Re: funny capacitor

[Bob Sciamanda <trebor@VELOCITY.NET>]

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

It is a fine reference point if you are only interested in differences of
potential in a given, single, system state.  But how do you examine the
behavior of the reference point V3 as the system changes from state to
state (ie, the Q's and V's all change - except of course your V3)?


> . . .  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.

The point is that your k = V3 is not a "constant " - it changes value
(relative to infinity) as the system goes into different states.  To
compare different states one must somewhere refer to a point whose
potential is unaffected by changing system states (eg: infinity).

Another way of saying this is that if one were to refer your calculated
potentials to infinity, each system state would need a different k (its
own gauge).

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "John S. Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, March 10, 2001 02:57 PM
Subject: Re: funny capacitor


> 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?