The uncertainty principle for energy and time. II

American Journal of Physics

Volumn 66, Issue 5, 1998, Pages 396-402

  Hilgevoord, Jan ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032389967     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18880     Document Type: Article

References (32)

1. Jan Hilgevoord, "The uncertainty principle for energy and time," Am. J. Phys. 64, 1451-1456 (1996).
2. Niels Bohr, "The Quantum Postulate and the Recent Development of Atomic Theory," Nature (London) 121, 580-590 (1928).
3. Niels Bohr, in Albert Einstein: Philospher-Scientist, edited by P. A. Schilpp, The Library of Living Philosophers Volume VII (Open Court, La Salle, IL, 1949), pp. 201-241.
4. With Bohr the symbol Δ does not denote the standard deviation but some unspecified relevant measure of width.
5. E. P. Wigner, "On the Time-Energy Uncertainty Relation," in Aspects of Quantum Theory, edited by Abdus Salam and E. P. Wigner (Cambridge U.P., Cambridge, 1972).
6. P. Busch, "On the Energy-Time Uncertainty Relation" (Parts I and II), Found. Phys. 20, 1-43 (1990), Sec. 3.3.3.
7. It should be noted that, even when the states are orthogonal, a measurement of φ may not be capable of distinguishing with certainty between them, i.e., the distributions of φ values in the two states may still overlap. For example, a measurement of the spin component of a spin one-half particle in any direction other than the z direction does not allow one to distinguish with certainty between the two orthogonal eigenstates of the spin in the z direction. However, a measurement of the spin component in the z direction does. Generally, if two states are orthogonal, there are variables a measurement result of which enables one to distinguish with certainty between the states.
8. J. Hilgevoord and J. Uffink, "The mathematical expression of the uncertainty principle," in Microphysical Reality and Quantum Formalism, edited by A. van der Merwe et al. (Kluwer, Dordrecht, 1988), pp. 91-114.
9. See the end of Sec. III.
10. The idea of a quantum clock orinates with Wigner: E. P. Wigner, "Relativistic Invariance and Quantum Phenomena," Rev. Mod. Phys. 29, 255-268 (1957); and H. Salecker and E. P. Wigner, "Quantum Limitations of the Measurement of Space-Time Distances," Phys. Rev. 109, 571-577 (1958).
11. The idea of a quantum clock orinates with Wigner: E. P. Wigner, "Relativistic Invariance and Quantum Phenomena," Rev. Mod. Phys. 29, 255- 268 (1957); and H. Salecker and E. P. Wigner, "Quantum Limitations of the Measurement of Space-Time Distances," Phys. Rev. 109, 571-577 (1958).
12. A. Peres, "Measurement of time by quantum clocks," Am. J. Phys. 48, 552-557 (1980); Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993).
13. A. Peres, "Measurement of time by quantum clocks," Am. J. Phys. 48, 552-557 (1980); Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993).
14. J. Uffink and J. Hilgevoord, "Uncertainty Principle and Uncertainty Relations," Found. Phys. 15, 925-944 (1985), Appendix D.
15. For an alternative derivation, see J. Uffink, "The rate of evolution of a quantum state," Am. J. Phys. 61, 935-936 (1993).
16. J. Hilgevoord and J. Uffink, "A new view on the uncertainty principle," in Sixty-Two Years of Uncertainty, Historical and Physical Inquiries into the Foundations of Quantum Mechanics, edited by A. I. Miller (Plenum, New York, 1990), pp. 121-139.
17. J. Hilgevoord and J. Uffink, "Uncertainty in Prediction and in Inference," Found. Phys. 21, 323-341 (1991).
18. P. Busch, "On the Energy-Time Uncertainty Relation" (Parts I and II), Found. Phys. 20, 1-43 (1990), Sec. 3.4.
19. See Jan Hilgevoord, "The uncertainty principle for energy and time," Am. J. Phys. 64, 1451-1456 (1996).
20. A. S. Wightman, "On the localizability of Quantum Mechanical Systems," Rev. Mod. Phys. 34, 845-872 (1962).
21. This article is reprinted in J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton U.P., Princeton, 1983), pp. 9-52, and in Niels Bohr, Collected Works, edited by J. Kalckar (Elsevier, Amsterdam, 1996), Vol. 7, pp. 339-381.
22. This article is reprinted in J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement (Princeton U.P., Princeton, 1983), pp. 9-52, and in Niels Bohr, Collected Works, edited by J. Kalckar (Elsevier, Amsterdam, 1996), Vol. 7, pp. 339-381.
23. Don Howard, "'Nicht Sein Kann Was Nicht Sein Darf,' Or the Prehistory of the EPR, 1909-1935: Einstein's Early Worries About the Quantum Mechanics of Composite Systems," in Ref. 14, pp. 61-113.
24. In Ref. 3, pp. 224-228.
25. This is Fig. 8 of Ref. 3.
26. A. Pais, 'Subtle is the Lord...' (Oxford U.P., Oxford, 1982), p. 447.
27. R. Peierls, Surprises in Theoretical Physics (Princeton U.P., Princeton, 1979), p. 36.
28. For a survey of the discussion up to 1974 see M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974), Chap. 5.
29. H.-H. von Borzeszkowski and H.-J. Treder, The Meaning of Quantum Gravity (Reidel, Dordrecht, 1987), p. 17.
30. Niels Bohr, Collected Works, edited by J. Kalckar (Elsevier, Amsterdam, 1996), Vol. 7, p. 286.
31. W. G. Unruh and G. I. Opat, "The Bohr-Einstein 'weighing of energy' debate," Am. J. Phys. 47, 743 (1979).
32. In Ref. 3, p. 215.