Now, some days ago, author of said paper contacted me to let me know I allegedly “completely failed to understand” what he wrote, and urged me to publish my writing in a journal so he could react to it, followed by “friendly warnings”. If I come around to converting my post appropriately, I might indeed send it somewhere, but it admittedly isn't very high on my list of priorities. As far as I am concerned, I said what I had to say, and the eternal reinterpretation of Special Relativity isn't a topic I am particularly keen on engaging in to begin with. It followed some back and forth of emails that did not amount to anything.
Such reminded that my statement might have confused some people, I thought it would be worthwhile to briefly summarize the point of my argument. It really isn't so hard to understand. Special Relativity is based on these axioms:
- Space and time form a 4-dimensional, flat, differentiable manifold with Lorentzian signature.
- The laws of physics are tensor equations over this manifold.
My argument is now simply, from these axioms you can not follow what “existence” means, thus you can not outrule presentism for it builds on this notion. You can then go ahead and produce a lot of fog by talking about clocks and rods and rulers and twins etc, but all of this is completely irrelevant. If you introduce additional assumptions about what constitutes a physical object then you might be able to come to conclusions. But these assumptions do not follow from Special Relativity and should be named explicitly.
As a concrete counter example for the claim that shows why this talk is empty, I suggested the following: Introduce an arbitrary time-like slicing in Minkowski-space and name it “existence slicing” to mean what is on the same slice “exists” together. This is not incompatible with Special Relativity.
No, there isn't anything more to this example, that was already it. I've shown one can define a notion of “existence” only on 3-dimensional submanifolds and this is compatible with Special Relativity. Now you can say you don't like this definition of “existence”. Fine. Nobody said you have to.
If you want you can understand “together” in the above example as “simultaneous”. This is not the notion of simultaneity commonly used in Special Relativity (based on inertial observers), but nobody forbids you to introduce a different one as you please. Again, you might not like that, but that was not a requirement I aimed to fulfill. For more precise statements, please see mentioned earlier post.
Just to make it clear, I personally don't even believe in presentism, I am just trying to say that the claim it is outruled through Special Relativity is logically false. If you want to come to any conclusions, you will need additional assumptions for what you mean with “existence”.