyclopedia_of_Mathematics</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Cartan, Élie (1981) [1938], The theory of spinors, New York: Dover Publications, p. 17, ISBN 978-0-486-64070-9, MR 0631850 <a href="978-0-486-64070-9" target="_blank">978-0-486-64070-9</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> </ol>