Twistors and holography

Abstract

We extend Bousso's notion of a lightsheet -a surface where entropy can be defined in a way so that the entropy bound is satisfied -to more general surfaces. Intuitively, these surfaces may be regarded as deformations of the Bousso choice; in general, these deformations will be timelike and so we refer to them as 'timesheets'. We show that a timesheet corresponds to a section of a certain twistor bundle over a given spacelike two-surface B. We further argue that increasing the entropy flux through a given region of spacetime corresponds to increasing the volume of certain regions in twistor space. Put another way, it would seem that entropy in spacetime corresponds to volume in twistor space. We argue that this formulation may point a way towards a version of the covariant entropy bound which allows for quantum fluctuations of the lightsheet. We also point out that in twistor space, it might be possible to give a purely topological characterization of a lightsheet, at least for suitably simple spacetimes. I. INTRODUCTIONThroughout history [1], one of the central problems faced by philosophers and scientists has been the simple query: How does one define the concepts of space and time? Are they merely abstractions which we have introduced in order to facilitate a description of the interrelationship between things which actually 'exist' (e.g., such as material bodies)? Or do space and time 'exist' in and of themselves, without any reference to observable consequences? Although such Machian musings may seem esoteric, they actually take on a new and exciting life when viewed in the light of modern ideas coming from theoretical physics, especially quantum gravity. Indeed, most theoretical physicists today would probably agree that 'space' and 'time' will be effective concepts which only emerge at low energies. At scales past the Planck energy, 'space' and 'time' will simply cease to have any operational meaning, and some more fundamental ideas (comprising quantum gravity) will have to take over.Of course, at first it seems nonsensical to assert that the 'ultimate theory' should be constructed without invoking the use of the words 'space' or 'time'. After all, from our earliest days of undergraduate physics, we were all weaned on physical theories which simply would not make any sense without reference to these concepts. More precisely, theories such as classical or quantum mechanics are useful precisely because they are bodies of knowledge which allow us to predict, with at least some probability, the nature of future events given some knowledge about present or past events. One of the conceptual obstructions to constructing a quantum theory of gravity is that it is unclear what the theory will have to do with prediction; although certain quantum gravity models do yield predictions (such as the No Boundary Proposal), much more work on connecting quantum gravity with the low energy world around us is needed.On the aesthetic level, however, the construction of a quantum theory of gravity may be the most beautiful way o...

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