Abstract
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space–time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theory makes it possible to perform a complete space–time analysis in various models that have been proposed in this setting. In spite of the background-independent starting point, all these models turned out to be non-geometrical and even inconsistent to varying degrees, unless strong modifications of Riemannian geometry are taken into account. This outcome leads to several implications for potential observations as well as lessons for other background-independent approaches.
Highlights
A key feature of general relativity is its ability to determine both the dynamics and the structure of space–time
Space–time structure must be derived after quantization for a subsequent physical analysis, and the result may be modified compared with the familiar Riemannian structure
A detailed analysis is available in models of loop quantum gravity, but it remains preliminary owing to the tentative nature of physical models of space–time in this theory
Summary
A key feature of general relativity is its ability to determine both the dynamics and the structure of space–time. If one accepts the possibility that quantum gravity may well lead to nonclassical space–time structures that require a modified and perhaps weakened version of general covariance, consistency requires a detailed demonstration of how one can avoid various low-energy problems that may trickle down from the Planck regime, as pointed out in [1,2] In such a situation, it is important to determine how a modified space–time structure can be described in meaningful terms, for instance by addressing the question of whether such a theory can still be considered geometrical and whether there is an extended range of parameters (such as h) in which effective line elements may still be available. Time with a certain generalized meaning compared with our classical notion
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