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1.1: Prelude Einstein’s equation $$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=8\pi GT_{\mu\nu}$$ takes the place of (1) the inverse square gravity law and (2) Newton’s second law. It relates the curvature of spacetime (LHS) to the effect it has on matter (RHS).
Free particles move along geodesics in spacetime.
“Special relativity: the theory of spacetime in the absence of…
1.1: Prelude Einstein’s equation $$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=8\pi GT_{\mu\nu}$$ takes the place of (1) the inverse square gravity law and (2) Newton’s second law. It relates the curvature of spacetime (LHS) to the effect it has on matter (RHS).
Free particles move along geodesics in spacetime.
“Special relativity: the theory of spacetime in the absence of gravity/curvature”.
1.2: Space and Time, Separately and Together A particle’s worldline is its four-dimensional trajectory $x^\mu(\tau)$.
Simultaneity: in Newtonian physics, there is a notion of “all space at a given time”, a cross-section in time.Read on /journal/carroll/1/ ↗
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