 Common textbook wisdom justifies the use of phase averages as follows. As we have seen, the Gibbs formalism associates physical quantities with functions on the system’s phase space. Making an experiment measuring one of these quantities takes time and it is assumed that what measurement devices register is not the instantaneous value of the function in question, but rather its time average over the duration of the measurement. Hence, time averages are what is empirically accessible. Then, so the argument continues, although measurements take an amount of time that is short by human standards, it is long compared to microscopic time scales on which typical molecular processes take place. For this reason it is assumed that the measured finite time average is approximately equal to the infinite time average of the measured function. If we now assume that the system is ergodic, then time averages equal phase averages. The latter can easily be obtained from the formalism. Hence we have found the sought-after connection: the Gibbs formalism provides phase averages which, due to ergodicity, are equal to infinite time averages, and these are, to a good approximation, equal to the finite time averages obtained from measurements.