Any pair of complementary observables cannot be determined simultaneously. In other words we cannot specify the eigenvalues of any two non-commuting operators. We have already seen in the previous subsection that the position along x axis and x component of the linear momentum are complementary variables. Hence they cannot be determined simultaneously.
Werner Heisenberg in 1927 proposed the following relation, now known as the famous Heisenberg's uncertainty principle:
x and px are the respective uncertainties in the simultaneous determination of x and px. Even if it be possible to measure x with certainty, according to the principle the determination of px would become totally uncertain.
In this context, it may be mentioned that the very act of measurement introduces uncertainties in the values of the complementary observables leading to a change of state of the system.
Heisenberg went on to receive the Nobel prize in Physics in the year 1932 for his contribution to the birth of quantum mechanics.