Abstract
It is suggested that anoversight occurred in classical mechanics when time-derivatives of observables were treated on the same footing as the undifferentiated observables. Removal of this oversight points in the direction of quantum mechanics. Additional light is thrown on uncertainty relations and on quantum mechanics, as a possible form of a subtle statistical mechanics, by the formulation of aclassical uncertainty relation for a very simple model. The existence of universal motion,i.e., of zero-point energy, is lastly made plausible in terms of a gravitational constant which is time-dependent. By these three considerations an attempt is made to link classical and quantum mechanics together more firmly, thus giving a better understanding of the latter.
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References
D. Bohm,Causality and Chance in Modern Physics (Routledge & Kegan Paul, London, 1957), p. 1.
P. T. Landsberg, “The uncertainty principle as a problem in philosophy,”Mind 56, 250–256 (1947).
M. Born, “Statistical interpretation of quantum mechanics,”Science 122 675–679 (1955) (Nobel prize lecture, translated by R. Schlapp, Edinburgh).
E. A. Gislason, N. H. Sabelli, and J. W. Wood, “New form of the time-energy uncertainty relation,”Phys. Rev. A31, 2078–2081 (1985).
E. Joos, “Continuous measurement: Watchdog effect versus golden rule,”Phys. Rev. D. 29, 1626–1633 (1984).
D. Home and M. A. B. Whitaker, “Reflections on the quantum Zeno paradox,”J. Phys. A19, 1847–1854 (1986).
J.-M. Lévy-Leblond, “Correlation of quantum properties and the generalised Heisenberg inequality,”Am. J. Phys. 54, 134–135 (1986).
R. Blankenbecler and M. H. Partovi, “Uncertainty, entropy and the statistical mechanics of microscopic systems,”Phys. Rev. Lett. 54, 373–376 (1985).
J. Hilgevoord and J. B. M. Uffink, “More certainty about the uncertainty principle,”Europ. J. Phys. 6, 165–170 (1985);Found. Phys. 15, 925 (1985).
L. de la Peña, “Conceptually interesting generalized Heisenberg inequality,”Am. J. Phys. 48, 775–776 (1980).
L. Mandelstam and I. Tamm, “The uncertainty relation between energy and time in non-relativistic quantum mechanics,”J. Phys. (USSR) 9, 249–254 (1945).
T. Padmanabhan and T. R. Seshadri, “The uncertainty principle and the horizon size of our universe,”Gen. Rel. Grav. 19, 791–796 (1987).
L. E. Ballentine, “The uncertainty principle and the statistical interpretation of quantum mechanics,”Canad. J. Phys. 47, 2417–2419 (1969).
F. J. Belinfante,Measurement and Time Reversal in Objective Quantum Theory (Pergamon, Oxford, 1975).
P. Busch and P. J. Lahti, “On various joint measurements of position and momentum observables in quantum theory,”Phys. Rev. D29 1634–1646 (1984).
P. T. Landsberg and D. Home, “An analysis of wave function collapse using the ensemble interpretation,”Am. J. Phys. 55, 226–230 (1987).
A. Einstein, “Elementary considerations about the interpretation of the foundations of quantum mechanics,” inScientific Papers presented to Max Born (Oliver & Boyd, Edinburgh, 1953), translated by the present author.
J. Peslak Jr., “Comparison of classical and quantum mechanical uncertainties,”Am. J. Phys. 47, 39–45 (1979).
M. Born and D. J. Hooton, “Statistical dynamics of multiply-periodic systems,”Proc. Camb. Phil. Soc. 52, 287–300 (1956).
V. V. Kuryshkin, “Uncertainty principle and the problem of joint coordinate-momentum probability density in quantum mechanics,” inThe Uncertainty Principle and Foundations of Quantum Mechanics, W. C. Price and S. S. Chissick, eds. (Wiley, New York, 1977), pp. 61–83.
P. S. Wesson,Cosmology and Geophysics (Adam Hilger, Bristol, 1978).
P. T. Landsberg and N. T. Bishop, “A principle of importance allowing for Newtonian cosmologies with a time-dependent gravitational constant,”Mon. Not. R. Astron. Soc. 171, 279–286 (1975).
N. T. Bishop and P. T. Landsberg, “Time-varying Newtonian gravity and universal motion,”Nature 264, 346 (1976).
S. R. Maiti, “Time-varying gravitation in Newtonian theory,”Mon. Not. R. Astron. Soc. 185, 293–295 (1978).
R. Lapiedra and J. A. Palacios, “Time-varying Newtonian gravity. An upper limit for the rate of change of the gravitational constant,”Astron. Astrophys. 98, 382–383 (1981).
A. Pais,‘Subtle is the Lord...’: The Science and Life of Albert Einstein (Clarendon Press, Oxford, 1982), p. 449.
E. Lasker,Die Philosophie des Unvollendbar (Veit, Leipzig, 1919).
P. T. Landsberg, “The search for completeness,”Nature and System 3, 236–242 (1981).
N. Rescher,The Limits of Science (University of California Press, Los Angeles, 1984).
P. T. Landsberg, “On matrices whose eigenvalues are in arithmetic progression,”Proc. Camb. Phil. Soc. 47, 585–590 (1951).
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Paper dedicated to David Bohm on the occasion of his 70th birthday.
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Landsberg, P.T. Why quantum mechanics?. Found Phys 18, 969–982 (1988). https://doi.org/10.1007/BF01909933
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DOI: https://doi.org/10.1007/BF01909933