imaginary numbers

madness

Maybe this should be in the philosophy of science/math forum, but i thought it fitted here. Why is it that variables taking imaginary values are inherently unobservable, whereas real numbered variables correspond to observables like position/momentum? As far as I can see there is no a priori reason why this should be the case.

rbj

we had a bit of a discussion about measuring complex quantities and whether or not (and why) "real" and "imaginary" were good labels for these numbers. check it out:

http://physicsforums.com/showthread.php?t=149195

madness

Thanks that's an interesting thread. Here is a more specific question to explain what i mean. Why is it that Hermitian operators in quantum mechanics (ones with real eigenvalues) correspond to observables. What is it about real numbers over complex ones that make them observable? I don't think this question was directly covered in that thread.

masudr

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 realised 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 realised in nature. There is no displacement in our space that is modelled by a complex number: this is why they have a slightly different status.

rbj

thank you for saying here about what it was that i was trying to say in the other thread (that got so contentious). i would say it as "the set of numbers are realized quantities in nature are called "real numbers".