Recent content by PAllen

To me, the idea is that formalizing the notion of global isotropy and homogeneity leads to both topological constraints and geometric constraints. The single statement that the spacetime must be a product of R and a maximally symmetric 3-manifold, contains both. A single statement can have...

It seems to me that global homogeneity and isotropy, formalized as requiring the product of R and a maximally symmetric, homeneous 3-manifold, is both a global topology constraint and a local geometric constraint. Of course it limits the EFE solutions since only those of the FLRW metric (in a...

I have bumped into problems that are trivial given the assumption that there is a well defined answer, but more tedious if you don't assume this and must establish that there is enough information. My favorite is a cylindrical hole cut out of the center of a ball. It turns out the volume of what...

Of course you can look at it either way. Another statement is that Minkowski spacetime is the analytic continuation of the geodesically incomplete Milne spacetime, similar to Kruskal for the exterior Schwarzschild.

Also, in the other thread you thread, you said "No, that's not Minkowski coordinates, that's Milne coordinates. You can't put the Minkowski metric in Minkowski coordinates in the FLRW form, so you can't even define an a(t) for the Minkowski metric in Minkowski coordinates.", referring to a(t) =...

I think you are missing my point. We start with just topology, no metric. The topology we start will is all of ##R^4##. In one case, we place the flat metric on it such that all geodesics are affine complete. In the other case, on the same starting topology, we place the flat metric such that no...

Correct. It’s occurs to me that there is another way to look at this that strongly justifies treating the Milne spacetime as a completely different manifold with metric than Minkowski spacetime. Note that each is homeomorphic to ##R^4##. Let me know if you need an argument to see this. So...

[Moderator's note: Spin-off from another thread due to question change. Edited to remove content specific to the other thread.] You can argue that Milne and Minkowski are different instances of manifold with metric, even though they are both flat, because there is no global isometry between...

Thanks.

A better wording is simply that the time coordinate in Milne coordinates is different than the time coordinate in standard Minkowski coordinates. This is simply because the foliations are different. In Milne coordinates, you are slicing Minkowski spacetime into hyperbolic spatial slices, while...

I think my objection to the utility of simultaneity is its use at large scales, rather than small. Tangents and normals are local objects, and a local frame makes sense. However, globally, giving credence to simultaneity (as an element of reality), even in SR, leads to such nonsense as: for a...

I think one aspect of @pervect 's view is that from the point of invariants, and also, for GR, it is arguably better to say that simultaneity is a concept that should be (almost completely) banished, rather than considered relative. Of, if you insist: any two events such that neither are in the...

Well, some philosophers of foundations of physics use math fully equal to any theoretical physicist. Of course, you can “claim them” as physicists in disguise.

So am I.

You can, but many people have a hard time picturing how this is possible. My suggestion provides a way to picture this that was helpful to me and many others, over the years.