ok I should be more clear: At least the thermodynamic arrow of time is not known to have reversed during cosmological evolution so far, in answering Yuvrak question on whether time reversal is possible
I don't know what happened to the other arrow of times in cosmological history, especially the quantum ones
@Slereah Thanks for the references on (2+1)-D gravity and junction conditions, made significant progress. Was wondering if you knew any papers which talk about computing the Einstein-Hilbert action with a source placed at the screen (at some r=R)?
You had suggested Carlip's book on (2+1)-D black holes, I was referring to that
As for the action question, we consider a spacetime with a source on a screen (shell at r=R). Now, at $V^{-}$ there's gonna be flat space and at $V^{+}$ space is gonna be Schwarzschild-like. I was wondering what the contribution of the source, say J(R), would be to the action.
@ACuriousMind Maybe I should start a meta post suggesting we make a new vote to close reason where the close banner is just a link to this comic
On a somewhat more serious note, would there be any way to have the site make some warning pop up if a user is making a question and types the words "My attempt"? I feel like usually questions that have that phrase are just "check my work" questions that should be closed.
@DanielSank Why do you think Banach-Tarski is nonsense? It doesn't apply to physical objects made of atoms, though. It only works on mathematical objects made of a continuous substance. It's trivial to construct a bijection between a 1×1×1 cube & a 2×2×2 cube.
Banach-Tarski is interesting because it says you can perform that bijection using a dissection into a small number of subsets that are translated (no rotation is required). But those subsets aren't simply connected, they're Cantor dusts, IIRC.
Here is a cute dissection "paradox" I first saw in a Martin Gardner column, it was possibly an April Fools Day article.
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He said that it works by virtue of Banach-Tarski, but of course he was only joking. In this dissection a 5×13 rectangle is transformed into a 8×8 square. Can you see how it works? If you're on a mobile device, you need to go to the desktop view to enable the display of the SVG animation, otherwise you'll just see the source code.
@Slereah I choose not to assume the negation of the axiom of choice. ;)
