Section 2.1.3 Energy and Momentum Exercise: A photon rocket accelerates in a straight line by emitting photons in the direction opposite its motion. If cβ is the final velocity of the rocket in its initial rest frame, show that the ratio of its initial mass to its final mass is

11

i

f

mm

ββ

+=−

Hint: find the increment of velocity in the instantaneous rest frame and use the Einstein velocity addition law. Exercise: A particle of mass m at rest in the laboratory decays to a particle of mass 'm and emits a photon. Use 4-vector arguments to show that the energies of the particle and the photon in the laboratory frame are

2 2

2

'2

m mc m

±=E

where the plus sign refers to the energy of the particle and the minus sign to that of the photon.