# Pairs of observables in uncertainty principle

1. Dec 18, 2015

### Negatratoron

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?)

2. Dec 18, 2015

### Staff: Mentor

In the formalism of quantum mechanics, an observable is represented by a Hermitian operator.
If the operators corresponding to two observables do not commute, then there will be an uncertainty relationship between them.