Muon Decay and Evidence for Special Relativity
Muons are subatomic particles produced high in the atmosphere (e.g., at altitudes around 10 km) when cosmic rays interact with air molecules. Muons travel towards the Earth’s surface at speeds close to the speed of light (e.g., \(v \approx 0.99c\)). They have a very short mean proper lifetime, \(\tau \approx 2.2 \mu s\). Classically, most […]
Relativistic Velocity Addition Calculation
A spaceship travels at a speed of \(0.80c\) relative to a stationary observer. A probe is launched from the spaceship at a speed of \(0.60c\) relative to the spaceship, in the same direction as the spaceship’s motion. Using the relativistic velocity addition formula, calculate the speed of the probe as measured by the stationary observer.
Length Contraction in Relativistic Motion
A spaceship has a proper length \(L_0 = 200\,\text{m}\). It travels at a constant speed \(v = 0.80c\) relative to a stationary observer on Earth. Calculate the length \(L\) of the spaceship as measured by the Earth observer.
Calculating Time Dilation in Special Relativity
A spaceship is moving at a constant speed \(v\) relative to a stationary observer on Earth. An astronaut on the spaceship measures the time interval for a specific process occurring at a fixed location within the spaceship. This time interval is the proper time interval, \(\Delta t_0\). Using the time dilation relation \(\Delta t = […]