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There is a little subtlety here. Calculation of the Lorentz contraction actually involves rod endpoints which appear to be different events to different observers. The example assumes the same two events are measured by both observers. However, the conclusion remains valid. If the endpoint events look simultaneous to two different observers, then the rod length measured must be the same for each. See Fig. 9 and the concomitant discussion in Sec. 5.2.
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