Electric fields, magnetic fields and Lorentz frames

[golfingboy07]

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.

 

[Meir Achuz]

Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.

 

[golfingboy07]

ok. would you be able to start me off though?

 

[Meir Achuz]

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.

 

[golfingboy07]

yes i know what the F tensor is in terms of the components of E and B

 

[Meir Achuz]

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.