Why do changing magnetic fields produce electric fields?

[Jeff Rosenbury]

Zahid Iftikhar asked why charges get separated in a changing magnetic field over in the EE forum. I pointed him to Maxwell's equations and also pointed out we took them to be observational and axiomatic.

Yet it occurred to me there might be an reason in quantum probability.

So is there a reason a time varying magnetic field produces an electric field and vice versa? (Of course I understand that any quantum explanation will also be predicated on observation, so it's at best part of the answer, but I'm curious. It's one of my vices.)

 

[DEvens]

The relationship between electric and magnetic fields is more to do with special relativity. It all comes down to the 4-vector potential $A_{\mu}$, its spatial and time derivatives, and how they vary under changes in velocity.

https://en.wikipedia.org/wiki/Relativistic_electromagnetism
https://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism

 

[jtbell]

By assuming that a particle's quantum field has U(1) gauge symmetry, one can derive Maxwell's equations in their QED formulation. Try a Google search for "u(1) gauge symmetry maxwell's equations" to turn up some information... I'm in a bit of a hurry right now.

Of course, this begs the question, "why do quantum fields have U(1) gauge symmetry?" Maybe a turtle somewhere knows...

 

[DEvens]

By assuming that a particle's quantum field has U(1) gauge symmetry, one can derive Maxwell's equations in their QED formulation. Try a Google search for "u(1) gauge symmetry maxwell's equations" to turn up some information... I'm in a bit of a hurry right now.

Of course, this begs the question, "why do quantum fields have U(1) gauge symmetry?"

Possibly you can do that with one or two more assumptions. For example, the assumptions that the field for the photon is a vector of spin 1, and that it sits in the spin rep corresponding to the usual $F_{\mu\nu}$. That would tell you that there is only one way that classical E&M could be quantized.

Historically it went the other way. The fields present in classical E&M were "turned into operators" to get a QM form of a field. With just a few little "tweaks" like making the matter fields spinors.

 

[Windadct]

Jeff, I follow your link over to here to see what is going on - I have never considered this to be QP -- in general the electrons are always moving (in orbit / cloud) around the atom / molecule. As such it still obeys Lenz and creates a Mag Field - the so as the general mag field near an electron changes it disrupts the electron with enough energy to separate from it's atom molecule ( the motion of the electron now will try to counter act the mag filed allied to it). Same as an electron beam is bent by a magnetic field ( there the electron can be moving though a fixed field).

So the QP question really would be is WHY is there Lenz Law - for this there may be a valid question. But I believe that is much more advanced than Zahid's original post - which I read as how does the changing magnetic field separate charge - which I took as separate an electron from it's atom, to that simply because a force is applied to it according to Lenz law, derived from Maxwels, and then beyond that may be a good QP. As Prof Lewin indicates this is similar to the force applied to an electron in an E field.

 

[Jeff Rosenbury]

Windadct, I assumed he was asking about a generator winding. But I decided to follow up on the more general question and I'm glad I did.

I'm sure prof. Lewin's lecture is great, but I have limited bandwidth, so can't watch it now. (@#$%^&* satellite connection.)

You are right that this is advanced stuff for us EEs. It's just at the edge of my learning envelope. For example, until today I thought all gauge groups were the same as U(1) groups and didn't have any of the words. I knew about quaternions, but I hadn't made the connection. At my advanced age, learning the vocabulary is maybe the hardest part.

I learned a lot. Thanks to everyone who responded.

 

[bhobba]

As pointed out in other posts U(1) gauge symmetry is its rock bottom essence:
http://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

But even without QM its pretty inevitable:
http://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html

Thanks
Bill