Length contraction in a current carrying wire?

[Per Oni]

Which is roughly the same answer I’ve given in post #44 .

So what’s the difference between us? I want to know why the –ve charge density doesn’t increase in a non moving lab frame, not even for the most massive currents. You are apparently happy to accept the facts and to get on with life. (perhaps not a bad idea).

 

[Dale]

I still don't understand your confusion on this point. Again, there is no lattice for the electrons so they are free to take any spacing that satisfies the laws and the boundary conditions.

You seem to understand that everything in the lab frame follows Maxwell's equations, and you seem to understand that when you Lorentz transform into the "drift" frame you get correct results in that frame also. Do you possibly think that Maxwell's equations should be violated in the lab frame for large currents?

I don't think it is a matter of me being happy to accept the facts. The facts are empirical data and there is never any question of accepting them or not; you must accept them or you are not doing science. In my mind the point is that the theories fit the facts and that is what makes me happy to accept the theories and get on with life.

 

[Per Oni]

there is no lattice for the electrons so they are free to take any spacing that satisfies the laws and the boundary conditions.

You seem to understand that everything in the lab frame follows Maxwell's equations, and you seem to understand that when you Lorentz transform into the "drift" frame you get correct results in that frame also.

That almost sounds that you could go along with the statement that in a drift frame conduction electrons are spread out.

 

[Dale]

Certainly. The distance between conduction electrons in the drift frame is larger than the distance between electrons in the lab frame. In fact, the distance between electrons in the drift frame is larger than the distance between electrons in any other frame since the proper distance is always greater than or equal to the coordinate distance.

 

[Per Oni]

Just some thoughts.

In their rest frame the conduction electrons must all move apart a little and therefore end up forming a longer length than the lattice. In the lab frame this expansion is not observed but it must be there in the drift frame to start with. These electrons see the lattice contracted but they still feel a force somehow which moves them apart. How do the electrons know how far to move? What force drives them apart?

 

[Dale]

How do the electrons know how far to move? What force drives them apart?

The EM-field (Maxwell's equations, especially Gauss' law). Just like in the lab frame.