EXCLUSION PRINCIPLE AND QUANTUM MECHANICS 31 tually had been lost since Plancks discovery of the quantum of action. with- out discussing further the change of the attitude of modern physics to such concepts as causality m and physical reality in comparison with the older classical physics I shall discuss more particularly in the following osition of the exclusion principle on the new quantum mechanics As it was first shown by Heisenberg, wave mechanics leads to quali tatively different conclusions for particles of the same kind(for instance for electrons)than for particles of different kinds. As a consequence of the im- possibility to distinguish one ofseveral like particles from the other, the wave functions describing an ensemble of a given number of like particles in the configuration space are sharply separated into different classes of symmetry which can never be transformed into each other by external perturbations In the term configuration space we are including here the spin degree of freedom, which is described in the wave function of a single particle by an index with only a finite number of possible values. For electrons this number is equal to two; the configuration space of N electrons has therefore 3 N space dimensions and N indices of two-valuedness >. Among the different classes of symmetry, the most important ones(which moreover for particles are the only ones)are the symmetrical class, in which the wave function does not change its value when the space and spin coordinates of Pmm么、emt, and the antisymmetrical class, in which for such wave function changes its sign. At this stage of the theory ee different hypotheses turned out to be logically possible concerning the actual ensemble of several like particles in Nature I. This ensemble is a mixture of all symmetry classes Il. Only the symmetrical class occurs Ill. only the antisymmetrical class occurs As we shall see, the first assumption is never realized in Nature. Moreover, it is only the third assumption that is in accordance with the exclusion prin ciple, since an antisymmetrical function containing two particles in the same state is identically zero. The assumption Ill can therefore be considered as the correct and general wave mechanical formulation of the exclusion principle It is this possibility which actually holds for electrons This situation appeared to me as disappointing in an important respect Already in my original paper I stressed the circumstance that I was unable to give a logical reason for the exclusion principle or to deduce it from moreEXCLUSION PRINCIPLE AND QUANTUM MECHANIC S 31 tually had been lost since Planck’s discovery of the quantum of action.With￾out discussing further the change of the attitude of modern physics to such concepts as « causality » and « physical reality » in comparison with the older classical physics I shall discuss more particularly in the following the position of the exclusion principle on the new quantum mechanics. As it was first shown by Heisenberg12 , wave mechanics leads to quali￾tatively different conclusions for particles of the same kind (for instance for electrons) than for particles of different kinds. As a consequence of the im￾possibility to distinguish one ofseveral like particles from the other, the wave functions describing an ensemble of a given number of like particles in the configuration space are sharply separated into different classes of symmetry which can never be transformed into each other by external perturbations. In the term « configuration space » we are including here the spin degree of freedom, which is described in the wave function of a single particle by an index with only a finite number of possible values. For electrons this number is equal to two; the configuration space of N electrons has therefore 3 N space dimensions and N indices of « two-valuedness ». Among the different classes of symmetry, the most important ones (which moreover for two particles are the only ones) are the symmetrical class, in which the wave function does not change its value when the space and spin coordinates of two particles are permuted, and the antisymmetrical class, in which for such a permutation the wave function changes its sign. At this stage of the theory three different hypotheses turned out to be logically possible concerning the actual ensemble of several like particles in Nature. I. This ensemble is a mixture of all symmetry classes. II. Only the symmetrical class occurs. III. Only the antisymmetrical class occurs. As we shall see, the first assumption is never realized in Nature. Moreover, it is only the third assumption that is in accordance with the exclusion prin￾ciple, since an antisymmetrical function containing two particles in the same state is identically zero. The assumption III can therefore be considered as the correct and general wave mechanical formulation of the exclusion principle. It is this possibility which actually holds for electrons. This situation appeared to me as disappointing in an important respect. Already in my original paper I stressed the circumstance that I was unable to give a logical reason for the exclusion principle or to deduce it from more