An alien spacecraft is flying overhead at a great distance...

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.190 s. The first officer on the spacecraft measures that the searchlight is on for 12.0 $\mathrm{ms}$ . (a) Which of these two measured times is the proper time? (b) What is the speed of the spacecraft relative to the earth expressed as a fraction of the speed of light $c$ ?

Key Concepts

Inertial Reference Frame

An inertial reference frame is one in which an observer is either at rest or moving with constant velocity, meaning no net forces are acting on the observer. In these frames, the laws of physics, including those of special relativity, hold in their simplest form, allowing for consistent and comparable measurements of time and space between different observers.

Lorentz Factor

The Lorentz factor, often represented by the symbol gamma (?), quantifies the amount by which time, length, and relativistic mass change for objects moving at a significant fraction of the speed of light relative to an observer. It is calculated using the relative speed and is essential for transforming measurements between different inertial reference frames in special relativity.

Time Dilation

Time dilation is a phenomenon predicted by special relativity where the elapsed time between two events is longer for an observer in motion relative to the events than for an observer at rest relative to them. This effect arises because time is not absolute and depends on the relative velocity between observers, causing moving clocks to appear to tick slower compared to stationary ones.

Proper Time

Proper time is the time interval measured by an observer for whom the events occur at the same location in space. It is the shortest elapsed time between two events and is measured in the observer’s rest frame. This concept is crucial in special relativity because it serves as the invariant measure of time when comparing observations from different reference frames.

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