@glS Yes this is what I wanna do. "how many eigenvalues there are" would depend on the dimension of the Hamiltonian right? Also one would in practice need to measure something else too since if I measure the same Hamiltonian's energy eigenvalue twice I get the same answer.

@MoreAnonymous but my question was: what do you mean exactly by "measure an energy eigenvalue". How do you measure those? This is a genuine question on my part, I'm not sure how one actually goes in measuring eigenvalues of an unknown observable

I'm not even sure that it makes sense to do it. After all, observables are used to encode a way to measure/interact with a system. What does it mean that "an observable is unknown and we want to find its eigenvalues"?

@glS I give you an energy measuring apparatus. You will measure eigenvalues of energy. If I limit the number of measurements available you will be forced to use probability of some sort to quantify what you measured

what = Hamiltonain

All (hey) does the measurement cause thermal fluctuations?

physicsoverflow.org/42577/…

@Mithrandir24601 I'm pretty sure I've seen someone posting it on twitter

hang on

@Mithrandir24601 yep, here you go twitter.com/sylvaingigan/status/1193472651018330112?s=20

the direct link to the video is youtu.be/FklMpRiTeTA

ah, but you were asking about the Q&A afterwards, not the walk, sorry

@MoreAnonymous yes that's the question, what is an "energy measurement apparatus"

@glS Dunno, you just trust your experimentalist friend who says here's one