A spaceship is moving at a constant velocity of 0.70 c...

A spaceship is moving at a constant velocity of $0.70 c$ relative to an Earth observer. The Earth observer measures the length of the spaceship to be $40.0 \mathrm{~m}$. How long is the spaceship as measured by its pilot?

Key Concepts

Special Relativity

Special relativity is a fundamental theory in physics formulated by Albert Einstein that describes how space and time are interwoven and vary for observers in different inertial frames. It introduces the concept that the laws of physics are the same for all non-accelerating observers and that the speed of light in a vacuum is constant, leading to surprising consequences such as time dilation and length contraction.

Inertial Frames

An inertial frame of reference is one in which objects obey Newton's first law, meaning they either remain at rest or move at a constant velocity unless acted upon by an external force. In special relativity, differences in measurements of time and space can arise when comparing observations made in different inertial frames moving relative to each other.

Length Contraction

Length contraction is a relativistic effect predicting that an object's length, as measured by an observer in relative motion to the object, appears shorter than its length measured in its own rest frame (the proper length). This contraction only occurs along the direction of relative motion and becomes significant at speeds close to the speed of light.

Lorentz Factor

The Lorentz factor, denoted as gamma (?), quantifies the degree of time dilation, length contraction, and mass increase experienced by objects moving at relativistic speeds. It is defined by the expression ? = 1/?(1 - v²/c²), where v is the relative velocity and c is the speed of light. This factor is central to calculating how measurements of space and time transform between different inertial frames.

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