Timeline for MTW Box 9.1 Tangent Vectors and Tangent Space of a metric-free, geodesic-free spacetime. What necessary properties remain?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2023 at 16:36 | answer | added | Steven Thomas Hatton | timeline score: 0 | |
| Jan 12, 2023 at 16:23 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
spelling
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| Jun 21, 2021 at 12:47 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
Res. recom. can usually not be mixed with an actual physics q
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| Jun 19, 2021 at 10:39 | vote | accept | Steven Thomas Hatton | ||
| Jun 19, 2021 at 6:20 | comment | added | Steven Thomas Hatton | I'm fairly convinced that more is intended than simply introducing tangent spaces, etc. In many places in the book, they show a great deal of enthusiasm for what can be accomplished without a metric. In Chapter 9 the notion of a tangent vector arrow in a tangent space becomes useful fiction. What remains is the ability to differentiate scalar functions with respect to a parameter. The books by Loring Tu and Frank Warner appear to share MTW's view. But they are formidable challenges. C. H. Edwards mumbles conspicuously in this area. Alfred Grey introduces arc-length almost immediately. | |
| Jun 19, 2021 at 5:35 | comment | added | peek-a-boo | it seems like this is just a heuristic idea to motivate the definition of a tangent vector (though I'm not a fan of such heuristics; I would much rather see the precise definition first and then look at the motivation). Also, I'm not really sure what your main concern is. Anyway, the concepts of differentiable manifolds, "curves" in a manifold (i.e just a smooth mapping of an interval into the manifold), and tangent space to a differentiable manifold are all standard topics, so once again, I'm not really sure what you're after. | |
| Jun 19, 2021 at 5:26 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
added resource=recommendations tag
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| Jun 18, 2021 at 11:52 | answer | added | Umaxo | timeline score: 1 | |
| Jun 18, 2021 at 9:44 | history | edited | Steven Thomas Hatton | CC BY-SA 4.0 |
added a comment about embedding spaces
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| Jun 18, 2021 at 9:35 | history | asked | Steven Thomas Hatton | CC BY-SA 4.0 |