Abstract
THE ratio of the action S to ħ (Planck's constant/2π) determines whether the physical system in question is to be treated classically or quantum mechanically. In the area of classical physics the ratio S/ħ is large compared with unity, and the governing equations are given by δS = 0. Quantum mechanics begins to be important when S ≲ ħ, and the definitive approach of classical physics is replaced by quantum uncertainty. We discuss here the behaviour of a physical system which is initially in the classical domain (S ≫ ħ) but whose later development may well take it into the region of quantum uncertainty. We consider a specific example of this—the gravitational collapse of a spherical dust ball. While classically such a dust ball ends up in a space–time singularity, the corresponding quantum mechanical result suggests a range of̄ final states some of̄ which are non-singular.
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References
Penrose, R. Phys. Rev. Lett. 14, 57 (1965).
Hawking, S. W. & Ellis, G. F. R. The Large Scale Structure of Space time (Cambridge University Press, Cambridge, 1973).
Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973).
Feynman, R. P. & Hibbs, A. R. Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
DeWitt, B. S. Phys. Rev. 162, 1239 (1967).
Hoyle, F. & Narlikar, V. V. Proc. R. Soc. A 278, 465 (1964).
Hoyle, F. & Narlikar, J. V. Nature 228, 544 (1970).
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NARLIKAR, J. Quantum uncertainty in the final state of gravitational collapse. Nature 269, 129–130 (1977). https://doi.org/10.1038/269129a0
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DOI: https://doi.org/10.1038/269129a0
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