Are Gandy Machines really local?

Abstract This paper discusses the empirical question concerning the physical realization (or implementation) of a computation. We give a precise definition of the realization of a Turing-computable algorithm into a physical situation. This definition is not based, as usual, on an interpretation function of physical states, but on an implementation function from machine states to physical states (as suggested by Piccinini 2012). We show that our definition avoids difficulties posed by Putnam’s theorem (1988) and Kripke’s objections (Stabler 1987; Scheutz 2001). Using our notion of representation, we analyse Gandy machines, intended in a physical sense, as a case study and show an inaccuracy in Gandy’s analysis with respect to the locality notion. This shows the epistemological relevance of our realization concept. We also discuss Gandy machines in quantum context. In fact, it is well known that in quantum mechanics, locality is seriously questioned, therefore it is worthwhile to analyse briefly, whether quantum machines are Gandy machines.