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So why was I confused? Because I accepted John's
potentials. They are not physical concepts defined
in terms of work per unit charge.
I wouldn't have said that.
1) What I call the potential most certainly is work per unit charge.
2) It is a potential in the mathematical sense.
3) It is agrees completely with what Feynman calls "the electric
potential" in section 4-3 of Volume II. He says (at the end of the
section) that it is measured relative to "some reference point".
I use delta_V to represent potential differences. Some of the
things I say about potential differences are not true about
absolute potentials (which I represent by V).
What is the evidence that my usage is less than 100%
traditional? I didn't invent gauge invariance!
A traditional model, on the other hand, does not
allow small objects to be references.
Says who?
(A traditional reference must be very very large to keep its
potential constant when its net charge is changing.
Hogwash. Anything you choose as a reference will be constant
by construction, by exercise of gauge freedom, no matter what
its size or location.
Remember this started with numerical Laplace-equation solvers.
The program is perfectly happy to find Q as a function of the _
four _absolute_potentials V (not delta_V). ...
Gauge theories are central to modern physics. The gauge of
electrostatics is just the teeniest tip of the iceberg.
http://www.nobel.se/physics/laureates/1999/press.html
http://www.nobel.se/physics/laureates/1982/wilson-autobio.html
http://www.nobel.se/physics/laureates/1979/press.html