View source for Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy

{{Infobox paper
| title = Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy
| author = [[Allen D Allen]]
| keywords = [[refraction]], [[Planck's equation]], [[Snell's law]], [[mass and energy conservation]], [[photon]], [[particle]], [[relativistic spacetime]], [[wavelength]], [[self-interference]], [[Heisenberg uncertainty principle]]
| published = 1988
| journal = [[Physics Essays]]
| volume = [[1]]
| number = [[2]]
| pages = 82-84
}}

==Abstract==

<em>By<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>direct substitution from</em> E = mc<sup><span style="FONT-SIZE: x-small">2</span></sup> ''and'' <img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" /> = h(mv)<sup><span style="FONT-SIZE: x-small">&#8722;1</span></sup>, ''energy becomes'' E = hc<sup><span style="FONT-SIZE: x-small">2</span></sup>(<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />v)<sup><span style="FONT-SIZE: x-small">&#8722;1</span></sup>. ''This<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>reduces to Planck's equation if, and only if'', v = c. ''It<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>follows from Snell's law that a photon undergoing refraction will<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>gain energy'' <img border="0" alt="sigma" align="bottom" src="http://physicsessays.aip.org/stockgif3/sgr.gif" />E = hc<sup><span style="FONT-SIZE: x-small">2</span></sup>[(<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />v)<sup><span style="FONT-SIZE: x-small">&#8722;1</span></sup> &#8722; (<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" /><sub><span style="FONT-SIZE: x-small">0</span></sub>C)<sup><span style="FONT-SIZE: x-small">&#8722;1</span></sup>], ''where'' <img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" /><sub><span style="FONT-SIZE: x-small">0</span></sub> ''is its wavelength'' in vacuo.<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>''This very small energy gain arises from work done on<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>the photon's mass by the refracting medium in decelerating the<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>photon from'' c ''to'' v. ''The medium therefore looses internal<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>energy while the photon is passing through, regaining it when<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>the photon leaves to resume speed'' c. ''Photon momentum is<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>a linear, monotone-increasing function of speed'', p = hc(<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" /><sub><span style="FONT-SIZE: x-small">0</span></sub>v)<sup><span style="FONT-SIZE: x-small">&#8722;1</span></sup>. ''The reason photons<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>do not have rest mass is because they cannot rest<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>in space'' (v = 0) ''for the same reason massive particles cannot<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>rest in time'' (v = c): ''In either case the energy would<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>be infinite. EPR-type paradoxes can be resolved by replacing the<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>notion of self-interference with recognition of the fact that'' <img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" /><span style="FONT-SIZE: x-small"><sub>''x''</sub><sup>&nbsp;</sup></span>''is the extent of the'' x-''axis that is instantaneously occupied<sup><span style="FONT-SIZE: x-small">&nbsp;</span></sup>by a particle''.[[Category:Scientific Paper]]

[[Category:Relativity]]