Re: funny capacitor

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

Now that I know that the letter "c" denotes the size of the third object in
our three-object system, let me take another stab at this:

At 01:43 PM 3/10/01 -0500, Bob Sciamanda wrote:
> Perhaps more to the point:
> Note that the only way to force V3 to always be zero, regardless of the Q
> values, is to let c=> infinity.
>
> Unless it is at infinity, forcing one of your conductors to always be at a
> fixed potential is adding a constraint to the set of independent
> variables.

No way!  Gauge invariance allows us to make the transformation
        (V1, V2, V3) --> (V1+k, V2+k, V3+k)
any time we want.  This applies to *any* system, no matter what the size /
shape / location of the objects.

As a special case, we can choose k=-V3, which is tantamount to forcing V3=0
and making all voltage measurements relative thereto.

This does not count as a "constraint" in the usual counting of constraints,
because it doesn't change the physics.  All the formulas used to calculate
physically-meaningful quantities were gauge invariant to begin with, so
choosing your favorite gauge won't cause any meaningful changes.

======

People seem to be having bad reactions to the notion of gauge
invariance.  All I can say is that gauge invariance is here to stay;  you'd
better get used to it.  It's a law of nature.
  -- Newton's laws are invariant under a Galilean change in reference frame.
  -- Maxwell's equations are invariant under a gauge transformation.

> Even if you are only interested in potential differences in a
> given system state, the meaning of your reference potential changes with
> each system state and you have offered no meaningful reference for
> comparison of these values.

Why is not object 3 a meaningful reference point, regardless of its size /
shape / location?