Timeline for Are 4-vectors really vectors in general relativity?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Oct 24 at 2:13 | history | edited | weeab00 | CC BY-SA 4.0 |
added 16 characters in body
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| Oct 23 at 17:32 | vote | accept | weeab00 | ||
| Oct 23 at 15:40 | history | became hot network question | |||
| Oct 23 at 11:45 | comment | added | Amit | Related: Does spacetime position not form a four-vector? | |
| Oct 23 at 10:48 | answer | added | KierD | timeline score: 9 | |
| Oct 23 at 10:28 | comment | added | Jeanbaptiste Roux | @OfekGillon What is your point, exactly? $\mathbb{R}^4$ is not "the" tangent space for the "manifold" $\mathbb{R}^4$. Plus, you are confusing the vector space $\mathbb{R}^4$ with a manifold $(\mathbb{R}^4,g)$. A tangent space is tangent to a point in a manifold. Vector fields are sections of the tangent bundle, vectors are restrictions of a section to a point of the manifold, that's all. | |
| Oct 23 at 10:14 | comment | added | Ofek Gillon | @user366875 Well $\mathbb{R^4}$ is the tangent space for the manifold $\mathbb{R^4}$, so points in that space can be considered vectors by your definition | |
| Oct 23 at 10:06 | comment | added | weeab00 | @OfekGillon A vector is an element of a tangent space. I think a point on a manifold cannot be a vector… point and vector are two different concepts | |
| Oct 23 at 9:57 | comment | added | Ofek Gillon | @user366875 , Agreed, if you first give a definition: what is a vector, and why is a point on a manifold ($M\subseteq \mathbb{R}^n , n\geq 3$) not a vector? | |
| Oct 23 at 9:53 | comment | added | weeab00 | @OfekGillon a point on a manifold is not necessarily a vector | |
| Oct 23 at 9:47 | comment | added | Ofek Gillon | @user366875 from the question: "...is what one calls "position 4-vector" but it is a point, not a vector, despite its name". It is not clear what you meant when you wrote it: on what basis are you making this distinction between a point and a vector? | |
| Oct 23 at 9:39 | comment | added | weeab00 | @OfekGillon I need to know the precise definition of 4-vectors to be sure. It seems to me that 4-velocity and 4-acceleration are nothing but proper time derivatives of 4-position components. | |
| Oct 23 at 9:21 | comment | added | Ofek Gillon | @user366875 I think you need to clarify in your question why do you think it is not considered a true vector | |
| Oct 23 at 9:07 | comment | added | Quillo | Points live on the manifold (i.e. spacetime), vectors on the tangent space. The 4-velocity is a legit vector (morally, differentiation takes you to the tangent space). This may also help: physics.stackexchange.com/q/489827/226902 | |
| Oct 23 at 7:39 | history | asked | weeab00 | CC BY-SA 4.0 |