Relative difference in laws of electrodynamics

[TrickyDicky]

Actually I see Dalespam already mentioned ROS in #26.

 

[Q-reeus]

It is IMHO as Q-reeus says, a paradox that is fully solved by the relativity of simultaneity set in Minkowski spacetime.
Just like two spacelike separated observers may not agree about the causality of certain events, if we consider the loop as spatially extended, two observers may disagree about what happens, that is because in relativity only spacetime is well defined, not the space slice.

Quite agree TrickyDicky and more succinctly expressed than myself, but (and it won't be real soon from me) looks like some convincing calculations will be in order, to prove it one way or the other. One thing I am almost 100% certain about is that length contraction of the moving loop in frame S' does not capture the non-simultaneity relevant here - those clocks on the periphery will be quite out of sync in S' notwithstanding the squashed shape of loop they ride on. Also, the circulation of E must be an intrinsic, intensive feature, not some effective internal field arising from any special material interactions in the loop conductor. Hence a Feynman disk or similar will rotate in response to an intrinsic curl E no differently than a current will circulate in a conducting loop - with the conceivable caveat that induced surface charges are negligible; well satisfied for a very thin loop. Must go.

 

[PAllen]

Quite agree TrickyDicky and more succinctly expressed than myself, but (and it won't be real soon from me) looks like some convincing calculations will be in order, to prove it one way or the other. One thing I am almost 100% certain about is that length contraction of the moving loop in frame S' does not capture the non-simultaneity relevant here - those clocks on the periphery will be quite out of sync in S' notwithstanding the squashed shape of loop they ride on. Also, the circulation of E must be an intrinsic, intensive feature, not some effective internal field arising from any special material interactions in the loop conductor. Hence a Feynman disk or similar will rotate in response to an intrinsic curl E no differently than a current will circulate in a conducting loop - with the conceivable caveat that induced surface charges are negligible; well satisfied for a very thin loop. Must go.

The problem is that in the frame of the wire loop at rest, you have some shape at rest. There can be nothing influencing the current except the precise E and B fields. These are the most complex in this frame (for this problem), but they are still nothing but a Poincare transform of an axially symmetric Coulomb field. This does lead to a field with mixed E and B, that does not have axial symmetry, and is time dependent. But the complete explanation must, then, boil down to how this field interacts with a stationary conducting loop of some general shape.

 

[pervect]

I spun off a new (but related) thread to explore what happens when you "boost" a neutral loop of wire carrying a current I. My initial results (I don't thin I've made an error, but it's possible) are that Kirchoff's current law is not satisfied in the usual manner after the boost.