The discussion revolves around the nature and origin of observables in quantum mechanics, specifically addressing why observables are typically represented by Hermitian operators, the implications of eigenstates and eigenvalues, and the conventions surrounding these definitions. The scope includes theoretical considerations and conceptual clarifications related to quantum mechanics.
Participants express a range of views on the necessity and implications of using Hermitian operators for observables. There is no consensus on whether the conventions surrounding observables are fundamentally necessary or merely historical artifacts. Multiple competing perspectives on the nature of observables and their mathematical representation remain unresolved.
Participants acknowledge that the discussion involves assumptions about the mathematical framework of quantum mechanics, including the definitions of observables and the nature of measurement. The implications of these assumptions on the interpretation of quantum mechanics are not fully resolved.
A. Neumaier said:In a damped harmonic oscillator, the complex-valued frequency has a nonzero real and imaginary part.
Nice post-editing :)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.
Take a wire and bend it to a sine wave :)Derek Potter said:I am surprised that nobody else seems to be interested in whether the idea of complex observables makes sense physically.