one boxers of the world unite!
I wrote a Galilean dialogue w James Read on the hole argument and determinism. It is essentially a fruitful email exchange we had after we each had published papers diametrically opposed to each other. It was a fun project!
philosophyofphysics.lse.ac.uk/articles/10....
Given your interests and your posts here, I think you'd love being a philosopher of physics! There are lots of grad students at LPS who switch out of math/physics after realizing it's not where their passion is. But with good technical skills (like you), they often pick things up very quickly...
The Bobs are indeed paragons of clarity! I was fortunate to have Bob G on my dissertation committee. I am perhaps a bit biased but the pinnacle of GR clarity is David Malament (also at Chicago during the golden age). His 2012 book is my bible. I don't believe in God but I do believe in David. #wwdd
Wiki is wrong! Wald (1984) will never lead you astray...
S spacetime is usually understand to be stationary, e.g. Wald in his book. This means there is a global timelike KF. The K extension doesn't have a global timelike KF for the reasons you give. So Wald and anyone else who claims S is stationary must also take S to be just the exterior region.
It's also good that you picked up on the difference between a global timelike KF and the stronger condition of a global timelike isometry. Imagine Minkowski spacetime with the t<0 region deleted. Still has a global timelike KF but there is no global timelike isometry!
Exactly! The Killing vector field d/dt becomes spacelike inside the EH. As you say: can't flow along d/dt into the singularity. So you are right that the Kruskal extension is not stationary (bc no global timelike KF) but S spacetime is (bc global timelike KF).
Hi Rochelle! S spacetime (M,g) has a timelike isometry! Write the metric g in (t,r, theta, phi) coordinates. Now consider the map f: M --> M defined by f(t,r,theta,phi)=(t+1,r, theta, phi). Notice that none of the metric components depend on t and d(t+1)=dt. So f*(g)=g and f is an isometry.
New piece on "Heraclitus spacetime" out today!
#physics #philsky #philsci
iai.tv/articles/the...
For example, Leibniz’ metaphysical principle of plenitude is connected to the arrow properties of a GR category. Plenitude is harder to defend if, for example, some spacetimes don’t have maximal extensions. This doesn’t happen when the GR objects are the standard collection (Geroch 1970).
In my paper “General Relativity As a Collection of Collections of Models”, I settle one of the open questions Geroch asks (concerning energy conditions) and I also explore many others. (By the way, this is the same volume as Jim’s paper!)
He highlights some open questions about spacetime maximality which are equivalent to questions about how the arrows work under various choices of categorical GR objects.
This turns the study of the property of the arrows into the study of spacetime (in)extendibility/maximality! Appendix B of Geroch’s paper “Singularities” is the place to start for foundational work on this.
From here on out, let’s restrict attention to the choice of isometric embeddings: there is an arrow from the spacetime (M,g) to the spacetime (M’,g’) iff (M,g) can isometrically embedded into (M’,g’), i.e. “extended” by (M’,g’).
the collection of vacuum solutions to Einstein’s equations, the collection of spacetimes without closed timelike curves, etc.
2. How does the choice of objects change the arrow properties of the category?
For (i) the objects, one could consider various collections of GR spacetimes. Of course, we have the standard collection of spacetimes (connected Hausdorff smooth Lorentzian manifolds) but have can also consider a number of subcollections defined by some physically reasonable property, like:
😍
What happens when you remove a carefully chosen Cantor set from time-rolled Minkowski spacetime? You settle a extendibility question posed by Bob Geroch 55 years ago!
Also, I want to add that I just yesterday saw that Krasnikov died last year. This made me sad. We had many lovely emails back and forth throughout the years and he was always very kind to me.
Nice connection re: "local" spacetime properties! The original Krasnikov theorem used a definition of "local" that turned out to be inadequate and rendered his theorem false. I published a counterexample and he later adopted a new definition of "local" fixed things up (see [v4] of the link you give)
Yes! Check out Wald (1984) for a nice discussion how the CBG theorem can be generalized to certain non-vacuum collections as well. Our paper mentions this and our results generalize in a natural way…
Indeed! We focus on the collection of spacetimes that was already known to be deterministic in the weaker sense due to the famous Choquet-Bruhat and Geroch (1969) theorem: four-dimensional, globally hyperbolic, maximal vacuum solutions to Einstein's equation.
Had an absolute blast writing this paper with Thomas, Hans, and
@jamesowenweatherall.com!
GR turns out to be way more deterministic than previously appreciated. The past determines the future not only up to isomorphism but up to *unique* isomorphism! 🤯
Haha. Symmetry buddies are really hard to find -- hang in there!
Oxford talk on Spacetime Asymmetry just uploaded...
Among other things, we show that the claim must fail for "Heraclitus" spacetimes -- models that have no local symmetries at all.
It is sometimes claimed that the "privileged coordinates" of geometric model (e.g. a relativistic spacetime) encode its "structure". In a paper just out in Philosophy of Science (open access), Thomas Barrett and I explore the limitations of this idea...
www.cambridge.org/core/journal...
New issue out now! Featuring evolutionary transitions and cumulative culture, hole arguments and jury theorems, Galileo’s ship and best laid plans, distinguishing the indistinguishable, and so much more…
Read it here: www.journals.uchicago.edu/toc/bjps/202...
#philsci #philsky #hps
Two new papers out today on "determinism" co-authored with the foundations of (a)symmetries dream team: @jimweatherall.bsky.social, Hans Halvorson, and Thomas Barrett. #philsci #philsky
philsci-archive.pitt.edu/24881/
philsci-archive.pitt.edu/24883/
