General Relativity: An Introduction for Physicists · Problem 5.19

Special relativity revisited — Hobson, Efstathiou & Lasenby

Physics · spatial-momentum-magnitude-4-vector

Problem

At some event PP in Minkowski spacetime, the worldline of a particle (either massive or massless) and an observer cross. If, at this event, the particle has 4-momentum p\boldsymbol{p} and the observer has 4-velocity u\boldsymbol{u} then show that the observer measures the magnitude of the spatial momentum of the particle to be ∣p⃗∣=[(p⋅u)2c2−p⋅p]1/2.|\vec{p}| = \left[\frac{(\boldsymbol{p}\cdot\boldsymbol{u})^2}{c^2} - \boldsymbol{p}\cdot\boldsymbol{p}\right]^{1/2}.

Related theory

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