Special Relativity and Riemannian Geometry -----------------------------------------------------------------------------

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Special Relativity and Riemannian Geometry

Special Relativity And Riemannian Geometry 1 (37.95 KiB) Viewed 38 times

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FORMULASHEET

Special Relativity And Riemannian Geometry 2 (26.61 KiB) Viewed 38 times

Special Relativity And Riemannian Geometry 3 (31.95 KiB) Viewed 38 times

QUESTION 3 = Consider a kaon particle with mass m = 498 MeV/c? that is moving along the x-axis of an inertial reference frame S with speed v = 0.8c. a) What is the momentum of the kaon? b) What is the total relativistic energy of the kaon? (3) c) Write down the four-momentum of the kaon. (3) d) What is the measured total relativistic energy and momentum of the kaon in an inertial frame S' that is moving in the standard configuration with speed 0.4c relative to S? (7) e) What is the kinetic energy of the kaon as measured in S'? (3)

FORMULA SHEET c= 3.00 x 108 ms -1 1eV = 1.60 x 10-19 J 1 GeV = 10eV = r = r - Vt E' = 7(E-VP2) VE = c2 py = Py p. = P: p's = 9 (p:-) y y 2 E = pc + m² ť = y(t - (V/c?) 2) 7.3 - Vt) y = y FVO - ای 2 F 7 (Fº-VF/C) (F! - VF/) F2 - F2 F3 = F3 free = fem Icv c+V

free - Ic-v femi c+V 2 271/2 Lc (PQ) L' [() 9+ ) + dy du du du Ic-V Tem = Trect V Arec Vetv im Σ дуmk, дујт ду;k + ari a.ch acm jk 172 V-V - de dirk d12 + ΣΓ' dx dx juk 1-V,V/e2 Vy 7(1 - 0 V/e2) - 0 ข U2 ve k sy - y (:2 + y2) 3/2 (1 - 0,V/2) R1212 K= ar ark 9 RE ijk aci ΣΓ"Γ" -Σ", Γ'πιά my i mk m m TWV = (p+p/c?) UMU” – pgh =