Incompatibility of Observables in Quantum Mechanics
A crucial difference between classical quantities and quantum mechanical observables is that the latter may not be simultaneously measurable. This is mathematically expressed by non-commutativity of the corresponding operators, to the effect that
This inequality expresses a dependence of measurement results on the order in which measurements of observables and are performed. Observables corresponding to non-commutative operators are called incompatible.
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“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)