Timeline for Does spacetime position not form a four-vector?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 23, 2021 at 9:14 | comment | added | Shashaank | @PraharMitra yeh I got confused because we lower indices on $dx^\mu$ and $\dot{x}^\{mu}, but there one is a basis covector ( one form) and the other is velocity contravariant vector. Is that right? | |
| Feb 23, 2021 at 9:01 | comment | added | Prahar | @Shashaank you are right. In GR, coordinates do NOT transform like that. You also cannot raise and lower indices on the coordinates. | |
| Feb 22, 2021 at 5:02 | comment | added | Shashaank | @BenceRacskó so will in GR $x^\mu$ ( where $x^\mu $is a coordinate) not transform via the rule $x^{\mu' }= \frac{\partial x^{\mu'}}{\partial x^\nu}x^\nu$( which is the rule for transformation of contravariant vectors? And also when we raise and index on $g^{ab}x_b=x^a$, this will only work when $x$ does not denote a coordinate but is an actual vector field? Do what I say above is correct, specially the first point? Let me know what you think. | |
| Feb 21, 2021 at 19:52 | comment | added | Bence Racskó | @Shashaank I don't have the book in front of me right now but presumably Carroll says that during the special relativity chapter where it is true (that is for Minkowski spacetime). It is not true for general manifolds. | |
| Feb 21, 2021 at 19:38 | comment | added | Shashaank | If the $x^\mu$ aren’t vectors, the why does Caroll say that the coordinates transform like contravariant vectors. And why do we raise and lower indices on them like they vectors | |
| Aug 4, 2020 at 20:39 | vote | accept | Ivan Burbano | ||
| Jul 7, 2015 at 7:38 | comment | added | CuriousOne | @WetSavannaAnimalakaRodVance: Amen to that. | |
| Jul 7, 2015 at 7:03 | comment | added | Selene Routley | @Mehrdad True, but the sound of Gennaro's phrase is pretty cool too! | |
| Jul 7, 2015 at 7:02 | comment | added | Selene Routley | @CuriousOne Your last sentence is an interesting one. It's certainly true that if a student has trouble grasping the difference, then maybe they wouldn't be ready for Riemannian geometry. On the other hand, a bad teacher is like a bad drawing partner in Pictionary: apt to send even the brightest students down the wrong path. | |
| Jul 7, 2015 at 6:22 | comment | added | CuriousOne | Upvote for your great answer, but I would remark that physicists in general are not mistaking position for a vector. We have spent a couple centuries arguing amongst ourselves about Galilean relativity and even a capable high school physics teacher can explain the difference between a map of points (labels) and physical vectors that live in tangent space without ever needing to go to the formal definition of manifolds. Unfortunately not every teacher is capable and not every student picks up the subtlety. OTOH, the students that don't won't profit from a lecture on Riemann manifolds, either. | |
| Jul 7, 2015 at 3:37 | comment | added | user541686 | @GennaroTedesco: It's called "succinct" :P | |
| Jul 7, 2015 at 0:15 | comment | added | gented | Concise and precise, +1! :) | |
| Jul 7, 2015 at 0:07 | history | answered | Bence Racskó | CC BY-SA 3.0 |