Electric fields, magnetic fields and Lorentz frames

golfingboy07
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Not sure how to go about proving that if E and B are perpendicular in one Lorentz frame they are perpendicular in all Lorentz frames.
 
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Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.
 
ok. would you be able to start me off though?
 
Do you know the tensor F in terms of E and B?
If you don't know that much, you can't start the problem.
Go back to the textbook.
 
yes i know what the F tensor is in terms of the components of E and B
 
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Find the dual tensor
{\cal F}_{\mu\nu}=\epsilon_{\mu\nu\rho\sigma}F^{\rho\sigma}.
Then form the scalar
{\cal F}_{\mu\nu}F^{\mu\nu}.
This will be proportional to {\bf E\cdot B}.
My latex didn't work, so try to read the above. Sorry.
 
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