Antigone M. Nounou

Scientific understanding comes in different kinds, and each kind comes in degrees. Two of these kinds are revealed by the examination of a recent episode from the history of physics: the making of the theory of strong interactions. The first of these kinds of understanding is associated with the realization that some mathematical formalism or theory may have a fruitful application to physical phenomena. This is what I call prior understanding. Yet another kind is associated with the development of the mathematical formalism into a physical theory that purports to be mathematically consistent and empirically complete –at least in the domain of its applicability. This second kind I call internal understanding. None of these two kinds is conferred by explanations; both are associated with what some authors have called genuine or scientific understanding; and both are epistemically relevant in that they are required for the achievement of some of science’s epistemic aims.

The modern debate around scientific structuralism has revealed the need to reassess the standing and role of both structure and objects in the metaphysics of physics. Ontic structural realism recommends that metaphysics be purged of objects. Nonetheless, its proponents have failed to specify what it means for properties to be relational and structural, and, consequently, to show how the elementary objects postulated by our best theories can be re-conceptualized in structural terms or altogether eliminated. In this paper, I draw from modern physics in order to untangle various types of relational properties and propose a definition for structural properties.

I argue that the Holonomy Interpretation, at least as it has been presented in Richard Healey’s Gauging What’s Real, faces serious problems. These problems are revealed when certain approximations and idealizations that are innate in the original formulation of the Aharonov-Bohm effect are thrust aside; in particular, when the temporal dimension is taken into account. There are two ways in which time re-appears in the picture: by considering complete solutions to the original problem, where the magnetic flux is static, and by examining the effects of time dependent magnetic fluxes. Both cases expose explanatory gaps in the Interpretation, as well as conflicts between it and customary ideas about relativistic locality and local action on which the Interpretation depends

Στις κβαντικές θεωρίες πεδίου, οι οποίες στην πιο ολοκληρωμένη τους μορφή εκφράζονται μέσω του μαθηματικού φορμαλισμού που ονομάζεται δεσμίδες ινών (fibre bundles), χρησιμοποιούνται εκτενώς η έννοια της συμμετρίας και η αλληλένδετη με αυτήν έννοια της διατήρησης. Ο στόχος του παρόντος άρθρου είναι η αποσαφήνιση του όρου συμμετρία, όπως αυτός εμφανίζεται στο εν λόγω πλαίσιο, καθώς και η εξέταση του ρόλου κάποιων συγκεκριμένων μαθηματικών δομών , οι οποίες εμφανίζονται ως αποτέλεσμα της χρήσης των συμμετριών, στην επιστημονική εξήγηση των φαινομένων που περιγράφονται από τις κβαντικές θεωρίες πεδίου.

To single one out of the infinitely many, empirically indistinguishable gauge potentials of classical electrodynamics, and to deem it `more real' than the rest is not trivial. Only two routes are open to one who might attempt to do so. The first leads to a slippery slope: if one singles out a potential solely by requiring it to admit well behaved propagations, and on the strength of this behavior one subscribes to its reality, one inevitably subscribes to the reality of infinitely many. As for the second, it seems to be barred from the beginning. But if, for reasons of metaphysical economy, one insisted on taking it, it would lead to a `truncated theory' that is physically and empirically inferior to the complete.

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the so-called holonomies are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function.