In the "funny capacitor" thread the question arose as to whether it is
correct to make statements that do not appear to embody the
gauge-invariance principle. The answer is, usually, yes, it's OK.
Here's an analogy. Compare the following statements about driving:
1a) Speed limit: 55 mph
1b) Speed limit: 55 mph relative to the nearby surface of the earth
Statement 1b is perfectly correct, and conforms to Galileo's principle of
equivalence. Statement 1a can be viewed as a convenient shorthand for
statement 1b.
Also compare the following statements about flying:
2a) Maneuvering speed: 110 knots
2b) Maneuvering speed: 110 knots relative to the surface of the earth
2c) Maneuvering speed: 110 knots relative to the local airmass
Statement 2c is perfectly correct, and conforms to Galileo's principle of
equivalence. Statement 2b is just plain wrong. Statement 2a can be viewed
as a convenient shorthand for statement 2c.
Note that 1a and 2a both contain implicit frames of reference -- but the
frames are different in the two cases.
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Now let's generalize these examples:
*) People make frame-dependent and gauge-dependent statements all the time.
*) There is nothing wrong with this, provide a few simple guidelines
are followed:
--) Make sure you realize that your statement is shorthand
for a more-precise statement.
--) Make sure the people you are talking to realize that it
is shorthand, and make sure everybody knows what the
implied frame of reference is.
Speaking in shorthand is not the same as repealing the laws of physics!