 Loop quantum gravity is seemingly less plagued by a lack of predictions, and indeed it is often claimed that the discreteness of area and volume operators are concrete predictions of the theory, with potentially testable consequences. Proponents of this approach argue that this makes the theory more susceptible to falsification, and thus more scientific (in the sense of Popper; see the entry on  Karl Popper)  than string theory (see Smolin 2006 for this line of argument). However, it is still quite unclear, in practice and even in principle, how one might actually observe these quantities. There have been recent suggestions that in order to probe the effects of the Planck scale (discreteness, or minimal length in particular) one needs to look to the cosmological level for tiny violations of Lorentz invariance. Rovelli and Speziale (2003) have argued that, in fact, the existence of a minimal length does not imply a violation of the Lorentz symmetry (a conclusion seconded by the proponents of the causal set programme). Their argument turns on the fact that in the context of quantum theory, symmetries act on states (and so on mean values) rather than eigenvalues (representing the discrete quantities in the theory). However, in any case, there remains a question mark over the theoretical status of the discreteness result which has been shown to hold only for operators on the kinematical Hilbert space, that is, for gauge-variant quantities. It is still an open question whether this result transfers to genuine observables (i.e. operators that satisfy all of the constraints and are defined on the physical Hilbert space: that gauge-invariant quantities). See Dittrich and Thiemann (2009) for a detailed investigation of the problem and a possible resolution employing suitably gauge-fixed (by matter) Dirac observables. Even if one overcomes this problem, and could observe evidence of the discreteness of space, so many approaches involve such discreteness that one would face a further problem in using this new data to decide between the discrete approaches. For a philosophical discussion of this and related issues (including the question of whether the proposed discreteness breaks Lorentz invariance), see Hagar (2009) — Hagar (2014) considers these and related issues in a book-length treatment.