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Year 3 of the physics course of the University of Oxford

Symmetry and relativity course of the University of Oxford

Past exam of the symmetry and relativity course of the University of Oxford

2017

The <centre-of-mass velocity> follows from the total <energy> and <momentum>:
$$
\boxed{\mathbf V_{\mathrm{CM}}=\frac{c^2\mathbf p_{\mathrm{tot}}}{E_{\mathrm{tot}}}
=\left(\frac c2,\frac c2,0\right),\qquad
|\mathbf V_{\mathrm{CM}}|=\frac c{\sqrt2}.}
$$
A boost in this direction with $\Gamma_{\mathrm{CM}}=\sqrt2$ gives zero total spatial <momentum> and total <energy> $\sqrt2\hbar\omega$. The constituent <photons> remain moving at $c$ in that frame.

Solution

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

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

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

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