In the book Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light by Grynberg, Aspect and Fabre I came across the following statement on page 385: "By the end of the nineteenth century, classical electromagnetism,.........., provided a wave description of almost all known optical phenomena (adding the postulate that the quantity measured in optics, called the light intensity, is proportional to the average of the squared electric field of the Maxwellian wave)." An analogous statement for quantum mechanics might read: the Schrodinger equation describes all known non-relativistic electronic phenomena (adding the postulate that the quantity measured, called electron probability density, is proportional to the squared modulus of the Schrodinger wavefunction.) Now I knew that the postulate concerning the squared modulus of the wavefunction is fundamental to interpreting measurements in quantum mechanics but I didn't know that you need a postulate concerning the square of the electric field to interpret measurements in optics. Can't you always (in principle at least) measure the electric field itself? Is this additional postulate concerning the intensity a fundamental part of classical electromagnetism?