Lecture 17
FYS3120 – Classical mechanics and electrodynamics Recap Relativistic four-momentum pμ is defined as where E and p is the relativistic energy and momentum. These reduce to ordinary kinetic energy plus rest energy, and to ordinary momentum in the non-relativistic limit. These lead to the energy-momentum relation which allows massless particles with E = pc. 𝑝 μ = 𝑚𝑈 μ = γ𝑚𝑐,γ𝑚 𝑣 = 𝐸 𝑐 , 𝑝 Lav totalenergi første tilgjengelig eksperimentelt i våre dager. 𝐸 2 = 𝑝 2 𝑐 2 + 𝑚 2 𝑐 4 / Are Raklev / 17.03.17 FYS3120 – Classical mechanics and electrodynamics
FYS3120 – Classical mechanics and electrodynamics Today Doppler effect for light Conservation of relativistic energy and momentum Leads to mass non-conservation. Centre-of-mass reference frame Just as in non-relativistic physics – the sum of momenta is zero. / Are Raklev / 17.03.17 FYS3120 – Classical mechanics and electrodynamics
FYS3120 – Classical mechanics and electrodynamics Summary We can derive the Doppler effect by looking at Lorentz transformations of the four-momentum Conservation of relativistic energy and momentum is given by the four-momenta The centre-of-mass reference frame is defined as the RF where ν′ = γ 1−βcosθ ν 𝑖 𝑝 𝑖 μ = 𝑓 𝑝 𝑓 μ Lav totalenergi første tilgjengelig eksperimentelt i våre dager. 𝑃 = 𝑖 𝑝 𝑖 = 0 / Are Raklev / 17.03.17 FYS3120 – Classical mechanics and electrodynamics