Most recent edit on 2007-10-27 01:37:53 by CharlesFrancis

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Lorentz Boost Applied to Faraday for a Static Electric Field

Write the first contraction in matrix form

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Lorentz Boost Applied to Faraday For a static Electric Field

Write the second multiplication in matrix form

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Edited on 2007-10-27 01:32:27 by CharlesFrancis

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Edited on 2007-10-27 01:28:54 by CharlesFrancis

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Edited on 2007-10-27 01:27:21 by CharlesFrancis

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Lorentz Boost Applied to Faraday For a static Electric Field

I include this calculation to illustrate that the very succinct Einstein notation for tensors should be understood as representing arrays, or matrices. Anyone learning general relativity should do a number of similar calculations in order to become comfortable with the notation. I make no apologies for errant minus signs — you should have done it yourself.
Cancel terms, using the Lorentz factor
← Return

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↑  Lorentz Boost Applied to Faraday For a static Electric Field

I include this calculation as an illustration that the very succinct Einstein notation for tensors should be understood as representing arrays, or matrices. Anyone learning general relativity should do a number of similar calculations in order to become comfortable with the notation. I make no apologies for any errant minus signs — you should have done it yourself.
cancel terms, using the Lorentz factor
Return ← Top ↑

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Edited on 2007-10-27 01:22:18 by CharlesFrancis

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cancel terms, using the Lorentz factor



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cancel terms, using the Lorentz factor

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Edited on 2007-10-27 01:19:31 by CharlesFrancis

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↑  Lorentz Boost Applied to Faraday For a static Electric Field

cancel terms, using the Lorentz factor



Deletions:

↑  Lorentz Boost Applied to Faraday For a static Electric Field

cancel terms, using the Lorentz factor

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Edited on 2007-10-27 01:15:05 by CharlesFrancis

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↑  Lorentz Boost Applied to Faraday For a static Electric Field

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↑  Lorentz Boost Applied to Faraday For a static Electric Field

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Edited on 2007-10-27 01:13:57 by CharlesFrancis

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↑  Lorentz Boost Applied to Faraday For a static Electric Field

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↑  Lorentz Boost Applied to Faraday For a static Electric Field

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Edited on 2007-10-27 01:13:25 by CharlesFrancis

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↑  Lorentz Boost Applied to Faraday For a static Electric Field Return ← Top ↑

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href="http://www.teleconnection.info/rqg/IntroductionToTensors#ElectromagneticForce"»> ↑</a>  Lorentz Boost Applied to Faraday For a static Electric Field href="http://www.teleconnection.info/rqg/IntroductionToTensors#ElectromagneticForce">Return ← Top ↑

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Oldest known version of this page was edited on 2007-10-27 01:12:42 by CharlesFrancis []
 

href="http://www.teleconnection.info/rqg/IntroductionToTensors#ElectromagneticForce"»> ↑</a>  Lorentz Boost Applied to Faraday For a static Electric Field I include this calculation as an illustration that the very succinct Einstein notation for tensors should be understood as representing arrays, or matrices. Anyone learning general relativity should do a number of similar calculations in order to become comfortable with the notation. I make no apologies for any errant minus signs — you should have done it yourself. Write the second multiplication in matrix form <img alt="TensorSub-1" src="images/tensors/TensorSub-1.gif" align="texttop" vspace="0"> Multiply matrices <img alt="TensorSub-2" src="images/tensors/TensorSub-2.gif" align="texttop" vspace="0"> Transpose, so that we can multiply rows by columns in the usual way. <img alt="TensorSub-3" src="images/tensors/TensorSub-3.gif" align="texttop" vspace="0"> Multiply matrices <img alt="TensorSub-4" src="images/tensors/TensorSub-4.gif" align="texttop" vspace="0"> cancel terms, using the Lorentz factor <img alt="TensorSub-5" src="images/tensors/TensorSub-5.gif" align="texttop" vspace="0"> <img alt="TensorSub-6" src="images/tensors/TensorSub-6.gif" align="texttop" vspace="0"> Transpose back <img alt="TensorSub-7" src="images/tensors/TensorSub-7.gif" align="texttop" vspace="0"> href="http://www.teleconnection.info/rqg/IntroductionToTensors#ElectromagneticForce">Return ← Top ↑