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Special Relativity Explained

Special Relativity is one of the most exciting topics in AQA A-Level Physics. Although it appears difficult at first, every concept follows logically from two surprisingly simple assumptions. Once these ideas are understood, equations such as time dilation and length contraction become much easier to apply.

Einstein's Two Postulates

Einstein built his theory upon two revolutionary principles:

  • The laws of physics are identical in every inertial frame.
  • The speed of light is constant for every observer.
c = 3.00 × 108 m s-1
Why is this important?

If the speed of light is always the same, then measurements of time and distance must change instead.

The Lorentz Factor

Every relativistic equation depends on the Lorentz factor.

γ = 1 / √(1 − v²/c²)
Symbol Meaning
γ Lorentz factor
v Object velocity
c Speed of light

Time Dilation

Moving clocks tick more slowly than stationary clocks.

Δt = γΔt₀
Exam Tip
The proper time (Δt₀) is always measured by the observer travelling with the clock.

Length Contraction

L = L₀ / γ

Objects become shorter only in the direction of motion.

Relativistic Momentum

p = γmv

Momentum increases rapidly as velocity approaches the speed of light.

Mass-Energy Equivalence

E = mc²

Mass and energy are two forms of the same physical quantity.

Remember:
Nothing with mass can reach the speed of light because the Lorentz factor tends towards infinity.

Real-World Applications

  • GPS satellites
  • Particle accelerators (CERN)
  • Cosmic ray muons
  • Nuclear power stations

Summary

Special Relativity explains how space and time behave at extremely high speeds. Understanding the Lorentz factor allows students to solve problems involving time dilation, length contraction, relativistic momentum and energy with confidence.

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