Quantum uncertainty in the final state of gravitational collapse


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1

    Penrose, R. Phys. Rev. Lett. 14, 57 (1965).

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    Hawking, S. W. & Ellis, G. F. R. The Large Scale Structure of Space time (Cambridge University Press, Cambridge, 1973).

    Google Scholar 

  3. 3

    Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  4. 4

    Feynman, R. P. & Hibbs, A. R. Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

    Google Scholar 

  5. 5

    DeWitt, B. S. Phys. Rev. 162, 1239 (1967).

    ADS  CAS  Article  Google Scholar 

  6. 6

    Hoyle, F. & Narlikar, V. V. Proc. R. Soc. A 278, 465 (1964).

    ADS  Google Scholar 

  7. 7

    Hoyle, F. & Narlikar, J. V. Nature 228, 544 (1970).

    ADS  CAS  Article  Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

NARLIKAR, J. Quantum uncertainty in the final state of gravitational collapse. Nature 269, 129–130 (1977). https://doi.org/10.1038/269129a0

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.