What is it about?
We consider the problem of the motion of N bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum–mechanical problem of an N-body generalization of the problem of the H+2 molecular ion in one dimension. The canonical gravitational N-body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.
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Why is it important?
This paper uncovers a previously unknown link between General Relativity (GRT) and Quantum Mechanics (QM). If we had a dilaton field to the Einstein-Hilbert metric, we find that the equation governing the dilaton field is none other than the Schrödinger Equation! This connection was found in 1+1 dimensions i.e. one spatial and one time dimension. In this dimensional range, all the Physics is contained within the dilaton.
Perspectives
Although this invaluable connection between GRT and QM is realized, it is found in 1+1 dimensions. It's a matter of finding out what happens in 3+1 dimensions i.e. OUR spacetime. This is later found in 2016.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: N-body gravity and the Schrödinger equation, Classical and Quantum Gravity, August 2007, Institute of Physics Publishing,
DOI: 10.1088/0264-9381/24/18/006.
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