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Feb14-13, 11:16 AM
P: 36
Quote Quote by jtbell View Post
[I took too long to write this, and Jano slipped in before me.]

Yes indeed! And so is the distinction between electric and magnetic fields.

Consider two stationary charges, one above the other from your point of view as you stand in front of them, and separated by some distance. Each charge produces (only) an electric field, which exerts an electric force on the other charge. If the charges are free to move, they move towards or away from each other depending on whether they are "like" or "unlike" charges.

Now imagine running past the two charges. From your new point of view, the charges are both in motion. In addition to the electric fields and forces, each charge now produces a magnetic field which exerts a magnetic force on the other charge.

Clearly the net effect of the electric and magnetic forces in the second case must be the "same" as the effect of the electric forces in the first case, in terms of the motion of the charges, after taking into account the the difference in your own motion. After all, the charges don't "know" whether you're standing still or running.

We say nowadays that electric and magnetic fields and forces are merely different aspects of a single unified electromagnetic field and electromagnetic force. If we know the electric and magnetic fields in one reference frame (e.g. the one you use when you're standing still), and the relative velocity of another reference frame (e.g. the one you use when you're running), we ought to be able to calculate the fields in the second frame. That is, we ought to be able to transform the fields from one frame to the other.

The question of how to do this in a way that is consistent with how the laws of mechanics transform between reference frames, was a major theoretical puzzle in the late 1800s, which led ultimately to Einstein's Special Theory of Relativity.
I had no idea that electromagnetics had so many relativistic components! So, correct me if i'm wrong, but let's say you're running towards the charges and observing an electric field:

There is one true underlying reality in regards to their actual state. To arrive at that state, various observers at various speeds will view differently rendered versions of the same event, witnessing varying proportions of electric and magnetic fields in use (depending on their speeds?), which all reconcile the event with it's true mathematical reality, where the specific nature of the "reconciliation" is based on their frame of reference?