A spaceship is moving with a speed of v =5 0.99 c. A...

A spaceship is moving with a speed of $v =5 0.99 c.$ A passenger in the spaceship heats her food for 2 minutes according to her watch. Calculate the duration of heating as observed from a fixed planet.

Key Concepts

Special Relativity

Special relativity is the branch of physics that examines how space and time are interwoven, especially when objects are moving at speeds close to the speed of light. It challenges our classical intuitions by showing that measurements of time and space depend on the relative motion between observers, leading to phenomena such as time dilation and length contraction.

Time Dilation

Time dilation is a key consequence of special relativity, where the time interval between two events is observed to be longer (or 'dilated') in a frame of reference that is in relative motion compared to the frame in which the events occur at the same location. This means a moving clock appears to tick slower when observed from a stationary frame, making time intervals appear longer.

Lorentz Factor

The Lorentz factor, denoted by ? (gamma), is a mathematical expression derived from the Lorentz transformations that quantifies the amount of time dilation (and length contraction) experienced at high velocities. It is given by the formula ? = 1/?(1 - v²/c²), indicating that as an object's speed v approaches the speed of light c, ? increases significantly, resulting in more pronounced relativistic effects.

Proper Time

Proper time refers to the time interval measured by an observer who is at rest relative to the event being timed, meaning it is the time measured in the object's own inertial frame. This concept is fundamental in relativity because it serves as a baseline for comparing time intervals observed in different frames, especially when computing time dilation effects.

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