Singularity and unanimity

Details Singularity and unanimity Singularity and unanimity

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..713w&link_type=abstract

General Relativity and Gravitation, vol. 8, Aug. 1977, p. 713-715.

Mathematics

7

Field Theory (Physics), Gravitational Collapse, Quantum Mechanics, Relativistic Theory, Singularity (Mathematics), Traveling Charge, Einstein Equations, Point Sources, Schroedinger Equation

Scientific paper

A 'unanimity query' is posed which, if correct, would imply that quantum mechanics does not provide an escape from gravitational collapse. According to this query, if all the solutions to the equations of motion for a classical dynamical problem encounter a singularity, except a set of measure zero, then all solutions for the corresponding quantum-mechanical problem are singular. To clarify the motivation for the unanimity query, three examples are discussed which involve the motion of a charged particle under the influence of a point center of attraction, the motion of a particle along a potential ridge of uniform height that runs to an infinite distance in the x-direction, and the motion of a particle under an inverse-cube central attraction. It is concluded that if the query is answered in the affirmative, every quantum solution for the problem of a closed universe in the framework of Einstein's field equations leads to a singularity.

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