A subatomic particle moves through the laboratory at 0.90 c....

A subatomic particle moves through the laboratory at $0.90 \mathrm{c}$. Laboratory experimenters measure its lifetime, from creation to annihilation, to be 2.3 ps $\left(1 \mathrm{ps}=1\right.$ picosecond $\left.=10^{-12} \mathrm{s}\right)$ According to the particle, how long did it live?

Key Concepts

Special Relativity

Special Relativity is a fundamental theory in physics that describes how measurements of space and time are relative to the state of motion of the observer. It introduces concepts such as time dilation and length contraction when objects move at speeds close to the speed of light, fundamentally altering our classical understanding of physics.

Time Dilation

Time dilation is a phenomenon predicted by Special Relativity in which a moving clock is observed to tick slower than a stationary clock. This means that the elapsed time between two events is longer when measured in a frame in which the events occur at different locations, compared to the proper time measured in the rest frame of the moving object.

Proper Time

Proper time is the time interval between two events measured by an observer for whom the events occur at the same location, meaning the observer is at rest relative to the events. It is a key concept in understanding time dilation, as it represents the true lifetime of an object in its own rest frame.

Lorentz Factor

The Lorentz factor quantifies the effects of time dilation and length contraction in Special Relativity. It is defined as gamma = 1/?(1 - v²/c²), where v is the velocity of the moving object and c is the speed of light. This factor is used to convert proper time (time in the object's rest frame) to dilated time (time observed in a different inertial frame) and vice versa.

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