A moving object's length in a given frame is defined to be the distance between two events that occur at opposite ends of the object and that are simultaneous in that frame. Why is it crucial that the events we use to define a moving object's length be simultaneous?
A) This is purely conventional: there is no other reason.
B) This choice makes it easier to use the Lorentz transformation equations to find the length.
C) If the events are not constrained to be simultaneous, then the length is poorly defined: its value would depend on the time interval between the events.
D) If the events are simultaneous, then the length will be a frame-independent quantity.
E) Other (specify)

Question

Quizplus · Accepted Answer

If the events used to measure the length of a moving object are not simultaneous in the given frame, the distance between these events will not accurately represent the object's length at a specific moment in time. Instead, it would vary depending on the time difference between the events, leading to an inconsistent and poorly defined measurement of length.  See the discussion in section R6.1.
Section R6.1: The Length of a Moving Object
We can precisely and operationally define an object's length in a given inertial frame in which it is moving to be the distance between simultaneous events occurring at the object's ends in that frame.

A Moving Object's Length in a Given Frame Is Defined