Invariance and Objectivity

Abstract

There are three strands to our ordinary notion of an objective fact or objective truth. First, an objective fact is accessible from different angles. It can be repeated by the same sense (sight, touch, etc.) at different times, it can be repeated by different senses of one observer, and by different observers. Different laboratories can replicate the phenomenon. What can be experienced only at one instant by one sense modality of one observer is indistinguishable from random noise, and does not (securely) count as an objective fact. second mark of an objective truth, related to the first, is that there is or can be intersubjective agreement about it. And the third feature concerns independence. If p is an objective truth, then it holds independently of people's beliefs, desires, hopes, and observations or measurements that p. These three features of objective truths certainly are in need of elaboration and refinement, if only to meet the counterexamples to thinking of them as individually necessary and jointly sufficient. We also may wonder how the notion of independence fares in the light of quantum mechanics. However, it is a fourth and more fundamental characteristic of objective truth that I want to investigate here today. An objective fact is invariant under various transformations. It is this invariance that constitutes something as an objective truth and it underlies and explains the first three features (to the extent that they hold). That invariance is importantly connected to something's being an objective fact is suggested by the practice of physicists, who treat what is invariant under Lorentz transformations as more objective than what varies under these transformations. Dirac writes, The important things in the world appear as the invariants... of ... transformations.1 Einstein taught us that spatial distance and temporal distance are relative to an observer; their magnitudes will be measured differently by different inertial observers, and spatial and temporal intervals are not invariant under Lorentz transformations. However, inertial observers will agree about another more complicated interval between events, involving not just spatial separations alone or temporal separations alone but a particular mixture of the two, namely, the square root of the square of the time separation minus the square of the spatial separation. This more complicated interval is invariant under Lorentz transformations. principle of relativity of Einstein's Special Theory holds that all laws of physics are the same for all inertial observers; they are the same in every inertial reference frame, and so are invariant under Lorentz transformations. That an interval involving both temporal and spatial separation is invariant, while no simpler interval involving only temporal or only spatial separation is