Daniel E. Barnett

Simon Saunders and Vesselin Petkov argue four-dimensionalism is the only ontology compatible with special relativity. Saunders argues the requirement of intersubjectivity requires four-dimensionalism, whereas Petkov argues the relativity of simultaneity, relativistic length contraction, and the twins paradox require a block universe model. Each succeeds in showing a certain species of presentism is not compatible with special relativity, but neither shows either that three-dimensionalism is incompatible with—or that four-dimensionalism is essential to—special relativity. Both fail to show three-dimensionalism is incompatible with special relativity because both erroneously conflate three-dimensionalism with the concept of a spatially extended present time. When the speed of light is finite in a three-dimensional world, though, the resulting world is special relativistic. In formulating their separate—but related—arguments for four-dimensionalism, Saunders and Petkov repeat the error of Putnam, Rietdijk, and others of conflating what exists with what lies on a perspectival line of simultaneity. Because their arguments ascribe ontological meaning to a perspectival feature, their ontological conclusions are unwarranted. Moreover, because the block universe argument relies on infinitely fast propagation of light signals, the block universe and special relativity are in fact mutually exclusive.

Neither eternalism nor standard presentism captures both all of the tenets of Special Relativity and our observation that the universe is dynamic. A three-dimensional universe of dynamic, space-like separated particles captures both. Although three-dimensionalism contemplates no spatially extended present, it is not solipsism because the things we see on our past light cones endure in some form. The ontology of a dynamic, three-dimensional universe allows us to quantify the rate at which time elapses as a function of the rate at which photons recede in vacuo. It is shown that intuitive ideas related to elapse of time that are argued by others to be philosophical dead ends in an eternalist block universe find ready explanation in a dynamic, three-dimensional universe.

Balashov and Janssen (2003) on the one hand and Brown and Pooley (2006) on the other hand debate whether the structure of Minkowski spacetime or the Lorentz invariance of physical laws fundamentally grounds Special Relativity. In addition to a debate about what is fundamental, it is a debate about whether the Minkowskian structure of spacetime explains the Lorentz invariance of physical laws or the Lorentz invariance of physical laws explains why spacetime is Minkowskian. I argue neither side states what fundamentally grounds Special Relativity. Instead, a constructive derivation of Special Relativity is provided based on the properties of light and a homogeneous, isotropic universe. Special Relativity is shown to be concerned with nothing more than the units of space and time and the effect of relative motion on those units as described by the Lorentz boost. Minkowski spacetime can be constructed from the Lorentz boost, but it does not add structure to spacetime. Dynamical laws governing the microstructure of matter in turn instantiate Lorentz boosts because they incorporate units of space and time in their equations.