Past exam of the symmetry and relativity course of the University of Oxford / 2017 / 2 / c / b

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- Solution b

Solution

The centre-of-mass velocity follows from the total energy and momentum:

V_{CM} = \frac{c ^{2} p _{tot}}{E _{tot}} = (\frac{c}{2}, \frac{c}{2}, 0), ∣ V_{CM} ∣ = \frac{c}{2} .

A boost in this direction with

Γ_{CM} = 2

gives zero total spatial momentum and total energy

2 ℏ ω

. The constituent photons remain moving at

c

in that frame.

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