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

374 A. Ashtekarthe big bang but has a long prior history. Through quantum dynamics, theuniverse tunnels from a contracting phase in the distant past (‘before thebang’) to an expanding phase in the distant future (‘now’) in a specificmanner. Classically, of course such a transition is impossible.To summarize, the infinities predicted by the classical theory at thebig-bang are artifacts of assuming that the classical, continuum space-timeapproximation is valid right up to the big-bang. In the quantum theory, thestate can be evolved through the big-bang without any difficulty. However,the classical, continuum completely fails near the big-bang; figuratively, theclassical space-time ‘dissolves’. This resolution of the singularity withoutany ‘external’ input (such as matter violating energy conditions) is dramaticallydifferent from what happens with the standard Wheeler-DeWittequation of quantum geometrodynamics 2,3,4,5,6 . However, for large values ofthe scale factor, the two evolutions are close; as one would have hoped, quantumgeometry effects intervene only in the ‘deep Planck regime’ resultingin a quantum bridge connecting two classically disconnected space-times.From this perspective, then, one is led to say that the most striking of theconsequences of loop quantum gravity are not seen in standard quantumcosmology because it ‘washes out’ the fundamental discreteness of quantumgeometry.4. Summary and OutlookFrom the historical and conceptual perspectives of section 1, loop quantumgravity has had several successes. Thanks to the systematic developmentof quantum geometry, several of the roadblocks encountered by quantumgeometrodynamics 2,3,4,5,6 were removed. There is a framework to resolvethe functional analytic issues related to the presence of an infinite numberof degrees of freedom. Integrals on infinite dimensional spaces are rigorouslydefined and the required operators have been systematically constructed.Thanks to this high level of mathematical precision, the canonical quantizationprogram has leaped past the ‘formal’ stage of development. Moreimportantly, although some key issues related to quantum dynamics still remain,it has been possible to use the parts of the program that are alreadywell established to extract useful and highly non-trivial physical predictions.In particular, some of the long standing issues about the nature ofthe big-bang and properties of quantum black holes have been resolved. Inthis section, I will further clarify some conceptual issues, discuss currentresearch and outline some directions for future.