New PDF release: Classical and quantum mechanics of the damped harmonic

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He also returned to the problem in an unpublished manuscript, entitled `Field and Charge Measurements in Quantum Theory' of 1937 (reproduced in Bohr, 1996, pp. 195±209), and after many further years he wrote a ®nal paper on the topic, again with Rosenfeld, which was published in the Physical Review after World War II (Bohr and Rosenfeld, 1950). 820 LeÂon Rosenfeld was born on 14 August 1904 at Charleroi, Belgium, and studied physics and mathematics at the University of LieÁge, obtaining his doctorate in 1926.

Planck, loc. , p. 20) After all of these complications, Planck frankly admitted that `only future will tell us' whether one might really be able to proceed successfully on the path indicated (Planck, loc. , pp. 20±21). But with respect to the causality problem, Planck remained optimistic, provided one would assume the following interpretation: The causal law is neither right nor wrong; it is rather a heuristic principle, a pathindicator (Wegweiser)Ðin my opinion the most valuable indicator we have at 708 Chapter IV The Conceptual Completion and the Extensions of Quantum Mechanics handÐfor us to ®nd our way in the colourful jumble of events and to indicate the direction in which physical research must go on to reach ®nal results.

57); hence, they also concluded: `If the wave function of the system cannot be determined by the measurement, it can have no meaning,' or `the existence of predictable measurements is an absolutely necessary condition for the validity of wave mechanics' (Landau and Peierls, loc. , p. 58). Now, in Bohr's scheme, every momentum measurement in time ht is connected with a de®nite change hP (in addition to the unknown change which restricts the accuracy of the measurement due to the indeterminacy relation), given by the relation …v À v H †hP b h Y ht …635† where v and v H denote the velocities of the particle before and after the change.

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