Difference between revisions of "Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy"
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==Abstract== | ==Abstract== | ||
| − | <em>By<sup><span style="FONT-SIZE: x-small"> </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">−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">−1</span></sup>. ''This<sup><span style="FONT-SIZE: x-small"> </span></sup>reduces to Planck's equation if, and only if'', v = c. ''It<sup><span style="FONT-SIZE: x-small"> </span></sup>follows from Snell's law that a photon undergoing refraction will<sup><span style="FONT-SIZE: x-small"> </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">−1</span></sup> − (<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">−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"> </span></sup>''This very small energy gain arises from work done on<sup><span style="FONT-SIZE: x-small"> </span></sup>the photon's mass by the refracting medium in decelerating the<sup><span style="FONT-SIZE: x-small"> </span></sup>photon from'' c ''to'' v. ''The medium therefore looses internal<sup><span style="FONT-SIZE: x-small"> </span></sup>energy while the photon is passing through, regaining it when<sup><span style="FONT-SIZE: x-small"> </span></sup>the photon leaves to resume speed'' c. ''Photon momentum is<sup><span style="FONT-SIZE: x-small"> </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">−1</span></sup>. ''The reason photons<sup><span style="FONT-SIZE: x-small"> </span></sup>do not have rest mass is because they cannot rest<sup><span style="FONT-SIZE: x-small"> </span></sup>in space'' (v = 0) ''for the same reason massive particles cannot<sup><span style="FONT-SIZE: x-small"> </span></sup>rest in time'' (v = c): ''In either case the energy would<sup><span style="FONT-SIZE: x-small"> </span></sup>be infinite. EPR-type paradoxes can be resolved by replacing the<sup><span style="FONT-SIZE: x-small"> </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> </sup></span>''is the extent of the'' x-''axis that is instantaneously occupied<sup><span style="FONT-SIZE: x-small"> </span></sup>by a particle''. | + | <em>By<sup><span style="FONT-SIZE: x-small"> </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">−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">−1</span></sup>. ''This<sup><span style="FONT-SIZE: x-small"> </span></sup>reduces to Planck's equation if, and only if'', v = c. ''It<sup><span style="FONT-SIZE: x-small"> </span></sup>follows from Snell's law that a photon undergoing refraction will<sup><span style="FONT-SIZE: x-small"> </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">−1</span></sup> − (<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">−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"> </span></sup>''This very small energy gain arises from work done on<sup><span style="FONT-SIZE: x-small"> </span></sup>the photon's mass by the refracting medium in decelerating the<sup><span style="FONT-SIZE: x-small"> </span></sup>photon from'' c ''to'' v. ''The medium therefore looses internal<sup><span style="FONT-SIZE: x-small"> </span></sup>energy while the photon is passing through, regaining it when<sup><span style="FONT-SIZE: x-small"> </span></sup>the photon leaves to resume speed'' c. ''Photon momentum is<sup><span style="FONT-SIZE: x-small"> </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">−1</span></sup>. ''The reason photons<sup><span style="FONT-SIZE: x-small"> </span></sup>do not have rest mass is because they cannot rest<sup><span style="FONT-SIZE: x-small"> </span></sup>in space'' (v = 0) ''for the same reason massive particles cannot<sup><span style="FONT-SIZE: x-small"> </span></sup>rest in time'' (v = c): ''In either case the energy would<sup><span style="FONT-SIZE: x-small"> </span></sup>be infinite. EPR-type paradoxes can be resolved by replacing the<sup><span style="FONT-SIZE: x-small"> </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> </sup></span>''is the extent of the'' x-''axis that is instantaneously occupied<sup><span style="FONT-SIZE: x-small"> </span></sup>by a particle''. |
| − | [[Category:Relativity]] | + | [[Category:Scientific Paper|work photons refraction improved symmetry consistent expression photon energy]] |
| + | |||
| + | [[Category:Relativity|work photons refraction improved symmetry consistent expression photon energy]] | ||
Latest revision as of 20:14, 1 January 2017
| Scientific Paper | |
|---|---|
| Title | Work Done on Photons During Refraction: Improved Symmetry From a More Consistent Expression for Photon Energy |
| Author(s) | 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
By direct substitution from E = mc2 and <img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" /> = h(mv)−1, energy becomes E = hc2(<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />v)−1. This reduces to Planck's equation if, and only if, v = c. It follows from Snell's law that a photon undergoing refraction will gain energy <img border="0" alt="sigma" align="bottom" src="http://physicsessays.aip.org/stockgif3/sgr.gif" />E = hc2[(<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />v)−1 − (<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />0C)−1], where <img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />0 is its wavelength in vacuo. This very small energy gain arises from work done on the photon's mass by the refracting medium in decelerating the photon from c to v. The medium therefore looses internal energy while the photon is passing through, regaining it when the photon leaves to resume speed c. Photon momentum is a linear, monotone-increasing function of speed, p = hc(<img border="0" alt="lambda" align="bottom" src="http://physicsessays.aip.org/stockgif3/lgr.gif" />0v)−1. The reason photons do not have rest mass is because they cannot rest in space (v = 0) for the same reason massive particles cannot rest in time (v = c): In either case the energy would be infinite. EPR-type paradoxes can be resolved by replacing the 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" />x is the extent of the x-axis that is instantaneously occupied by a particle.
