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

Space Time in String Theory 333branes. To put it another way, we have no positive evidence of the utilityof the field theory notion of effective potential, as a tool for finding validstringy models of quantum gravity. Indeed, what evidence exists 47 suggeststhat this is not a useful tool for this purpose.The global space-time picture one is forced to consider if one believes inthe “landscape of string theory” most likely has a Hot Big Bang in its past,and almost certainly has the fractal Penrose diagram of eternal inflation 48as its future. We do not know how to talk about well defined observablesin either of these contexts, so it is a bit premature to conclude that any ofthe meta-stable dS minima that are found by the procedures of KKLT andtheir followers, have anything to do with what we know as string theory. Ona practical level, our lack of knowledge of what the basic setup is, makes itimpossible to set up, even in principle, the computation of the next ordercorrection to the large radius, and weak coupling approximations, whichare invoked by landscape enthusiasts. We don’t know what it is that theseare approximations to.If we accept the existence of the landscape, we are faced with a phenomenologicaldilemma. Many of the parameters in the standard model ofparticle physics and cosmology are much more finely tuned than would berequired by anthropic considerations alone. A landscape model would haveto predict that most of the parameters did not fluctuate much around theircentral values, and that these central values coincided with what we findin nature in order to give reasonable agreement with experiment. Only twoor three parameters, notably the c.c. and the VEV of the standard modelHiggs field, can be well fixed by anthropic considerations o . There is as yetno indication that the stringy landscape really makes such predictions.A more conservative interpretation of the existence of the stringy landscapeis simply that string theory gives us a lot of possible low energytheories of the world, and we should simply fit the data to determine whichone we are experiencing. It is not clear whether there is any predictivepower left in such a strategy. This is made even more problematic by thesuggestion p that even given all the resources in the universe, we might notbe able to build a computer capable of exploring the vast set of meta-stablestates in the theory.This subject is still unfinished and there is undoubtedly a lot left to besaid about it, so I will have to leave the reader stranded in the midst of theo And even this is only true if all other parameters are fixed by the theory to their realworld values.p Due to E. Witten.