Studia Logica

, Volume 95, Issue 1, pp 279–300

Physical Oracles: The Turing Machine and the Wheatstone Bridge

  • Edwin J. Beggs
  • José Félix Costa
  • John V. Tucker
Article

DOI: 10.1007/s11225-010-9254-6

Cite this article as:
Beggs, E.J., Costa, J.F. & Tucker, J.V. Stud Logica (2010) 95: 279. doi:10.1007/s11225-010-9254-6

Abstract

Earlier, we have studied computations possible by physical systems and by algorithms combined with physical systems. In particular, we have analysed the idea of using an experiment as an oracle to an abstract computational device, such as the Turing machine. The theory of composite machines of this kind can be used to understand (a) a Turing machine receiving extra computational power from a physical process, or (b) an experimenter modelled as a Turing machine performing a test of a known physical theory T.

Our earlier work was based upon experiments in Newtonian mechanics. Here we extend the scope of the theory of experimental oracles beyond Newtonian mechanics to electrical theory. First, we specify an experiment that measures resistance using a Wheatstone bridge and start to classify the computational power of this experimental oracle using non-uniform complexity classes. Secondly, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on our ability to measure resistance by the Wheatstone bridge.

The connection between the algorithm and physical test is mediated by a protocol controlling each query, especially the physical time taken by the experimenter. In our studies we find that physical experiments have an exponential time protocol; this we formulate as a general conjecture. Our theory proposes that measurability in Physics is subject to laws which are co-lateral effects of the limits of computability and computational complexity.

Keywords

Turing machine physical oracle experimental procedure theory of measurement Wheatstone bridge physically measurable numbers 

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Edwin J. Beggs
    • 1
  • José Félix Costa
    • 2
    • 3
  • John V. Tucker
    • 1
  1. 1.School of Physical SciencesSwansea UniversitySwanseaWales, United Kingdom
  2. 2.Department of Mathematics, Instituto Superior TécnicoUniversidade Técnica de LisboaLisboaPortugal
  3. 3.Centro de Matemática e Aplicações, Fundamentais do Complexo InterdisciplinarUniversidade de LisboaLisboaPortugal