Abstract
The monoaxial torsional pendulum's angle Θ relative to the lab is free real, neither mod 2π nor 4π. Hence the conjugate angular momentum is alsofree real, even quantum mechanically. If the 1/2kΘ2 potential is relaxed at large Θ to 2πN periodicity, then the quantum of angular momentum is partially reestablished, to fractionalħ / N. If the pendulum were built by tensor product from designated constituent atoms, addition of angular momentum would deny the foregoing; however, the tie to atoms is as a collective mode instead. Similarly, theL-C oscillator hasfree real electric charge Q onone plate of the capacitor: The other plate, accommodating —Q, is here “the lab” or “ground”; observability ofcurrent breaks superselection of charge. These comments should alternatively develop from a Born-Oppenheimer approximation.
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