Newtonian Quantum Gravity

We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schrödinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space–time. Consideration of quasi–classical conservation laws selects the reduced one–body quantities as the basis for an explicit quasi–classical coarse–graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localize this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self–potential. A nonlinear treatment of gravitational self–energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantization is re–interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self–bound solitary waves. Contrasting this theory with its canonically quantized analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantized gravity. Expanded version of a talk presented at the Inaugural Australian General Relativity Workshop, CMA, A.N.U., Canberra, September 30th 1994 (to app. Australian Journal of Physics, Nov. ’95).