 b

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2015/11/b

Let

S^{'}

be the runner's inertial frame, with origin at the entry event. The Lorentz transformation is

x^{'} = γ (x - v t), t^{'} = γ (t - \frac{vx}{c ^{2}}), γ = (1 - β^{2})^{- 1/2} .

The emission event

E = (L, 0)

has coordinates

x_{E}^{'} = γ L

t_{E}^{'} = - γ vL / c^{2}

. It is earlier than entry in

S^{'}

: entry and far-end emission are simultaneous only in the tunnel frame. This is relativity of simultaneity, not an extra delay of the light source.

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