 Different worlds correspond to different classically described states of at least one object. Different classically described states correspond to orthogonal quantum states. Therefore, different worlds correspond to orthogonal states: all states \(\ket{\Psi_{\world\ i}}\) are mutually orthogonal and consequently, \(\sum \lvert\alpha_i\rvert^2 = 1\) (here we include as a “world” a situation in which there are no macroscopic objects).