View source for The de Broglie Relations: Lorentz Invariance and Photons

{{Infobox paper
| title = The de Broglie Relations: Lorentz Invariance and Photons
| author = [[]]
| keywords = [[quantum optics]], [[anisotropic media]], [[special theory of relativity]], [[covariance]]
| published = 1988
| journal = [[Physics Essays]]
| volume = 1
| number = 2
| pages = 102-108
}}

==Abstract==

<em>A<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>simple covariant derivation of the de Broglie relations breaks down<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>when one considers propagation of light in an anisotropic medium.<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>This breakdown results in two distasteful conclusions. The first is<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>that the de Broglie relations are not completely universal and<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>their covariance is restricted. The second is that wave-particle duality<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>is not universal. In this paper a resolution of these<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>problems is suggested, a resolution that is an extrapolation of<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>ideas of de Broglie and Andrade e Silva. The relations<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>are generalized for propagation in anisotropic media by defining a<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>new phase wave with wave vector</em> <img border="0" alt="1-vector" align="bottom" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000001000002000102000001%3A0%3A0%3A28&amp;t=a&amp;d=a" /> ''in the direction<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>of energy transport and distinct from the conventional electromagnetic wave.<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>The introduction of'' <img border="0" alt="1-vector" align="bottom" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000001000002000102000001%3A0%3A0%3A28&amp;t=a&amp;d=a" /> ''follows the method by which de<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>Broglie associated a wave with an electron. The magnitude of''<span style="FONT-SIZE: x-small"><sup>&nbsp;</sup><img border="0" alt="1-vector" align="bottom" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000001000002000102000001%3A0%3A0%3A28&amp;t=a&amp;d=a" /></span> ''is'' <img border="0" alt="omega" align="bottom" src="http://physicsessays.aip.org/stockgif3/ohgr.gif" />u/c<sup><span style="FONT-SIZE: x-small">2</span></sup> ''where <img border="0" alt="omega" align="bottom" src="http://physicsessays.aip.org/stockgif3/ohgr.gif" /> is the angular frequency and''<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>u ''the velocity of energy transport. The physical meaning of''<span style="FONT-SIZE: x-small"><sup>&nbsp;</sup><img border="0" alt="1-vector" align="bottom" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000001000002000102000001%3A0%3A0%3A28&amp;t=a&amp;d=a" /></span> ''and the covariance of physical laws in the presence<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>of matter are discussed. An experiment is described that would<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>test the existence of the phase wave associated with the<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>new wave vector'' <img border="0" alt="1-vector" align="bottom" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000001000002000102000001%3A0%3A0%3A28&amp;t=a&amp;d=a" />. ''This experiment is essentially a Hanbury<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>Brown-Twiss correlation experiment carried out within an anisotropic crystal.''

[[Category:Scientific Paper|broglie relations lorentz invariance photons]]

[[Category:Relativity|broglie relations lorentz invariance photons]]

[[Category:Quantum Theory]]