Index notation for inverse Lorentz transform

Click For Summary

Discussion Overview

The discussion revolves around the use of tensor and matrix notation in the context of the inverse Lorentz transform, particularly as it relates to equations presented in Schutz's "Introduction to General Relativity." Participants explore the implications of different notational conventions and the correctness of specific mathematical expressions.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant presents an equation for the inverse Lorentz transform and questions the correctness of their reasoning regarding tensor and matrix indices.
  • Another participant challenges the validity of a specific equation, asserting that the left-hand side does not equal the right-hand side as proposed.
  • A later reply suggests that the participant should clarify their notation by explicitly indicating the dependence on different velocities in the transformation.
  • Discussion arises about the appropriateness of using different indices to denote components with respect to different bases, with some arguing it is a bad habit while others defend the practice as a matter of notation preference.
  • One participant emphasizes that the components of a vector should be labeled consistently to avoid confusion, while another reflects on their own learning experience with different notational conventions.
  • References to other threads and literature are made to support various viewpoints on notation and its implications for understanding tensor transformations.

Areas of Agreement / Disagreement

Participants express differing opinions on the use of notation for tensor components, with no consensus reached on whether certain practices are strictly correct or merely a matter of convenience. The mathematical correctness of specific equations remains contested.

Contextual Notes

Participants acknowledge that their discussions involve assumptions about notation and definitions, which may not be universally accepted. The implications of these assumptions on the mathematical expressions are not resolved.

Who May Find This Useful

Readers interested in tensor notation, Lorentz transformations, and the nuances of mathematical conventions in physics may find this discussion insightful.

  • #31
As I said, I find this utmost confusing. If it takes effort to understand something only because of a bad choice of notation, it's better to change the notation!
 
  • Like
Likes   Reactions: cianfa72

Similar threads

Graduate Is the variation of the metric ##\delta g_{\mu\nu}## a tensor?
  • · Replies 49 ·
2
Replies
49
Views
2K
Graduate Show Lagrangian is invariant under a Lorentz transformation without using generators
  • · Replies 3 ·
Replies
3
Views
1K
High School Transforming the Electric Field Measured by an Observer with 4-velocity U
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Lorentz transformation on mode functions
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Yang-Mills Stress-Energy Tensor Explained
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Solving Spherically Symmetric Static Star Equations of Motion
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Transpose and Inverse of Lorentz Transform Matrix
  • · Replies 89 ·
3
Replies
89
Views
15K
Undergrad Proof of Lorentz Gauge Existence: Help Understanding Schutz 8.3
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Can gravitational energy be localized in the case of plane waves?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Index-Free Expressions & Unique Metric-Compatible Connections
  • · Replies 1 ·
Replies
1
Views
1K