P. Piot, PHYS 571 – Fall 2007Last lesson in a nutshell!• Proper time defined as• Minkowski space:• A 4-vector is an object that conforms to LT• Introduced–4-velocity– 4-momentumP. Piot, PHYS 571 – Fall 2007More on Lorentz Transform• Invariant• The Lorentz transform conserve (ds)2.rotationLorentz transformationsγδβδαγαβγδδβγααβδγγδβααβgggdxdxdxdxgdxdxgdxdxg=ΛΛ==''''βααβdxdxgdxdxdxdxds =−−−=222221202)()()()()(Determinants: -1 |Λ| |Λ| -1 so |Λ|2=1P. Piot, PHYS 571 – Fall 2007Particle dynamics in SR: example 1• Consider w one incident n at restQuestionQuestion: Minimum required energy for the incoming n to enable the reaction?AnswerAnswer: At threshold the 4 final neutrons are at rest in the lab framewith we finally get the threshold energyP. Piot, PHYS 571 – Fall 2007Photon emission & absorption• Consider• Then•soPhoton 4-momentumThis also applies to accelerating frames!P. Piot, PHYS 571 – Fall 2007Photon emission & absorption: example 2• In emitter’s frame• In absorber frame• On another hand we have:for photons ⇒P. Piot, PHYS 571 – Fall 2007Photon emission & absorption: example 2• Expliciting the velocity• For f=90 deg this reduces to(Doppler shift)P. Piot, PHYS 571 – Fall 2007SI (système International) versus CGS (cm Gram Second)• The prescription to convert from CGS to SI and vice versa is• Example: Lorentz forceP. Piot, PHYS 571 – Fall 2007SI versus CGS (cnt’d)• Maxwell’s equations in SI and CGS are• The “real pros” also take c=1 (pros because the accept the equivalence between space and time)… but we won’t do
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