Abstract
There is only one well-known application for the time—energy uncertainty relation: the connection between the life-time and the energy-width of resonance states. The relation in question was commonly known even before quantum mechanics was established; its first quantum mechanical derivation was based on Dirac’s original theory of the interaction between matter and radiation.1 The point which should be noted is that the uncertainty relation does not apply to time and energy in abstracto but to the life-time of a definite state of a system. In the example referred to, this is the state in which an atom is in an excited state but there is no radiation present.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. A. M. Dirac, Proc. Roy. Soc. (London) A114 243, 710 (1927). The calculation was carried out by V. Weisskopf and E. Wigner, Z. Physik 6354 (1930). See also the article of the same authors, ibid. 65 18 (1930) and many subsequent discussions of the same subject and of resonance states decaying by the emission of particles rather than radiation.
W. Heisenberg, Z. Physik 43 172 (1927). For a rigorous derivation, see H. P. Robertson, Phys. Rev. 34 163 (1929). The derivation of section 5 is patterned on that of this article.
G. R. Allcock, Ann. Phys. (N.Y.) 53, 253, 286, 311 (1969). Section II of the first of these articles gives a very illuminating discussion of the ideas which underlie also the present section. It also contains a review of the literature of the time—energy uncertainty principle, making it unnecessary to give such a review here. The review also gives a criticism of some of the unprecise interpretations of the time—energy uncertainty relation which are widely spread in the literature. The later parts of the aforementioned articles arrive at a pessimistic view on the possibility of incorporating into the present framework of quantum mechanics time measurements as described by Allcock in section n or in the present section. This pessimism, which is not shared by the present writer, is expressed, however, quite cautiously and is mitigated by the various assumptions on which it is based.
The notation of chapter xx of P. A. M. Dirac’s The Principles of Quantum Mechanics (Oxford University Press, various editions) is used.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wigner, E.P. (1997). On the Time—Energy Uncertainty Relation. In: Wightman, A.S. (eds) Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics. The Scientific Papers, vol A / 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09203-3_58
Download citation
DOI: https://doi.org/10.1007/978-3-662-09203-3_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08179-8
Online ISBN: 978-3-662-09203-3
eBook Packages: Springer Book Archive