Discussion Overview
The discussion centers around the adequacy of the textbook "Misner Thorne and Wheeler" (MTW) for understanding tensors in the context of General Relativity (GR). Participants express their concerns about the complexity of tensors and seek alternative resources or clarifications on the subject.
Discussion Character
- Exploratory
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- Some participants express that MTW may not be the best source for learning tensor calculus due to its intimidating nature.
- One participant suggests Sean Carroll's online lecture notes as a gentler introduction to tensors and GR.
- Several participants discuss the importance of correctly following the "commandments" of tensor calculus, particularly regarding the ordering of indices.
- There is mention of confusion regarding the interpretation of indices in tensor notation, particularly in relation to matrix representations.
- Some participants highlight that the distinction between upper and lower indices is significant for understanding tensor transformations.
- One participant notes that while the Lorentz group is an orthogonal group, the properties of matrices can vary, leading to confusion in specific cases.
- There are requests for recommendations on textbooks that clearly explain tensor notation and the relationships between indices.
Areas of Agreement / Disagreement
Participants do not reach a consensus on whether MTW is sufficient for understanding tensors. Multiple competing views exist regarding the best resources for learning tensor calculus, and there is ongoing confusion about tensor notation and index conventions.
Contextual Notes
Participants express uncertainty about the clarity of various resources and the potential limitations of matrix notation in conveying the properties of tensors, particularly regarding the distinction between upper and lower indices.