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Electric fields, magnetic fields and Lorentz frames

  1. Oct 21, 2006 #1
    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.
     
  2. jcsd
  3. Oct 22, 2006 #2

    Meir Achuz

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    Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.
     
  4. Oct 23, 2006 #3
    ok. would you be able to start me off though?
     
  5. Oct 23, 2006 #4

    Meir Achuz

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    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.
     
  6. Oct 24, 2006 #5
    yes i know what the F tensor is in terms of the components of E and B
     
    Last edited: Oct 24, 2006
  7. Oct 24, 2006 #6

    Meir Achuz

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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.
     
    Last edited: Oct 24, 2006
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