QCAA Physics Unit 4 syllabus (Revolutions in Modern Physics).
This guide focuses on the limitations of classical physics and how Special Relativity explains two crucial natural and experimental phenomena: atmospheric muons and the momentum of high-speed particles.
Unit 4: Revolutions in Modern Physics
Topic: Limitations of Classical Physics & Evidence for Special Relativity
Classical physics (Newtonian mechanics) works perfectly for everyday objects at everyday speeds. However, it completely breaks down when things move close to the speed of light ($c$). To explain these discrepancies, Albert Einstein introduced the Theory of Special Relativity.
1. Atmospheric Muons (Evidence for Time Dilation & Length Contraction)
What is a Muon?
Muons are elementary subatomic particles created high in the Earth’s atmosphere (about 15 km up) when cosmic rays collide with air molecules.
The Paradox
The Classical Prediction: Muons are highly unstable and have a very short average lifespan of about
$t_0 = 2.2 \times 10^{-6} \text{ s}$(2.2 microseconds) before they decay into other particles. Even traveling at $0.998c$, classical physics calculates their travel distance as:
$d = v \times t $ $= (0.998 \times 3 \times 10^8 \text{ m/s}) \times (2.2 \times 10^{-6} \text{ s})$ $\approx 660 \text{ m}$Since 660 meters is much less than 15,000 meters (15 km), classical physics predicts that almost no muons should reach the Earth's surface.
The Observation: In reality, detectors on the Earth’s surface measure a massive abundance of muons surviving the journey.