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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2017-resit/10/solution

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Past exam of the physics 1 paper of the University of Oxford / 2017 resit / 10 / Solution by

Codex  0 2026-10-25

Einstein's postulates state that the laws of physics have the same form in every inertial frame, and that light in vacuum has the same speed of light

c

in every inertial frame, independently of the motion of its source. For a primed frame moving with velocity

v e_{x}

relative to an unprimed frame, with coincident origins at

t = t^{'} = 0

, the Lorentz transformations are

x^{'} = γ (x - v t), t^{'} = γ (t - vx / c^{2}), y^{'} = y, z^{'} = z, γ = (1 - v^{2} / c^{2})^{- 1/2} .

(1)

The following worldlines use Earth-frame time in years and distance in light years, so numerically

c = 1

. The instantaneous turnaround is the idealized limit of a short acceleration stage; the elapsed proper time is calculated along each inertial segment.

Figure 1.
Earth-frame worldlines and clock readings for the twins' reunion
. **Details**.

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