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.(adsbygoogle = window.adsbygoogle || []).push({});

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?)

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# Pairs of observables in uncertainty principle

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