Averaging and the statistical postulate

From what has been said it is dear that the calculation of the macroscopic properties of a body involves a process of averaging. Let it be supposed that the precise position and velocity of every molecule in the body could be determined. Then it would appear that we could, at least in principle, compute the future state of the i stem at any moment, and also its average properties over a long period, by using only the laws of mechanics. But this completely detailed knowledge of the instantaneous state of a qrstem is clearly impossible in practice and also, according to the uncertainty prindple, it is impossible even in theory. Any measurement of the position of a molecule disturbs the velocity and vice versa. 

A specification of the state of a system in complete detail is therefore unattainable. This is one of the bases of the second law, as discussed already in 1 18, and it is for the same reason that it is impossible to calculate the average properties of a i stem by seeking to apply the laws of mechanics to the individual molectdes. In order to calculate this average U is necessary to use an extra postulate, over and above the postulates of mechanics. This postulate is of a statistical character, and it asserts that if there are Cl quantum states of an isolated system, all of them compatible with the fixed value of the energy, then the system is as likely to be found in any one of the states as in any other. Thus each of these quantum states is to be t For further diecussion on this point see Tolman, Prineiples of SiaHoHeal Mechanics (Oxford, 1938), 5, and Bom, Natural PhUoeophy of Cause and Chance (Oxford, 1949). 

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