Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-12-21
Class.Quant.Grav. 19 (2002) 3217-3248
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
minor revisions, accepted for publication by Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/19/12/308
We give a derivation of general relativity and the gauge principle that is novel in presupposing neither spacetime nor the relativity principle. We consider a class of actions defined on superspace with two key properties. The first is 3-coordinate invariance. This is the only postulated symmetry, and it leads to the standard momentum constraint. The second property is that the Lagrangian is constructed from a `local' square root of an expression quadratic in the velocities, `local' because it is taken before integration over 3-space. It gives rise to quadratic constraints that do not correspond to any symmetry and are not, in general, propagated by the Euler-Lagrange equations. Therefore these actions are internally inconsistent. Only one action of this form is well behaved: the Baierlein-Sharp-Wheeler reparametrisation-invariant action for GR. From this viewpoint, spacetime symmetry is emergent. It appears as a `hidden' symmetry in the (underdetermined) solutions of the evolution equations, without being manifestly coded into the action itself. In addition, propagation of the constraints acts as a striking selection mechanism beyond pure gravity. If a scalar field is included in the configuration space, it must have the same characteristic speed as gravity. Thus Einstein causality emerges. Finally, self-consistency requires that any 3-vector field must satisfy Einstein causality, the equivalence principle and, in addition, the Gauss constraint. Therefore we recover the standard (massless) Maxwell equations.
Barbour Julian
Foster Brendan
Murchadha Niall Ó
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