Author(s): Schmitz, Timothy | Advisor(s): Barrett, Jeffrey A | Abstract: Our epistemic limits depend on the nature of the physical world we inhabit and the ways in which we can observe and manipulate it. This dissertation examines these limits in the realm of physical computation. It focuses on quantum computing and particularly computing in GRW quantum mechanics, although it has implications for both quantum computing in particular and physical computation more broadly. By rigorously investigating the conceptual issues that arise when looking at computation in GRW, we see how the conceptual issues in the foundations of quantum mechanics and our solutions to these issues determine what models of quantum computation can be realized and what quantum computing can achieve. More broadly, we see how grounding our discussions of physical computation in precise physical theories informs our understanding of computational and epistemic limits and illustrates the challenges and nuances involved in the work of developing a rigorous understanding of what is physically computable.
The purpose of this talk is to single out some physical assumptions that commonly underpin physical computation, several models of computation (discrete and continuous) as well as the notion of "algorithm" itself. In particular, it is argued that scientific representation is inextricably intertwined with physical computation, and so necessary conditions for the former are also necessary conditions for the latter (and for computation in general). I discuss some physical situations where such conditions are violated and show that uncomputability results arise in such situations as well.