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

Gravity, Geometry and the Quantum 351offered by general relativity while dealing with cosmological and astrophysicalphenomena, and the quantum-mechanical world of chance and intrinsicuncertainties while dealing with atomic and subatomic particles. Clearly,this strategy is quite appropriate as a practical stand. But it is highly unsatisfactoryfrom a conceptual viewpoint. Everything in our past experiencein physics tells us that the two pictures we currently use must be approximations,special cases that arise as appropriate limits of a single, universaltheory. That theory must therefore represent a synthesis of general relativityand quantum mechanics. This would be the quantum theory of gravity.The burden on this theory is huge: Not only should it correctly describe allthe known physical phenomena, but it should also adequately handle thePlanck regime. This is the theory that we invoke when faced with phenomena,such as the big bang and the final state of black holes, where the worldsof general relativity and quantum mechanics must unavoidably meet.The challenge of constructing a quantum gravity theory has been with usfor many decades now. The long series of investigations in the ensuing yearshas unveiled a number of concrete problems. These come in two varieties.First, there are the issues that are ‘internal’ to individual programs: For example,the incorporation of physical —rather than half flat— gravitationalfields in the twistor program discussed by Roger Penrose; mechanisms forbreaking of supersymmetry and dimensional reduction in string theory reviewedby Tom Banks; and issues of space-time covariance in the canonicalapproach discussed in this chapter. The second category consists of physicaland conceptual questions that underlie the whole subject. To set the stagefrom which one can gauge overall progress, I will now focus on the secondtype of issues by recalling three long standing issues that any satisfactoryquantum theory of gravity should address.• Black holes: In the early seventies, using imaginative thought experiments,Bekenstein argued that black holes must carry an entropy proportionalto their area 7,19,28 . a About the same time, Bardeen, Carter andHawking (BCH) showed that black holes in equilibrium obey two basiclaws, which have the same form as the zeroth and the first laws of thermodynamics,provided one equates the black hole surface gravity κ withsome multiple of the temperature T in thermodynamics and the horizonarea a hor to a corresponding multiple of the entropy S. 7,19,28 However, ata Since this article is addressed to non-experts, except in the discussion of very recentdevelopments, I will generally refer to books and review articles which summarize thestate of the art at various stages of development of quantum gravity. References tooriginal papers can be found in these reviews.