- #1
Negatratoron
- 25
- 7
Observables are paired up in the uncertainty principle such that we can't measure both to a high degree of accuracy. Specifically, ## \sigma_x \sigma_y>\frac{\hbar}{2} ## where ## \sigma_x ## and ## \sigma_y ## are the standard deviations of our measurements.
I've got two lines of questions related to this.
1: How are observables specified by physicists? Is an observable any physical action you can carry out to obtain a number?
I suspect that when people say "Position is an observable", they really mean: "Given an object O, the position of O is an observable". So the abstract idea of 'position' is not an observable, but rather a function that takes a physical system and outputs an observable. Is that correct?
2: How are observables paired off in the uncertainty principle? Given one observable, can you find the other? (if I specified a position observable to you, could you define the corresponding momentum observable from it?)
I've got two lines of questions related to this.
1: How are observables specified by physicists? Is an observable any physical action you can carry out to obtain a number?
I suspect that when people say "Position is an observable", they really mean: "Given an object O, the position of O is an observable". So the abstract idea of 'position' is not an observable, but rather a function that takes a physical system and outputs an observable. Is that correct?
2: How are observables paired off in the uncertainty principle? Given one observable, can you find the other? (if I specified a position observable to you, could you define the corresponding momentum observable from it?)