B What is the origin of Observables?

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Observables in quantum mechanics are conventionally required to be Hermitian to ensure that measured values are real numbers, which is critical for the validity of Born's rule. This requirement arises from historical postulates and the mathematical framework of quantum mechanics, particularly the use of complex Hilbert spaces and probability distributions. While Hermitian operators are commonly used due to their properties, it is noted that they are not strictly necessary for all observables, as other mathematical constructs like Positive Operator Valued Measures (POVMs) can also be employed. The discussion emphasizes that the focus should be on maintaining a self-consistent probability calculus rather than strictly adhering to the historical conventions of Hermitian operators. Ultimately, the effectiveness of the mathematical formalism in predicting experimental outcomes is what underpins these conventions.
  • #31
A. Neumaier said:
In a damped harmonic oscillator, the complex-valued frequency has a nonzero real and imaginary part.
A. Neumaier said:
The real observables are the points on the oscillating curve; the observable complex frequency is extracted from these and produces the physical way of summarizing the behavior of the oscillator.

It is always the summary that carries the physics. Without summarizing what happens in Nature we cannot form a single concept. Every observable is an abstraction of the real thing, and as an abstraction it may be a real number, a complex number, or an even more complicated object such as a vector or a tensor.
Nice post-editing :)

Sure, that's what I said, the real variable is a projection of the complex representation.

I am surprised that nobody else seems to be interested in whether the idea of complex observables makes sense physically. You and I are clearly not going to agree about that so we must agree to differ.
 
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  • #32
Derek Potter said:
I am surprised that nobody else seems to be interested in whether the idea of complex observables makes sense physically.
Take a wire and bend it to a sine wave :)
 

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