INDETERMINACY ASSOCIATED WITH THE MEASUREMENT OF AN OBSERVABLE

For simplicity, consider that only the Z-component of the electron’s spin, ˆ S_z is measured. To do this, a sample consisting of many electrons is collected, and a spin measurement device is employed to measure the spins of the sample. Why are measurements performed on a sample of electrons instead of a single electron? We need a sample to be statistically correct; the same value of the spin must be measured from the whole sample of electrons. When measurements are performed on the whole sample consisting of N number of electrons, to measure the Z-component of the spin of the electrons, some of the electrons yield spin up (+ h /2)values, some of them yield spin down (− h/2) values, and h is Planck’s constant. This implies that the measurement of the Z-component does not yield a definite value. Thus, the spin of an electron has indeterminacy associated with it. This is unlike any classical system where the outcome of a measurement for any dynamical variable is always definite. Classically, for such a sample of electrons prepared under identical conditions, measurement outcome would yield only one value of the spin from all the electrons. This special feature of a quantum mechanical system requires a different mathematical approach than that of classical mechanics. In the section that follows, the concept of states and indeterminacy in the outcome of a measurement is described.