Relativistic Invariance

  • Thread starter Ed Quanta
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If I were to attempt to prove that the dot product of an electric and magnetic field is invariant under the conditions of Einstein's Special Theory of Relativity, how would I do this? Would the proof be very involved and complicated? Or should I just use hypothetical magnetic and electric fields and demonstrate how the dot product is unchanged when dealing with relativistic frames of reference?
 

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DW
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Originally posted by Ed Quanta
If I were to attempt to prove that the dot product of an electric and magnetic field is invariant under the conditions of Einstein's Special Theory of Relativity, how would I do this? Would the proof be very involved and complicated? Or should I just use hypothetical magnetic and electric fields and demonstrate how the dot product is unchanged when dealing with relativistic frames of reference?
Its not too complicated. E dot B is what you get for 1/4 the inner product of the electromagnetic tensor with the electromagnetic duel tensor. Inner products of tensors resulting in scalars are invariant which is suffucient to prove that E dot B is invariant. Why do you ask?
 

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