Data acquisition systems' ADCs use differential amplifiers at inputs. So with respect to a common ground(for example earth-ground reference), I apply 3V to one input and 1V to the other input of the differential amplifier; and the amplifier will measure the difference which is 3-1 = 2V. And if perfectly balanced system is used I guess it will reject 50Hz common mode noise which is capacitively coupled to both input wires from mains for instance.
When I approach a live mains cable to a scope's coax cable input, I see 50Hz noise appears on scope screen. So I guess the system is balanced since no input is connected and the system is balanced. Since I still see this 50Hz noise I wonder how does a digital the scope subtracts the voltages. It doesn't use a differential amplifier? Why wouldn't it use a differential amplifier, so it could reject common mode inferences like in an ADC input?