Timeline for Question on how to think about diffeomorphism invariance
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2018 at 18:54 | comment | added | lurscher | well @JohnRennie , arguably one can extend Newton's first law to include Coriolis and Centripetal terms to account for noninertial frames. Probably something similar is true of electromagnetism | |
| Jun 29, 2018 at 16:46 | comment | added | John Rennie | @lurscher for example Newton's first law is not valid if you use accelerating coordinates. However the geodesic equation (probably the closest to Newton's first law in GR) is valid for all coordinate systems, accelerating, curved or whatever. | |
| Jun 29, 2018 at 16:33 | comment | added | Creo | I'm by no means an expert, but for example in Yang Mills theory, the laws are only preserved by gauge transformations, which are a special kind of diffeomorphisms on the bundle used to describe the theory, so its more a question of in what model you what to impose which kind of symmetry(?) So I'd say false in general, it should hold for theorys described by tensorial equations. | |
| Jun 29, 2018 at 16:32 | comment | added | Bob | So if I have a funky metric (in terms of $t,r,\theta\phi$) that can be written as Minkowski after a change of coordinates ($t\rightarrow \tilde{t}$, etc.) , would the proper way forward to work with this metric be to change coordinates to $\tilde{t},\tilde{r},\tilde{\theta},\tilde{\phi}$, solve the Einstein Field Equations in terms of those tilde'd coordinates where the metric is Minkowski, and then switch back to the usual $t,r,\theta,\phi$ coordinates to connect predictions from my original funky metric with observation? | |
| Jun 29, 2018 at 16:15 | comment | added | lurscher | if diffeomorphism invariance is only about coordinate invariance, then it is trivial and all physical laws and forces must be "diffeomorphic invariant". True or False? | |
| Jun 29, 2018 at 16:14 | history | answered | Creo | CC BY-SA 4.0 |