Re: "4/3 Problem" Resolution (fwd), comment on

["John S. Denker" <jsd@MONMOUTH.COM>]

At 12:35 AM 5/16/01 -0700, David Rutherford wrote:

> "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 as
> -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.

5) There is nothing wrong with choosing to work in a particular gauge,
provided you follow some simple rules:
 -- Keep track of whatever assumptions have been made.
 -- Communicate these assumptions clearly.  Don't claim that a
    non-invariant result represents the general case.
 -- Don't change horses in mid-stream, i.e. don't take a non-invariant
    expression (valid under one set of assumptions) and try to apply it
    under some other set of assumptions.