The Gauge Interpretation of the Conventionality of Simultaneity

In this work we will consider gauge interpretations of the conventionality of simultaneity as developed initially by Anderson and Stedman, and later by Rynasiewicz. We will make a critical reassessment of these interpretations in relation to the “tradition” as developed in particular by Reichenbach, Grünbaum, and Edwards. This paper will address different issues, including: the relation between these two gauge interpretations; what advantages or defects these gauge approaches might have; how “new” Rynasiewicz’s approach in relation to the previous ones is; how much of the gauge interpretation Rynasiewicz actually applies to deal with objections to the conventionality of simultaneity thesis. The conclusion is that the gauge interpretations, in their current formulation, do not provide a better “rationale” of the conventionality of simultaneity thesis that supersedes the “tradition”.

The Conventionality of Simultaneity and Einstein’s Conventionality of Geometry

The conventionality of simultaneity thesis as established by Reichenbach and Grünbaum is related to the partial freedom in the definition of simultaneity in an inertial reference frame. An apparently altogether different issue is that of the conventionality of spatial geometry, or more generally the conventionality of chronogeometry when taking also into account the conventionality of the uniformity of time. Here we will consider Einstein’s version of the conventionality of (chrono)geometry, according to which we might adopt a different spatial geometry and a particular definition of equality of successive time intervals. The choice of a particular chronogeometry would not imply any change in a theory, since its “physical part” can be changed in a way that, regarding experimental results, the theory is the same. Here, we will make the case that the conventionality of simultaneity is closely related to Einstein’s conventionality of chronogeometry, as another conventional element leading to it.

Time in the Special Theory of Relativity

Restricted to special relativity, this chapter observes that the most significant change in the concept of time is certainly the relativity of simultaneity. What events are simultaneous with some event for one observer are different from those that are simultaneous with respect to an object traveling in a different inertial frame. Many believe that this relativity can play a role in an argument for eternalism. This chapter critically surveys these arguments before taking on the implications of relativity for the metaphysics of time. It also tackles the conventionality of simultaneity. Many philosophers of science, especially during the early days of relativity, felt that simultaneity is not only relative but also conventional—there is a crucial element of choice in deciding what events are simultaneous for any other in a given inertial reference frame, so that there is no fact of the matter about what is simultaneous.