The Time-Energy Uncertainty Relation

The time-energy uncertainty relation ΔT ΔE ≥ 1/2ħ (3.1) has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. Already the first formulations due to Bohr, Heisenberg, Pauli and Schrodinger are very different, as are the interpretations of the terms used. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer [1], Bauer and Mello [2], and Busch [3,4]. More recent reviews are concerned with different specific aspects of the subject: [5,6,7]. 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 (Sects. 3.3,3.4, and 3.6). In view of the existing reviews, references to older work will be restricted to a few key sources. A distinction of three aspects of time in quantum theory introduced in [3] will serve as a guide for a systematic classification of the different approaches (Sect. 3.2).

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