- #1
- 24,775
- 792
Rovelli has introduced an extended idea of diffeomorphism which is smooth except at a finite number of points.
The group of extended (or 'almost smooth') diffeomorphisms plays a role in the Fairbairn/Rovelli paper that just came out
and also in the key chapter 6 of the new book "Quantum Gravity".
Someone I exchange emails with has been wondering what to call these
morphisms and one possibility that really ought to be considered, in my view, is to follow the example of the Skippy Peanut Butter people.
For them, peanut butter is either Smooth
or else it is smooth except at a finite number of points in which case
it is Chunky
almost smooth peanut butter is chunky
so almost smooth homeomorphisms are chunkymorphisms
----------------
Einstein's original vintage 1915 General Relativity was, it seems, "diffeomorphism invariant" meaning that if you had some matter and a geometry which was a solution to the equation then you could skootch the matter and the metric around by a smooth map and it would still be a solution.
As far as I know the original GR is not however invariant under chunkymorphisms. [correction: it seems it may be after all! one can extend the idea of a solution of the einstein equation to almost smooth metrics! see a later post in this thread] One thing about Rovelli is his audacity. I don't know how to spell it in Yiddish but there is a word for it. It is high risk to contemplate extending the diffeomorphism group.
Maybe someone will have some thoughts about this. or maybe I will have some to add later.
If you want background on chunkymorphisms (called by the correct name that Rovelli uses) its all thru Chapter 6 of the book and especially around pages 170-173 and 192
The book is online here
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
or else look at Fairbairn/Rovelli
http://arxiv.org/gr-qc/0403047
here is an earlier thread on the Fairbairn/Rovelli paper
https://www.physicsforums.com/showthread.php?t=16144
I think there probably is a differentiable-with-finite-number-of-singularities
category, maybe someone who does category theory can look at it and see what it would be like. Fairbairn and Rovelli make a start on this. It seems potentially interesting.
The group of extended (or 'almost smooth') diffeomorphisms plays a role in the Fairbairn/Rovelli paper that just came out
and also in the key chapter 6 of the new book "Quantum Gravity".
Someone I exchange emails with has been wondering what to call these
morphisms and one possibility that really ought to be considered, in my view, is to follow the example of the Skippy Peanut Butter people.
For them, peanut butter is either Smooth
or else it is smooth except at a finite number of points in which case
it is Chunky
almost smooth peanut butter is chunky
so almost smooth homeomorphisms are chunkymorphisms
----------------
Einstein's original vintage 1915 General Relativity was, it seems, "diffeomorphism invariant" meaning that if you had some matter and a geometry which was a solution to the equation then you could skootch the matter and the metric around by a smooth map and it would still be a solution.
As far as I know the original GR is not however invariant under chunkymorphisms. [correction: it seems it may be after all! one can extend the idea of a solution of the einstein equation to almost smooth metrics! see a later post in this thread] One thing about Rovelli is his audacity. I don't know how to spell it in Yiddish but there is a word for it. It is high risk to contemplate extending the diffeomorphism group.
Maybe someone will have some thoughts about this. or maybe I will have some to add later.
If you want background on chunkymorphisms (called by the correct name that Rovelli uses) its all thru Chapter 6 of the book and especially around pages 170-173 and 192
The book is online here
http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html
or else look at Fairbairn/Rovelli
http://arxiv.org/gr-qc/0403047
here is an earlier thread on the Fairbairn/Rovelli paper
https://www.physicsforums.com/showthread.php?t=16144
I think there probably is a differentiable-with-finite-number-of-singularities
category, maybe someone who does category theory can look at it and see what it would be like. Fairbairn and Rovelli make a start on this. It seems potentially interesting.
Last edited by a moderator: