Okay, I said I'd look at Wigner, page 10, so here is a relevant quote. The subject matter is electric charge conservation, the idea that the total amount of charge in the universe doesn't change. Charge can be created and destroyed, but only in pairs of plus and minus charges. Nowadays, there is a popular idea for why charge is conserved. It's related to the phase of the electron's "matter wave." The dissonance still exists, if you ask me--to be discussed later! Here's Eugene:
"My account of the role of invariance in quantum
mechanics would remain grossly incomplete if I did not mention a dissonant
sound in the harmony of quantum mechanics and the older theorems of
invariance. This is the conservation law
for the electrical charge. While the
conservation laws for all other quantities, such as energy or angular momentum,
follow in a natural way from the principles of invariance, the conservation law
for electric charge so far has defied all attempts to place it on an equally general
basis. The situation was, of course, the
same in classical mechanics but the simplicity of the connection between
invariance and the ordinary conservation laws makes the situation even more
conspicuous in quantum mechanics."
From Symmetries and Reflections: Scientific Essays of
Eugene P. Wigner, Indiana University Press, Bloomington and London, 1967. This essay is called
“Invariance in Physical Theory.” It was first presented as a talk at “the
celebration honoring Professor Albert Einstein on March 19, 1949, in
Princeton.” Einstein had turned 70 years old on March 14 of that year, thus the celebration.
