Timeline for Observer Transformation in general relativity
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2023 at 16:48 | comment | added | Toyesh Jayaswal | What are PG coordinates? Sure, there will always be coordinate transformations to compare the tangent space of one coordinate to another, but the issue is that there are many. If you fix some convention for some very particular scenario, then sure you can talk about relative velocity relative to this fixed identification of tangent spaces, but in general, there is no canonical way to identify them at different points. This is why we need connections, but connections only serve to canonically compare infinitesimally close tangent spaces and not far away ones. | |
| Dec 23, 2023 at 16:06 | comment | added | Chandra Prakash | But we have coordinate transformations, like PG coordinate describes metric for freely Falling observer. They are derived via coordinate transformation of schwarzschild metric. So, theoretically we could use the transformation to change observer. So again my question is why is relative velocity ill defined? | |
| Dec 22, 2023 at 19:28 | comment | added | Toyesh Jayaswal | bit of a run on sentence, but I think yes this is the right idea | |
| Dec 22, 2023 at 18:39 | comment | added | Chandra Prakash | So it's something like, we have different vectors in different tangent spaces when we are trying to evaluate acceleration but in that case it's remedied by connection term. However when we wanna transform observers, we need to do the transformation and for that we need all the velocities to be in same tangent space so we can transform them into one another but they don't live in same tangent space and connection term is path dependent so there's no unique way to define relative velocity due to this ambiguity. | |
| Dec 22, 2023 at 18:35 | vote | accept | Chandra Prakash | ||
| Dec 22, 2023 at 18:35 | vote | accept | Chandra Prakash | ||
| Dec 22, 2023 at 18:35 | |||||
| Dec 22, 2023 at 14:40 | history | answered | Toyesh Jayaswal | CC BY-SA 4.0 |