Key Concepts: Special Relativity

Einstein's Two Postulates

• 1. The laws of physics are the same in all inertial reference frames.
• 2. The speed of light in vacuum (c ≈ 3 × 10⁸ m/s) is the same for all observers, regardless of their motion.

Key Consequences

• Time Dilation: Moving clocks run slow. t = γt₀, where γ = 1/√(1 − v²/c²).
• Length Contraction: Moving objects are shorter in the direction of motion. L = L₀/γ.
• Mass-Energy Equivalence: E = mc². A small amount of mass corresponds to a huge amount of energy.

The Lorentz Factor (γ)

• γ = 1 at v = 0 (no relativistic effects).
• γ → ∞ as v → c (effects become extreme).
• At everyday speeds, γ ≈ 1 and effects are negligible.

Relativistic Energy: E² = (pc)² + (mc²)². For a photon (m = 0): E = pc.