> If there is 120V AC between the two wires, doesn't this mean that there has to be at least 60V AC potential between at least one of the wires and earth ground?
Yes, it does, but that's fine. The moment you touch a wire in an ungrounded system, that wire is connected to ground through your body, and the voltage between it and ground "floats" harmlessly and instantly to zero, with negligible current passing through you.
Practically, the system is always weakly grounded through mega-ohms of resistance in the insulation. Typically, this means that one wire is better grounded than the other (through a ground plane or part case), and it floats closer to one wire or the other. You can measure the voltage of the "ungrounded" system with a high-impedance multimeter or oscilloscope probe; I've probably done this more times by accident ("105 volts!?? Now 100 volts....Why is my motor ground at 95 volts and falling without turning the motor?") than on purpose.
Yes, it does, but that's fine. The moment you touch a wire in an ungrounded system, that wire is connected to ground through your body, and the voltage between it and ground "floats" harmlessly and instantly to zero, with negligible current passing through you.
Practically, the system is always weakly grounded through mega-ohms of resistance in the insulation. Typically, this means that one wire is better grounded than the other (through a ground plane or part case), and it floats closer to one wire or the other. You can measure the voltage of the "ungrounded" system with a high-impedance multimeter or oscilloscope probe; I've probably done this more times by accident ("105 volts!?? Now 100 volts....Why is my motor ground at 95 volts and falling without turning the motor?") than on purpose.