Logic, methodology and philosophy of science VIII proceedings of the eighth international congress of logic, methodology and philosophy of science, and philosophy of science proceedings) ( PDFDrive ) 59

40 ILYA PRIGOGINE ApAqZh (4.4) Its interpretation is standard: it expresses that the operators associated to momentum p , and to coordinate x are non-commuting Let us next consider the uncertainty relation AEAtzh (4.5) Its interpretation is somewhat subtler, as there is no operator corresponding to time Still, in many situations, there is no real difficulty to give a meaning to this relation For example, if we take a wave packet, its lifetime will be related to its spectral representation, through this uncertainty relation We may then consider the case of an unstable state, characterized by a lifetime As well known, we have h AEr27 However, this uncertainty relation has a quite different meaning Indeed, the lifetime has a well-defined value for a given quantum state and a given experimental device Therefore, this uncertainty relation limits the measurement of a single quantum observable, in this case the energy of the unstable quantum state We may write this relation in the form - h E - (B)22 (%) (4.7) It expresses a dispersion in the values of the energy The existence of a finite lifetime leads to a lack of control of the energy of the unstable quantum state, as manifested by the natural line width We consider this fact as fundamental, as it suggests that a new form of quantum theory is necessary Not only we need non-commuting operators, but we also need operators which would be non-distributive Indeed, if we represent the observable energy as some operator A acting on the hamiltonian AH, we should have A H 2# ( A H ) ’ (4.8) This gives us a hint about the direction in which we have to develop quantum theory to deal with unstable systems Since the oral presentation