100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Gravity, Geometry and the Quantum 353Geometry itself is dynamical. Therefore, as indicated above, one expectsthat a fully satisfactory quantum gravity theory would also be free of abackground space-time geometry. However, of necessity, a background independentdescription must use physical concepts and mathematical toolsthat are quite different from those of the familiar, low energy physics whichtakes place on a flat, background space-time. A major challenge then is toshow that this low energy description does arise from the pristine, Planckianworld in an appropriate sense, bridging the vast gap of some 16 ordersof magnitude in the energy scale. In this ‘top-down’ approach, does thefundamental theory admit a ‘sufficient number’ of semi-classical states? Dothese semi-classical sectors provide enough of a background geometry toanchor low energy physics? Can one recover the familiar description? If theanswers to these questions are in the affirmative, can one pin point why thestandard ‘bottom-up’ perturbative approach fails in the gravitational case?That is, what is the essential feature which makes the fundamental descriptionmathematically coherent but is absent in the standard perturbativequantum gravity?There are of course many other challenges as well. Here are a few examples.A primary goal of physics is to predict the future from the past. Butif there is no space-time in the background, what does time-evolution evenmean? How does one extend the measurement theory and the associatedinterpretation of the quantum framework when space-time geometry is itselfa part of the quantum system? On a more technical level, how does oneconstruct gauge (i.e. diffeomorphism) invariant quantum observables andintroduce practical methods of computing their properties? Are there manageableways of computing S-matrices? Of exploring the role of topologyand the phenomenon of topology change? Should the structure of quantummechanics itself be modified, e.g., through a gravity induced non-linearity?The list continues.Every approach sets its own priorities as to which of these are morecentral than the others and several of these questions are discussed in articlesby Banks, Dowker, Gambini and Pullin and Penrose. In loop quantumgravity described in this chapter, one adopts the view that one should firsttackle squarely the three issues discussed in some detail above and thenexplore other questions. Indeed, these three issues are rooted in deep conceptualchallenges at the interface of general relativity and quantum theoryand all three have been with us longer than any of the current leadingapproaches.