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Background: The following two observations are , in my understanding, pretty much accepted in quantum theory:

  1. Location is a property which is not preexisting but is established by measurement. It is conjugate to momentum. There is a limit to joint precision when measuring location and momentum (Heisenberg). There is a limit to absolute precision in measuring location (Compton).

  2. Momentum is a property which ... We can formulate essentially the same observation with swapped roles wrt to momentum.

Question: In which regard is (electrical) charge different? Why do we treat it as constant with full precision and without conjugate property? As fact and not as property established by measurement.

Of course, quantum theory is not built that way. But that's no reason. Which physical observation gives a reason for treating charge differently.

Some misguided attempts: Let's try to measure charge. Our experiments will involve some time / location measurements. So we expect some form of limitation in measurement precision (relative wrt to a conjugate variable, also in an absolute sense) and some form of Kopenhagen argument "charge as property does not exist unless measured". Maybe it is the fact that it is a discrete value? But we also find discrete values for spin and we treat spin on a measurement footing as well, similar to location and momentum. Maybe it is the constancy of that value? But how do we know that? First, it is not constant (we find +1, 0, -1 as measured elementary charge, and there are the fractional quark charges). Second, how would we confirm this empirically? (If we use measurements involving location and momentum, energy and time, we have imprecision again.)

So if we measure charge - what would be a conjugate variable then? What would that mean for charge conservation? How would a theory look like? Well, probably that's not a reasonable approach. But why?

I am specifically looking for observational reasons, as, of course, the theory as we constructed it, just provides a conventional or historical reason. Or is it, in the end, only a convention after all?

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    $\begingroup$ physics.stackexchange.com/questions/235449/… $\endgroup$
    – safesphere
    Jul 3, 2019 at 13:20
  • $\begingroup$ This seems more like a ontological/ epistemological question that would be better suited in the philosophy stack exchange. $\endgroup$ Jul 3, 2019 at 13:21
  • $\begingroup$ @Oбжорoв While the question has ontological aspects I am interested in the experimenters answer which is why I placed it here. But I was considering... $\endgroup$ Jul 3, 2019 at 20:31

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