Are Virtual Quanta Nothing but Formal Tools?

Abstract

The received view in philosophical studies of quantum field theory is that Feynman diagrams are simply calculational devices. Alongside this view we have the one that takes virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of physics by Mario Bunge, Paul Teller, Michael Redhead, Robert Weingard, Brigitte Falkenburg, and others. In this article I present an alternative to the received view.

Acknowledgements

I thank two anonymous referees of this journal for helpful comments on a previous draft.

Notes

[1] The philosophical debate about virtual quanta is usually developed as if we had to choose between just two possibilities: (1) see virtual quanta just as formal tools resulting from a diagrammatic approach to a perturbative calculation; (2) treat virtual quanta realistically (i.e. at an ‘ontological level’) as the bearers of the quantum interaction. I consider that there are alternatives to (1) and (2). One example is Rom Harré’s (1988) view which while not agreeing with (1) does not go as far as defending (2). Here I will make the case that there is no solid argument that proves (1) and that there are reasons to take virtual quanta to be more than just formal tools. However this, by itself, does not imply (2). In particular I will focus more on making epistemic and operational claims regarding virtual quanta than on presenting any positive argument regarding a possible ontological structure of the quantum interaction in which virtual quanta might have a role.

[2] The S‐matrix program was originally developed by Werner Heisenberg as an alternative to quantum field theory. His idea was to sidestep the problem of divergences in quantum field theory—in his view due to the point‐like interaction between the fields—by considering only what he saw as measurable quantities (Miller 1994, 97). Heisenberg’s idea was to retain only the basic elements of quantum field theory, like the conservation laws, relativistic invariance, unitarity, and others, and to make the S‐matrix the central element of a new theory (Pais 1986, 498). This was not done because, in practice, it was not possible to define an S‐matrix without a specific use of the theory it was intended to avoid (Cushing 1986, 118). The S‐matrix later reappeared in mainstream physics with Dyson’s use of it as a calculational tool. In Dyson’s view the ‘Feynman theory will provide a complete fulfilment of Heisenberg’s S‐matrix program. The Feynman theory is essentially nothing more than a method of calculating the S‐matrix for any physical system from the usual equations of electrodynamics’ (quoted in Cushing 1986, 122).

[3] For example, Mario Bunge takes the virtual quanta (and interaction processes described as exchange of virtual quanta) to be ‘fictions and as such have no rightful place in a physical theory’ (Bunge 1970, 508); Paul Teller’s view is that ‘a Feynman diagram is only a component in a much larger superposition’ (Teller 1995, 139); and Fritz Rohrlich considers that ‘virtual particles are an artifact of the perturbation expansion into free particle states’ (Rohrlich 1999, 363).

[4] There might appear to be ways of sidestepping this type of approach by considering the Feynman path integral approach (Weingard 1988, 54). But again, when considering the specific applications of the theory there is no infinite expansion of the transition amplitudes. In the mathematical expression for the transition amplitudes there are propagators, and the interpretation of the propagators relating them to quanta cannot be overturned in a (finite expansion) application based on path integrals.

[5] The philosophical implications of this situation are certainly important. However any tentative treatment of this subject would go far beyond the topic of this article.

[6] For details on the operational meaning of ‘single out’ see Falkenburg (2007, 237–238).