Interpretation Formalism

Dean Rickles

1.1 INTERPRETATION AND ONTOLOGY

Can philosophers really contribute to the project of reconciling general relativity and quantum field theory? Or is this a technical business best left to the experts? [.] General relativity and quantum field theory are based on some profound insights about the nature of reality. These insights are crystallized in the form of mathematics, but there is a limit to how much progress we can make by just playing around with this mathematics. We need to go back to the insights behind general relativity and quantum field theory, learn to hold them together in our minds, and dare to imagine a world more strange, more beautiful, but ultimately more reasonable than our current theories of it. For this daunting task, philosophical reflection is bound to be of help. ([Baez, 2001], p. 177)

Although one might not guess it from the above quote, in recent times physicists and philosophers of physics have tended to tread very different paths, and they have generally been a little suspicious of one another. As Michael Redhead points out in the first of his Tarner lectures, "many physicists would dismiss the sort of question that philosophers of physics tackle as irrelevant to what they see themselves as doing" while "philosophers generally regard physicists as naive people, who do physics in an uncritical way" ([1996], pp. 1-2). Reichenbach expresses much the same point even more strongly, suggesting that there is a "mutual contempt in which each misunderstands the purposes of the other's endeavours" ([1958], p. xi).

This hasn't always been the case, of course. As Reichenbach notes, "[t]he classical philosophers had a close connection with the science of their times" (ibid.), Descartes and Leibniz being fine examples. In addition to this, historically, each time a fundamental revolution has occurred in physics (Newtonian mechanics; the relativity theories; quantum theory, etc.) there has generally been an associated shift to a more critical, reflective attitude towards theory construction. Indeed, Kuhn appears to suggest that such a shift is a necessary part of scientific revolutions:

Kuhn also seems to give a very accurate depiction of the present situation in quantum gravity1 when he writes that:

One of the main aims of this book is to highlight the extent to which many problems of quantum gravity are predominantly 'philosophical' in their nature and origin—these spring in large part from aspects of the classical theory. But despite this, though physicists have been known to take up more philosophical attitudes in times of crisis, 'the philosophers' have previously remained firmly divided from the constructive practice of theory building in physics, waiting in the wings, as it were, until the theories were deemed sufficiently well established to warrant their attention.

The strange case of quantum gravity, as this book will try to show, offers us a place where philosophers might play a role in the more constructive parts of the foundations of physics—though, of course, it is highly doubtful that this will include an involvement in the technical foundations. Tian Yu Cao, believing consistency and conceptual clarity to be of the essence in quantum gravity (his point being, there is no experimental basis), makes a similar point:

There are at least three reasons behind this possibility as I see it: (1) these days philosophers of physics are simply better equipped in terms of their command of the necessary parts of mathematics and physics required—most of them having done their original training and research in physics, and often publishing in physics journals, (2) quantum gravity is an area of physics lacking an experimental basis from which to test the various proposals, thus forcing conceptual and mathematical consistency to take center stage. What's more, (3) it appears that the kinds of conceptual problem that litter the field of quantum gravity are ones that philosophers are already well familiar with, as I have already suggested, and aim to show in more detail.2

Philosophers, however, have generally been rather slow to pick up the challenge of quantum gravity, seemingly more content to flog poor old non-relativistic quantum mechanics to death! This is made all the more surprising given that many researchers engaged in quantum gravity actively encourage the involvement of philosophers in their discipline. For example, Carlo Rovelli (one of the physicists who created the popular approach known as 'loop quantum gravity'—a genuinely viable alternative to string theory) explicitly voices this opinion:

Up until very recently the same might have been said of (specially) relativistic quantum field theory, though lately there has been a definite shift of emphasis from non-relativistic quantum mechanics to relativistic quantum field theory— a very welcome move in my opinion. As welcome as this shift is though, methodologically the philosophy of relativistic quantum field theory is the same as non-relativistic quantum mechanics (and likewise subject to Rovelli's gripe): the mathematical and theoretical framework exists (admittedly, modulo certain nasty consistency problems in the interacting theory—i.e., Haag's theorem) and the experimental data is there to confirm this pre-given framework; the job of the philosopher of physics is to examine and interpret this framework and its relation to the world. The uniqueness of quantum gravity as a challenge to philosophers arises precisely from the lack of such an established framework and associated medley of confirming experiments, and philosophers would do well to shift their gaze in its direction because of this feature.

Of course, some might suggest that, quite to the contrary, this in fact gives one more reason to divert one's gaze! The worry here, if I understand the objection's direction correctly, is that it is pointless3 for philosophers to apply their skills to a theory that does not yet exist, and they should, therefore, stand on the sidelines until the theory has sufficiently matured to warrant such attention. I don't think we need take this stance. Although it is true that there is no definitive theory of quantum gravity—nor does it look likely that there will be for some time to come—, there are a number of ways in which one can approach the theories we do have without risking irrelevance. The crucial philosophical aspect concerning quantum gravity is how to interpret a background free (i.e. diffeomorphism invariant) quantum field theory—the technical aspect is, of course, how to construct one!4 This notion can be analyzed independently of specific proposals that aim to implement it; moreover, we can be fairly confident (given what we know about general relativity) that the 'final' theory of quantum gravity will implement this feature.5 It is, therefore, to this aspect that I devote my attention and, in particular, to the specific conceptual problems that result from background independence and symmetry (the former involving the latter in a highly non-trivial way).

To understand what background independence is, I first need to say something about the relationship between ontology and interpretation, and the way in which symmetry blackens the already muddy waters. My account of this relationship is based upon models that encode information about a theory's (possible) ontology (or ontologies). Background independence is then seen to be a feature of these models that is caused by a high degree of symmetry. It is a certain class of symmetry that I am interested in: those that preserve all qualitative structure of a model or world (see below for more on the notion of 'qualitative'). One of the central themes of this work is that these symmetries cause ontology to be radically underdetermined, making the task of the interpreter very difficult indeed. As I will show, it is always possible to choose a formalism (or an interpretation) without these symmetries but this too will be underdetermined by the...