A spaceship traveling at 0.8c passes parallel to Earth. A...

A spaceship traveling at 0.8$c$ passes parallel to Earth. A rod of length $L$ is inside the spaceship. According to an astronaut inside the spaceship, what is the length of the rod?
(A) 0.2$L$
(B) 0.8$L$
(C) $L$
(D) 1.2$L$
(E) 1.8$L$

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Key Concepts

Proper Length

The proper length of an object is defined as the length measured in the reference frame in which the object is at rest. For an astronaut aboard the spacecraft, the rod is at rest relative to them, and thus, the measurement obtained is the proper length. This concept is central in distinguishing measurements made by observers in different inertial frames.

Inertial Frames

An inertial frame of reference is one in which an observer is either at rest or moving at a constant velocity, with no acceleration. In the context of special relativity, measurements of time and length depend on the inertial frame of the observer, which illustrates the relativity of measurements when comparing different frames, such as those of the spacecraft and Earth.

Length Contraction

Length contraction is a phenomenon predicted by special relativity where an object moving relative to an observer appears shorter along the direction of motion compared to its proper length. However, this effect is only observed by an observer in a different inertial frame than that of the object, meaning that an observer sharing the object's frame (in which it is at rest) will measure its actual proper length.

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