Large fluctuations in the horizon area and what they can tell us about entropy and quantum gravity

We evoke situations where large fluctuations in the entropy are induced, our main example being a spacetime containing a potential black hole whose formation depends on the outcome of a quantum mechanical event. We argue that the teleological character of the event horizon implies that the consequent entropy fluctuations must be taken seriously in any interpretation of the quantal formalism. We then indicate how the entropy can be well defined despite the teleological character of the horizon, and we argue that this is possible only in the context of a spacetime or 'histories' formulation of quantum gravity, as opposed to a canonical One, concluding that only a spacetime formulation has the potential to compute-from first principles and in the general case-the entropy of a black hole. From the entropy fluctuations in a related example, we also derive a condition governing the form taken by the entropy, when it is expressed as a function of the quantal density operator.