Computation in Nested Closed Timelike Curves

Abstract

How powerful computers are depends on the laws of physics that govern the behaviour of a computer. So to determine what problems can be solved by computers, we have to consider the physical model they are present in. In general relativity theory, spacetime can curve so much that loops are formed, potentially allowing travel back in time. It might even be possible for there to be loops within other loops. By considering these loops quantum mechanically, a consistent physical model can be formulated. This thesis investigates what computational problems can be solved by computers with access to such loops. I show that more and more problems that are impossible to solve on our current computers, can be solved as the computer gets access to more and more of such loops.