 Solution

ID: past-exam-of-the-symmetry-and-relativity-course-of-the-university-of-oxford/2017/2/c/a/solution

Put

ε = ℏ ω

P_{tot} = (\frac{2 ε}{c}, \frac{ε}{c}, \frac{ε}{c}, 0) .

Although each constituent is massless, the sum has

P_{tot}^{2} = 2 ε^{2} / c^{2}

. Its invariant mass is therefore

M_{sys} = \frac{2 ℏ ω}{c ^{2}} .

The rest energy is the total energy in the frame where the two photon momenta cancel, not the sum of individual photon rest energies.

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