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I know that electric charge is lorentz invariant quantity and I can easily think of experiment to check that. Is a though experiment that can prove that also?

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Rather than on a thought experiment, our assumption of Lorentz invariance of electric charge is based on Lorentz invariance of Maxwell's equations. The latter was the reason for developing the theory of relativity and invariance of electric charge came as a natural consequence. If charge were not invariant, the theory would have to be strongly modified (Maxwell's equations would break down when changing reference frames).

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  • $\begingroup$ I agree what you said is right but I don't feel it's a fully satisfying answer. The question could be stated without a reference to Maxwell equations / Special relativity. How is it a priori possible to conclude that two observers agree on the electric content of an electron? $\endgroup$ – Yair Jan 16 '14 at 3:57
  • $\begingroup$ @Yair Surely you would look at the way the effects of that charge transformed, which would lead you to ... Maxwell's equations plus the Lorentz force rule. $\endgroup$ – dmckee --- ex-moderator kitten Jan 16 '14 at 4:09
  • $\begingroup$ Can I say that the invariance of electic charge cannot be deduced from though expriments only but is a consequence of experimental fact? $\endgroup$ – Yair Jan 16 '14 at 4:28
  • $\begingroup$ Even thought experiments are based on $some$ experimental facts. So if you could find example of a thought experiment from which the Lorentz invariance of electric charge could be derived, still it would be a consequence of $some$ experimental fact. $\endgroup$ – Ján Lalinský Jan 16 '14 at 13:49
  • $\begingroup$ @Yair You always measure charge by it's effects. There is no other way to measure charge. Note that the Coulomb is defined as a Ampere-second and the Ampere is defined in terms of the force between current carrying wires. $\endgroup$ – dmckee --- ex-moderator kitten Jan 16 '14 at 14:57
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My textbook says that if electric charge was not invariant under Lorentz's transformation, then atoms would have charge. We know that atoms are neutral, so electric charge must be invariant.

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