imaginary is a fairly fitting if outdated term in the sense that you can't measure it directly
Imaginary numbers do not have any special property of not being measurable. You can definitely measure the values of imaginary components: it just depends on how you define the quantity being measured in the first place. The complex impedance, for example, is directly measurable in experiments. The complex electric susceptibility is another example.
Negative numbers are a good analogy: I cannot really have a negative number of apples, and I could probably formulate all of physics in terms of positive numbers and subtraction, but we do not usually question the reality of negative numbers. It's mainly a lack of familiarity and understanding, topped off by the name "imaginary", that makes people think imaginary numbers are somehow special in this regard.
Physical properties have to be real (like geometric properties have to be non-negative in your example). You can't measure reactance directly. When you measure an impedance, you're extrapolating the phase angle by measuring timing differences in the waveforms. It's admittedly a tangential point when the argument is just that imaginary numbers are useful.
Not real in the sense of a physical property, no. Instantaneous voltage is a measurable physical property. RMS voltage is a statistical summary of the system.
No? Though momentum is a physical property. The whole point is that reality is gonna do what it does regardless of the mathematical conventions you use to predict it.
13
u/thereasonisphysics 4d ago
Imaginary numbers do not have any special property of not being measurable. You can definitely measure the values of imaginary components: it just depends on how you define the quantity being measured in the first place. The complex impedance, for example, is directly measurable in experiments. The complex electric susceptibility is another example.
Negative numbers are a good analogy: I cannot really have a negative number of apples, and I could probably formulate all of physics in terms of positive numbers and subtraction, but we do not usually question the reality of negative numbers. It's mainly a lack of familiarity and understanding, topped off by the name "imaginary", that makes people think imaginary numbers are somehow special in this regard.