Retrieving "Coordinate Transformations" from the archives

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1. General Covariance

   Linked via "coordinate transformations"

   The core mechanism by which General Relativity enforces general covariance is the metric tensor $g{\mu\nu}$. The metric is not just a passive background field; it actively describes the geometry of spacetime, and crucially, it is a tensor. All fundamental physical quantities (like the Riemann curvature tensor, $R{\rho\sigma\mu\nu}$) must also be tensors.
   This tensor nature guarantees covariance. A [tensor field](/entries/tensor-fi…

2. Spatial Coordinate

   Linked via "coordinate transformations"

   A spatial coordinate is a quantifiable parameter used to precisely define the location or orientation of a point, object, or vector (mathematics)/) within a defined geometric space. These coordinates are fundamentally dependent on the chosen reference frame, which dictates the zero point (origin) and the orientation of the foundational axes. While the most commonly encountered systems rely on three dimensions ($x, y, z$), [theoreti…