The discussion revolves around the nature of imaginary numbers in relation to observables in physics, particularly focusing on why variables with imaginary values are considered inherently unobservable compared to real-numbered variables that correspond to measurable quantities like position and momentum. The scope includes philosophical implications, mathematical definitions, and quantum mechanics concepts.
Participants express differing views on the nature of imaginary numbers and their relation to observables. There is no consensus on the reasons behind the distinction between real and imaginary numbers, and the discussion remains unresolved.
The discussion touches on philosophical and mathematical assumptions regarding the definitions of real and imaginary numbers, as well as the implications of these definitions in physical measurements. Some claims rely on historical perspectives that may not be universally accepted.
masudr said:Well, ultimately everything boils down to measurements of position: whether it's where the pointer is pointing to, or which LEDs are lit etc. The Ancient Greeks discovered (much to their dismay) that irrational numbers are realized in nature (e.g. the right-angled triangle with the two smaller unit sides has a hypotenuse of irrational length).
And so it was known, that the set of real numbers were realized in nature. There is no displacement in our space that is modeled by a complex number: this is why they have a slightly different status.