Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [123]
Heisenberg was delighted as he saw the pieces fit neatly together. His version of quantum mechanics was built out of matrices representing observables such as position and momentum that do not commute. Ever since he discovered the strange rule that made the order in which two arrays of numbers were multiplied an essential component of the mathematical scheme of his new mechanics, the physical reason why this was so had been shrouded in mystery. Now he had lifted the veil. It was, according to Heisenberg, 'only the uncertainty specified by pqh/2', that 'creates room for the validity of the relations' in pq–qp=–ih/2.39 It was uncertainty, he claimed, that 'makes possible this equation without requiring that the physical meaning of the quantities p and q be changed'.40
The uncertainty principle had exposed a deep fundamental difference between quantum and classical mechanics. In classical physics both the position and momentum of an object can in principle be simultaneously determined to any degree of accuracy. If the position and velocity were known precisely at any given moment, then the path of an object, past, present and future, could also be exactly mapped out. These long-established concepts of everyday physics 'can also be defined exactly for the atomic processes', said Heisenberg.41 However, the limitations of these concepts are laid bare when attempts are made to measure simultaneously a pair of conjugate variables: position and momentum or energy and time.
For Heisenberg the uncertainty principle was the bridge between the observation of what appeared to be electron tracks in a cloud chamber and quantum mechanics. As he built that bridge between theory and experiment, he assumed that 'only such experimental situations can arise in nature as can be expressed in the mathematical formalism' of quantum mechanics.42 He was convinced that if quantum mechanics said it could not happen, then it did not. 'The physical interpretation of quantum mechanics is still full of internal discrepancies,' Heisenberg wrote in his uncertainty paper, 'which show themselves in arguments about continuity versus discontinuity and particle versus wave.'43
It was a sorry state of affairs that arose because concepts that had been the foundation of classical physics ever since Newton 'fit nature only inaccurately' at the atomic level.44 He believed that with a more precise analysis of concepts such as position, momentum, velocity, and the path of an elec-tron or atom it might be possible to eliminate 'the contradictions evident up to now in the physical interpretations of quantum mechanics'.45
What is meant by 'position' in the quantum realm? Nothing more or less, Heisenberg answered, than the result of a specific experiment designed to measure, say, the 'position of the electron' in space at a given moment, 'otherwise this word has no meaning'.46 For him there simply is no electron with a well-defined position or a well-defined momentum in the absence of an experiment to measure its position or momentum. A measurement of an electron's position creates an electron-with-a-position, while a measurement of its momentum creates an electron-with-a-momentum. The very idea of an electron with a definite 'position' or 'momentum' is meaningless prior to an experiment that measures it. Heisenberg had adopted an approach to defining concepts through their measurement that harked back to Ernst Mach and what philosophers called operationalism. But it was more than just a redefinition of old concepts.
With the track left behind by an electron passing through a cloud chamber firmly on his mind, Heisenberg examined the concept of the 'path of the electron'. A path is an unbroken, continuous series of positions taken up by