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

344 T. Banksthetical space-time probably involves a Big Bang, while its future is almostcertainly the fractal Penrose diagram of eternal inflation. It is alleged thatthe fundamental string theory observables of this system will be related tomeasurements done in the non-accelerating region, and that these will allowone to define the measurements done in our own universe in a rigorous, ifapproximate, way (much as scattering experiments define the properties ofa meta-stable resonance). This proposal faces many phenomenological andfundamental challenges, as well as issues of computability associated withthe huge number of meta-stable states. Work is in progress to address someof these issues.The second approach to space-times with positive c.c. is based on theassertion that the quantum theory of dS space has a finite number, N, ofstates, related to the value of the cosmological constant in Planck units.As in the case of AdS space, the c.c. is a discrete high energy input. Thefiniteness of the state space poses problems of quantum measurement theory:such a theory can describe neither arbitrarily accurate measurements,nor measurements which remain robust over arbitrarily long time intervals.However, for the value of the c.c. indicated by observations, the limit onaccuracy is about one part in e 1090 , and this number (in any units you careto choose) is also the size of the time over which measurements will bedestroyed by quantum fluctuations. The phenomenology of this proposal isbased on the idea of Cosmological SUSY Breaking. It seems to lead to arather predictive framework for both particle physics and cosmology. Someprogress has also been made in constructing a fundamental Hamiltoniandescription of this system. Progress on all fronts is incremental but slow.Finally, I described a general holographic quantum theory of space-time.According to the covariant entropy bound, a causal diamond is describedby a finite number of states, related to the area of its holographic screen.In the quantum theory this translates into a finite Clifford algebra of operatorsS a (n). The classical Cartan-Penrose equation tells us how to describethe conformal structure of the holographic screen of a causal diamond interms of a section of the spinor bundle over the screen (viewed as a d − 2dimensional manifold). The S a (n) are a quantization of this spinor section.The topology of the screen is pixelated by replacing its function algebraby a finite dimensional associative (and generally non-commutative) algebraand the spinor bundle is a finite projective module over this algebra.The S a (n) are quantum operators corresponding to a basis of this module.The dimension of the irreducible representation of the Clifford algebra forfixed n determines the area of a pixel, via the Bekenstein-Hawking rela-