Approaches to Quantum Gravity

572 Questions and answerssay much about what this theory must be. But if you do have a candidatefor what this fundamental theory is, the effective theory is among the mostefficient ways to identify its observational consequences (and so to comparebetween different candidates for the fundamental theory). For instance, calculatingthe effective theory which is appropriate requires first identifying whatthe low-energy degrees of freedom are and what are their approximate lowenergysymmetries. Then computing the coefficients of the relevant effectivetheory efficiently identifies what combination of the properties of the underlyingtheory are relevant in low-energy observables, and so can be accessedexperimentally.For gravity, the process of identifying the relevant low-energy theory is fairlywell developed for the case where the candidate fundamental theory is stringtheory, with the result being supergravity theories in various dimensions.The comparison of string theory with its competitors in their implicationsfor observations would be much easier if the implications of the alternativetheories in weakly-curved spaces were similarly expressed.• Q - D. Sudarsky - to S. Majid:1. Regarding eqs. (24.1) and (24.2): what are we to make of their meaning? IfX i has anything to do with the coordinates X that we use to parameterize spacetime(in a given frame, and having chosen an origin for them), it would follow(using the interpretation you suggest in Section 24.5.1) that one can not measureposition and time simultaneously except if we are considering located at theorigin of coordinates (i.e. the uncertainty relation is X 0 DeltaX i ≤ 1κ〈X i 〉).Even if the X are not precisely the space-time positions that we measure, buthave anything to do with them, it seems clear that the precision limitations tocoincident measurements of space and time would increase with the distance tosome origin. In fact in eq. (1.27) the quantities of order λ are also of order 〈X〉.So where in the universe is this special point?2. If on the other hand, these quantities above have nothing to do with the spacetimecoordinates we might measure, why do we talk about non-commutativespace-time?3. You say that the model in Section 24.5.1 has been “taken to the point offirst predictions”, but then you acknowledge that without answering your questionsabout the physical (i.e. measurement related) meaning of the momentumcoordinates, and the physical meaning of the order of addition in momentumaddition law, you can have no predictions at all! Can you explain this apparentcontradiction?– A-S.Majid:1. Indeed eq. (24.1) is in a specific frame of reference as is the conclusionthat the uncertainty in that frame gets worse further out from the origin in that