An adapted form of this law applies to energy and time; it applies directly to any two components of spin, but it is best known in its application to position and momentum, the product of the standard deviations of which is at least h-bar over two.
This rule holds if the operator algebra for some set of observables is non-trivial; that is true because it is derived via the Schwarz inequality applied to the expectation value of the commutator of two observables' operators. It formally bounds the product of the dispersions in two observables. An adapted form of this law applies to energy and time; it applies directly to any two components of spin, but it is best known in its application to position and momentum, the product of the standard deviations of which is at least h-bar over two. FTP, name this principle from quantum mechanics that limits the precision of measurements.
This rule holds if the operator algebra for some set of observables is non-trivial; that is true because it is derived via the Schwarz inequality applied to the expectation value of the commutator of two observables' operators.
the Heisenberg {uncertainty} principle