Re: funny capacitor

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

At 08:48 AM 3/5/01 -0500, Ludwik Kowalski wrote:
> 1) A cold triode is a "funny capacitor". For any chosen set
> of Vj we would have a specific Qi set, and VICE VERSA.

Really?  Vice versa?  How do we know that?
 -- Is this the 11th commandment?  Is it a newly-enacted law of nature?
 -- Has gauge invariance been repealed?
 -- Is this a consequence of Maxwell's equations?
    If so, how is it derived?

I claim that gauge invariance _is_ a direct consequence of Maxwell's equations:
        Q = del^2(phi) = del^2(phi + const)

for any distribution of potential phi and for any const independent of
position.


> 2) The VICE VERSA implies that the inversion should be
> possible. If it does happen in reality (as one and only one
> reproducible solution) then our description of reality should
> match it.

Where is there the slightest evidence that this does happen in reality?

There is abundant evidence that the opposite happens in reality.

Specifically, consider a DC circuit consisting of a number of batteries and
capacitors.  We wish to find the voltage Vi at each node (i), and the
corresponding charge distribution.

Now, every voltmeter I've ever seen has *two* leads.  WLoG let's call them
the black lead and the red lead.  Now I choose to hook the black lead to
node 17 and measure all the other nodes with the red lead.  You choose to
hook the black lead to node 7 and measure all the other nodes with the red
lead.

We get two different sets of voltage numbers, but there is only one charge
distribution.  The two different voltage-distributions differ by a gauge
transformation.  That's what happens in reality.  Get used to it.

> But JohnD discovered that this is not true. How come
> > that others were wrong for so long?

I'm not responsible for what other people say.  I'm only responsible for
what I say.