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At 12:35 AM 5/16/01 -0700, David Rutherford wrote:as
"How can you admit that vxE/c^2, which is the same as curl(A), is
specified, and then turn around and deny that v.E/c^2, which is the same
-div(A), is specified?"
1) Let's tone down the rhetoric. This is not a cross-examination.
2) It is not generally true that v.E is related to div(A).
3) Let's focus on A, and use the standard textbook definition thereof. And
let's start by asking which things are _observable_ (which is not quite the
same as _specified_; see item (4)).
3a) It turns out that curl(A) is observable.
Specifically: curl(A) = B, and B is observable.
3b) It turns out that div(A) is not observable.
4) Gauge invariance is a freedom.
4a) If you want, you can _specify_ div(A), by exercise of gauge freedom.
That's your freedom.
4b) If I want, I can specify div(A) differently, or not at all.
That's my freedom.