Hidden Underdetermination: A Case Study in Classical Electrodynamics

Abstract

In this article, I present a case study of underdetermination in nineteenth-century electrodynamics between a pure field theory and a formulation in terms of action at a distance. A particular focus is on the question if and how this underdetermination is eventually resolved. It turns out that after a period of overt underdetermination, during which the approaches are developed separately, the two programmes are merged. On the basis of this development, I argue that the original underdetermination survives in hidden form in ontological and methodological redundancies of the subsequent particle–field electrodynamics. Implications regarding criteria for theory choice and the realism debate are briefly addressed.

Acknowledgements

I am much indebted to Mathias Frisch and to two anonymous referees, as well as the editor of this journal, for helpful comments and criticism. Thanks also to audiences at the Pittsburgh Center for Philosophy of Science and at the 2010 Foundations of Physics Meeting in Aberdeen.

Notes

Some authors (e.g. Bonk 2008, 79–82) discuss the equivalence of Wheeler–Feynman electrodynamics with particle–field electrodynamics, which is however only remotely connected with the case study in this essay. A further case of underdetermination in electrodynamics is discussed in Pitts (2011).

It has of course been a long-standing tradition for scientists to discuss methodological questions in the preface to their works. Maxwell is no exception in this respect.

The fact that Duhem distinguishes English, French, and German research styles in physics somewhat suggests that Duhem might even allow for sociological influences in physics.

What we would today call a vacuum is also a dielectric medium in Maxwell's sense.

The interested reader might look at Spohn (2004) or references therein.

These problems are mainly inherited from Dirac's treatment of radiation reaction about which more will be said later on. It is rather unfortunate that action-at-a-distance approaches in classical electrodynamics have been tied so closely to the Wheeler–Feynman theory.

Zeh (2001, 36) cautiously hints that under certain cosmological conditions action at a distance might be ruled out experimentally.

For a detailed exposition of these issues, see Pietsch (2010), 73–74.

Emitter conditions are generally not addressed since they do not form part of the currently most influential action-at-a-distance approach due to Wheeler and Feynman.

For details, consult Rohrlich (2007).

A more detailed critique of the Dirac programme is left for another occasion.

Of course, this is not to claim that pure particle and pure field approaches are without problems.

Although in his later years Feynman largely abandoned the theory, he nevertheless continued insisting on the possibility of action-at-a-distance electrodynamics, e.g. in his Nobel lecture: ‘The fact that electrodynamics can be written in so many ways—the differential equations of Maxwell, various minimum principles with fields, minimum principles without fields, all different kinds of ways, was something I knew, but I have never understood’ (Feynman 1972).

For a recent discussion see for example Worrall (2009).

A further separate issue in this regard is Stanford's problem of recurrent, transient underdetermination (Stanford 2006).

As the discussion of surplus structure shows, structural realists do acknowledge pragmatic criteria like heuristic fruitfulness in theory choice. However, in such instances the surplus structure that serves the pragmatic means should be clearly identifiable.

Additional information

Notes on contributors

Wolfgang Pietsch

Wolfgang Pietsch is at the Lehrstuhl für Philosophie und Wissenschaftstheorie, Carl von Linde-Akademie, Technische Universität München.