David Braddon-Mitchell and Kristie Miller have a fun new paper arguing that we can both believe in spatially extended mereological simples and agree that every extended object o has a part at each sub-region of the region which o occupies. The trick which is supposed to enable us to marry these two theses is to claim that space has smallest regions which have no sub-regions. (This is a position I've heard defended in conversation by others as well, so I'm coming round to the view that it ought to be taken seriously.)
For many of us, quantized space seems a very strange idea on the face of it, but Braddon-Mitchell and Miller argue that it must be taken seriously because of certain results in physics. They claim that 'physicists tell us that we cannot divide up space into any finer-grained regions than those constituted by Planck squares [i.e. areas of 10 to the power -66 centimetres squared]' and that physics 'tells us that talk of space breaks down altogether once we talk about regions smaller than the Planck square'. 'Hence', they conclude, 'we know that talking about something occupying a sub-region of a Planck square makes no sense: there is no such sub-region' (p. 224).
When they give a few details of what the physics actually shows, it turns out to be that 'there is nothing that could be taking place within these squares'. Braddon-Mitchell and Miller take it (and this is where I get puzzled) that this 'is to say that in principle, there cannot be anything that occupies the sub-regions of such a square' (p. 224, their emphasis).
For all I know, physicsists may well be claiming this sort of import for that sort of result, but I can't see how the transition could be that straightforward. What I can't understand is how any claim about what can or cannot take place with a Planck square - which is of course the sort of thing physicists can helpfully tell us about - could settle the question of whether such a square has sub-regions. Specifically, I wonder what sort of results are supposed to distinguish between the hypotheses:
1. that Planck squares have no sub-regions
2. that any Planck square (and therefore any sub-region of a Planck square) must, as a matter of nomic necessity, be uniformly filled.
The claim that nothing can be 'taking place' within a Planck square seems at best to get us as far as 2. What justifies the further step to 1? What sort of result from physics as it is currently practiced could possibly justify this further step?
(I ask these questions in self-confessed ignorance of the physics, but with a dose of scepticism as to whether we can get this much metaphysics out of it, whatever it is!)