It is the purpose of the following remarks to clear up misunderstandings which apparently arise sometimes in the popular literature on quantum mechanics and its implications on hazard and causality.The theoretical description of the microscopical behaviour of particles like the electron necessitates a quantum mechanical framework. In this framework the notions of position and velocity of a particle lose their sense. The particle is described in terms of waves (wave mechanics).
The unusual point of quantum mechanics, however, is that these waves are not measurable directly but only in the sense that they predict the probability distribution of experiments, where the particles are registered as whole (in this sense classical) particles. In these macroscopic measurements the notions of position and velocity of the particle are valid, however, not precisely. It is an important result of the theory of measurements within quantum mechanics, that the precision of a simultaneous measurement of position and velocity is limited by the microscopical wave character of the particle. This is expressed by Heisenberg’s uncertainty principle.
The theory of quantum mechanics is a causal theory for the time evolution of the quantum mechanical waves. The only point where hazard plays a role is in the prediction of the outcome of measurements: The prediction of the result of a single measurement is impossible, only a prediction of the probability distribution produced by many measurements can be made. Thus quantum theory is more modest than a classical theory. To derive from this structure a lack of causality in our world or a dominance of hazard in our universe is a pure philosophical speculation.
There is also no contradiction to the causal nature of Newtonian mechanics valid in the macroscopic world. The Newtonian theory is derivable from quantum mechanics by using the characteristics of the modification of quantum mechanics when applied to the macroscopic world.
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