Perdurance, Relativity and Quantum Mechanics

It is known that perdurantists, who hold that objects persisting in time are made of infinitely thin temporal slices, have to deny that fundamental particles are simple (i.e., do not have (integral) parts). For a fundamental particle is an object persisting in time, and hence will be made of particle-slices.

But what is perhaps not so well-known is that on perdurantism, the temporal slices a particle is made of will typically not be simple either, given some claims from standard interpretations of Quantum Mechanics and Special Relativity. The quick version of the argument is this: the spatial non-localizability of quantum particles requires typical temporal slices to be non-localized simples (e.g., extended simples), but this runs into relativistic problems.

Here is a detailed argument.

A perdurantist who takes Relativity seriously will say that for each inertial reference frame R and each persistent object, the object is made of R-temporal slices, where an R-temporal slice is a slice all of whose points are simultaneous according to R.

Now, suppose that p is a fundamental particle and that p is made up of a family F₁ of temporal slices defined by an inertial reference frame R₁. Now, particles are rarely if ever perfectly localized spatially on standard interpretations of Quantum Mechanics (Bohmianism is an exception): except perhaps right after a collapse, their position is fuzzy and wavelike. Thus, most particle-slices in F₁ will not be localized at a single point. Consider one of the typical unlocalized particle-slices, call it S. Since it’s not localized, S must cover (be at least partially located at) at least two distinct spacetime points a and b. These points are simultaneous according to R₁.

But for two distinct spacetime points that are simultaneous according to one frame, there will be another frame according to which they are not simultaneous. Let R₂, thus, be a frame according to which a and b are not simultaneous. Let F₂ be the family of temporal slices making up p according to R₂. Then S is not a part (proper or improper) of any slice in F₂, since S covers the points a and b of spacetime, but no member of F₂ covers these two points. But:

1. If a simple x is not a part of any member of a family F of objects, then x is not a part of any object made up of the members of that family.

Thus, if S is simple, then S is not a part of our particle p, which is absurd. Therefore, for any reference frame R and particle p, a typical R-temporal slice of p is not simple.

I think the perdurantist’s best bet is supersubstantialism, the view that particles are themselves made out of points of spacetime. But I do not think this is a satisfactory view. After all, two bosons could exist for all eternity in the same place.

Without Relativity, the problem is easily solved: particle-slices could be extended simples.

It is, I think, ironic that perdurantism would have trouble with Relativity. After all, a standard path to perdurantism is: Special Relativity → four-dimensionalism → perdurantism.

I myself accept four-dimensionalism but not perdurantism.