Criteria of physical significance for quantities in physics

Abstract

Criteria of physical significance for quantities in physics Philosophers of physics like to describe their task as that of interpreting physical theories. The most famous debate over the interpretation of a physical theory is undoubtedly the interpretation of quantum mechanics, but other theories, like the special and general theories of relativity, classical electromagnetism, and quantum field theory have also seen controversial attempts at interpretation. One of the key elements of providing an interpretation of a given theory in physics is to distinguish the ‘physically significant’ elements of a theory from those that are ‘merely mathematical’. This raises the question of what exactly distinguishes the former from the latter. In my paper I address that questions specifically with respect to quantities, where the matter of physical significance has often seemed especially pressing. The reason the question of physical significance has often seemed especially pressing in the case of quantities, is that quantities are entities which can be characterized mathematically: they can appear in mathematical equations. Since it is common in the philosophy of physics to regard the mathematical formalism of a theory to be open to physical and philosophical interpretation, those equations are usually what is taken to be the theory to be interpreted. The question faced by anybody trying to interpret a theory is then to decide, which of the quantities appearing in the equations can be regarded as physical. My strategy in the paper is as follows: First I develop a list of criteria, which have de facto been employed in arguments in favor or against the physical reality of particular quantities: observability, causal efficacy, scale invariance and observer independence. I sort those criteria into ones which have been taken as necessary, sufficient, and necessary and sufficient respectively. Second I ask whether these criteria are ever in conflict, and if so, which criteria win out. The history and philosophy of physics offer several important examples of this: electric and magnetic fields, absolute acceleration, vector potentials in electromagnetism. From these examples I develop a distinction between criteria, which aim at the causal significance of a quantity, and those, which aim at the invariance of a quantity. I then go on to use this distinction to re-evaluate the conflicts in question. I conclude that the conflict between such criteria and the ensuing philosophical debates over the ontological status of particular quantities arises typically from a conflict between the apparent causal efficacy of a quantity and the failure of that quantity to be sufficiently invariant. But since these two sorts of criteria are not on a par, I suggest that the conflict in question can be understood as a sign of the gap between two ideals of scientific theorizing: to include all causally relevant factors, on the one hand, and on the other hand to have a theory that is maximally invariant. Any actual theory will only be adequate if it takes into account all (seemingly) relevant causal factors in the description and explanation of a particular phenomenon. But the extent to which such a theory fails to do so using only maximally invariant quantities can be regarded as a measure of the distance the actual theory bears to the ideal theory.