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# Classical Theory of Measurement: A Big Step Towards the Quantum Theory of Measurement

## Abstract

One of us, in previous years, has published several articles [1–8] the quantum theory of measurement. These papers have not been much quoted, perhaps because they have been difficult to understand. After a review of the history of the subject, the present paper outlines a purely classical approach to the measurement problem in nonrelativistic classical mechanics. We regard this as a very simple and trivial problem. In fact, it is so simple and trivial that no one has treated it until now. The remarkable fact is that, once one learns how to treat this completely classical problem, a literal translation of the calculation into the quantum domain provides a very fine model for the quantum theory of measurement.

### Keywords

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### References

- [1]W. E. Lamb Jr., “Interpretation of Nonrelativistic Quantum Mechanics”, Physics Today 22, 23 (1969).CrossRefGoogle Scholar
- [2]W. E. Lamb, Jr., “Theory of Quantum Mechanical Measurements”, Ann. N. Y. Acad. Sci. 480, 407 (1986).ADSCrossRefGoogle Scholar
- [3]W. E. Lamb, Jr., “Theory of Quantum Mechanical Measurement”,
*Proceedings of the 2nd International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, August*,*1986*, edited by M. Namiki, Y. Ohnuki, Y. Murayama and S. Normura ( Physical Society of Japan, Tokyo, 1987 ), pp. 185 – 192.Google Scholar - [4]W. E. Lamb, Jr., “Sequential Measurements in Quantum Mechanics”. Lecture at Como NATO Advanced Research Workshop in Quantum Optics, September, 1986.
*Quantum Measurement and Chaos*, ed. E. R. Pike and S. Sarkar, pp. 183–193 ( Plenum Press, New York and London, 1987 ).Google Scholar - [5]W. E. Lamb, Jr., “Quantum Theory of Measurement,”
*Proceedings of the Nato Advanced Research Workshop on Noise and Chaos in Nonlinear Dynamical Systems*, edited by F. Moss, L. Lugiato and W. Schleich (Cambridge University Press, 1990 ).Google Scholar - [6]W. E. Lamb, Jr., “Classical Measurements on a Quantum Mechanical System” in
*Proceedings of the International Symposium on Spacetime Symmetries*, eds. Y. S. Kim and W. M. Zachary, pp. 197–201, reprinted from Nuclear Physics B (Proc. Suppl.) 6 ( North-Holland, Amsterdam, 1989 ).Google Scholar - [7]W. E. Lamb, “Suppose Newton had Invented Wave Mechanics,” Am. J. Phys. 62, 201 (1994).ADSCrossRefGoogle Scholar
- W. E. Lamb Jr., “Schrödinger’s Cat,” in
*Paul Adrien Maurice Dirac*, eds. B. N. Kursunoglu and E. P. Wigner, pp. 249 - 261 ( Cambridge University Press, 1987 ).Google Scholar - L. de Broglie,
*Thesis*( Masson et Cie, Paris, 1924 ).Google Scholar - [10]D. Bohm, and B. Hiley,
*The Undivided Universe*, (Routledge, London, 1993), and P. R. Holland,*The Quantum Theory of Motion; an Account of the DeBroglie-Bohm Causal Interpretation of Quantun Mechanics*(Cambridge University Press, 1993 ).Google Scholar - W. Heisenberg, “Quantum Theoretic Re-interpretation of Kinematic and Mechanical Relations,” (1925), translated in [13].Google Scholar
- [12]B. L. van der Waerden,
*Sources of Quantum Mechanics*(Dover, 1968 ).Google Scholar - [13]J. A. Wheeler and W. H. Zurek, editors,
*Quantum Theory and Measurement*(Princeton University Press, 1983 ).Google Scholar - W. Heisenberg, “The Physical Content of Quantum Kinematics and Mechanics” (1927), translated in [13].Google Scholar
- [15]E. Schrödinger,
*Collected Papers on Wave Mechanics*( Blackie, London, 1928 ).MATHGoogle Scholar - [16]W. Heisenberg,
*The Physical Principles of the Quantum Theory*(Chicago University Press, 1930 ).Google Scholar - E. Schrödinger, “The Uncertainty Principle,” Sitzungberichte, Preuss. Akad. Wiss., 296(1930).Google Scholar
- [18]H. P. Robertson, “The Uncertainty Principle,” Phys. Rev. 34, 163 – 164 (1929).CrossRefGoogle Scholar
- E. Schrodinger, a translation of the ‘cat paradox’ papers appears in Proc. Am. Phil. Soc. 124, 323–338 and in [13].Google Scholar
- [20]E. Schrödinger,
*What is Life?*, (Cambridge University Press, 1944 ).Google Scholar - [21]K. B. Mullis, “The Polymerase Chain Reaction,” pp. 102–117, Les Prix Nobel, 1993 ( Almqvist and Wiksell, Stockholm, 1994 ).Google Scholar
- See reference [12].Google Scholar
- A. Einstein, M. Born and H. Bohr,
*The Einstein-Born Letters*,*1916–1955*( Macmillan, London, 1971 ).Google Scholar - [24]P. A. M. Dirac,
*The Principles of Quantum Mechanics*, 1st ed. ( Oxford University Press, London 1930 ).Google Scholar - [25]J. von Neumann,
*Mathematische Grundlagen der Quantenmechanik*(Springer, Berlin, 1932). English translation by R. T. Beyer (Princeton University, Princeton, N.J., 1955 ).Google Scholar - E. Arthurs and J. Kelly, “On the Simultaneous Measurement of a Pair of Conjugate Variables,” Bell Syst. Tech. J. 44, 725 – 729, (1965).Google Scholar
- [27]M. A. Bunge,
*Foundations in Physics*, especially Chapter 5, Section 8 ( Springer, New York, 1967 ).Google Scholar - See reference [2] for a discussion of the classical version of von Neumann’s X-meter.Google Scholar
- [29]W. Pauli, “General Principles of Wave Mechanics,”
*Handbuch der Physik*, vol. 24/1 ( Springer, Berlin, 1933 ).Google Scholar - [30]V. B. Braginsky, K. Khalili and K. Thorne,
*Quantum Measurements*, (Cambridge University Press, 1992). Also, M. B. Menski,*Continuous Quantum Measurements and Path Integrals*( IOP Pub., London, 1992 ).Google Scholar - [31]C. M. Caves, “Quantum Mechanics of Measurements Distributed in Time,” Phys. Rev. D 33, 1643 (1986).CrossRefGoogle Scholar
- [32]S. Weinberg, “Testing Quantum Mechanics,” Annals of Physics, 194, 336 – 386 (1989).MathSciNetADSCrossRefGoogle Scholar
- [33]M. Gell-Mann and J. B. Hartle, “Classical Equations for Quantum Systems,” Phys. Rev. D 47, 3345 – 3382 (1993).MathSciNetCrossRefGoogle Scholar
- [34]R. Omnes,
*The Interpretation of Quantum Mechanics*(Princeton University Press, 1994 ).Google Scholar - E. P. Wigner, “Remarks on the Mind-Body Question,” in
*The Scientist Speculates*eds I. J. Good (Heineman, London, 1961 ).Google Scholar - [36]See, for example, R. Penrose,
*The Emperor’s New Mind*(Oxford University Press, 1989); R. Penrose, Shadows of the Mind (Oxford University Press, 1994); and H. P. Stapp,*Mind, Matter and Quantum Mechanics*( Springer, N.Y., 1993 ).Google Scholar