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1. Minkowski Metric

   Linked via "four-vectors"

   The Minkowski metric ($\eta_{\mu\nu}$) is the fundamental mathematical object defining the geometry of flat, four-dimensional spacetime as described by the theory of Special Relativity. It establishes the structure for measuring intervals in a spacetime manifold devoid of gravitational fields or intrinsic curvature, often referred to as Minkowski space. This metric dictates the rules for four-vectors and the transformations that preserve the spacetime interval, primarily the [Lorentz transformations](/en…

2. Minkowski Metric

   Linked via "four-vectors"

   $$\eta{\rho\sigma} = \frac{\partial x^\mu}{\partial x'^\rho} \frac{\partial x^\nu}{\partial x'^\sigma} \eta{\mu\nu}$$
   This invariance principle ensures that physical laws expressed in terms of four-vectors (like the four-momentum or four-current) retain the same form for all observers moving at constant relative velocities with respect to one another.
   Metric Tensor Components

3. Relativistic Kinematics

   Linked via "four-vectors"

   The Four-Vector Formalism
   Relativistic kinematics is often simplified and generalized through the use of four-vectors, which transform predictably under Lorentz transformations, behaving similarly to a standard spatial vector under rotation (see Conic Sections for analogues in geometry). The spacetime position $\mathbf{X}$ is defined as:
   $$
   \mathbf{X} = (ct, x, y, z)