Physics and the measurement of continuous variables

Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the measurement problem (collapse of the wave packet) in quantum mechanics and extending it to the measurement of operators with continuous spectra, we are able to compare the situation in quantum mechanics with that in quantum mechanics. Our conclusion is that the notion of a geometrical point is as meaningful in quantum mechanics as it is in classical mechanics.Comment: 20 page

The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur