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Why is not object 3 a meaningful reference point, regardless of its size/
shape / location?
. . . 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.V3=0
As a special case, we can choose k=-V3, which is tantamount to forcing
and making all voltage measurements relative thereto.
Now that I know that the letter "c" denotes the size of the third objectin
our three-object system, let me take another stab at this:Q
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
at avalues, is to let c=> infinity.
Unless it is at infinity, forcing one of your conductors to always be
/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.V3=0
As a special case, we can choose k=-V3, which is tantamount to forcing
and making all voltage measurements relative thereto.constraints,
This does not count as a "constraint" in the usual counting of
because it doesn't change the physics. All the formulas used tocalculate
physically-meaningful quantities were gauge invariant to begin with, soyou'd
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;
better get used to it. It's a law of nature.frame.
-- Newton's laws are invariant under a Galilean change in reference
-- Maxwell's equations are invariant under a gauge transformation.with
Even if you are only interested in potential differences in a
given system state, the meaning of your reference potential changes
/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?