Perdurance and particles

A perdurantist who believes that particles are fundamental will typically think that the truly fundamental physical entities are instantaneous particle-slices.

But particles are not spatially localized, unless we interpret quantum mechanics in a Bohmian way. They are fuzzily spread over space. So particle-slices have the weird property that they are precisely temporally located—by definition of a slice—but spatially fuzzily spread out. Of course, it is not too surprising if fundamental reality is strange, but maybe the strangeness here should make one suspicious.

There is a second problem. According to special relativity, there are infinitely many spacelike hyperplanes through spacetime at a given point z of spacetime, corresponding to the infinitely many inertial frames of reference. If particles are spatially localized, this isn’t a problem: all of these hyperplanes slice a particle that is located at z into the same slice-at-z. But if the particles are spatially fuzzy, we have different slices corresponding to different hyperplanes. Any one family of slices seems sufficient to ground the properties of the full particle, but there are many families, so we have grounding overdetermination of a sort that seems to be evidence against the hypothesis that the slices are fundamental. (Compare Schaffer’s tiling requirement on the fundamental objects.)

A perdurantist who thinks the fundamental physical entities are fields has a similar problem.

A supersubstantialist perdurantist, who thinks that the fundamental entities are points of spacetime, doesn’t run into this problem. But that’s a really, really radical view.

An “Aristotelian” perdurantist who thinks that particles (or macroscopic entities) are ontologically prior to their slices also doesn’t have this problem.